### Re: Bruno's mathematical reality

```
On 12/29/2013 11:42 PM, Bruno Marchal wrote:

On 29 Dec 2013, at 20:25, meekerdb wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate computationally a
random number, and that is right, if we want generate only that numbers. but a
simple counting algorithm generating all numbers, 0, 1, 2,  6999500235148668,
... generates all random finite incompressible strings,

How can a finite string be incompressible? 6999500235148668 in base 6999500235148669
is just 10.

You can define a finite string as incompressible when the shorter combinators to
generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short sequences which indeed
will depend of the language used (here combinators).

Then you can show that such a definition can be made universal by adding some
constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base, are random in that
sense.

Of course, 10 is a sort of compression of any string X in some base, but if you allow
change of base, you will need to send the base with the number in the message. If you
fix the base, then indeed 10 will be a compression of that particular number base, for
that language, and it is part of incompressibility theory that no definition exist
working for all (small) numbers.

Since all finite numbers are small, I think this means the theory only holds in
the limit.

The definition will work for all numbers reasonably bigger than the code of the
universal machine used. That is what determine the constant. Not all numbers are small
relatively to the size of the universal number/machine used to compress information.

Maybe you can clarify this point which seemed to arise in my discussion with JR.  Are you

Brent

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### Re: Bruno's mathematical reality

```

On 29 Dec 2013, at 22:51, meekerdb wrote:

On 12/29/2013 1:28 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 2:25 PM, meekerdb meeke...@verizon.net
wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want
generate only that numbers. but a simple counting algorithm
generating all numbers, 0, 1, 2,  6999500235148668, ...
generates all random finite incompressible strings,

How can a finite string be incompressible?  6999500235148668 in
base 6999500235148669 is just 10.

You can define a finite string as incompressible when the shorter
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short
sequences which indeed will depend of the language used (here
combinators).

Then you can show that such a definition can be made universal by
adding some constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base,
are random in that sense.

Of course, 10 is a sort of compression of any string X in some
base, but if you allow change of base, you will need to send the
base with the number in the message. If you fix the base, then
indeed 10 will be a compression of that particular number base,
for that language, and it is part of incompressibility theory that
no definition exist working for all (small) numbers.

Since all finite numbers are small, I think this means the theory
only holds in the limit.

Brent

Brent,

It is easy to see with the pigeon hole principal.  There are more 2
digit numbers than 1 digit numbers, and more 3 digit numbers than 2
digit numbers, and so on.  For any string you can represent using a
shorter string, another shorter string must necessarily be
displaced.  You can't keep replacing things with shorter strings
because there aren't enough of them, so as a side-effect, every
compression strategy must represent some strings by larger ones.
In fact, the average size of all possible compressed messages (with
some upper-bound length n) can never be smaller than the average
size of all uncompressed messages.

The only reason compression algorithms are useful is because they
are tailored to represent some class of messages with shorter
strings, while making (the vast majority of) other messages
slightly larger.

A good explanation.  But just because you cannot compress all
numbers of a given size doesn't imply that any particular number is
incompressible.  So isn't it the case that every finite number
string is compressible in some algorithm?  So there's no sense to
saying 6999500235148668 is random, but 11 is not, except
relative to some given compression algorithm.

It works up to a constant related to the choice of the universal base
to do the compression. 11 is probably random in the SK
combinator language. But for strings which are greater than the
description of the universal bases used, the same strings will be
random or not.

Bruno

Brent

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### Re: Bruno's mathematical reality

```

On 29 Dec 2013, at 23:42, meekerdb wrote:

On 12/29/2013 2:08 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 4:51 PM, meekerdb meeke...@verizon.net
wrote:

On 12/29/2013 1:28 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 2:25 PM, meekerdb meeke...@verizon.net
wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want
generate only that numbers. but a simple counting algorithm
generating all numbers, 0, 1, 2,  6999500235148668, ...
generates all random finite incompressible strings,

How can a finite string be incompressible?  6999500235148668 in
base 6999500235148669 is just 10.

You can define a finite string as incompressible when the shorter
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short
sequences which indeed will depend of the language used (here
combinators).

Then you can show that such a definition can be made universal by
adding some constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base,
are random in that sense.

Of course, 10 is a sort of compression of any string X in some
base, but if you allow change of base, you will need to send the
base with the number in the message. If you fix the base, then
indeed 10 will be a compression of that particular number base,
for that language, and it is part of incompressibility theory
that no definition exist working for all (small) numbers.

Since all finite numbers are small, I think this means the theory
only holds in the limit.

Brent

Brent,

It is easy to see with the pigeon hole principal.  There are more
2 digit numbers than 1 digit numbers, and more 3 digit numbers
than 2 digit numbers, and so on.  For any string you can represent
using a shorter string, another shorter string must necessarily
be displaced.  You can't keep replacing things with shorter
strings because there aren't enough of them, so as a side-effect,
every compression strategy must represent some strings by larger
ones.  In fact, the average size of all possible compressed
messages (with some upper-bound length n) can never be smaller
than the average size of all uncompressed messages.

The only reason compression algorithms are useful is because they
are tailored to represent some class of messages with shorter
strings, while making (the vast majority of) other messages
slightly larger.

A good explanation.

Thanks.

But just because you cannot compress all numbers of a given size
doesn't imply that any particular number is incompressible.

That is true if you consider the size of the compression program to
be of no relevance.  In such a case, you can of course have a
number of very small strings map directly to very large ones.

So isn't it the case that every finite number string is
compressible in some algorithm?  So there's no sense to saying
6999500235148668 is random, but 11 is not, except
relative to some given compression algorithm.

Right, but this leads to the concept of Kolmogorov complexity. If
you consider the size of the minimum string and algorithm together,
necessary to represent some number, you will find there are some
patterns of data that are more compressible than others.  In your
previous example with base 6999500235148668, you would need to
include both that base, and the string 10 in order to encode
6999500235148669.

But that seems to make the randomness of a number dependent on the
base used to write it down? Did I have to write down And this is in
base 10 to show that 6999500235148668 is random?  There seems to be
an equivocation here on computing a number and computing a
representation of a number.

Only for the numbers or strings with size similar to the size of the
universal number use for the compression. This means it works for
almost all numbers (= all except a finite number of exception).

For the majority of numbers, you will find the Kolmogorov
complexity of the number to almost always be on the order of the
number of digits in that number.  The exceptions like 11
are few and far between.

1 looks a lot messier in base 9.

Sure.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```

On 30 Dec 2013, at 05:54, meekerdb wrote:

On 12/29/2013 7:45 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 6:58 PM, meekerdb meeke...@verizon.net
wrote:

On 12/29/2013 3:49 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 5:42 PM, meekerdb meeke...@verizon.net
wrote:

On 12/29/2013 2:08 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 4:51 PM, meekerdb meeke...@verizon.net
wrote:

On 12/29/2013 1:28 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 2:25 PM, meekerdb meeke...@verizon.net
wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we
want generate only that numbers. but a simple counting
algorithm generating all numbers, 0, 1, 2,
6999500235148668, ... generates all random finite
incompressible strings,

How can a finite string be incompressible?  6999500235148668
in base 6999500235148669 is just 10.

You can define a finite string as incompressible when the
shorter combinators to generate it is as lengthy
as  the
string itself.
This definition is not universal for a finite amount of short
sequences which indeed will depend of the language used (here
combinators).

Then you can show that such a definition can be made universal
by adding some constant, which will depend of the universal
language.

It can be shown that most (finite!) numbers, written in any
base, are random in that sense.

Of course, 10 is a sort of compression of any string X in some
base, but if you allow change of base, you will need to send
the base with the number in the message. If you fix the base,
then indeed 10 will be a compression of that particular number
base, for that language, and it is part of incompressibility
theory that no definition exist working for all (small) numbers.

Since all finite numbers are small, I think this means the
theory only holds in the limit.

Brent

Brent,

It is easy to see with the pigeon hole principal.  There are
more 2 digit numbers than 1 digit numbers, and more 3 digit
numbers than 2 digit numbers, and so on.  For any string you can
represent using a shorter string,
another
shorter string must necessarily be displaced.  You can't keep
replacing things with shorter strings because there aren't
enough of them, so as a side-effect, every compression strategy
must represent some strings by larger ones.  In fact, the
average size of all possible compressed messages (with some
upper-bound length n) can never be smaller than the average size
of all uncompressed messages.

The only reason compression algorithms are useful is because
they are tailored to represent some class of messages with
shorter strings, while making (the vast majority of) other
messages slightly larger.

A good explanation.

Thanks.

But just because you cannot compress all numbers of a given size
doesn't imply that any particular number is incompressible.

That is true if you consider the size of the compression program
to be of no relevance.  In such a case, you can of course have a
number of very small strings map directly to very large ones.

So isn't it the case that every finite number string is
compressible in some algorithm?  So there's no sense to saying
6999500235148668 is random, but 11 is not, except
relative to some given compression algorithm.

Right, but this leads to the concept of Kolmogorov complexity. If
you consider the size of the minimum string and algorithm
together, necessary to represent some number, you will find there
are some patterns of data that are
more  compressible
than others.  In your previous example with base
6999500235148668, you would need to include
both  that base, and
the string 10 in order to encode 6999500235148669.

But that seems to make the randomness of a number dependent on the
base used to write it down? Did I have to write down And this is
in base 10 to show that 6999500235148668 is random?  There seems
to be an equivocation here on computing a number and computing
a representation of a number.

A number containing regular patterns in some base, will also
contain regular patterns in some other base (even if they are not
obvious to us), compression algorithms are good at recognizing them.

The text of this sentence may not seem very redundant, but english
text can generally be compressed somewhere between 20% - 30% of
its original size.  If you convert a number like 555 to
base 2, its patterns should be more evident in the pattern of bits.

For the majority of numbers, you will find the ```

### Re: Bruno's mathematical reality

```

On 30 Dec 2013, at 06:28, Jason Resch wrote:

In the space of all possible movies, the ones that are watchable or
meaningful to human viewers would all be highly compressible. The
would not make interesting movies.  So maybe there is something to
your idea that interesting is related to short descriptions. We did
evolve to find entirely predictable and entirely unpredictable
things boring, there may be some ideal blend of predictability and
unpredicability that we find most engaging.

Yes, it is the redundancy of the information related to the notion of
universal machine. It is contained in Post numbers, which is a sort of
UD by itself (when seen in some way): 0,
00110001011000100101001001110 ... with nth digit = 0 or 1
according to the fact that the nth programs (with 0 input) stop or
not. (It is an halting oracle, and of course is not computable, but it
is compressible).

The non computable maximal compression of Post number gives Chaitin
Omega number, which delete all redundancies in the UD, and thus the
whole physics!

Anything interesting and beautiful is highly redundant, like the
Mandelbrot set for example.

In recursion theory, it is the difference between two
complementarities: the simple/immune complementarity discovered by
Post (and rediscovered by Chaitin in term of algorithmic compression)
on one par, and the creative/productive complementarity, also
discovered by Post, where creative has been shown later to be
equivalent with Turing universality (or sigma_1 completeness) by John
Myhill, (using Kleene second recursion theorem).

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```

On 30 Dec 2013, at 09:01, meekerdb wrote:

On 12/29/2013 11:42 PM, Bruno Marchal wrote:

On 29 Dec 2013, at 20:25, meekerdb wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want
generate only that numbers. but a simple counting algorithm
generating all numbers, 0, 1, 2,  6999500235148668, ...
generates all random finite incompressible strings,

How can a finite string be incompressible?  6999500235148668 in
base 6999500235148669 is just 10.

You can define a finite string as incompressible when the shorter
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short
sequences which indeed will depend of the language used (here
combinators).

Then you can show that such a definition can be made universal by
adding some constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base,
are random in that sense.

Of course, 10 is a sort of compression of any string X in some
base, but if you allow change of base, you will need to send the
base with the number in the message. If you fix the base, then
indeed 10 will be a compression of that particular number base,
for that language, and it is part of incompressibility theory
that no definition exist working for all (small) numbers.

Since all finite numbers are small, I think this means the theory
only holds in the limit.

The definition will work for all numbers reasonably bigger than the
code of the universal machine used. That is what determine the
constant. Not all numbers are small relatively to the size of the
universal number/machine used to compress information.

Maybe you can clarify this point which seemed to arise in my
of digits that name numbers?

I am talking about string of digits (naming or not numbers). Sometimes
I call them number, as all strings on a fixed alphabet can be seen as
a number written in the base defined by that alphabet. But compression
is a notion concerning strings of symbols.

Bruno

Brent

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 16:51, Jason Resch wrote:

On Dec 28, 2013, at 6:09 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 28 Dec 2013, at 04:56, Jason Resch wrote:

On Fri, Dec 27, 2013 at 10:42 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

Any program, and whether or not it ever terminates can be
translated to a statement concerning numbers in arithmetic. Thus
mathematical truth captures the facts concerning whether or not
any program executes forever, and what all of its intermediate
states are.

this also captures every instance of random numbers as well.

It is not clear to me what random means in arithmetical truth.

Randomness can appear from the perspectives of observers, but I
don't see how it can arise in arithmetic.

?

It appears in all numbers written in any base. Most numbers are

I guess you know that.

I agree most numbers are incompressible, but I was using random in a
different sense than the unpredictability of the next digits of the
number given previous ones.

OK. But in the iterated self-duplication, both form of indeterminacy
can be mixed.

In the phi_i(j) in the UD, randomness can appear in the many j used
as input, as we usually dovetail on the function of one variable.
(but such input can easily be internalized in 0-variable programs).

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want
generate only that numbers.

Right, all the random numbers are there, the question is how to
throw the dart so that it lands on one.

Of course. And here the 1-indetermlinacy provides one answer.

but a simple counting algorithm generating all numbers, 0, 1,
2,  6999500235148668, ... generates all random finite
incompressible strings, and even all the infinite one (for the 1p
view, notably).

I think we are using the term in a slightly different sense.
Certainly any number in the range 1 - N can be considered as a
random number in that range (as it is a candidate to be output by
some RNG), but the problem is selecting it in a random (in the sense
of not-predictable) way.

Yes. here I just point on the fact that random number (with random
digits) exists.

There was a joke cartoon of some computer code:

int getRandomNumber()
{
return 4; // this number was determined by a random die roll
}

Lol
Close to my favorite infinite binary random sequence:
...

The term random is very large.

While a number can be interpreted as random once, it might not be
the second time.

While selecting and using all possibilities is arguably a way to
achieve randomness (unpredictibilty), (from some points of view) it
is often not practical nor useful.  Consider encrypting a message
with all possible keys and sending the recipient all possible
messages.

Not only might you need to send 2^256 possible ciphertexts but any
eavesdropper could use the first possible key to decrypt it. This
achieves randomness from the POV of the cipher, but not for the user
or the attackers.

In quantum cryptography this is essentially what is done, but it
requires that the sender and reciever (and attackers) be duplicated
for each possible key. So they need to be embedded in that larger
program that provides all possible inputs for it to seem random.
This is just FPI though, is it not?

Yes.

Bruno

Jason

In that (trivial) sense, arithmetic contains a lot of 3p
randomness, even perhaps too much. Then 1p randomeness appears too,
by the 1p indeterminacy (and that one is in the eyes of the machine).

Chaitin's results can also explain why we cannot filter out that 3p
randomness from arithmetic.

Bruno

What method is deployed to ensure that a program is not just a
regular random number and not some random number prefixed on a
real halting program?

It don't see how it makes a difference.

Truth is not a measure zero set, or is it?

I don't understand this question..  Could you clarify?

Jason

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch
jasonre...@gmail.com wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

Could you discuss the trace of the UD that LizR mentioned? How
is it computed? Could you write an explicit example? I have never
been able to grok it.

Bruno has written an actual UD in the LISP programming language.
I will write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i

Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far

# For each program we have generated that has not halted,
execute one instruction of ```

### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 17:16, Stephen Paul King wrote:

Dear Bruno,

On Sat, Dec 28, 2013 at 4:54 AM, Bruno Marchal marc...@ulb.ac.be
wrote:

On 27 Dec 2013, at 17:51, Stephen Paul King wrote:

Dear Bruno,

On Fri, Dec 27, 2013 at 11:11 AM, Bruno Marchal marc...@ulb.ac.be
wrote:

On 25 Dec 2013, at 18:40, spudboy...@aol.com wrote:

Are we not presuming, structure, or a-priori, existence of
something, doing this processing, this work?

In the UDA we assume a Turing universal, or sigma_1-complete
physical reality, in some local sense.

Could this Turing universal/sigma_1-complete in a local sense be
the exact criteria required to define the observations 3-
experiences of individuals or is it the 1-experiences of
individuals (observers) in keeping with the definition of an
observer as the intersection of infinitely many computations?

I think the UDA answers this question. You need Turing universality,
but also the FPI, which in some sense comes from mechanism, but not
necessarily universality, which has, here, only an indirect
relevance in the definition of what is a computation in arithmetic.

I suspect that the FPI results from the underlap or failure to
reach exact overlap between observers. As if a small part of the
computations that are observers is not universal. This would
effectively induce FPI as any one observer would be forever unable
to exactly match its experience of being in the world with that of
another.

,

We need this to just explain what is a computer, alias, universal
machine, alias universal number (implemented or not in a physical
reality).
Note that we do not assume a *primitive physical reality*. In comp,
we are a priori agnostic on this. The UDA, still will explains that
such primitiveness cannot solve the mind-body problem when made
into a dogma/assumption-of-primitiveness.

It has always seemed to me that UDA cannot solve the mind-body
problem strictly because it cannot comprehend the existence of
other minds.

UDA formulates the problem, and show how big the mind-body problem
is, even before tackling the other minds problem. But something is
said. In fact it is easy to derive from the UDA the following
assertions:

comp + explicit non-solipsism entails sharable many words or a core
linear physical reality.

I do not comprehend this. It is easy for us to see that solipsism
is false,

?

but how can a computation see anything? I do not understand how it
is that you can claim that computations will not be solipsistic by
default.

The 1p is solipsist, but not in a public way, just in the trivial way
that nobody can see that solipsism is false, as the dream argument
justifies. Solipsism is irrefutable, and hopefully false.

Now, if you remember the definition of first person plural (which is
just when different people enter the same annihilation-reconstitution
box), if we add non solipsism, it means that when machine interact,
they share the computations. So, the only way to avoid solipsism in
comp, is that the measure is sharable by interacting machine, and so
they have to live in a quantum-lile many worlds.

But comp in fact has to justify the non-solipsism, and this is begun
through the nuance Bp  p versus Bp  Dt. Normally the linearity
should allow the first person plural in the  Dt nuance case.

Exactly! I am looking forward to the explanation of this  nuance Bp
p versus Bp  Dt. :-

Keep in mind that UDA does not solve the problem, but formulate it.
AUDA go more deep in a solution, and the shape of that solution
Aristotelian theology (used by atheists and the main part of
institutionalized abramanic religion).

Sure. My main worry is that your wonderful result obtains at too
high a price: the inability to even model interactions and time.

If you show that, you extend the UDA in a full proof refutation of
comp. Good luck!
I thought this would be easy, but the simplicity of this is
counterbalanced by the self-referential constraints. On p-sigma_1, we
get already three arithmetical (quantum) quantizations.

Keep in mind that I offer a problem, not a solution (although I offer
a path toward it, and some shaping of the possible solutions, notably
that they belong to (neo)platonism and refute Aristotle).

Bruno

Bruno

Then in AUDA, keeping comp at the meta-level, I eliminate all
assumptions above very elementary arithmetic (Robinson Arithmetic).

The little and big bangs, including the taxes, and why it hurts is
derived from basically just

Kxy = x
Sxyz = xz(yz)

or just

x + 0 = x
x + s(y) = s(x + y)

x *0 = 0
x*s(y) = x*y + x

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 17:30, Stephen Paul King wrote:

Dear Bruno,

On Sat, Dec 28, 2013 at 6:53 AM, Bruno Marchal marc...@ulb.ac.be
wrote:

On 28 Dec 2013, at 04:39, Stephen Paul King wrote:

Dear Jason,

ISTM that the line  For each program we have generated that has
not halted, execute one instruction of it for each (Program p in
listOfPrograms) is buggy.

It assumes that the space of programs that do not halt is
accessible. How?

The space of all programs that do not halt is not Turing accessible.
The space of all programs that do halt is not Turing accessible.

The space of all programs (that do halt of do not halt) *is*
accessible.

Could you elaborate on this claim. I wish to be sure that I
understand it. Is it really a space?

It is a recursively enumerable set.

Would it have metrics and topological properties?

As a set, you can endow it with some structure, if you have the
motivation.

All what happen is that we have no general systematic,
computational, means to distinguish the programs that halt from the
programs that does not halt (on their inputs), and that is why the
universal dovetailer must *dovetail* on the executions of all
programs.

Not having a general systematic, computational, means to
distinguish.. has not stopped Nature.

Nor the FPI. Right.

She solves the problem by the evolution of physical worlds.

That's too quick, especially that we don't assume nature.

I propose that physical worlds ARE a form of non-universal
computation.

Then brain and computers cannot exist in those physical world.

I still think that the UD lives only in Platonia and is timeless and
static.

That's correct.

Only its projections (to use Plato's cave metaphor) are run as
physical worlds

OK. The FPI projections. But they are not run, only selected. The
computation are run, not the projection from inside.

Bruno

if they can survive the challenge of mutual consistency.

Bruno

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch
jasonre...@gmail.com wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

Could you discuss the trace of the UD that LizR mentioned? How
is it computed? Could you write an explicit example? I have never
been able to grok it.

Bruno has written an actual UD in the LISP programming language.  I
will write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i

Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far

# For each program we have generated that has not halted,
execute one instruction of it

for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next
time through

i = i + 1;
}

Any program, and whether or not it ever terminates can be
translated to a statement concerning numbers in arithmetic. Thus
mathematical truth captures the facts concerning whether or not any
program executes forever, and what all of its intermediate states
are. If these statements are true independently of you and me, then
the executions of these programs are embedded in arithmetical truth
and have a platonic existence.  The first, second, 10th,
1,000,000th, and 10^100th, and 10^100^100th state of the UD's
execution are mathematical facts which have definite values, and
all the conscious beings that are instantiated and evolve and write
books on consciousness, and talk about the UD on their Internet,
etc. as part of the execution of the UD are there, in the math.

Jason

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 17:35, Stephen Paul King wrote:

Dear Bruno,

On Sat, Dec 28, 2013 at 7:09 AM, Bruno Marchal marc...@ulb.ac.be
wrote:

On 28 Dec 2013, at 04:56, Jason Resch wrote:

On Fri, Dec 27, 2013 at 10:42 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

Any program, and whether or not it ever terminates can be
translated to a statement concerning numbers in arithmetic. Thus
mathematical truth captures the facts concerning whether or not any
program executes forever, and what all of its intermediate states
are.

this also captures every instance of random numbers as well.

It is not clear to me what random means in arithmetical truth.

Randomness can appear from the perspectives of observers, but I
don't see how it can arise in arithmetic.

?

It appears in all numbers written in any base. Most numbers are
I guess you know that. In the phi_i(j) in the UD, randomness can
appear in the many j used as input, as we usually dovetail on the
function of one variable. (but such input can easily be internalized
in 0-variable programs).

OK, I must agree, but can you see how this removes our ability to
use the natural ordering of the integers as an explanation of the
appearance of time?

Of the physical time? yes, that is right. That is a consequence of the
delay invariance of the FPI.  But we can still use it indirectly. It
is part of the additive-multiplicative structure of the numbers that
we assume (through the numbers laws).

Since there are multiple and equivalent (as to their properties)
sequences of integers that have very different orders relative to
each other, if we use these ordering as our time we would have a
different dimension of time for every one!

?
On the contrary. As you just said, the appearance of time is not
dependent on that order.

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want
generate only that numbers. but a simple counting algorithm
generating all numbers, 0, 1, 2,  6999500235148668, ...
generates all random finite incompressible strings, and even all the
infinite one (for the 1p view, notably).

In that (trivial) sense, arithmetic contains a lot of 3p randomness,
even perhaps too much. Then 1p randomeness appears too, by the 1p
indeterminacy (and that one is in the eyes of the machine).

Chaitin's results can also explain why we cannot filter out that 3p
randomness from arithmetic.

Have you had any more thoughts on the book keeping problem we have
discussed in the past?

Can you remind me? Thanks.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 17:43, Stephen Paul King wrote:

Dear Bruno,

On Sat, Dec 28, 2013 at 7:30 AM, Bruno Marchal marc...@ulb.ac.be
wrote:

On 28 Dec 2013, at 05:27, Stephen Paul King wrote:

Hi LizR and Jason,

Responding to both of you. I don't understand the claim of
determinism is random noise is necessary for the computations.
Turing machines require exact pre-specifiability. Adding noise
oracles is cheating!

But it exist in arithmetic. Subtracting it would be cheating. the
silmple counting algorith generates all random finite strings
(random in the strong Chaitin sense).

Almost all numbers are random, when written in some base. And you
can define the notion of base *in* arithmetic, so they exist in all
models of arithmetic. We can't subtract them.

With respect: No! We cannot wait forever (literally) to obtain
consistency of our data bases in the face of the inability to know
in advance the arrival time of messages in the network.

The fact that arithmetic contains all finite (even the random
ones) strings is an ontological claim. I have no problem with the
claim. My problem is that we cannot reason as if time does not exist
when we are trying to construct real computers.

We have to use different ideas, for example: competition for
resources! Platonic computers do not compete for resources nor
change. They are static and fixed eternally...

In God's eyes. We already know that from inside, except for the
measure problem which remains to be solved, things look very dynamical
and changing all the times. Bp  p is already a logic of (subjective)
time. Bp  Dt gives a quantum logic, Bp  Dt  p gives a subjective or
intuitionist quantum logic full of percepts including a time which can
be felt.

It is a trivial exercise to show that all diophantine approximation of
anything physical is emulated in arithmetic, so Platonia contains all
possible competition on all conceivable resources, and actually
anything that you can live, or not live, like the collision between
the Milky Way and Andromeda is emulated statically in arithmetic, and
lived temporally by its emulated persons.

Platonia is static from outside, not from inside. Arithmetic becomes a
block universe(s), although it is more like a block-mindscape or a
block multi-dreams.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 18:10, Stephen Paul King wrote:

Dear Bruno,

On Sat, Dec 28, 2013 at 7:37 AM, Bruno Marchal marc...@ulb.ac.be
wrote:

On 28 Dec 2013, at 05:27, LizR wrote:

On 28 December 2013 17:23, Edgar L. Owen edgaro...@att.net wrote:
Jason,

You might be able to theoretically simulate it but certainly not
compute it in real time which is what reality actually does which
is my point.

In real time ?! In comp (and many TOEs) time is emergent.

Physical times and subjective time emerge. OK. But let us be honest,
comp assumes already a sort of time, through the natural order: à,
1, 2, 3, ...

Then you have all UD-time step of the computations emulated by the UD:

phi_444(6) first step
...
phi_444(6) second step
... ...  (meaning greater delay
in the UD-time steps).

ph_444(6) third  step
... ... ...
ph_444(6) fourth  step
... ...
ph_444(6) fifth step
etc.

This would explain the sequencing of events aspect of time, but it
does nothing to address the concurrency problem.

Nor dark matter, nor visible matter, nor

That is the problem I offer to you, as a result of the translation of
he mind-body problem in arithmetic, enforced by the comp hypothesis.

We need a theory of time that has an explanation of both sequencing
and transition. I wish you could study GR, say from Penrose's math
book, and Prof. Hitoshi Kitada's Local Time interpretation of QM.

I did, and we have already discussed this. That can be used to
progress, may be. If you find that it would be very nice.
Right now, we need to solve much more simpler problem in logic to
proceed in a way such that we keep into account the communicable/non-
communicable self-referential constraints, in the way imposed by the
FPI.

It gives a nice set of concepts that help solve the problem of
time: there is no such thing as a global time; there is only local
time. Local for each individual observer. Synchronizations of these
local times generates the appearance of global time for a collection
that is co-moving or (equivalently) have similar inertial frames.

That's physics. But physics is given by a precise equation in comp.
You are free to use *any* papers and results to solve that equation.
You need to study logic to make the link properly.

(Of course you can also do physics, without tackling the comp mind-
body problem. That's what physicists do since a long time)

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 18:43, Stephen Paul King wrote:

Dear Bruno,

On Sat, Dec 28, 2013 at 12:34 PM, Bruno Marchal marc...@ulb.ac.be
wrote:

On 28 Dec 2013, at 07:34, LizR wrote:

On 28 December 2013 19:31, Stephen Paul King stephe...@provensecure.com
wrote:

Computed how? By what?

I know the answer to this one! To quote Brent -- He proposes to
dispense with any physical computation and have the UD exist via
arithmetical realism as an abstract, immaterial computation.

Assuming comp, there is not much choice in the matter. That is the
point.

I will agree.

Above the substitution level: interaction between universal
machines, including one apparently sustained from below the
substitution level by the statistical interference between
infinities of universal machines getting your actual states.

But the actual states are not just some random string from my
point of view!

Nor for me. They are state brought by some computation above the S-
level, and supported by infinitely many computation below the S-level.
The result is indeterminate, but not itself random. In The WM-
duplication, the result is indeterminate or random, but W or M
themselves are not random.

The very fact that we can (somewhat) communicate is an important
fact. There is a selection mechanism: interaction.

That's part of the problem. Showing this.

I don't know how to avoid those infinities without reifying some God-
of-the-gap or Matter-of-the-gap notion to singularize a computation
for consciousness, but if that is needed for consciousness, then
comp is false.

Umm, that is a false choice! The FPI is good enough to do the job
without resorting to a 'god/matter in the gap solution. The
singularization of consciousness is easy, as you have shown.

No it is not! There is a lot of work to be done before we have a realm
in which words like interaction can make sense.

It is the concurrent interaction problem that is not easy.

So let us concentrate on what is more easy first.

I cannot exactly predict your actions and thus can only bet on
action with my physical behaviors even if the physical world is an
illusion. The fact that it is a common and persistent illusion makes
it a ground of commonality from which we can distinguish ourselves 3-
p wise from each other.

We cannot use physics.

True, you still survive with a digital brain, but no more through
comp, it is true from comp + some explicit magic to make disappear
the other realities. You get an irrefutable form of cosmic solipsism.

There is no magic here, there is the SAT problem. Boolean algebras
do not automatically pop out with global consistency over their
arguments/propositions. One has to actually physically run a
physical world to know what it will do. Claiming that it exists in
Platonia is not a solution.

No, it is a problem. And thanks to the work done, it is (with comp) a
problem in arithmetic. That is the result.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 22:12, meekerdb wrote:

On 12/28/2013 3:13 AM, Bruno Marchal wrote:
Perhaps; but only for nano second. you real mind overlap on
sequence of states, with the right probabilities, and for this you
need the complete run of the UD, because your next moment is
determioned by the FPI on all computations.

That's a point that bothers me.  It seems that you require a
completed, realized uncountable inifinity.

Not in the ontology, where I can use only 0 and its successors, and
the numbers laws (+ and *).

What the theology and physics need from inside is indeed not bound-
able, and is bigger than anything we can conceive. That is in part a
reason why I use the term theology. from inside arithmetic, we are
eventually confronted with some thing very big.

Bruno

Brent

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 22:19, meekerdb wrote:

On 12/28/2013 3:43 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 04:36, Stephen Paul King wrote:

I loath Kronecker's claim! It is synonymous to Man is the measure
of all things.

What is his claim?  I am not familiar with it.

God created the Integers, all else is the invention of man.

man is a measure of all things is a quote from a french
philosopher (I just forget right now his name) itself taken from a
greek general, which cut the feet or head of all soldier having not
the right size (!).  (Sorry for those vague memories, learn this in
highschool)

Man is the measure of all things. is usually attributed to
Protagoras (a student of Plato).

Ah! Thanks. Protagoras is also the one asking if virtue are teachable.
I define a virtue Protagorean when it is not teachable by words, but
still by practice/example.

Procrustes, who stretched or chopped guests to fit his iron bed, was
a metal smith, not a general.

OK, I remember! Thanks.

Now, of course, comp saves Kronecker from anthropomorphism, as with
comp we can say that:
God created the integers, all else is the invention of ...
integers.

Die ganze Zahl schuf der liebe Gott, alles Übrige ist Menschenwerk
--- Kronecker

Die ganze Zahl schuf der liebe Gott, alles Übrige ist Zahlenwerk

:)

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want
generate only that numbers. but a simple counting algorithm
generating all numbers, 0, 1, 2,  6999500235148668, ...
generates all random finite incompressible strings,

How can a finite string be incompressible?  6999500235148668 in base
6999500235148669 is just 10.

You can define a finite string as incompressible when the shorter
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short
sequences which indeed will depend of the language used (here
combinators).

Then you can show that such a definition can be made universal by
adding some constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base, are
random in that sense.

Of course, 10 is a sort of compression of any string X in some base,
but if you allow change of base, you will need to send the base with
the number in the message. If you fix the base, then indeed 10 will be
a compression of that particular number base, for that language, and
it is part of incompressibility theory that no definition exist
working for all (small) numbers. Each particular language will have
some exception on the incompressibility issue. That should be part of
the role of the variable constant in the general universal definition.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```
On 12/29/2013 5:56 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate computationally a random
number, and that is right, if we want generate only that numbers. but a simple
counting algorithm generating all numbers, 0, 1, 2,  6999500235148668, ...
generates all random finite incompressible strings,

How can a finite string be incompressible? 6999500235148668 in base 6999500235148669 is
just 10.

You can define a finite string as incompressible when the shorter combinators to
generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short sequences which indeed
will depend of the language used (here combinators).

Then you can show that such a definition can be made universal by adding some constant,
which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base, are random in
that sense.

Of course, 10 is a sort of compression of any string X in some base, but if you allow
change of base, you will need to send the base with the number in the message. If you
fix the base, then indeed 10 will be a compression of that particular number base, for
that language, and it is part of incompressibility theory that no definition exist
working for all (small) numbers.

Since all finite numbers are small, I think this means the theory only holds in
the limit.

Brent

Each particular language will have some exception on the incompressibility issue. That
should be part of the role of the variable constant in the general universal definition.

Bruno

http://iridia.ulb.ac.be/~marchal/ http://iridia.ulb.ac.be/%7Emarchal/

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### Re: Bruno's mathematical reality

```On Sun, Dec 29, 2013 at 2:25 PM, meekerdb meeke...@verizon.net wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want generate
only that numbers. but a simple counting algorithm generating all numbers,
0, 1, 2,  6999500235148668, ... generates all random finite
incompressible strings,

How can a finite string be incompressible?  6999500235148668 in base
6999500235148669 is just 10.

You can define a finite string as incompressible when the shorter
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short sequences
which indeed will depend of the language used (here combinators).

Then you can show that such a definition can be made universal by adding
some constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base, are
random in that sense.

Of course, 10 is a sort of compression of any string X in some base, but
if you allow change of base, you will need to send the base with the number
in the message. If you fix the base, then indeed 10 will be a compression
of that particular number base, for that language, and it is part of
incompressibility theory that no definition exist working for all (small)
numbers.

Since all finite numbers are small, I think this means the theory only
holds in the limit.

Brent

Brent,

It is easy to see with the pigeon hole principal.  There are more 2 digit
numbers than 1 digit numbers, and more 3 digit numbers than 2 digit
numbers, and so on.  For any string you can represent using a shorter
string, another shorter string must necessarily be displaced.  You can't
keep replacing things with shorter strings because there aren't enough of
them, so as a side-effect, every compression strategy must represent some
strings by larger ones.  In fact, the average size of all possible
compressed messages (with some upper-bound length n) can never be smaller
than the average size of all uncompressed messages.

The only reason compression algorithms are useful is because they are
tailored to represent some class of messages with shorter strings, while
making (the vast majority of) other messages slightly larger.

Jason

Each particular language will have some exception on the
incompressibility issue. That should be part of the role of the variable
constant in the general universal definition.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```
On 12/29/2013 1:28 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 2:25 PM, meekerdb meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally a
random number, and that is right, if we want generate only that numbers.
but a
simple counting algorithm generating all numbers, 0, 1, 2,
6999500235148668,
... generates all random finite incompressible strings,

How can a finite string be incompressible? 6999500235148668 in base
6999500235148669 is just 10.

You can define a finite string as incompressible when the shorter
combinators to
generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short sequences
which
indeed will depend of the language used (here combinators).

Then you can show that such a definition can be made universal by adding
some
constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base, are
random in
that sense.

Of course, 10 is a sort of compression of any string X in some base, but if
you
allow change of base, you will need to send the base with the number in the
message. If you fix the base, then indeed 10 will be a compression of that
particular number base, for that language, and it is part of
incompressibility
theory that no definition exist working for all (small) numbers.

Since all finite numbers are small, I think this means the theory only
holds in the
limit.

Brent

Brent,

It is easy to see with the pigeon hole principal.  There are more 2 digit numbers than 1
digit numbers, and more 3 digit numbers than 2 digit numbers, and so on.  For any string
you can represent using a shorter string, another shorter string must necessarily be
displaced.  You can't keep replacing things with shorter strings because there aren't
enough of them, so as a side-effect, every compression strategy must represent some
strings by larger ones.  In fact, the average size of all possible compressed messages
(with some upper-bound length n) can never be smaller than the average size of all
uncompressed messages.

The only reason compression algorithms are useful is because they are tailored to
represent some class of messages with shorter strings, while making (the vast majority
of) other messages slightly larger.

A good explanation.  But just because you cannot compress all numbers of a given size
doesn't imply that any particular number is incompressible.  So isn't it the case that
every finite number string is compressible in some algorithm?  So there's no sense to
saying 6999500235148668 is random, but 11 is not, except relative to some
given compression algorithm.

Brent

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### Re: Bruno's mathematical reality

```Dear Brent and Jason,

I think that this is an important idea: the relationship between
compression algorithms and numbers. It does not look like a simple
one-to-one and onto map!

On Sun, Dec 29, 2013 at 4:51 PM, meekerdb meeke...@verizon.net wrote:

On 12/29/2013 1:28 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 2:25 PM, meekerdb meeke...@verizon.net wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want generate
only that numbers. but a simple counting algorithm generating all numbers,
0, 1, 2,  6999500235148668, ... generates all random finite
incompressible strings,

How can a finite string be incompressible?  6999500235148668 in base
6999500235148669 is just 10.

You can define a finite string as incompressible when the shorter
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short sequences
which indeed will depend of the language used (here combinators).

Then you can show that such a definition can be made universal by
adding some constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base, are
random in that sense.

Of course, 10 is a sort of compression of any string X in some base,
but if you allow change of base, you will need to send the base with the
number in the message. If you fix the base, then indeed 10 will be a
compression of that particular number base, for that language, and it is
part of incompressibility theory that no definition exist working for all
(small) numbers.

Since all finite numbers are small, I think this means the theory only
holds in the limit.

Brent

Brent,

It is easy to see with the pigeon hole principal.  There are more 2
digit numbers than 1 digit numbers, and more 3 digit numbers than 2 digit
numbers, and so on.  For any string you can represent using a shorter
string, another shorter string must necessarily be displaced.  You can't
keep replacing things with shorter strings because there aren't enough of
them, so as a side-effect, every compression strategy must represent some
strings by larger ones.  In fact, the average size of all possible
compressed messages (with some upper-bound length n) can never be smaller
than the average size of all uncompressed messages.

The only reason compression algorithms are useful is because they are
tailored to represent some class of messages with shorter strings, while
making (the vast majority of) other messages slightly larger.

A good explanation.  But just because you cannot compress all numbers of a
given size doesn't imply that any particular number is incompressible.  So
isn't it the case that every finite number string is compressible in some
algorithm?  So there's no sense to saying 6999500235148668 is random, but
11 is not, except relative to some given compression algorithm.

Brent

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Senior Researcher

Mobile: (864) 567-3099

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http://www.provensecure.us/

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### Re: Bruno's mathematical reality

```On Sun, Dec 29, 2013 at 4:51 PM, meekerdb meeke...@verizon.net wrote:

On 12/29/2013 1:28 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 2:25 PM, meekerdb meeke...@verizon.net wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want generate
only that numbers. but a simple counting algorithm generating all numbers,
0, 1, 2,  6999500235148668, ... generates all random finite
incompressible strings,

How can a finite string be incompressible?  6999500235148668 in base
6999500235148669 is just 10.

You can define a finite string as incompressible when the shorter
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short sequences
which indeed will depend of the language used (here combinators).

Then you can show that such a definition can be made universal by
adding some constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base, are
random in that sense.

Of course, 10 is a sort of compression of any string X in some base,
but if you allow change of base, you will need to send the base with the
number in the message. If you fix the base, then indeed 10 will be a
compression of that particular number base, for that language, and it is
part of incompressibility theory that no definition exist working for all
(small) numbers.

Since all finite numbers are small, I think this means the theory only
holds in the limit.

Brent

Brent,

It is easy to see with the pigeon hole principal.  There are more 2
digit numbers than 1 digit numbers, and more 3 digit numbers than 2 digit
numbers, and so on.  For any string you can represent using a shorter
string, another shorter string must necessarily be displaced.  You can't
keep replacing things with shorter strings because there aren't enough of
them, so as a side-effect, every compression strategy must represent some
strings by larger ones.  In fact, the average size of all possible
compressed messages (with some upper-bound length n) can never be smaller
than the average size of all uncompressed messages.

The only reason compression algorithms are useful is because they are
tailored to represent some class of messages with shorter strings, while
making (the vast majority of) other messages slightly larger.

A good explanation.

Thanks.

But just because you cannot compress all numbers of a given size doesn't
imply that any particular number is incompressible.

That is true if you consider the size of the compression program to be of
no relevance.  In such a case, you can of course have a number of very
small strings map directly to very large ones.

So isn't it the case that every finite number string is compressible in
some algorithm?  So there's no sense to saying 6999500235148668 is random,
but 11 is not, except relative to some given compression
algorithm.

Right, but this leads to the concept of Kolmogorov complexity. If you
consider the size of the minimum string and algorithm together, necessary
to represent some number, you will find there are some patterns of data
that are more compressible than others.  In your previous example with base
6999500235148668, you would need to include both that base, and the string
10 in order to encode 6999500235148669.  For the majority of numbers, you
will find the Kolmogorov complexity of the number to almost always be on
the order of the number of digits in that number.  The exceptions like
11 are few and far between.

Jason

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### Re: Bruno's mathematical reality

```On Sun, Dec 29, 2013 at 5:03 PM, Stephen Paul King
stephe...@provensecure.com wrote:

Dear Brent and Jason,

I think that this is an important idea: the relationship between
compression algorithms and numbers. It does not look like a simple
one-to-one and onto map!

Stephen,

For any loss-less (full-fidelity) compression algorithm, the mapping is
one-to-one.  There are other compression algorithms, like jpeg or mp3 which
are lossy (they discard some information in the process), and hence they
are many-to-one.

Jason

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### Re: Bruno's mathematical reality

```
On 12/29/2013 2:08 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 4:51 PM, meekerdb meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 12/29/2013 1:28 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 2:25 PM, meekerdb meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want generate
only
that numbers. but a simple counting algorithm generating all numbers,
0, 1,
2,  6999500235148668, ... generates all random finite incompressible
strings,

How can a finite string be incompressible? 6999500235148668 in base
6999500235148669 is just 10.

You can define a finite string as incompressible when the shorter
combinators
to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short sequences
which
indeed will depend of the language used (here combinators).

Then you can show that such a definition can be made universal by
constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base, are
random
in that sense.

Of course, 10 is a sort of compression of any string X in some base,
but if
you allow change of base, you will need to send the base with the
number in
the message. If you fix the base, then indeed 10 will be a compression
of that
particular number base, for that language, and it is part of
incompressibility
theory that no definition exist working for all (small) numbers.

Since all finite numbers are small, I think this means the theory only
holds in
the limit.

Brent

Brent,

It is easy to see with the pigeon hole principal.  There are more 2 digit
numbers
than 1 digit numbers, and more 3 digit numbers than 2 digit numbers, and so
on.
For any string you can represent using a shorter string, another shorter
string
must necessarily be displaced.  You can't keep replacing things with shorter
strings because there aren't enough of them, so as a side-effect, every
compression
strategy must represent some strings by larger ones.  In fact, the average
size of
all possible compressed messages (with some upper-bound length n) can never
be
smaller than the average size of all uncompressed messages.

The only reason compression algorithms are useful is because they are
tailored to
represent some class of messages with shorter strings, while making (the
vast
majority of) other messages slightly larger.

A good explanation.

Thanks.

But just because you cannot compress all numbers of a given size doesn't
imply that
any particular number is incompressible.

That is true if you consider the size of the compression program to be of no relevance.
In such a case, you can of course have a number of very small strings map directly to
very large ones.

So isn't it the case that every finite number string is compressible in
some
algorithm?  So there's no sense to saying 6999500235148668 is random, but
11 is not, except relative to some given compression algorithm.

Right, but this leads to the concept of Kolmogorov complexity. If you consider the size
of the minimum string and algorithm together, necessary to represent some number, you
will find there are some patterns of data that are more compressible than others.  In
your previous example with base 6999500235148668, you would need to include both that
base, and the string 10 in order to encode 6999500235148669.

But that seems to make the randomness of a number dependent on the base used to write it
down? Did I have to write down And this is in base 10 to show that 6999500235148668 is
random?  There seems to be an equivocation here on computing a number and computing a
representation of a number.

For the majority of numbers, you will find the Kolmogorov complexity of the number to
almost always be on the order of the number of digits in that number.  The exceptions
like 11 are few and far between.

1 looks a lot messier in base 9.

Berent

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To unsubscribe from this group and stop receiving emails from it, send an email
To post to this group, send email to everything-list@googlegroups.com.

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### Re: Bruno's mathematical reality

```On Sun, Dec 29, 2013 at 5:42 PM, meekerdb meeke...@verizon.net wrote:

On 12/29/2013 2:08 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 4:51 PM, meekerdb meeke...@verizon.net wrote:

On 12/29/2013 1:28 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 2:25 PM, meekerdb meeke...@verizon.net wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want generate
only that numbers. but a simple counting algorithm generating all numbers,
0, 1, 2,  6999500235148668, ... generates all random finite
incompressible strings,

How can a finite string be incompressible?  6999500235148668 in base
6999500235148669 is just 10.

You can define a finite string as incompressible when the shorter
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short sequences
which indeed will depend of the language used (here combinators).

Then you can show that such a definition can be made universal by
adding some constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base, are
random in that sense.

Of course, 10 is a sort of compression of any string X in some base,
but if you allow change of base, you will need to send the base with the
number in the message. If you fix the base, then indeed 10 will be a
compression of that particular number base, for that language, and it is
part of incompressibility theory that no definition exist working for all
(small) numbers.

Since all finite numbers are small, I think this means the theory only
holds in the limit.

Brent

Brent,

It is easy to see with the pigeon hole principal.  There are more 2
digit numbers than 1 digit numbers, and more 3 digit numbers than 2 digit
numbers, and so on.  For any string you can represent using a shorter
string, another shorter string must necessarily be displaced.  You can't
keep replacing things with shorter strings because there aren't enough of
them, so as a side-effect, every compression strategy must represent some
strings by larger ones.  In fact, the average size of all possible
compressed messages (with some upper-bound length n) can never be smaller
than the average size of all uncompressed messages.

The only reason compression algorithms are useful is because they are
tailored to represent some class of messages with shorter strings, while
making (the vast majority of) other messages slightly larger.

A good explanation.

Thanks.

But just because you cannot compress all numbers of a given size doesn't
imply that any particular number is incompressible.

That is true if you consider the size of the compression program to be
of no relevance.  In such a case, you can of course have a number of very
small strings map directly to very large ones.

So isn't it the case that every finite number string is compressible in
some algorithm?  So there's no sense to saying 6999500235148668 is random,
but 11 is not, except relative to some given compression
algorithm.

Right, but this leads to the concept of Kolmogorov complexity. If you
consider the size of the minimum string and algorithm together, necessary
to represent some number, you will find there are some patterns of data
that are more compressible than others.  In your previous example with base
6999500235148668, you would need to include both that base, and the string
10 in order to encode 6999500235148669.

But that seems to make the randomness of a number dependent on the base
used to write it down? Did I have to write down And this is in base 10 to
show that 6999500235148668 is random?  There seems to be an equivocation
here on computing a number and computing a representation of a number.

A number containing regular patterns in some base, will also contain
regular patterns in some other base (even if they are not obvious to us),
compression algorithms are good at recognizing them.

The text of this sentence may not seem very redundant, but english text can
generally be compressed somewhere between 20% - 30% of its original size.
If you convert a number like 555 to base 2, its patterns should
be more evident in the pattern of bits.

For the majority of numbers, you will find the Kolmogorov complexity
of the number to almost always be on the order of the number of digits in
that number.  The exceptions like 11 are few and far between.

1 looks a lot messier in base 9.

base 10: 111
base 9: 7355531854711617707
base 2: 011010110111010110101011001010000100011100

In base 9, there is a high proportion of 7's compared to other digits. In
base 2, the sequence '110' seems more common than ```

### Re: Bruno's mathematical reality

```
On 12/29/2013 3:49 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 5:42 PM, meekerdb meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 12/29/2013 2:08 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 4:51 PM, meekerdb meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 12/29/2013 1:28 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 2:25 PM, meekerdb meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want
generate
only that numbers. but a simple counting algorithm generating all
numbers, 0, 1, 2,  6999500235148668, ... generates all random
finite incompressible strings,

How can a finite string be incompressible? 6999500235148668 in base
6999500235148669 is just 10.

You can define a finite string as incompressible when the shorter
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short
sequences
which indeed will depend of the language used (here combinators).

Then you can show that such a definition can be made universal by
some constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base,
are
random in that sense.

Of course, 10 is a sort of compression of any string X in some
base, but
if you allow change of base, you will need to send the base with the
number in the message. If you fix the base, then indeed 10 will be a
compression of that particular number base, for that language, and
it is
part of incompressibility theory that no definition exist working
for all
(small) numbers.

Since all finite numbers are small, I think this means the theory
only
holds in the limit.

Brent

Brent,

It is easy to see with the pigeon hole principal.  There are more 2
digit
numbers than 1 digit numbers, and more 3 digit numbers than 2 digit
numbers,
and so on.  For any string you can represent using a shorter string,
another
shorter string must necessarily be displaced.  You can't keep
replacing
things with shorter strings because there aren't enough of them, so as a
side-effect, every compression strategy must represent some strings by
larger
ones.  In fact, the average size of all possible compressed messages
(with
some upper-bound length n) can never be smaller than the average size
of all
uncompressed messages.

The only reason compression algorithms are useful is because they are
tailored
to represent some class of messages with shorter strings, while making
(the
vast majority of) other messages slightly larger.

A good explanation.

Thanks.

But just because you cannot compress all numbers of a given size
doesn't imply
that any particular number is incompressible.

That is true if you consider the size of the compression program to be of no
relevance.  In such a case, you can of course have a number of very small
strings
map directly to very large ones.

So isn't it the case that every finite number string is compressible
in some
algorithm?  So there's no sense to saying 6999500235148668 is random,
but
11 is not, except relative to some given compression
algorithm.

Right, but this leads to the concept of Kolmogorov complexity. If you
consider the
size of the minimum string and algorithm together, necessary to represent
some
number, you will find there are some patterns of data that are more
compressible
than others.  In your previous example with base 6999500235148668, you
would need
to include both that base, and the string 10 in order to encode
6999500235148669.

But that seems to make the randomness of a number dependent on the base
used to
write it down? Did I have to write down And this is in base 10 to show
that
6999500235148668 is random?  There seems to be an equivocation here on
computing a
number and computing a representation of a number.

A number containing regular patterns in some base, will also contain regular patterns in
some other base (even if they are not obvious to us), compression algorithms are good at
recognizing them.

The text of this sentence may not seem very redundant, but english text can generally be
compressed somewhere between 20% - 30% of ```

### Re: Bruno's mathematical reality

```On Sun, Dec 29, 2013 at 6:58 PM, meekerdb meeke...@verizon.net wrote:

On 12/29/2013 3:49 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 5:42 PM, meekerdb meeke...@verizon.net wrote:

On 12/29/2013 2:08 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 4:51 PM, meekerdb meeke...@verizon.net wrote:

On 12/29/2013 1:28 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 2:25 PM, meekerdb meeke...@verizon.net wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want generate
only that numbers. but a simple counting algorithm generating all numbers,
0, 1, 2,  6999500235148668, ... generates all random finite
incompressible strings,

How can a finite string be incompressible?  6999500235148668 in base
6999500235148669 is just 10.

You can define a finite string as incompressible when the shorter
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short sequences
which indeed will depend of the language used (here combinators).

Then you can show that such a definition can be made universal by
adding some constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base, are
random in that sense.

Of course, 10 is a sort of compression of any string X in some base,
but if you allow change of base, you will need to send the base with the
number in the message. If you fix the base, then indeed 10 will be a
compression of that particular number base, for that language, and it is
part of incompressibility theory that no definition exist working for all
(small) numbers.

Since all finite numbers are small, I think this means the theory only
holds in the limit.

Brent

Brent,

It is easy to see with the pigeon hole principal.  There are more 2
digit numbers than 1 digit numbers, and more 3 digit numbers than 2 digit
numbers, and so on.  For any string you can represent using a shorter
string, another shorter string must necessarily be displaced.  You can't
keep replacing things with shorter strings because there aren't enough of
them, so as a side-effect, every compression strategy must represent some
strings by larger ones.  In fact, the average size of all possible
compressed messages (with some upper-bound length n) can never be smaller
than the average size of all uncompressed messages.

The only reason compression algorithms are useful is because they are
tailored to represent some class of messages with shorter strings, while
making (the vast majority of) other messages slightly larger.

A good explanation.

Thanks.

But just because you cannot compress all numbers of a given size
doesn't imply that any particular number is incompressible.

That is true if you consider the size of the compression program to be
of no relevance.  In such a case, you can of course have a number of very
small strings map directly to very large ones.

So isn't it the case that every finite number string is compressible
in some algorithm?  So there's no sense to saying 6999500235148668 is
random, but 11 is not, except relative to some given
compression algorithm.

Right, but this leads to the concept of Kolmogorov complexity. If you
consider the size of the minimum string and algorithm together, necessary
to represent some number, you will find there are some patterns of data
that are more compressible than others.  In your previous example with base
6999500235148668, you would need to include both that base, and the string
10 in order to encode 6999500235148669.

But that seems to make the randomness of a number dependent on the base
used to write it down? Did I have to write down And this is in base 10 to
show that 6999500235148668 is random?  There seems to be an equivocation
here on computing a number and computing a representation of a number.

A number containing regular patterns in some base, will also contain
regular patterns in some other base (even if they are not obvious to us),
compression algorithms are good at recognizing them.

The text of this sentence may not seem very redundant, but english text
can generally be compressed somewhere between 20% - 30% of its original
size.  If you convert a number like 555 to base 2, its patterns
should be more evident in the pattern of bits.

For the majority of numbers, you will find the Kolmogorov complexity
of the number to almost always be on the order of the number of digits in
that number.  The exceptions like 11 are few and far between.

1 looks a lot messier in base 9.

base 10: 111
base 9: 7355531854711617707
base 2: ```

### Re: Bruno's mathematical reality

```
On 12/29/2013 7:45 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 6:58 PM, meekerdb meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 12/29/2013 3:49 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 5:42 PM, meekerdb meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 12/29/2013 2:08 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 4:51 PM, meekerdb meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 12/29/2013 1:28 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 2:25 PM, meekerdb meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want
generate only that numbers. but a simple counting algorithm
generating all numbers, 0, 1, 2,  6999500235148668, ...
generates all random finite incompressible strings,

How can a finite string be incompressible? 6999500235148668 in
base
6999500235148669 is just 10.

You can define a finite string as incompressible when the
shorter
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short
sequences which indeed will depend of the language used (here
combinators).

Then you can show that such a definition can be made universal
by
adding some constant, which will depend of the universal
language.

It can be shown that most (finite!) numbers, written in any
base,
are random in that sense.

Of course, 10 is a sort of compression of any string X in some
base,
but if you allow change of base, you will need to send the base
with
the number in the message. If you fix the base, then indeed 10
will
be a compression of that particular number base, for that
language,
and it is part of incompressibility theory that no definition
exist
working for all (small) numbers.

Since all finite numbers are small, I think this means the
theory
only holds in the limit.

Brent

Brent,

It is easy to see with the pigeon hole principal.  There are more 2
digit
numbers than 1 digit numbers, and more 3 digit numbers than 2 digit
numbers, and so on.  For any string you can represent using a
shorter
string, another shorter string must necessarily be displaced.  You
can't keep replacing things with shorter strings because there
aren't
enough of them, so as a side-effect, every compression strategy must
represent some strings by larger ones.  In fact, the average size
of all
possible compressed messages (with some upper-bound length n) can
never
be smaller than the average size of all uncompressed messages.

The only reason compression algorithms are useful is because they
are
tailored to represent some class of messages with shorter strings,
while
making (the vast majority of) other messages slightly larger.

A good explanation.

Thanks.

But just because you cannot compress all numbers of a given size
doesn't
imply that any particular number is incompressible.

That is true if you consider the size of the compression program to be
of no
relevance.  In such a case, you can of course have a number of very
small
strings map directly to very large ones.

So isn't it the case that every finite number string is
compressible in
some algorithm?  So there's no sense to saying 6999500235148668 is
random,
but 11 is not, except relative to some given compression
algorithm.

Right, but this leads to the concept of Kolmogorov complexity. If you
consider
the size of the minimum string and algorithm together, necessary to
represent
some number, you will find there are some patterns of data that are more
compressible than others.  In your previous example with base
6999500235148668, you would need to include both that base, and the
string
10 in order to encode 6999500235148669.

But that seems to make the randomness of a number dependent on the base
used to
write it down? Did I have to write down And this is in base 10 to
show that
6999500235148668 is random? ```

### Re: Bruno's mathematical reality

```On Sun, Dec 29, 2013 at 11:54 PM, meekerdb meeke...@verizon.net wrote:

On 12/29/2013 7:45 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 6:58 PM, meekerdb meeke...@verizon.net wrote:

On 12/29/2013 3:49 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 5:42 PM, meekerdb meeke...@verizon.net wrote:

On 12/29/2013 2:08 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 4:51 PM, meekerdb meeke...@verizon.net wrote:

On 12/29/2013 1:28 PM, Jason Resch wrote:

On Sun, Dec 29, 2013 at 2:25 PM, meekerdb meeke...@verizon.net wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want generate
only that numbers. but a simple counting algorithm generating all numbers,
0, 1, 2,  6999500235148668, ... generates all random finite
incompressible strings,

How can a finite string be incompressible?  6999500235148668 in base
6999500235148669 is just 10.

You can define a finite string as incompressible when the shorter
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short
sequences which indeed will depend of the language used (here
combinators).

Then you can show that such a definition can be made universal by
adding some constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base,
are random in that sense.

Of course, 10 is a sort of compression of any string X in some base,
but if you allow change of base, you will need to send the base with the
number in the message. If you fix the base, then indeed 10 will be a
compression of that particular number base, for that language, and it is
part of incompressibility theory that no definition exist working for all
(small) numbers.

Since all finite numbers are small, I think this means the theory
only holds in the limit.

Brent

Brent,

It is easy to see with the pigeon hole principal.  There are more 2
digit numbers than 1 digit numbers, and more 3 digit numbers than 2 digit
numbers, and so on.  For any string you can represent using a shorter
string, another shorter string must necessarily be displaced.  You can't
keep replacing things with shorter strings because there aren't enough of
them, so as a side-effect, every compression strategy must represent some
strings by larger ones.  In fact, the average size of all possible
compressed messages (with some upper-bound length n) can never be smaller
than the average size of all uncompressed messages.

The only reason compression algorithms are useful is because they are
tailored to represent some class of messages with shorter strings, while
making (the vast majority of) other messages slightly larger.

A good explanation.

Thanks.

But just because you cannot compress all numbers of a given size
doesn't imply that any particular number is incompressible.

That is true if you consider the size of the compression program to be
of no relevance.  In such a case, you can of course have a number of very
small strings map directly to very large ones.

So isn't it the case that every finite number string is compressible
in some algorithm?  So there's no sense to saying 6999500235148668 is
random, but 11 is not, except relative to some given
compression algorithm.

Right, but this leads to the concept of Kolmogorov complexity. If you
consider the size of the minimum string and algorithm together, necessary
to represent some number, you will find there are some patterns of data
that are more compressible than others.  In your previous example with base
6999500235148668, you would need to include both that base, and the string
10 in order to encode 6999500235148669.

But that seems to make the randomness of a number dependent on the
base used to write it down? Did I have to write down And this is in base
10 to show that 6999500235148668 is random?  There seems to be an
equivocation here on computing a number and computing a representation
of a number.

A number containing regular patterns in some base, will also contain
regular patterns in some other base (even if they are not obvious to us),
compression algorithms are good at recognizing them.

The text of this sentence may not seem very redundant, but english text
can generally be compressed somewhere between 20% - 30% of its original
size.  If you convert a number like 555 to base 2, its patterns
should be more evident in the pattern of bits.

For the majority of numbers, you will find the Kolmogorov
complexity of the number to almost always be on the order of the number of
digits in that number.  The exceptions like 11 are few and far
between.

1 looks a lot messier in ```

### Re: Bruno's mathematical reality

```

On 29 Dec 2013, at 20:25, meekerdb wrote:

On 12/29/2013 5:56 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 22:23, meekerdb wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want
generate only that numbers. but a simple counting algorithm
generating all numbers, 0, 1, 2,  6999500235148668, ...
generates all random finite incompressible strings,

How can a finite string be incompressible?  6999500235148668 in
base 6999500235148669 is just 10.

You can define a finite string as incompressible when the shorter
combinators to generate it is as lengthy as the string itself.
This definition is not universal for a finite amount of short
sequences which indeed will depend of the language used (here
combinators).

Then you can show that such a definition can be made universal by
adding some constant, which will depend of the universal language.

It can be shown that most (finite!) numbers, written in any base,
are random in that sense.

Of course, 10 is a sort of compression of any string X in some
base, but if you allow change of base, you will need to send the
base with the number in the message. If you fix the base, then
indeed 10 will be a compression of that particular number base, for
that language, and it is part of incompressibility theory that no
definition exist working for all (small) numbers.

Since all finite numbers are small, I think this means the theory
only holds in the limit.

The definition will work for all numbers reasonably bigger than the
code of the universal machine used. That is what determine the
constant. Not all numbers are small relatively to the size of the
universal number/machine used to compress information.

Bruno

Brent

Each particular language will have some exception on the
incompressibility issue. That should be part of the role of the
variable constant in the general universal definition.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```

On 27 Dec 2013, at 17:51, Stephen Paul King wrote:

Dear Bruno,

On Fri, Dec 27, 2013 at 11:11 AM, Bruno Marchal marc...@ulb.ac.be
wrote:

On 25 Dec 2013, at 18:40, spudboy...@aol.com wrote:

Are we not presuming, structure, or a-priori, existence of
something, doing this processing, this work?

In the UDA we assume a Turing universal, or sigma_1-complete
physical reality, in some local sense.

Could this Turing universal/sigma_1-complete in a local sense be
the exact criteria required to define the observations 3-experiences
of individuals or is it the 1-experiences of individuals (observers)
in keeping with the definition of an observer as the intersection of
infinitely many computations?

I think the UDA answers this question. You need Turing universality,
but also the FPI, which in some sense comes from mechanism, but not
necessarily universality, which has, here, only an indirect
relevance in the definition of what is a computation in arithmetic.

We need this to just explain what is a computer, alias, universal
machine, alias universal number (implemented or not in a physical
reality).
Note that we do not assume a *primitive physical reality*. In comp,
we are a priori agnostic on this. The UDA, still will explains that
such primitiveness cannot solve the mind-body problem when made
into a dogma/assumption-of-primitiveness.

It has always seemed to me that UDA cannot solve the mind-body
problem strictly because it cannot comprehend the existence of
other minds.

UDA formulates the problem, and show how big the mind-body problem is,
even before tackling the other minds problem. But something is said.
In fact it is easy to derive from the UDA the following assertions:

comp + explicit non-solipsism entails sharable many words or a core
linear physical reality.

But comp in fact has to justify the non-solipsism, and this is begun
through the nuance Bp  p versus Bp  Dt. Normally the linearity
should allow the first person plural in the  Dt nuance case.

Keep in mind that UDA does not solve the problem, but formulate it.
AUDA go more deep in a solution, and the shape of that solution (like
Aristotelian theology (used by atheists and the main part of
institutionalized abramanic religion).

Bruno

Then in AUDA, keeping comp at the meta-level, I eliminate all
assumptions above very elementary arithmetic (Robinson Arithmetic).

The little and big bangs, including the taxes, and why it hurts is
derived from basically just

Kxy = x
Sxyz = xz(yz)

or just

x + 0 = x
x + s(y) = s(x + y)

x *0 = 0
x*s(y) = x*y + x

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```

On 27 Dec 2013, at 23:50, LizR wrote:

On 28 December 2013 05:51, Stephen Paul King stephe...@provensecure.com
wrote:

It has always seemed to me that UDA cannot solve the mind-body
problem strictly because it cannot comprehend the existence of
other minds.

computation which are assumed to exist in arithmetic actually
manage to communicate with each other?

Some universal system (in arithmetic, thus), can emulate interacting
universal systems. Indeed the UD simulates even all possible
interactions between universal systems. The only problem which remains
is in the search of why such universal systems (allowing interactions)
win the measure battle, but for this we have to extract the measure
first, and then the interaction from them. If we add interaction,
without extracting it from comp, we are doing traditional physics, and
we lost the qualia and all the non communicable stuff, and we put
again the mind under the rug.

Stephen critics seems to miss the point that UDA *formulates* the
constraints we have to follow in solving the mind body problem. he
could as well say that UDA miss the gravitation law, Maxwell's
equation, the H bosons, and actually even space and time. We are only
at the beginning here.  All what comp already say, is that the
possible answer are closer to Plato's theology than Aristotle
theology, which means that comp forces us to backtrack on 1500 years
on theology, to get the comp-correct physics.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 00:20, Jason Resch wrote:

On Fri, Dec 27, 2013 at 6:03 PM, LizR lizj...@gmail.com wrote:
On 28 December 2013 11:55, Stephen Paul King stephe...@provensecure.com
wrote:

Hi LizR,

That is what is not explicitly explained! I could see how one
might make an argument based on Godel numbers and a choice of a
numbering scheme could show the existence of a string of numbers
that, if run on some computer, would generate a description of the
interaction of several actors. But this ignores the problems of
concurrency and point of view. The best one might be able to do,
AFAIK, is cook up a description of the interactions of many
observers -each one is an intersection of infinitely many
computations, but such a description would itself be the content of
some observer's point of view that assumes a choice of Godel
numbering scheme.

It seems to suggest multi-solipsism or something along those lines
- which doesn't make it wrong, of course.

I await Bruno's answer with interest. I think he has already said
least to my limited understanding.

I am also interested to hear what Bruno has to say.

I should have read this before answering. Hope you are not too much
disappointed :)

My perspective is that most of the computations that support you and
I are not isolated and short-lived computational Boltzmann brains
but much larger, long-running computations such as those that
correspond to a universe in which life adapts and evolves.

Yes. I suspect both deep (in Bennett sense) computations, + the
physical symmetrical and linear core. This would makes us both
relatively very numerous in our type of reality, and relatively very
rare at some other level. I suspect also the FPI relative random
oracles to play some role in the continuous self-multiplication. But
this is speculation, and should be derived from self-reference alone,
to keep intact the exploitation of the G* minus G difference, on the
intensional variants, to have the qualia and their non communicable
feature.

The starting conditions for these is much less constrained, and
therefore it is far more probable to result in conscious
computations such as ours than the case where the computation
supporting your brain experiencing this moment is some initial
condition of a very specific program. Certainly, those programs
exist too, but they are much rarer. They appear in the UD much less
frequently than say the program corresponding to the approximate
laws of physics of this universe.  It takes far more data to
describe your brain than it does to describe the physical system on
which it is based.

That is right. I think it is the correct intuition, but unfortunately,
we cannot use it per se, we have to derive it from the math to be able
to exploit the whole theology of the numbers. Universal system like
the braids group, or the unitary group, might solve this, but we
cannot use them directly, we have to derived them from the comp mind-
body constraints.

So we are (mostly) still in the same universe, and so we can
interact with and affect the consciousness of other people.

Hopefully. The existence of 3 different sort of physical realities
seems to give sense to a pretension of salvia (i), which is that a
form of plural first person reality might still exists near and after
clinical death. this is not obvious. A priori, with comp, we might
surivive in solipsist state, but apparently, there are entities with
which we can communicate. In fact our own consciousness here and now,
seems to involve many internal dialog and interaction.
Note that no Boltzman brain can ever implement a UD, nor even
arbitrary part of UD*, which involves very long and stable
computations. Eventually the simple but global and complete
arithmetical reality is a very highly structured reality.

Bruno

Jason

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 01:56, Jason Resch wrote:

Somewhat. I think how frequently a program is referenced /
instantiated by other non-halting programs may play a role.

Yes. It has to be like that. Stopping programs should contribute to 0,
in the measure conflict.

So we are (mostly) still in the same universe, and so we can
interact with and affect the consciousness of other people.

From my reasoning, the appearance that we are in the same universe
is a by product of bisimilarities in the infinity of computations
that are each of us. In other words, there  are many computations
that are running Stephen that are identical to and thus are the same
computation to many of the computations that are running Jason.

Yes. We would be programs instantiated within a (possibly but not
necessarily) shared, larger program.

This gives an overlap between our worlds and thus the appearance
of a common world for some collection of observers.

Right.

The cool thing is that this implies that there are underlaps;
computations that are not shared or bisimilar between all of us.

Yes, I agree.  In some branches of the MW, perhaps you were born but
I was not, or I was, and you weren't.

COuld those be the ones that we identify as ourselves?

Personal identity can become a very difficult subject, since there
may be paths through which my program evolves to become you, and
vice versa.

Yes, indeed.

Bruno

Jason

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 02:03, Edgar L. Owen wrote:

Jason,

You state The UD is a comparatively short program, and provably
contains the program that is identical to your mind.

You can't be serious! As stated that's the most ridiculous statement
I've heard here today in all manner of respects!

If you believe this, you cannot believe in computationalism.  If your
brain work  is Turing emulable, that emulation is provably in
arithmetic, which emulates all (it is a theorem in arithmetic) all
computations. It is long to prove, but not so much difficult if you
add some axioms like the exponentiation axioms. It is a hell of a
difficulty to eliminate that exponentiation axioms, but that has been
done, even in some strong way (eliminating universal quantifiers
altogether) by Matiyasevitch, and that is well known (by logicians).

That the UD itself exist is a consequence of Church thesis, and is
obvious to many for wrong reason. If you know Cnator diagonalization,
then at first sight, it looks we can diagonalized against the UD
existence, but it happens that the UD and arithmetic is close for the
diagonalization procedure, making the UD, or equivalently the sigma_1
part of arithmetic, complete for the computational reality (of course
not complete for truth: that never happens by incompleteness à-la
Gödel).

Bruno

Edgar

On Friday, December 27, 2013 7:56:44 PM UTC-5, Jason wrote:

On Fri, Dec 27, 2013 at 6:33 PM, Stephen Paul King
step...@provensecure.com wrote:

Dear Jason,

Interleaving below.

On Fri, Dec 27, 2013 at 6:20 PM, Jason Resch jason...@gmail.com
wrote:

On Fri, Dec 27, 2013 at 6:03 PM, LizR liz...@gmail.com wrote:
On 28 December 2013 11:55, Stephen Paul King
step...@provensecure.com wrote:

Hi LizR,

That is what is not explicitly explained! I could see how one
might make an argument based on Godel numbers and a choice of a
numbering scheme could show the existence of a string of numbers
that, if run on some computer, would generate a description of the
interaction of several actors. But this ignores the problems of
concurrency and point of view. The best one might be able to do,
AFAIK, is cook up a description of the interactions of many
observers -each one is an intersection of infinitely many
computations, but such a description would itself be the content of
some observer's point of view that assumes a choice of Godel
numbering scheme.

It seems to suggest multi-solipsism or something along those lines
- which doesn't make it wrong, of course.

I await Bruno's answer with interest. I think he has already said
least to my limited understanding.

I am also interested to hear what Bruno has to say.  My perspective
is that most of the computations that support you and I are not
isolated and short-lived computational Boltzmann brains but much
larger, long-running computations such as those that correspond to a
universe in which life adapts and evolves.

I agree. I have never been happy with the Boltzman brain argument
because it seems to assume that the probability distribution of
spontaneous BBs is independent of the complexity of the content of
the minds associated with those brains. I have been studying this
relationship between complexity or expressiveness of a B.B. My
first guesstimation is that there is something like a Zift's Law in
the distribution: the more expressive a BB the less chance it has to
exist and evolve at least one cycle of its computation. (After
all, computers have to be able to run one clock cycle to be said
that they actually compute some program...)

The starting conditions for these is much less constrained, and
therefore it is far more probable to result in conscious
computations such as ours than the case where the computation
supporting your brain experiencing this moment is some initial
condition of a very specific program. Certainly, those programs
exist too, but they are much rarer.

RIght, but how fast do they get rarer?

It's hard to say. We would have to develop some model for estimating
the Kolmogorov complexity (and maybe also incorporate frequency) of
different programs and their relation to a given mind.

They appear in the UD much less frequently than say the program
corresponding to the approximate laws of physics of this universe.

It takes far more data to describe your brain than it does to
describe the physical system on which it is based.

How do you estimate this?

The UDA is a comparatively short program, and provably contains the
program that is identical to your mind.  Similarly, all of the known
laws of physics could fit on a couple sheets of paper.  QM seems to
suggest that all possible solutions to certain equations exist, and
so there is no need to specify the initial conditions of the
```

### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 02:04, LizR wrote:

On 28 December 2013 13:56, Jason Resch jasonre...@gmail.com wrote:

The UDA is a comparatively short program, and provably contains the
program that is identical to your mind.

To be more precise (I hope) - assuming that thoughts, experiences
etc are a form of computation at some level, the output (or trace)
of the UDA, which I seem to recall is designated UDA*, will
eventually generate those thoughts, experiences etc. Though if run
on a PC it would probably take a few googol years to do so (and
require many hubble volumes of storage space too, I imagine).

However, arithmetical realism assumes that the trace of the UDA

Of the UD. UD is the program doing the universal dovetailing.

UDA is for the 8 step argument showing that if we are machine, physics
is a brnach of machine's theology, itself a branch of arithmetic or
computer science.

Bruno

Similarly, all of the known laws of physics could fit on a couple
sheets of paper.  QM seems to suggest that all possible solutions to
certain equations exist, and so there is no need to specify the
initial conditions of the universe (which would require much more
information to describe than your brain).

This sounds like the Theory of Nothing again.?

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 03:29, LizR wrote:

What I think Jason is saying is that the TRACE of the UD (knowns as
UD* - I made the same mistake!)

Good :)

Perhaps; but only for nano second. you real mind overlap on sequence
of states, with the right probabilities, and for this you need the
complete run of the UD, because your next moment is determioned by
the FPI on all computations. Here the invariance of first person
experience for the UD time delays is capital. But I see your point.

Bruno

See my previous post for an elaboration.

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 04:36, Stephen Paul King wrote:

I loath Kronecker's claim! It is synonymous to Man is the measure
of all things.

What is his claim?  I am not familiar with it.

God created the Integers, all else is the invention of man.

man is a measure of all things is a quote from a french philosopher
(I just forget right now his name) itself taken from a greek general,
which cut the feet or head of all soldier having not the right size
(!).  (Sorry for those vague memories, learn this in highschool)

Now, of course, comp saves Kronecker from anthropomorphism, as with
comp we can say that:

God created the integers, all else is the invention of ... integers.

Of course it made comp number-centered, but this we knew at the start
with comp, and ... with christianism, in which it is important to
realize our finiteness.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 04:41, Jason Resch wrote:

On Fri, Dec 27, 2013 at 10:20 PM, LizR lizj...@gmail.com wrote:
There is one point to add which I think you've missed, Jason
(apologies if I've misunderstood). The UD generates the first
instruction of the first programme, then the first instruction of
the second programme, and so on. Once it has generated the first
instruction of every possible programme, it then adds the second
instruction of the first programme, the second instruction of the
second programme, and so on.

If it did work like this, it would never get to run the second
instruction of any program, since there is a countable infinity of
possible programs.

This is why it's called a dovetailer, I believe, and stops it
running into problems with non-halting programmes, or programmes
that would crash, or various other contingencies...

This is addressed by not trying to run any one program to its
completion, instead it gives each program it has generated up to
that point some time on the CPU.

This isn't intrinsic to the UD, which could in principle write the
first programme before it moves on to the next one - but it allows
it to avoid certain problems caused by having a programme that
writes other programmes.

There is no program with the UD encountering programs that
themselves instantiate other programs.

I guess you mean there is no problem with the UD encountering
programs ..., and you are right.

Indeed, the UD encounters itself, infinitely often.

...I think. I'm sure Bruno will let me know if that's wrong.

:)

Jason did it. Liz, Stephen, Are you OK with the UD and UD*. Both the
list of all programs AND their execution are done little bit by little
bit.

Thanks to Jason for a code. With the phi_i, you can code the UD by

For all i, j, k,
execute k steps of phi_i(j)

Bruno

PS I like the while (true) statement. What would Pontius Pilate

:-)  Good question, I haven't the faintest idea.  I could have used
while (i == i) but then if someday Brent's paralogic takes over,
it might fail.

Jason

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 04:39, Stephen Paul King wrote:

Dear Jason,

ISTM that the line  For each program we have generated that has
not halted, execute one instruction of it for each (Program p in
listOfPrograms) is buggy.

It assumes that the space of programs that do not halt is
accessible. How?

The space of all programs that do not halt is not Turing accessible.
The space of all programs that do halt is not Turing accessible.

The space of all programs (that do halt of do not halt) *is* accessible.

All what happen is that we have no general systematic, computational,
means to distinguish the programs that halt from the programs that
does not halt (on their inputs), and that is why the universal
dovetailer must *dovetail* on the executions of all programs.

Bruno

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch jasonre...@gmail.com
wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

Could you discuss the trace of the UD that LizR mentioned? How
is it computed? Could you write an explicit example? I have never
been able to grok it.

Bruno has written an actual UD in the LISP programming language.  I
will write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i

Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far

# For each program we have generated that has not halted, execute
one instruction of it

for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next
time through

i = i + 1;
}

Any program, and whether or not it ever terminates can be translated
to a statement concerning numbers in arithmetic. Thus mathematical
truth captures the facts concerning whether or not any program
executes forever, and what all of its intermediate states are. If
these statements are true independently of you and me, then the
executions of these programs are embedded in arithmetical truth and
have a platonic existence.  The first, second, 10th, 1,000,000th,
and 10^100th, and 10^100^100th state of the UD's execution are
mathematical facts which have definite values, and all the conscious
beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part
of the execution of the UD are there, in the math.

Jason

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 04:44, Stephen Paul King wrote:

Hi Jason,

The first, second, 10th, 1,000,000th, and 10^100th, and
10^100^100th state of the UD's execution are mathematical facts ...
Umm, how? Godel and Matiyasevich would disagree!

No logicians at all would ever disagree on this. They are the one who
proved this.

If there does not exist a program that can evaluate whether or not a
UD substring is a faithful representation of a true theorem, then
how is it a fact?

It does not need to be a fact. *you* recognize you are conscious, even
if no one can prove it by looking at your code and state, and that is
enough to proceed in the reasoning.

bruno

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch jasonre...@gmail.com
wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

Could you discuss the trace of the UD that LizR mentioned? How
is it computed? Could you write an explicit example? I have never
been able to grok it.

Bruno has written an actual UD in the LISP programming language.  I
will write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i

Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far

# For each program we have generated that has not halted, execute
one instruction of it

for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next
time through

i = i + 1;
}

Any program, and whether or not it ever terminates can be translated
to a statement concerning numbers in arithmetic. Thus mathematical
truth captures the facts concerning whether or not any program
executes forever, and what all of its intermediate states are. If
these statements are true independently of you and me, then the
executions of these programs are embedded in arithmetical truth and
have a platonic existence.  The first, second, 10th, 1,000,000th,
and 10^100th, and 10^100^100th state of the UD's execution are
mathematical facts which have definite values, and all the conscious
beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part
of the execution of the UD are there, in the math.

Jason

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Mobile: (864) 567-3099

stephe...@provensecure.com

http://www.provensecure.us/

“This message (including any attachments) is intended only for the
use of the individual or entity to which it is addressed, and may
contain information that is non-public, proprietary, privileged,
confidential and exempt from disclosure under applicable law or may
be constituted as attorney work product. If you are not the intended
recipient, you are hereby notified that any use, dissemination,
distribution, or copying of this communication is strictly
prohibited. If you have received this message in error, notify
sender immediately and delete this message immediately.”

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 04:52, Jason Resch wrote:

On Fri, Dec 27, 2013 at 10:39 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Dear Jason,

ISTM that the line  For each program we have generated that has
not halted, execute one instruction of it for each (Program p in
listOfPrograms) is buggy.

It assumes that the space of programs that do not halt is
accessible. How?

We never know a prior if a program will halts or not.  However, once
a program has reached a halted stated it is immediately apparent.
If the function name was willThisProgramHalt(), then I agree it
would be a buggy program. :-)

The UD as I wrote it executes all programs, whether they will halt
or not, but it never wastes time trying to run another instruction
of a program that has halted.  This is only an optimization, and I
added it only to reduce the ambiguity of running another
instruction of a program that has halted.

OK. The LISP UD is even more optimized, and the small UD I just gave
is not optimal at all. Of course, to optimize a UD is a bit like pure
coquetry :)   (it should not change anything in the measure conflicts,
a priori).

Bruno

Jason

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch jasonre...@gmail.com
wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

Could you discuss the trace of the UD that LizR mentioned? How
is it computed? Could you write an explicit example? I have never
been able to grok it.

Bruno has written an actual UD in the LISP programming language.  I
will write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i

Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far

# For each program we have generated that has not halted, execute
one instruction of it

for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next
time through

i = i + 1;
}

Any program, and whether or not it ever terminates can be translated
to a statement concerning numbers in arithmetic. Thus mathematical
truth captures the facts concerning whether or not any program
executes forever, and what all of its intermediate states are. If
these statements are true independently of you and me, then the
executions of these programs are embedded in arithmetical truth and
have a platonic existence.  The first, second, 10th, 1,000,000th,
and 10^100th, and 10^100^100th state of the UD's execution are
mathematical facts which have definite values, and all the conscious
beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part
of the execution of the UD are there, in the math.

Jason

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Stephen Paul King

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Mobile: (864) 567-3099

stephe...@provensecure.com

http://www.provensecure.us/

“This message (including any attachments) is intended only for the
use of the individual or entity to which it is addressed, and may
contain information that is non-public, proprietary, privileged,
confidential and exempt from disclosure under applicable law or may
be constituted as attorney work product. If you are not the intended
recipient, you are hereby notified that any use, dissemination,
distribution, or copying of this communication is strictly
prohibited. If you have received this message in error, notify
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send an email to ```

### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 04:56, Jason Resch wrote:

On Fri, Dec 27, 2013 at 10:42 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

Any program, and whether or not it ever terminates can be
translated to a statement concerning numbers in arithmetic. Thus
mathematical truth captures the facts concerning whether or not any
program executes forever, and what all of its intermediate states
are.

this also captures every instance of random numbers as well.

It is not clear to me what random means in arithmetical truth.

Randomness can appear from the perspectives of observers, but I
don't see how it can arise in arithmetic.

?

It appears in all numbers written in any base. Most numbers are
I guess you know that. In the phi_i(j) in the UD, randomness can
appear in the many j used as input, as we usually dovetail on the
function of one variable. (but such input can easily be internalized
in 0-variable programs).

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want
generate only that numbers. but a simple counting algorithm generating
all numbers, 0, 1, 2,  6999500235148668, ... generates all random
finite incompressible strings, and even all the infinite one (for the
1p view, notably).

In that (trivial) sense, arithmetic contains a lot of 3p randomness,
even perhaps too much. Then 1p randomeness appears too, by the 1p
indeterminacy (and that one is in the eyes of the machine).

Chaitin's results can also explain why we cannot filter out that 3p
randomness from arithmetic.

Bruno

What method is deployed to ensure that a program is not just a
regular random number and not some random number prefixed on a
real halting program?

It don't see how it makes a difference.

Truth is not a measure zero set, or is it?

I don't understand this question..  Could you clarify?

Jason

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch jasonre...@gmail.com
wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

Could you discuss the trace of the UD that LizR mentioned? How
is it computed? Could you write an explicit example? I have never
been able to grok it.

Bruno has written an actual UD in the LISP programming language.  I
will write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i

Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far

# For each program we have generated that has not halted, execute
one instruction of it

for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next
time through

i = i + 1;
}

Any program, and whether or not it ever terminates can be translated
to a statement concerning numbers in arithmetic. Thus mathematical
truth captures the facts concerning whether or not any program
executes forever, and what all of its intermediate states are. If
these statements are true independently of you and me, then the
executions of these programs are embedded in arithmetical truth and
have a platonic existence.  The first, second, 10th, 1,000,000th,
and 10^100th, and 10^100^100th state of the UD's execution are
mathematical facts which have definite values, and all the conscious
beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part
of the execution of the UD are there, in the math.

Jason

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Mobile: (864) 567-3099

stephe...@provensecure.com

http://www.provensecure.us/

“This message (including any attachments) is intended only for the
use of the individual or entity to which it is addressed, and may
contain information that is non-public, proprietary, privileged,
confidential and exempt from disclosure under applicable law or may
be constituted as attorney work product. If you are not the intended
recipient, you are hereby notified that any use, dissemination,
distribution, or ```

### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 05:01, Stephen Paul King wrote:

How do we distinguish a program from a string of random numbers.
(Consider OTP encryptions).

In which language?

A program fortran will be distinguished by the grammar of Fortran.

In some language all numbers will be program.

Then , for all language question like does that progream compute this
or that are non algorithmically solvable (and undecidable in most
theories).

Bruno

On Fri, Dec 27, 2013 at 10:56 PM, Jason Resch jasonre...@gmail.com
wrote:

On Fri, Dec 27, 2013 at 10:42 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

Any program, and whether or not it ever terminates can be
translated to a statement concerning numbers in arithmetic. Thus
mathematical truth captures the facts concerning whether or not any
program executes forever, and what all of its intermediate states
are.

this also captures every instance of random numbers as well.

It is not clear to me what random means in arithmetical truth.

Randomness can appear from the perspectives of observers, but I
don't see how it can arise in arithmetic.

What method is deployed to ensure that a program is not just a
regular random number and not some random number prefixed on a
real halting program?

It don't see how it makes a difference.

Truth is not a measure zero set, or is it?

I don't understand this question..  Could you clarify?

Jason

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch jasonre...@gmail.com
wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

Could you discuss the trace of the UD that LizR mentioned? How
is it computed? Could you write an explicit example? I have never
been able to grok it.

Bruno has written an actual UD in the LISP programming language.  I
will write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i

Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far

# For each program we have generated that has not halted, execute
one instruction of it

for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next
time through

i = i + 1;
}

Any program, and whether or not it ever terminates can be translated
to a statement concerning numbers in arithmetic. Thus mathematical
truth captures the facts concerning whether or not any program
executes forever, and what all of its intermediate states are. If
these statements are true independently of you and me, then the
executions of these programs are embedded in arithmetical truth and
have a platonic existence.  The first, second, 10th, 1,000,000th,
and 10^100th, and 10^100^100th state of the UD's execution are
mathematical facts which have definite values, and all the conscious
beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part
of the execution of the UD are there, in the math.

Jason

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stephe...@provensecure.com

http://www.provensecure.us/

“This message (including any attachments) is intended only for the
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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 05:03, Stephen Paul King wrote:

I ask this because I am studying Carl Hewitt's Actor Model...

Also know today as object oriented languages. c++ win against
smaltalk, which won against the Actor model, but the idea is the same,
basically. It is efficacious, but the math and semantics is still
unclear to me. It is a sort of vague polymorphic lambda calculus. I
did love a long time ago, the actor model. It is somewhat
psychologically sad that the term object replaced the term actor.

bruno

On Fri, Dec 27, 2013 at 11:03 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi jason,

Do programs have to be deterministic. What definition of
deterministic are you using?

On Fri, Dec 27, 2013 at 11:00 PM, Jason Resch jasonre...@gmail.com
wrote:

On Fri, Dec 27, 2013 at 10:54 PM, LizR lizj...@gmail.com wrote:
On 28 December 2013 16:44, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

The first, second, 10th, 1,000,000th, and 10^100th, and
10^100^100th state of the UD's execution are mathematical facts ...
Umm, how? Godel and Matiyasevich would disagree! If there does not
exist a program that can evaluate whether or not a UD substring is a
faithful representation of a true theorem, then how is it a fact?

That depends on whether the UD is deterministic or not.

It is. The evolution of any Turing machines is deterministic.

If it is, then, its Nth state is a fact. (It doesn't need to be run
or evaluated, and the Nth state may be a fact that nobody knows,
like the googolth digit of pi, assuming no one's worked that out.)

Right. :-)

The fact that I remember drinking a glass of water is as much a
mathematical fact about the UD, as the fact as the third decimal
digit of Pi is 4.

Jason

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Mobile: (864) 567-3099

stephe...@provensecure.com

http://www.provensecure.us/

“This message (including any attachments) is intended only for the
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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 05:06, LizR wrote:

Clearly programmes don't have to be deterministic. They could
contain a source of genuine randomness, in principle.

I don't think the UD does, however.

The UD emulates all quantum computer and many sort of non
deterministic processes, including all randomness (through the
inputs), even deterministically.

Just think about the fact that the UD does emulate infinite iteration
of the WM duplication.

Bruno

The definition of deterministic would be - gives the same output on
each run (given that the UD has no input).

On 28 December 2013 17:03, Stephen Paul King stephe...@provensecure.com
wrote:

I ask this because I am studying Carl Hewitt's Actor Model...

On Fri, Dec 27, 2013 at 11:03 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi jason,

Do programs have to be deterministic. What definition of
deterministic are you using?

On Fri, Dec 27, 2013 at 11:00 PM, Jason Resch jasonre...@gmail.com
wrote:

On Fri, Dec 27, 2013 at 10:54 PM, LizR lizj...@gmail.com wrote:
On 28 December 2013 16:44, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

The first, second, 10th, 1,000,000th, and 10^100th, and
10^100^100th state of the UD's execution are mathematical facts ...
Umm, how? Godel and Matiyasevich would disagree! If there does not
exist a program that can evaluate whether or not a UD substring is a
faithful representation of a true theorem, then how is it a fact?

That depends on whether the UD is deterministic or not.

It is. The evolution of any Turing machines is deterministic.

If it is, then, its Nth state is a fact. (It doesn't need to be run
or evaluated, and the Nth state may be a fact that nobody knows,
like the googolth digit of pi, assuming no one's worked that out.)

Right. :-)

The fact that I remember drinking a glass of water is as much a
mathematical fact about the UD, as the fact as the third decimal
digit of Pi is 4.

Jason

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Mobile: (864) 567-3099

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 05:27, Stephen Paul King wrote:

Hi LizR and Jason,

Responding to both of you. I don't understand the claim of
determinism is random noise is necessary for the computations.
Turing machines require exact pre-specifiability. Adding noise
oracles is cheating!

But it exist in arithmetic. Subtracting it would be cheating. the
silmple counting algorith generates all random finite strings (random
in the strong Chaitin sense).

Almost all numbers are random, when written in some base. And you can
define the notion of base *in* arithmetic, so they exist in all models
of arithmetic. We can't subtract them.

Bruno

On Fri, Dec 27, 2013 at 11:22 PM, LizR lizj...@gmail.com wrote:
On 28 December 2013 17:15, Jason Resch jasonre...@gmail.com wrote:
On Fri, Dec 27, 2013 at 11:06 PM, LizR lizj...@gmail.com wrote:
Clearly programmes don't have to be deterministic. They could
contain a source of genuine randomness, in principle.

That source, if it is within the program, would necessarily be
deterministic.  If it is external to the program, then it is more
properly treated as an input to the program rather than a part of
the program itself.

In practice, computers draw on sources of environmental noise such
as delays between keystrokes, timing of the reception of network
traffic, and delays in accessing data off of hard drives, etc. These
steps are necessary precisely because programs cannot produce
randomness on their own.

I knew that - honest! :-)

I was answering the question as posed. I believe that in practice
all real-world programmes are deterministic, and (more to the point)
the UD is.

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 05:27, LizR wrote:

On 28 December 2013 17:23, Edgar L. Owen edgaro...@att.net wrote:
Jason,

You might be able to theoretically simulate it but certainly not
compute it in real time which is what reality actually does which is
my point.

In real time ?! In comp (and many TOEs) time is emergent.

Physical times and subjective time emerge. OK. But let us be honest,
comp assumes already a sort of time, through the natural order: à, 1,
2, 3, ...

Then you have all UD-time step of the computations emulated by the UD:

phi_444(6) first step
...
phi_444(6) second step
... ...  (meaning greater delay in
the UD-time steps).

ph_444(6) third  step
... ... ...
ph_444(6) fourth  step
... ...
ph_444(6) fifth step
etc.

To take a parallel example that should be close to your heart,
suppose you're an AI living in the matrix and it's simulating
reality for you. You aren't aware of this but believe yourself to be
say a human writer who is participating in an online discussion.
Suppose it takes a million years to simulate one second of your
experience. How would you know? You can only compare your experience
of time with in-matrix clocks, which all run at the speed you'd
expect.

It's the same for any theory which tries to compute reality.

But the physical time is not Turing emulable, and perhaps is not even
existing, like in Dewitt-Wheeler equation: H = 0.
if it exist, it depends on all computations instantaneously, by the
delay invariance of the FPI.

Bruno

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 05:31, LizR wrote:

On 28 December 2013 17:27, Stephen Paul King stephe...@provensecure.com
wrote:

Hi LizR and Jason,

Responding to both of you. I don't understand the claim of
determinism is random noise is necessary for the computations.
Turing machines require exact pre-specifiability. Adding noise
oracles is cheating!

Who said random noise was necessary? I said the UD, at least, is
completely deterministic.

The UD is indeed totally deterministic. but it still generates all
random strings, and all executions of all programs on all random
streams. This has consequences on the FPI, but is not a consequences
of the FPI. The UD generates deterministically 3P randomness. 1p
randomness exists too in arithmetic, but cannot be said being
generated by the UD. That one is an illusion in the mind of the
observers.

Bruno

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 05:31, Stephen Paul King wrote:

Hi Jason,

On Fri, Dec 27, 2013 at 11:23 PM, Jason Resch jasonre...@gmail.com
wrote:

On Fri, Dec 27, 2013 at 11:09 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

It is not a question of whether or not that binary string refers
to anything that is true or not, only what its particular value
happens to be. No no no! We can not make statements without showing
how their proof are accessible!

The proof is straight forward. Run the UD and see what the state is.

Run it, on what hardware? ??

Are you objecting that it does not have a definite value because you
or I are not capable of computing it?

Did the 100th digit of Pi not exist until the first human computed it?

Pfft, that is a red herring and you know it! Why even mention
humans? If numbers exist, then that existence has nothing at all to
do with humans or aliens of black clouds. It is merely the necessary
possibility that the numbers are not inconsistent. If they were
inconsistent, then all that would exist is noise. And we are back to
my question. What decodes the noise into meaningful strings?

The universal numbers, through the laws (in this case with arithmetic
beeing the base) of addition and multiplication. Arithmetic dovetail
on programs, and consciousness filter out the meaningfull one (as we
assume comp).

Consider the i-th through j_th values of pi's expansion in binary.
If it is a finite string, how do we know that it is a Turing machine
program?

All integers can be mapped directly to Turing machine programs.
Consider Java: it uses a byte-code where every byte is an
instruction for the Java virtual machine.  Every string of bytes can
therefore be considered as a sequence of instructions for the Java
virtual machine to execute.

SO it is OK to include the java code that generates noise. There are

Like in the WM duplication. By self-reference.

bruno

Jason

On Fri, Dec 27, 2013 at 11:06 PM, Jason Resch jasonre...@gmail.com
wrote:

On Fri, Dec 27, 2013 at 10:44 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

The first, second, 10th, 1,000,000th, and 10^100th, and
10^100^100th state of the UD's execution are mathematical facts ...
Umm, how? Godel and Matiyasevich would disagree! If there does not
exist a program that can evaluate whether or not a UD substring is a
faithful representation of a true theorem, then how is it a fact?

The mathematical fact to which I am referring is only a basic and
straight-forward statement like the binary representation of the
state of UD after executing 100..00th steps is
'101010010...0010. It is not a question of whether or not that
binary string refers to anything that is true or not, only what its
particular value happens to be.

Jason

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch jasonre...@gmail.com
wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

Could you discuss the trace of the UD that LizR mentioned? How
is it computed? Could you write an explicit example? I have never
been able to grok it.

Bruno has written an actual UD in the LISP programming language.  I
will write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i

Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far

# For each program we have generated that has not halted, execute
one instruction of it

for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next
time through

i = i + 1;
}

Any program, and whether or not it ever terminates can be translated
to a statement concerning numbers in arithmetic. Thus mathematical
truth captures the facts concerning whether or not any program
executes forever, and what all of its intermediate states are. If
these statements are true independently of you and me, then the
executions of these programs are embedded in arithmetical truth and
have a platonic existence.  The first, second, 10th, 1,000,000th,
and 10^100th, and 10^100^100th state of the UD's execution are
mathematical facts which have definite values, and all the conscious
beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part
of the execution of the UD are there, in the math.

Jason

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 05:53, Stephen Paul King wrote:

Hi LizR,

This is fun! :-) We must remember that we are defining People as
intersections of infinitely many computations. Right?

This is a very loose way to talk. Computations are not sets, so
intersection of computations is very ill defined. We can say more
easily and clearly that machines cannot know which computations they
are supported by, and that the statistics will have to take into
account the distribution of 3p states in all computations.

Their perceptions of themselves as physical being having some
particular set of configuration, for example bilateral symmetry,
etc. is not really relevant to UDA.

?

So, if there is a change in accessibility to data, facts, etc. Where
is that change coming from.

From the computations (in arithmetic) which supports you,

This is my problem: We are presented with an argument that works
in Platonia and we have no explanation as to the relation it has
with the real world where things change and degrade and evolve,
etc. What is measuring that change?

We are already in Platonia. After Gödel + comp, we know that Platonia
(arithmetic) is full of change, when viewed from inside.
That should not seem so strange, as the 0 - s(0) - s(s(0)) -
implements  already a sort of atomic change.

Bruno

On Fri, Dec 27, 2013 at 11:49 PM, LizR lizj...@gmail.com wrote:
On 28 December 2013 17:46, Stephen Paul King stephe...@provensecure.com
wrote:
Ah, but they do degrade. Consider your ability to access a '80s
floppy drive's data.

Well, that's because people haven't worked out how to do it
perfectly. I agree digital archaeology is a real problem, but so
would analogue be without the relevant machines to play it back
(admittedly it's easier to decode analogue from first principles).
But that is a different form of degrading. If you have a system
capable of copying the data it should be more or less 100% accurate.

On Fri, Dec 27, 2013 at 11:44 PM, LizR lizj...@gmail.com wrote:
On 28 December 2013 17:41, Jason Resch jasonre...@gmail.com wrote:
On Fri, Dec 27, 2013 at 11:27 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi LizR and Jason,

Responding to both of you. I don't understand the claim of
determinism is random noise is necessary for the computations.
Turing machines require exact pre-specifiability. Adding noise
oracles is cheating!

I think you misunderstand.  Computers are deterministic, but they
often need randomness to implement things such as cryptography or
monte-carlo simulations, etc.  Due to this need for true
unpredictability, our computers must harness environmental noise if
they are to have any hope of being unpredictable.  This is because
computers cannot generate unpredictability on their own.

They are engineered not to! This is why digital recordings don't

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### Re: Bruno's mathematical reality

```

On Dec 28, 2013, at 6:09 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 28 Dec 2013, at 04:56, Jason Resch wrote:

On Fri, Dec 27, 2013 at 10:42 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

Any program, and whether or not it ever terminates can be
translated to a statement concerning numbers in arithmetic. Thus
mathematical truth captures the facts concerning whether or not any
program executes forever, and what all of its intermediate states
are.

this also captures every instance of random numbers as well.

It is not clear to me what random means in arithmetical truth.

Randomness can appear from the perspectives of observers, but I
don't see how it can arise in arithmetic.

?

It appears in all numbers written in any base. Most numbers are

I guess you know that.

I agree most numbers are incompressible, but I was using random in a
different sense than the unpredictability of the next digits of the
number given previous ones.

In the phi_i(j) in the UD, randomness can appear in the many j used
as input, as we usually dovetail on the function of one variable.
(but such input can easily be internalized in 0-variable programs).

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want
generate only that numbers.

Right, all the random numbers are there, the question is how to throw
the dart so that it lands on one.

but a simple counting algorithm generating all numbers, 0, 1,
2,  6999500235148668, ... generates all random finite
incompressible strings, and even all the infinite one (for the 1p
view, notably).

I think we are using the term in a slightly different sense.
Certainly any number in the range 1 - N can be considered as a random
number in that range (as it is a candidate to be output by some RNG),
but the problem is selecting it in a random (in the sense of not-
predictable) way.

There was a joke cartoon of some computer code:

int getRandomNumber()
{
return 4; // this number was determined by a random die roll
}

While a number can be interpreted as random once, it might not be the
second time.

While selecting and using all possibilities is arguably a way to
achieve randomness (unpredictibilty), (from some points of view) it is
often not practical nor useful.  Consider encrypting a message with
all possible keys and sending the recipient all possible messages.

Not only might you need to send 2^256 possible ciphertexts but any
eavesdropper could use the first possible key to decrypt it. This
achieves randomness from the POV of the cipher, but not for the user
or the attackers.

In quantum cryptography this is essentially what is done, but it
requires that the sender and reciever (and attackers) be duplicated
for each possible key. So they need to be embedded in that larger
program that provides all possible inputs for it to seem random. This
is just FPI though, is it not?

Jason

In that (trivial) sense, arithmetic contains a lot of 3p randomness,
even perhaps too much. Then 1p randomeness appears too, by the 1p
indeterminacy (and that one is in the eyes of the machine).

Chaitin's results can also explain why we cannot filter out that 3p
randomness from arithmetic.

Bruno

What method is deployed to ensure that a program is not just a
regular random number and not some random number prefixed on a
real halting program?

It don't see how it makes a difference.

Truth is not a measure zero set, or is it?

I don't understand this question..  Could you clarify?

Jason

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch
jasonre...@gmail.com wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

Could you discuss the trace of the UD that LizR mentioned? How
is it computed? Could you write an explicit example? I have never
been able to grok it.

Bruno has written an actual UD in the LISP programming language.  I
will write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i

Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far

# For each program we have generated that has not halted,
execute one instruction of it

for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next
time through

i = i + 1;
}

Any program, and whether or not it ever terminates can be
translated to a statement concerning numbers in arithmetic. Thus
mathematical truth captures the facts concerning whether or not any
program executes forever, and what all ```

### Re: Bruno's mathematical reality

```Dear Bruno,

On Sat, Dec 28, 2013 at 4:54 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 27 Dec 2013, at 17:51, Stephen Paul King wrote:

Dear Bruno,

On Fri, Dec 27, 2013 at 11:11 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 25 Dec 2013, at 18:40, spudboy...@aol.com wrote:

Are we not presuming, structure, or a-priori, existence of something,
doing this processing, this work?

In the UDA we assume a Turing universal, or sigma_1-complete physical
reality, in some local sense.

Could this Turing universal/sigma_1-complete in a local sense be the
exact criteria required to define the observations 3-experiences of
individuals or is it the 1-experiences of individuals (observers) in
keeping with the definition of an observer as the intersection of
infinitely many computations?

I think the UDA answers this question. You need Turing universality, but
also the FPI, which in some sense comes from mechanism, but not necessarily
universality, which has, here, only an indirect relevance in the
definition of what is a computation in arithmetic.

I suspect that the FPI results from the underlap or failure to reach
exact overlap between observers. As if a small part of the computations
that are observers is not universal. This would effectively induce FPI as
any one observer would be forever unable to exactly match its experience of
being in the world with that of another.

We need this to just explain what is a computer, alias, universal
machine, alias universal number (implemented or not in a physical reality).
Note that we do not assume a *primitive physical reality*. In comp, we
are a priori agnostic on this. The UDA, still will explains that such
primitiveness cannot solve the mind-body problem when made into a
dogma/assumption-of-primitiveness.

It has always seemed to me that UDA cannot solve the mind-body problem
strictly because it cannot comprehend the existence of other minds.

UDA formulates the problem, and show how big the mind-body problem is,
even before tackling the other minds problem. But something is said. In
fact it is easy to derive from the UDA the following assertions:

comp + explicit non-solipsism entails sharable many words or a core linear
physical reality.

I do not comprehend this. It is easy for us to see that solipsism is
false, but how can a computation see anything? I do not understand how it
is that you can claim that computations will not be solipsistic by default.

But comp in fact has to justify the non-solipsism, and this is begun
through the

nuance Bp  p versus Bp  Dt. Normally the linearity should allow the
first person plural in the  Dt nuance case.

Exactly! I am looking forward to the explanation of this

nuance Bp  p versus Bp  Dt. :-)

Keep in mind that UDA does not solve the problem, but formulate it. AUDA
go more deep in a solution, and the shape of that solution (like UDA
theology (used by atheists and the main part of institutionalized abramanic
religion).

Sure. My main worry is that your wonderful result obtains at too high a
price: the inability to even model interactions and time.

Bruno

Then in AUDA, keeping comp at the meta-level, I eliminate all assumptions
above very elementary arithmetic (Robinson Arithmetic).

The little and big bangs, including the taxes, and why it hurts is
derived from basically just

Kxy = x
Sxyz = xz(yz)

or just

x + 0 = x
x + s(y) = s(x + y)

x *0 = 0
x*s(y) = x*y + x

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 07:32, LizR wrote:

On 28 December 2013 18:03, Stephen Paul King stephe...@provensecure.com
wrote:

Hi Jason,

I would like to know the definition of reality that you are
using here.

I quite like whatever doesn't go away when you stop believing in it.

I quite like too.

Bruno

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### Re: Bruno's mathematical reality

```Dear Bruno,

On Sat, Dec 28, 2013 at 6:53 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 28 Dec 2013, at 04:39, Stephen Paul King wrote:

Dear Jason,

ISTM that the line  For each program we have generated that has not
halted, execute one instruction of it for each (Program p in
listOfPrograms) is buggy.

It assumes that the space of programs that do not halt is accessible.
How?

The space of all programs that do not halt is not Turing accessible.
The space of all programs that do halt is not Turing accessible.

The space of all programs (that do halt of do not halt) *is* accessible.

Could you elaborate on this claim. I wish to be sure that I understand
it. Is it really a space? Would it have metrics and topological
properties?

All what happen is that we have no general systematic, computational,
means to distinguish the programs that halt from the programs that does not
halt (on their inputs), and that is why the universal dovetailer must
*dovetail* on the executions of all programs.

Not having a general systematic, computational, means to distinguish..
has not stopped Nature. She solves the problem by the evolution of physical
worlds. I propose that physical worlds ARE a form of non-universal
computation.

I still think that the UD lives only in Platonia and is timeless and
static. Only its projections (to use Plato's cave metaphor) are run as
physical worlds if they can survive the challenge of mutual consistency.

Bruno

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch jasonre...@gmail.comwrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King
stephe...@provensecure.com wrote:

Hi Jason,

Could you discuss the trace of the UD that LizR mentioned? How is it
computed? Could you write an explicit example? I have never been able to
grok it.

Bruno has written an actual UD in the LISP programming language.  I will
write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i
Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far

# For each program we have generated that has not halted, execute one
instruction of it
for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next time
through
i = i + 1;
}

Any program, and whether or not it ever terminates can be translated to a
statement concerning numbers in arithmetic. Thus mathematical truth
captures the facts concerning whether or not any program executes forever,
and what all of its intermediate states are. If these statements are true
independently of you and me, then the executions of these programs are
embedded in arithmetical truth and have a platonic existence.  The first,
second, 10th, 1,000,000th, and 10^100th, and 10^100^100th state of the UD's
execution are mathematical facts which have definite values, and all the
conscious beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part of the
execution of the UD are there, in the math.

Jason

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### Re: Bruno's mathematical reality

```Dear Bruno,

On Sat, Dec 28, 2013 at 7:09 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 28 Dec 2013, at 04:56, Jason Resch wrote:

On Fri, Dec 27, 2013 at 10:42 PM, Stephen Paul King
stephe...@provensecure.com wrote:

Hi Jason,

Any program, and whether or not it ever terminates can be translated to
a statement concerning numbers in arithmetic. Thus mathematical truth
captures the facts concerning whether or not any program executes forever,
and what all of its intermediate states are.

this also captures every instance of random numbers as well.

It is not clear to me what random means in arithmetical truth.

Randomness can appear from the perspectives of observers, but I don't see
how it can arise in arithmetic.

?

It appears in all numbers written in any base. Most numbers are already
random (even incompressible).
I guess you know that. In the phi_i(j) in the UD, randomness can appear in
the many j used as input, as we usually dovetail on the function of one
variable. (but such input can easily be internalized in 0-variable
programs).

OK, I must agree, but can you see how this removes our ability to use the
natural ordering of the integers as an explanation of the appearance of
time? Since there are multiple and equivalent (as to their properties)
sequences of integers that have very different orders relative to each
other, if we use these ordering as our time we would have a different
dimension of time for every one!

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want generate
only that numbers. but a simple counting algorithm generating all numbers,
0, 1, 2,  6999500235148668, ... generates all random finite
incompressible strings, and even all the infinite one (for the 1p view,
notably).

In that (trivial) sense, arithmetic contains a lot of 3p randomness, even
perhaps too much. Then 1p randomeness appears too, by the 1p indeterminacy
(and that one is in the eyes of the machine).

Chaitin's results can also explain why we cannot filter out that 3p
randomness from arithmetic.

Have you had any more thoughts on the book keeping problem we have
discussed in the past?

Bruno

What method is deployed to ensure that a program is not just a regular
random number and not some random number prefixed on a real halting
program?

It don't see how it makes a difference.

Truth is not a measure zero set, or is it?

I don't understand this question..  Could you clarify?

Jason

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch jasonre...@gmail.comwrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King
stephe...@provensecure.com wrote:

Hi Jason,

Could you discuss the trace of the UD that LizR mentioned? How is
it computed? Could you write an explicit example? I have never been able to
grok it.

Bruno has written an actual UD in the LISP programming language.  I will
write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the
integer i
Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far

# For each program we have generated that has not halted, execute one
instruction of it
for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next time
through
i = i + 1;
}

Any program, and whether or not it ever terminates can be translated to
a statement concerning numbers in arithmetic. Thus mathematical truth
captures the facts concerning whether or not any program executes forever,
and what all of its intermediate states are. If these statements are true
independently of you and me, then the executions of these programs are
embedded in arithmetical truth and have a platonic existence.  The first,
second, 10th, 1,000,000th, and 10^100th, and 10^100^100th state of the UD's
execution are mathematical facts which have definite values, and all the
conscious beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part of the
execution of the UD are there, in the math.

Jason

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 07:35, Stephen Paul King wrote:

An observer can only experience a reality that is not

Tell this to the dictators.

Usually a reality guarantied some local consistency by definition of a
reality (modeled by the notion of models in logic).

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```Dear Bruno,

On Sat, Dec 28, 2013 at 7:17 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 28 Dec 2013, at 05:03, Stephen Paul King wrote:

I ask this because I am studying Carl Hewitt's Actor Model...

Also know today as object oriented languages. c++ win against smaltalk,
which won against the Actor model, but the idea is the same, basically. It
is efficacious, but the math and semantics is still unclear to me. It is a
sort of vague polymorphic lambda calculus. I did love a long time ago, the
actor model. It is somewhat psychologically sad that the term object
replaced the term actor.

Yes, Carl Hewitt claims that the Actor model has unbounded indeterminacy
as it does not assume an upper bound on the length of a path of a message
from one actor to another. We see this as a security feature, not a
problem. Our goal is inherently secure computation. We are using Marius
Buliga's graphic lambda calculus that very elegantly allows for the
construction of topological graphs that are both models of computation and
computer programs via a natural graph rewrite scheme.

bruno

On Fri, Dec 27, 2013 at 11:03 PM, Stephen Paul King
stephe...@provensecure.com wrote:

Hi jason,

Do programs have to be deterministic. What definition of
deterministic are you using?

On Fri, Dec 27, 2013 at 11:00 PM, Jason Resch jasonre...@gmail.comwrote:

On Fri, Dec 27, 2013 at 10:54 PM, LizR lizj...@gmail.com wrote:

On 28 December 2013 16:44, Stephen Paul King
stephe...@provensecure.com wrote:

Hi Jason,

The first, second, 10th, 1,000,000th, and 10^100th, and 10^100^100th
state of the UD's execution are mathematical facts ... Umm, how?
Godel and Matiyasevich would disagree! If there does not exist a program
that can evaluate whether or not a UD substring is a faithful
representation of a true theorem, then how is it a fact?

That depends on whether the UD is deterministic or not.

It is. The evolution of any Turing machines is deterministic.

If it is, then, its Nth state is a fact. (It doesn't need to be run or
evaluated, and the Nth state may be a fact that nobody knows, like the
googolth digit of pi, assuming no one's worked that out.)

Right. :-)

The fact that I remember drinking a glass of water is as much a
mathematical fact about the UD, as the fact as the third decimal digit of
Pi is 4.

Jason

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### Re: Bruno's mathematical reality

```Dear Bruno,

On Sat, Dec 28, 2013 at 7:30 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 28 Dec 2013, at 05:27, Stephen Paul King wrote:

Hi LizR and Jason,

Responding to both of you. I don't understand the claim of determinism
is random noise is necessary for the computations. Turing machines
require exact pre-specifiability. Adding noise oracles is cheating!

But it exist in arithmetic. Subtracting it would be cheating. the silmple
counting algorith generates all random finite strings (random in the strong
Chaitin sense).

Almost all numbers are random, when written in some base. And you can
define the notion of base *in* arithmetic, so they exist in all models of
arithmetic. We can't subtract them.

With respect: No! We cannot wait forever (literally) to obtain consistency
of our data bases in the face of the inability to know in advance the
arrival time of messages in the network.

The fact that arithmetic contains all finite (even the random ones)
strings is an ontological claim. I have no problem with the claim. My
problem is that we cannot reason as if time does not exist when we are
trying to construct real computers.

We have to use different ideas, for example: competition for resources!
Platonic computers do not compete for resources nor change. They are static
and fixed eternally...

Bruno

On Fri, Dec 27, 2013 at 11:22 PM, LizR lizj...@gmail.com wrote:

On 28 December 2013 17:15, Jason Resch jasonre...@gmail.com wrote:

On Fri, Dec 27, 2013 at 11:06 PM, LizR lizj...@gmail.com wrote:

Clearly programmes don't have to be deterministic. They could contain a
source of genuine randomness, in principle.

That source, if it is within the program, would necessarily be
deterministic.  If it is external to the program, then it is more properly
treated as an input to the program rather than a part of the program itself.

In practice, computers draw on sources of environmental noise such as
delays between keystrokes, timing of the reception of network traffic, and
delays in accessing data off of hard drives, etc. These steps are necessary
precisely because programs cannot produce randomness on their own.

I knew that - honest! :-)

I was answering the question as posed. I believe that in practice all
real-world programmes are deterministic, and (more to the point) the UD is.

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 07:26, meekerdb wrote:

He proposes to dispense with any physical computation and have the
UD exist via arithmetical realism as an abstract, immaterial
computation.

What does a physicist? It looks outside, and seem to be believe in a
special unique universal number, the physical TOE, describing what he
observed.

But comp say that if we share realities, like Everett QM seems to
suggest, then we share a rather low comp substitution level, and that
below it we should see the trace of the interference of the infinitely
many computations in arithmetic.

What we need to do is to compare the quantum observed multiverse with
the comp multi-dream which is inside the head of all universal
numbers. (That is begun in AUDA).

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 07:30, meekerdb wrote:

On 12/27/2013 8:24 PM, Stephen Paul King wrote:

Hi Edgar,

But here is the thing. If we assume timelessness, Bruno is
CORRECT! THe question then becomes: What is time?

It's a computed partial ordering relation between events.

The 1p time looks like that, but this is of course still an open
problem (both in comp and physics, I would say).

Such partial ordering gives models of the S4Grz logic (Bp  p).  It is
more the subjective time than the physical time, which is just not on
a comp horizon soon.

Bruno

Brent

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### Re: Bruno's mathematical reality

```Dear Bruno,

On Sat, Dec 28, 2013 at 7:37 AM, Bruno Marchal marc...@ulb.ac.be wrote:

On 28 Dec 2013, at 05:27, LizR wrote:

On 28 December 2013 17:23, Edgar L. Owen edgaro...@att.net wrote:

Jason,

You might be able to theoretically simulate it but certainly not compute
it in real time which is what reality actually does which is my point.

In real time ?! In comp (and many TOEs) time is emergent.

Physical times and subjective time emerge. OK. But let us be honest, comp
assumes already a sort of time, through the natural order: à, 1, 2, 3, ...

Then you have all UD-time step of the computations emulated by the UD:

phi_444(6) first step
...
phi_444(6) second step
... ...  (meaning greater delay in the
UD-time steps).
ph_444(6) third  step
... ... ...
ph_444(6) fourth  step
... ...
ph_444(6) fifth step
etc.

This would explain the sequencing of events aspect of time, but it does
nothing to address the concurrency problem. We need a theory of time that
has an explanation of both sequencing and transition. I wish you could
study GR, say from Penrose's math book, and Prof. Hitoshi Kitada's Local
Time interpretation of QM.
It gives a nice set of concepts that help solve the problem of time:
there is no such thing as a global time; there is only local time. Local
for each individual observer. Synchronizations of these local times
generates the appearance of global time for a collection that is co-moving
or (equivalently) have similar inertial frames.

To take a parallel example that should be close to your heart, suppose
you're an AI living in the matrix and it's simulating reality for you. You
aren't aware of this but believe yourself to be say a human writer who is
participating in an online discussion. Suppose it takes a million years to
simulate one second of your experience. How would you know? You can only
compare your experience of time with in-matrix clocks, which all run at the
speed you'd expect.

It's the same for any theory which tries to compute reality.

But the physical time is not Turing emulable, and perhaps is not even
existing, like in Dewitt-Wheeler equation: H = 0.

Indeed! The common idea of physical time is an illusion! See:
http://arxiv.org/abs/gr-qc/9408027

What is and What should be Time?
Lancelot
R. Fletcher http://arxiv.org/find/gr-qc/1/au:+Fletcher_L/0/1/0/all/0/1
(Submitted on 20 Aug 1994 (v1 http://arxiv.org/abs/gr-qc/9408027v1), last
revised 16 Mar 1996 (this version, v4))

The notions of time in the theories of Newton and Einstein are reviewed so
that certain of their assumptions are clarified. These assumptions will be
seen as the causes of the incompatibility between the two different ways of
understanding time, and seen to be philosophical hypotheses, rather than
purely scientific ones. The conflict between quantum mechanics and
(general) relativity is shown to be a consequence of retaining the
Newtonian conception of time in the context of quantum mechanics. As a
remedy for this conflict, an alternative definition of time -- earlier
presented in Kitada 1994a and 1994b -- is reviewed with less mathematics
and more emphasis on its philosophical aspects. Based on this revised
understanding of time it is shown that quantum mechanics and general
relativity are reconciled while preserving the current mathematical
formulations of both theories.

if it exist, it depends on all computations instantaneously, by the
delay invariance of the FPI.

Bruno

http://iridia.ulb.ac.be/~marchal/

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### Re: Bruno's mathematical reality

```

On 28 Dec 2013, at 07:34, LizR wrote:

On 28 December 2013 19:31, Stephen Paul King stephe...@provensecure.com
wrote:

Computed how? By what?

I know the answer to this one! To quote Brent -- He proposes to
dispense with any physical computation and have the UD exist via
arithmetical realism as an abstract, immaterial computation.

Assuming comp, there is not much choice in the matter. That is the
point.

Above the substitution level: interaction between universal machines,
including one apparently sustained from below the substitution level
by the statistical interference between infinities of universal

I don't know how to avoid those infinities without reifying some God-
of-the-gap or Matter-of-the-gap notion to singularize a computation
for consciousness, but if that is needed for consciousness, then comp
is false. True, you still survive with a digital brain, but no more
through comp, it is true from comp + some explicit magic to make
disappear the other realities. You get an irrefutable form of cosmic
solipsism.

Bruno

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### Re: Bruno's mathematical reality

```Dear Bruno,

On Sat, Dec 28, 2013 at 12:34 PM, Bruno Marchal marc...@ulb.ac.be wrote:

On 28 Dec 2013, at 07:34, LizR wrote:

On 28 December 2013 19:31, Stephen Paul King
stephe...@provensecure.comwrote:

Computed how? By what?

I know the answer to this one! To quote Brent -- He proposes to dispense
with any physical computation and have the UD exist via arithmetical
realism as an abstract, immaterial computation.

Assuming comp, there is not much choice in the matter. That is the point.

I will agree.

Above the substitution level: interaction between universal machines,
including one apparently sustained from below the substitution level by the
statistical interference between infinities of universal machines getting

But the actual states are not just some random string from my point of
view! The very fact that we can (somewhat) communicate is an important
fact. There is a selection mechanism: interaction.

I don't know how to avoid those infinities without reifying some
God-of-the-gap or Matter-of-the-gap notion to singularize a computation for
consciousness, but if that is needed for consciousness, then comp is false.

Umm, that is a false choice! The FPI is good enough to do the job
without resorting to a 'god/matter in the gap solution. The
singularization of consciousness is easy, as you have shown. It is the
concurrent interaction problem that is not easy. I cannot exactly predict
your actions and thus can only bet on your future states, but I can
constrain your possible choices of action with my physical behaviors even
if the physical world is an illusion. The fact that it is a common and
persistent illusion makes it a ground of commonality from which we can
distinguish ourselves 3-p wise from each other.

True, you still survive with a digital brain, but no more through comp, it
is true from comp + some explicit magic to make disappear the other
realities. You get an irrefutable form of cosmic solipsism.

There is no magic here, there is the SAT problem. Boolean algebras do not
automatically pop out with global consistency over their
arguments/propositions. One has to actually physically run a physical
world to know what it will do. Claiming that it exists in Platonia is not
a solution.

Bruno

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### Re: Bruno's mathematical reality

```
On 12/28/2013 3:13 AM, Bruno Marchal wrote:
Perhaps; but only for nano second. you real mind overlap on sequence of states, with the
right probabilities, and for this you need the complete run of the UD, because your next
moment is determioned by the FPI on all computations.

That's a point that bothers me.  It seems that you require a completed, realized
uncountable inifinity.

Brent

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### Re: Bruno's mathematical reality

```
On 12/28/2013 3:43 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 04:36, Stephen Paul King wrote:

I loath Kronecker's claim! It is synonymous to Man is the measure of all
things.

What is his claim?  I am not familiar with it.

God created the Integers, all else is the invention of man.

man is a measure of all things is a quote from a french philosopher (I just forget
right now his name) itself taken from a greek general, which cut the feet or head of all
soldier having not the right size (!).  (Sorry for those vague memories, learn this in
highschool)

Man is the measure of all things. is usually attributed to Protagoras (a
student of Plato).
Procrustes, who stretched or chopped guests to fit his iron bed, was a metal smith, not a
general.

Now, of course, comp saves Kronecker from anthropomorphism, as with comp we can
say that:
God created the integers, all else is the invention of ... integers.

Die ganze Zahl schuf der liebe Gott, alles Übrige ist Menschenwerk
--- Kronecker

Brent

Of course it made comp number-centered, but this we knew at the start with comp, and ...
with christianism, in which it is important to realize our finiteness.

Bruno

http://iridia.ulb.ac.be/~marchal/ http://iridia.ulb.ac.be/%7Emarchal/

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### Re: Bruno's mathematical reality

```
On 12/28/2013 4:09 AM, Bruno Marchal wrote:
For a long time I got opponent saying that we cannot generate computationally a random
number, and that is right, if we want generate only that numbers. but a simple counting
algorithm generating all numbers, 0, 1, 2,  6999500235148668, ... generates all
random finite incompressible strings,

How can a finite string be incompressible? 6999500235148668 in base 6999500235148669 is
just 10.

Brent

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### Re: Bruno's mathematical reality

```
On 12/28/2013 4:37 AM, Bruno Marchal wrote:

On 28 Dec 2013, at 05:27, LizR wrote:

On 28 December 2013 17:23, Edgar L. Owen edgaro...@att.net mailto:edgaro...@att.net
wrote:

Jason,

You might be able to theoretically simulate it but certainly not compute it
in real
time which is what reality actually does which is my point.

In real time ?! In comp (and many TOEs) time is emergent.

Physical times and subjective time emerge. OK. But let us be honest, comp assumes
already a sort of time, through the natural order: à, 1, 2, 3, ...

Then you have all UD-time step of the computations emulated by the UD:

phi_444(6) first step
...
phi_444(6) second step
... ...  (meaning greater delay in the
UD-time steps).
ph_444(6) third  step
... ... ...
ph_444(6) fourth  step
... ...
ph_444(6) fifth step
etc.

To take a parallel example that should be close to your heart, suppose you're an AI
living in the matrix and it's simulating reality for you. You aren't aware of this but
believe yourself to be say a human writer who is participating in an online discussion.
Suppose it takes a million years to simulate one second of your experience. How would
you know? You can only compare your experience of time with in-matrix clocks, which all
run at the speed you'd expect.

It's the same for any theory which tries to compute reality.

But the physical time is not Turing emulable, and perhaps is not even existing, like in
Dewitt-Wheeler equation: H = 0.
if it exist, it depends on all computations instantaneously, by the delay invariance
of the FPI.

Which seems like a flaw in trying to recover physics from comp - but maybe not, physics
has it's own problems with time.

Brent

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### Re: Bruno's mathematical reality

```On 29 December 2013 00:26, Bruno Marchal marc...@ulb.ac.be wrote:

On 28 Dec 2013, at 03:53, Jason Resch wrote:

Would any universal number do?

That is what Bruno speculatively has suggested. I am not so sure.
Sometimes I think an if-then-else-statement contains all that is
fundamentally required for consciousness, or at least, to be an atom of
consciousness.

As the base of the UD, any universal numbers will do. That is why I can
chose arithmetic or combinators etc.
For raw consciousness, I am prety sure that universality is already too
much, now just if then else might be not enough, I don't know, and I
don't thinks it is important. I will not found a society to protect the
private life of thermostat. I think.

Fair dos for thermostats! Like us, they have their ups and downs...

(Or is that thermometers?)

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### Re: Bruno's mathematical reality

```On Sat, Dec 28, 2013 at 4:23 PM, meekerdb meeke...@verizon.net wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want generate
only that numbers. but a simple counting algorithm generating all numbers,
0, 1, 2,  6999500235148668, ... generates all random finite
incompressible strings,

How can a finite string be incompressible?  6999500235148668 in base
6999500235148669 is just 10.

It took you 2 more digits to represent that number in that way.

Jason

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### Re: Bruno's mathematical reality

```
On 12/28/2013 3:00 PM, Jason Resch wrote:

On Sat, Dec 28, 2013 at 4:23 PM, meekerdb meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally a
random number, and that is right, if we want generate only that numbers.
but a
simple counting algorithm generating all numbers, 0, 1, 2,
6999500235148668,
... generates all random finite incompressible strings,

How can a finite string be incompressible? 6999500235148668 in base
6999500235148669
is just 10.

It took you 2 more digits to represent that number in that way.

But I wouldn't have if everybody knew that our numbering system was base
6999500235148669.

Brent
There are only 10 kind of people in the world. Those who think in binary and those who
don't.

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### Re: Bruno's mathematical reality

```On Sat, Dec 28, 2013 at 6:52 PM, meekerdb meeke...@verizon.net wrote:

On 12/28/2013 3:00 PM, Jason Resch wrote:

On Sat, Dec 28, 2013 at 4:23 PM, meekerdb meeke...@verizon.net wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want generate
only that numbers. but a simple counting algorithm generating all numbers,
0, 1, 2,  6999500235148668, ... generates all random finite
incompressible strings,

How can a finite string be incompressible?  6999500235148668 in base
6999500235148669 is just 10.

It took you 2 more digits to represent that number in that way.

But I wouldn't have if everybody knew that our numbering system was base
6999500235148669.

You should patent this and sell the compression algorithm to youtube. :-)

Jason

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### Re: Bruno's mathematical reality

```
On 12/28/2013 4:47 PM, Jason Resch wrote:

On Sat, Dec 28, 2013 at 6:52 PM, meekerdb meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 12/28/2013 3:00 PM, Jason Resch wrote:

On Sat, Dec 28, 2013 at 4:23 PM, meekerdb meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally
a random number, and that is right, if we want generate only that
numbers. but
a simple counting algorithm generating all numbers, 0, 1, 2,
6999500235148668, ... generates all random finite incompressible
strings,

How can a finite string be incompressible? 6999500235148668 in base
6999500235148669 is just 10.

It took you 2 more digits to represent that number in that way.

But I wouldn't have if everybody knew that our numbering system was base
6999500235148669.

You should patent this and sell the compression algorithm to youtube. :-)

Actually it's a commonly used one.  It's a one-time-pad; you and your communicant agree
before hand on the basis or the pad and then you only have to send 10 to communicate
6999500235148668.  It's the most secure form of cryptography.

Brent

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### Re: Bruno's mathematical reality

```On Sat, Dec 28, 2013 at 8:35 PM, meekerdb meeke...@verizon.net wrote:

On 12/28/2013 4:47 PM, Jason Resch wrote:

On Sat, Dec 28, 2013 at 6:52 PM, meekerdb meeke...@verizon.net wrote:

On 12/28/2013 3:00 PM, Jason Resch wrote:

On Sat, Dec 28, 2013 at 4:23 PM, meekerdb meeke...@verizon.net wrote:

On 12/28/2013 4:09 AM, Bruno Marchal wrote:

For a long time I got opponent saying that we cannot generate
computationally a random number, and that is right, if we want generate
only that numbers. but a simple counting algorithm generating all numbers,
0, 1, 2,  6999500235148668, ... generates all random finite
incompressible strings,

How can a finite string be incompressible?  6999500235148668 in base
6999500235148669 is just 10.

It took you 2 more digits to represent that number in that way.

But I wouldn't have if everybody knew that our numbering system was
base 6999500235148669.

You should patent this and sell the compression algorithm to youtube. :-)

Actually it's a commonly used one.  It's a one-time-pad; you and your
communicant agree before hand on the basis or the pad and then you only
have to send 10 to communicate 6999500235148668.  It's the most secure form
of cryptography.

Agreeing on a base wouldn't enable you to send a message securely if you
are constrained to sending 10. With OTPs, you agree on the pad
beforehand, then combine the pad with the message before sending it where
it can be de-combined.  In your example there is no act of combining or
de-combining involved.

Jason

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### Re: Bruno's mathematical reality

``` everything-list@googlegroups.com
Sent: Wed, Dec 25, 2013 6:18 am
Subject: Re: Bruno's mathematical reality

On 22 Dec 2013, at 20:04, spudboy...@aol.com wrote:

Your theory comes from Von Neumann, and Chaitin, and Wolfram, does
it not, Edgar? That everything is a program or cellular automata,
and in the beginning was a program. Following along, what is this
Logic comprised of (sort of like SPK's query) is it electrons, is
it virtual particles, is it field lines? Where doth the logical
structure sleep? In Planck Cells? I apologize if my questions
annoy, but where is the computer network that computes the current
state of the universe.

In the arithmletical reality which probably emulates all
computations (in the standard sense of computer science).

But the Wolfram theory is incorrect, as it assumes comp, and don't
take the FPI into account (nor even the quantum one).

Bruno

Can we get MIT physicist Seth Lloyd to shake a stick or a laser
pointer, or otherwise, display, where this abacus dwells?

Thanks,
Mitch
-Original Message-
From: Stephen Paul King stephe...@charter.net
Sent: Sun, Dec 22, 2013 1:36 pm
Subject: Re: Bruno's mathematical reality

Dear Edger,

Where does the fire come from that animates the logic?

On Friday, December 20, 2013 6:52:54 PM UTC-5, Edgar L. Owen wrote:
All,

The fundamental nature of reality is examined in detail in my
recent book on Reality available on Amazon under my name.

Marchal is on the right track, but reality consists not just of
numbers (math) but is a running logical structure analogous to
software that continually computes the current state of the
universe. Just as software includes but doesn't consist only of
numbers and math, so does reality. In fact the equations of
physical science make sense only when embedded in a logical
structure just as is the case in computational reality.

Modern science has a major lacuna, the notion that all of reality
is mathematical, that prevents science from grasping the complete
nature of reality. In truth all of reality is logical, as is
software, and the mathematics is just a subset of the logic. After
all, modern science with its misguided insistence that all of
nature of either consciousness or the present moment, the two most
fundamental aspects of experience. However I present a
computational based information approach to these in my book among
many other things.

The second clarification that needs to be made to the post on
Marchal's work is that human math and logic are distinct from the
actual math and logic that computes reality. The human version is a
generalized and extended approximation of the actual that differs
from the actual logico-mathematical structure of reality in
important ways (e.g. infinities and infinitesimals which don't
actually exist in external reality).

I can explain further if anyone is interested, or you can read

Edgar Owen

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### Re: Bruno's mathematical reality

``` the whole mathematical (in the current sense of
mathematical).

I am not proposing anything new, just pointing on the incompatibility
between mechanist and materialist cognitive sciences, and showing how
computer science translates the mind-body problem into a body belief
problem in arithmetic. The conversation with the Lôbian machine is just
the beginning of the solution, in the most ideal case.

Bruno

-Original Message-
From: Bruno Marchal marc...@ulb.ac.be
Sent: Wed, Dec 25, 2013 6:18 am
Subject: Re: Bruno's mathematical reality

On 22 Dec 2013, at 20:04, spudboy...@aol.com wrote:

Your theory comes from Von Neumann, and Chaitin, and Wolfram, does it not,
Edgar? That everything is a program or cellular automata, and in the
beginning was a program. Following along, what is this Logic comprised of
(sort of like SPK's query) is it electrons, is it virtual particles, is it
field lines? Where doth the logical structure sleep? In Planck Cells? I
apologize if my questions annoy, but where is the computer network that
computes the current state of the universe.

In the arithmletical reality which probably emulates all computations
(in the standard sense of computer science).

But the Wolfram theory is incorrect, as it assumes comp, and don't take
the FPI into account (nor even the quantum one).

Bruno

Can we get MIT physicist Seth Lloyd to shake a stick or a laser pointer,
or otherwise, display, where this abacus dwells?

Thanks,
Mitch
-Original Message-
From: Stephen Paul King stephe...@charter.net
Sent: Sun, Dec 22, 2013 1:36 pm
Subject: Re: Bruno's mathematical reality

Dear Edger,

Where does the fire come from that animates the logic?

On Friday, December 20, 2013 6:52:54 PM UTC-5, Edgar L. Owen wrote:

All,

The fundamental nature of reality is examined in detail in my recent
book on Reality available on Amazon under my name.

Marchal is on the right track, but reality consists not just of numbers
(math) but is a running logical structure analogous to software that
continually computes the current state of the universe. Just as software
includes but doesn't consist only of numbers and math, so does reality. In
fact the equations of physical science make sense only when embedded in a
logical structure just as is the case in computational reality.

Modern science has a major lacuna, the notion that all of reality is
mathematical, that prevents science from grasping the complete nature of
reality. In truth all of reality is logical, as is software, and the
mathematics is just a subset of the logic. After all, modern science with
its misguided insistence that all of reality is mathematical, has had
nothing useful to say about the nature of either consciousness or the
present moment, the two most fundamental aspects of experience. However I
present a computational based information approach to these in my book
among many other things.

The second clarification that needs to be made to the post on Marchal's
work is that human math and logic are distinct from the actual math and
logic that computes reality. The human version is a generalized and
extended approximation of the actual that differs from the actual
logico-mathematical structure of reality in important ways (e.g. infinities
and infinitesimals which don't actually exist in external reality).

I can explain further if anyone is interested, or you can read about it
in my book...

Edgar Owen

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### Re: Bruno's mathematical reality

```On 28 December 2013 05:51, Stephen Paul King stephe...@provensecure.comwrote:

It has always seemed to me that UDA cannot solve the mind-body problem
strictly because it cannot comprehend the existence of other minds.

computation which are assumed to exist in arithmetic actually manage to
communicate with each other?

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### Re: Bruno's mathematical reality

```Hi LizR,

That is what is not explicitly explained! I could see how one might make
an argument based on Godel numbers and a choice of a numbering scheme could
show the existence of a string of numbers that, if run on some computer,
would generate a description of the interaction of several actors. But this
ignores the problems of concurrency and point of view. The best one might
be able to do, AFAIK, is cook up a description of the interactions of many
observers -each one is an intersection of infinitely many computations,
but such a description would itself be the content of some observer's point
of view that assumes a choice of Godel numbering scheme.

On Fri, Dec 27, 2013 at 5:50 PM, LizR lizj...@gmail.com wrote:

On 28 December 2013 05:51, Stephen Paul King
stephe...@provensecure.comwrote:

It has always seemed to me that UDA cannot solve the mind-body problem
strictly because it cannot comprehend the existence of other minds.

computation which are assumed to exist in arithmetic actually manage to
communicate with each other?

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Stephen Paul King

Senior Researcher

Mobile: (864) 567-3099

stephe...@provensecure.com

http://www.provensecure.us/

“This message (including any attachments) is intended only for the use of
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### Re: Bruno's mathematical reality

```On 28 December 2013 11:55, Stephen Paul King stephe...@provensecure.comwrote:

Hi LizR,

That is what is not explicitly explained! I could see how one might
make an argument based on Godel numbers and a choice of a numbering scheme
could show the existence of a string of numbers that, if run on some
computer, would generate a description of the interaction of several
actors. But this ignores the problems of concurrency and point of view.
The best one might be able to do, AFAIK, is cook up a description of the
interactions of many observers -each one is an intersection of infinitely
many computations, but such a description would itself be the content of
some observer's point of view that assumes a choice of Godel numbering
scheme.

It seems to suggest multi-solipsism or something along those lines -
which doesn't make it wrong, of course.

I await Bruno's answer with interest. I think he has already said something
limited understanding.

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### Re: Bruno's mathematical reality

```Dear LizR,

Multi-solipsism, exactly! We each live in our very own world and all
interactions between pairs of separable entities are supported at lower
levels where the pair collapse to a single entity. This would be very
similar to Bruno's substitution level.

On Fri, Dec 27, 2013 at 6:03 PM, LizR lizj...@gmail.com wrote:

On 28 December 2013 11:55, Stephen Paul King
stephe...@provensecure.comwrote:

Hi LizR,

That is what is not explicitly explained! I could see how one might
make an argument based on Godel numbers and a choice of a numbering scheme
could show the existence of a string of numbers that, if run on some
computer, would generate a description of the interaction of several
actors. But this ignores the problems of concurrency and point of view.
The best one might be able to do, AFAIK, is cook up a description of the
interactions of many observers -each one is an intersection of infinitely
many computations, but such a description would itself be the content of
some observer's point of view that assumes a choice of Godel numbering
scheme.

It seems to suggest multi-solipsism or something along those lines -
which doesn't make it wrong, of course.

I await Bruno's answer with interest. I think he has already said
my limited understanding.

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Mobile: (864) 567-3099

stephe...@provensecure.com

http://www.provensecure.us/

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### Re: Bruno's mathematical reality

```On Fri, Dec 27, 2013 at 6:03 PM, LizR lizj...@gmail.com wrote:

On 28 December 2013 11:55, Stephen Paul King
stephe...@provensecure.comwrote:

Hi LizR,

That is what is not explicitly explained! I could see how one might
make an argument based on Godel numbers and a choice of a numbering scheme
could show the existence of a string of numbers that, if run on some
computer, would generate a description of the interaction of several
actors. But this ignores the problems of concurrency and point of view.
The best one might be able to do, AFAIK, is cook up a description of the
interactions of many observers -each one is an intersection of infinitely
many computations, but such a description would itself be the content of
some observer's point of view that assumes a choice of Godel numbering
scheme.

It seems to suggest multi-solipsism or something along those lines -
which doesn't make it wrong, of course.

I await Bruno's answer with interest. I think he has already said
my limited understanding.

I am also interested to hear what Bruno has to say.  My perspective is that
most of the computations that support you and I are not isolated and
short-lived computational Boltzmann brains but much larger, long-running
computations such as those that correspond to a universe in which life
adapts and evolves.  The starting conditions for these is much less
constrained, and therefore it is far more probable to result in conscious
computations such as ours than the case where the computation supporting
your brain experiencing this moment is some initial condition of a very
specific program. Certainly, those programs exist too, but they are much
rarer. They appear in the UD much less frequently than say the program
corresponding to the approximate laws of physics of this universe.  It
takes far more data to describe your brain than it does to describe the
physical system on which it is based.

So we are (mostly) still in the same universe, and so we can interact
with and affect the consciousness of other people.

Jason

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### Re: Bruno's mathematical reality

```Dear Jason,

Interleaving below.

On Fri, Dec 27, 2013 at 6:20 PM, Jason Resch jasonre...@gmail.com wrote:

On Fri, Dec 27, 2013 at 6:03 PM, LizR lizj...@gmail.com wrote:

On 28 December 2013 11:55, Stephen Paul King
stephe...@provensecure.comwrote:

Hi LizR,

That is what is not explicitly explained! I could see how one might
make an argument based on Godel numbers and a choice of a numbering scheme
could show the existence of a string of numbers that, if run on some
computer, would generate a description of the interaction of several
actors. But this ignores the problems of concurrency and point of view.
The best one might be able to do, AFAIK, is cook up a description of the
interactions of many observers -each one is an intersection of infinitely
many computations, but such a description would itself be the content of
some observer's point of view that assumes a choice of Godel numbering
scheme.

It seems to suggest multi-solipsism or something along those lines -
which doesn't make it wrong, of course.

I await Bruno's answer with interest. I think he has already said
my limited understanding.

I am also interested to hear what Bruno has to say.  My perspective is
that most of the computations that support you and I are not isolated and
short-lived computational Boltzmann brains but much larger, long-running
computations such as those that correspond to a universe in which life

I agree. I have never been happy with the Boltzman brain argument because
it seems to assume that the probability distribution of spontaneous BBs
is independent of the complexity of the content of the minds associated
with those brains. I have been studying this relationship between
complexity or expressiveness of a B.B. My first guesstimation is that
there is something like a Zift's Law in the distribution: the more
expressive a BB the less chance it has to exist and evolve at least one
cycle of its computation. (After all, computers have to be able to run
one clock cycle to be said that they actually compute some program...)

The starting conditions for these is much less constrained, and therefore
it is far more probable to result in conscious computations such as ours
than the case where the computation supporting your brain experiencing this
moment is some initial condition of a very specific program. Certainly,
those programs exist too, but they are much rarer.

RIght, but how fast do they get rarer?

They appear in the UD much less frequently than say the program
corresponding to the approximate laws of physics of this universe.

It takes far more data to describe your brain than it does to describe the
physical system on which it is based.

How do you estimate this? Are you assuming that a lot of data can be
compressed using symmetries and redundancies. This looks like a Kolmogorov
complexity/entropy...

So we are (mostly) still in the same universe, and so we can interact
with and affect the consciousness of other people.

From my reasoning, the appearance that we are in the same universe is a
by product of bisimilarities in the infinity of computations that are each
of us. In other words, there  are many computations that are running
Stephen that are identical to and thus are the same computation to many of
the computations that are running Jason.
This gives an overlap between our worlds and thus the appearance of a
common world for some collection of observers. The cool thing is that
this implies that there are underlaps; computations that are not shared or
bisimilar between all of us. COuld those be the ones that we identify as
ourselves?

Jason

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### Re: Bruno's mathematical reality

```On 28 December 2013 12:20, Jason Resch jasonre...@gmail.com wrote:

On Fri, Dec 27, 2013 at 6:03 PM, LizR lizj...@gmail.com wrote:

On 28 December 2013 11:55, Stephen Paul King
stephe...@provensecure.comwrote:

Hi LizR,

That is what is not explicitly explained! I could see how one might
make an argument based on Godel numbers and a choice of a numbering scheme
could show the existence of a string of numbers that, if run on some
computer, would generate a description of the interaction of several
actors. But this ignores the problems of concurrency and point of view.
The best one might be able to do, AFAIK, is cook up a description of the
interactions of many observers -each one is an intersection of infinitely
many computations, but such a description would itself be the content of
some observer's point of view that assumes a choice of Godel numbering
scheme.

It seems to suggest multi-solipsism or something along those lines -
which doesn't make it wrong, of course.

I await Bruno's answer with interest. I think he has already said
my limited understanding.

I am also interested to hear what Bruno has to say.  My perspective is
that most of the computations that support you and I are not isolated and
short-lived computational Boltzmann brains but much larger, long-running
computations such as those that correspond to a universe in which life
adapts and evolves.  The starting conditions for these is much less
constrained, and therefore it is far more probable to result in conscious
computations such as ours than the case where the computation supporting
your brain experiencing this moment is some initial condition of a very
specific program. Certainly, those programs exist too, but they are much
rarer. They appear in the UD much less frequently than say the program
corresponding to the approximate laws of physics of this universe.  It
takes far more data to describe your brain than it does to describe the
physical system on which it is based.

This sounds like a way to get Max Tegmark's mathematical universe
hypothesis out of comp. It also sounds like a way to get Edgar Owen's
cellular automaton universe, or whatever it should be called (though not
the part about the present moment being the only thing that exists, but
that's an unnecessary add-on anyway imho).

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### Re: Bruno's mathematical reality

```On Fri, Dec 27, 2013 at 6:33 PM, Stephen Paul King
stephe...@provensecure.com wrote:

Dear Jason,

Interleaving below.

On Fri, Dec 27, 2013 at 6:20 PM, Jason Resch jasonre...@gmail.com wrote:

On Fri, Dec 27, 2013 at 6:03 PM, LizR lizj...@gmail.com wrote:

On 28 December 2013 11:55, Stephen Paul King stephe...@provensecure.com
wrote:

Hi LizR,

That is what is not explicitly explained! I could see how one might
make an argument based on Godel numbers and a choice of a numbering scheme
could show the existence of a string of numbers that, if run on some
computer, would generate a description of the interaction of several
actors. But this ignores the problems of concurrency and point of view.
The best one might be able to do, AFAIK, is cook up a description of the
interactions of many observers -each one is an intersection of infinitely
many computations, but such a description would itself be the content of
some observer's point of view that assumes a choice of Godel numbering
scheme.

It seems to suggest multi-solipsism or something along those lines -
which doesn't make it wrong, of course.

I await Bruno's answer with interest. I think he has already said
my limited understanding.

I am also interested to hear what Bruno has to say.  My perspective is
that most of the computations that support you and I are not isolated and
short-lived computational Boltzmann brains but much larger, long-running
computations such as those that correspond to a universe in which life

I agree. I have never been happy with the Boltzman brain argument because
it seems to assume that the probability distribution of spontaneous BBs
is independent of the complexity of the content of the minds associated
with those brains. I have been studying this relationship between
complexity or expressiveness of a B.B. My first guesstimation is that
there is something like a Zift's Law in the distribution: the more
expressive a BB the less chance it has to exist and evolve at least one
cycle of its computation. (After all, computers have to be able to run
one clock cycle to be said that they actually compute some program...)

The starting conditions for these is much less constrained, and
therefore it is far more probable to result in conscious computations such
as ours than the case where the computation supporting your brain
experiencing this moment is some initial condition of a very specific
program. Certainly, those programs exist too, but they are much rarer.

RIght, but how fast do they get rarer?

It's hard to say. We would have to develop some model for estimating the
Kolmogorov complexity (and maybe also incorporate frequency) of different
programs and their relation to a given mind.

They appear in the UD much less frequently than say the program
corresponding to the approximate laws of physics of this universe.

It takes far more data to describe your brain than it does to describe
the physical system on which it is based.

How do you estimate this?

The UDA is a comparatively short program, and provably contains the program
that is identical to your mind.  Similarly, all of the known laws of
physics could fit on a couple sheets of paper.  QM seems to suggest that
all possible solutions to certain equations exist, and so there is no need
to specify the initial conditions of the universe (which would require much

Are you assuming that a lot of data can be compressed using symmetries and
redundancies. This looks like a Kolmogorov complexity/entropy...

Somewhat. I think how frequently a program is referenced / instantiated by
other non-halting programs may play a role.

So we are (mostly) still in the same universe, and so we can interact
with and affect the consciousness of other people.

From my reasoning, the appearance that we are in the same universe is a
by product of bisimilarities in the infinity of computations that are each
of us. In other words, there  are many computations that are running
Stephen that are identical to and thus are the same computation to many of
the computations that are running Jason.

Yes. We would be programs instantiated within a (possibly but not
necessarily) shared, larger program.

This gives an overlap between our worlds and thus the appearance of a
common world for some collection of observers.

Right.

The cool thing is that this implies that there are underlaps; computations
that are not shared or bisimilar between all of us.

Yes, I agree.  In some branches of the MW, perhaps you were born but I was
not, or I was, and you weren't.

COuld those be the ones that we identify as ourselves?

Personal identity can become a very difficult subject, since there may be
paths through which my program evolves ```

### Re: Bruno's mathematical reality

```Jason,

You state The UDA is a comparatively short program, and provably contains
the program that is identical to your mind.

You can't be serious! As stated that's the most ridiculous statement I've
heard here today in all manner of respects!

Edgar

On Friday, December 27, 2013 7:56:44 PM UTC-5, Jason wrote:

On Fri, Dec 27, 2013 at 6:33 PM, Stephen Paul King
step...@provensecure.com javascript: wrote:

Dear Jason,

Interleaving below.

On Fri, Dec 27, 2013 at 6:20 PM, Jason Resch jason...@gmail.comjavascript:
wrote:

On Fri, Dec 27, 2013 at 6:03 PM, LizR liz...@gmail.com javascript:wrote:

On 28 December 2013 11:55, Stephen Paul King
step...@provensecure.comjavascript:
wrote:

Hi LizR,

That is what is not explicitly explained! I could see how one might
make an argument based on Godel numbers and a choice of a numbering
scheme
could show the existence of a string of numbers that, if run on some
computer, would generate a description of the interaction of several
actors. But this ignores the problems of concurrency and point of view.
The best one might be able to do, AFAIK, is cook up a description of the
interactions of many observers -each one is an intersection of
infinitely
many computations, but such a description would itself be the content of
some observer's point of view that assumes a choice of Godel numbering
scheme.

It seems to suggest multi-solipsism or something along those lines -
which doesn't make it wrong, of course.

I await Bruno's answer with interest. I think he has already said
to
my limited understanding.

I am also interested to hear what Bruno has to say.  My perspective is
that most of the computations that support you and I are not isolated and
short-lived computational Boltzmann brains but much larger, long-running
computations such as those that correspond to a universe in which life

I agree. I have never been happy with the Boltzman brain argument because
it seems to assume that the probability distribution of spontaneous BBs
is independent of the complexity of the content of the minds associated
with those brains. I have been studying this relationship between
complexity or expressiveness of a B.B. My first guesstimation is that
there is something like a Zift's Law in the distribution: the more
expressive a BB the less chance it has to exist and evolve at least one
cycle of its computation. (After all, computers have to be able to run
one clock cycle to be said that they actually compute some program...)

The starting conditions for these is much less constrained, and
therefore it is far more probable to result in conscious computations such
as ours than the case where the computation supporting your brain
experiencing this moment is some initial condition of a very specific
program. Certainly, those programs exist too, but they are much rarer.

RIght, but how fast do they get rarer?

It's hard to say. We would have to develop some model for estimating the
Kolmogorov complexity (and maybe also incorporate frequency) of different
programs and their relation to a given mind.

They appear in the UD much less frequently than say the program
corresponding to the approximate laws of physics of this universe.

It takes far more data to describe your brain than it does to describe
the physical system on which it is based.

How do you estimate this?

The UDA is a comparatively short program, and provably contains the
program that is identical to your mind.  Similarly, all of the known laws
of physics could fit on a couple sheets of paper.  QM seems to suggest that
all possible solutions to certain equations exist, and so there is no need
to specify the initial conditions of the universe (which would require much

Are you assuming that a lot of data can be compressed using symmetries
and redundancies. This looks like a Kolmogorov complexity/entropy...

Somewhat. I think how frequently a program is referenced / instantiated by
other non-halting programs may play a role.

So we are (mostly) still in the same universe, and so we can interact
with and affect the consciousness of other people.

From my reasoning, the appearance that we are in the same universe is
a by product of bisimilarities in the infinity of computations that are
each of us. In other words, there  are many computations that are running
Stephen that are identical to and thus are the same computation to many of
the computations that are running Jason.

Yes. We would be programs instantiated within a (possibly but not
necessarily) shared, larger program.

This gives an overlap between our worlds and thus the appearance of a
common world for ```

### Re: Bruno's mathematical reality

```On 28 December 2013 13:56, Jason Resch jasonre...@gmail.com wrote:

The UDA is a comparatively short program, and provably contains the
program that is identical to your mind.

To be more precise (I hope) - assuming that thoughts, experiences etc are a
form of computation at some level, the output (or trace) of the UDA, which
I seem to recall is designated UDA*, will eventually generate those
thoughts, experiences etc. Though if run on a PC it would probably take a
few googol years to do so (and require many hubble volumes of storage space
too, I imagine).

However, arithmetical realism assumes that the trace of the UDA already
exists timelessly.

Similarly, all of the known laws of physics could fit on a couple sheets
of paper.  QM seems to suggest that all possible solutions to certain
equations exist, and so there is no need to specify the initial conditions
of the universe (which would require much more information to describe than

This sounds like the Theory of Nothing again.?

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### Re: Bruno's mathematical reality

```On 28 December 2013 14:03, Edgar L. Owen edgaro...@att.net wrote:

Jason,

You state The UDA is a comparatively short program, and provably
contains the program that is identical to your mind.

You can't be serious! As stated that's the most ridiculous statement I've
heard here today in all manner of respects!

Jason was shorthanding somewhat. I've expanded on his statement in my last
post.

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### Re: Bruno's mathematical reality

```Hi Jason,

I snipped the portion of the thread out to cut of the tail... Interleaving
in Blue.

I am also interested to hear what Bruno has to say.  My perspective is that
most of the computations that support you and I are not isolated and
short-lived computational Boltzmann brains but much larger, long-running
computations such as those that correspond to a universe in which life

I agree. I have never been happy with the Boltzman brain argument because
it seems to assume that the probability distribution of spontaneous BBs
is independent of the complexity of the content of the minds associated
with those brains. I have been studying this relationship between
complexity or expressiveness of a B.B. My first guesstimation is that
there is something like a Zift's Law in the distribution: the more
expressive a BB the less chance it has to exist and evolve at least one
cycle of its computation. (After all, computers have to be able to run
one clock cycle to be said that they actually compute some program...)

The starting conditions for these is much less constrained, and
therefore it is far more probable to result in conscious computations such
as ours than the case where the computation supporting your brain
experiencing this moment is some initial condition of a very specific
program. Certainly, those programs exist too, but they are much rarer.

RIght, but how fast do they get rarer?

It's hard to say. We would have to develop some model for estimating the
Kolmogorov complexity (and maybe also incorporate frequency) of different
programs and their relation to a given mind.

{spk} Do you have an candidate toy models of a mind that would work? What
can be constructed following Bruno's idea of an observer: an intersection
of infinitely many computations (of finite length?)

Would any universal number do? Isn't a Universal number always at max
Kolmogorov entropy? If we add arbitrary prefixes to a Universal number,
does it remain Universal?

They appear in the UD much less frequently than say the program
corresponding to the approximate laws of physics of this universe.

It takes far more data to describe your brain than it does to describe
the physical system on which it is based.

How do you estimate this?

The UDA is a comparatively short program, and provably contains the program
that is identical to your mind.  Similarly, all of the known laws of
physics could fit on a couple sheets of paper.  QM seems to suggest that
all possible solutions to certain equations exist, and so there is no need
to specify the initial conditions of the universe (which would require much

{spk} Sure! Any finite program will be smaller an an infinite one! LOL.
But I am skeptical of the claim that even if it exists, finding it is HARD.
If you don't actually have a means to implement it on a physical machine
what good is an existential proof of it in some theory?

This is why I often wonder if this entire conversation exercise in
futility! :_( What does it really mean to say that a mind is a finite
program when such has measure zero in the Reals (which is where we should
embed the NxN-N idea in the first place. I loath Kronecker's claim! It is
synonymous to Man is the measure of all things.

Are you assuming that a lot of data can be compressed using symmetries and
redundancies. This looks like a Kolmogorov complexity/entropy...

Somewhat. I think how frequently a program is referenced / instantiated by
other non-halting programs may play a role.

{spk} Like citations or Friending. LOL, nice! But what prevents such a
scheme from being regular, generating a complete graph with a homogeneous
connectedness or a purely random connectedness?

Real world networks are, at best, small
worldhttp://en.wikipedia.org/wiki/Small-world_network
on average and thus are far different from what we expect from our
considerations of ensembles of NxN-N strings.
http://en.wikipedia.org/wiki/Small-world_network
A *small-world network* is a type of mathematical
graphhttp://en.wikipedia.org/wiki/Graph_(mathematics)
in which most nodes are not neighbors of one another, but most nodes can
be reached from every other by a small number of hops or steps.
Specifically, a small-world network is defined to be a network where the
typical distance *L* between two randomly chosen nodes (the number of steps
required) grows proportionally to the logarithm of the number of nodes *N* in
the network, that
is:[1]http://en.wikipedia.org/wiki/Small-world_network#cite_note-1
[image: L \propto \log N]

So we are (mostly) still in the same universe, and so we can interact
with and affect the consciousness of other people.

From my reasoning, the appearance that we are in the same universe is a
by product of bisimilarities in the infinity of computations that are each
of us. In other words, there  are many computations that are running
Stephen ```

### Re: Bruno's mathematical reality

```On Fri, Dec 27, 2013 at 8:03 PM, Edgar L. Owen edgaro...@att.net wrote:

Jason,

You state The UDA is a comparatively short program, and provably
contains the program that is identical to your mind.

My apologies, I meant the UD which short for Universal Dovetailer, not
the UDA, which is the Universal Dovetailer Argument.

You can't be serious!

I am.

As stated that's the most ridiculous statement I've heard here today in
all manner of respects!

The UD is a program that executes all programs. If your mind is a program,
then it is executed by the UD.

Jason

On Friday, December 27, 2013 7:56:44 PM UTC-5, Jason wrote:

On Fri, Dec 27, 2013 at 6:33 PM, Stephen Paul King
step...@provensecure.com wrote:

Dear Jason,

Interleaving below.

On Fri, Dec 27, 2013 at 6:20 PM, Jason Resch jason...@gmail.com wrote:

On Fri, Dec 27, 2013 at 6:03 PM, LizR liz...@gmail.com wrote:

On 28 December 2013 11:55, Stephen Paul King step...@provensecure.com
wrote:

Hi LizR,

That is what is not explicitly explained! I could see how one
might make an argument based on Godel numbers and a choice of a numbering
scheme could show the existence of a string of numbers that, if run on
some
computer, would generate a description of the interaction of several
actors. But this ignores the problems of concurrency and point of view.
The best one might be able to do, AFAIK, is cook up a description of the
interactions of many observers -each one is an intersection of
infinitely
many computations, but such a description would itself be the content of
some observer's point of view that assumes a choice of Godel numbering
scheme.

It seems to suggest multi-solipsism or something along those lines
- which doesn't make it wrong, of course.

I await Bruno's answer with interest. I think he has already said
to
my limited understanding.

I am also interested to hear what Bruno has to say.  My perspective is
that most of the computations that support you and I are not isolated and
short-lived computational Boltzmann brains but much larger, long-running
computations such as those that correspond to a universe in which life

I agree. I have never been happy with the Boltzman brain argument
because it seems to assume that the probability distribution of
spontaneous BBs is independent of the complexity of the content of the
minds associated with those brains. I have been studying this relationship
between complexity or expressiveness of a B.B. My first guesstimation is
that there is something like a Zift's Law in the distribution: the more
expressive a BB the less chance it has to exist and evolve at least one
cycle of its computation. (After all, computers have to be able to run
one clock cycle to be said that they actually compute some program...)

The starting conditions for these is much less constrained, and
therefore it is far more probable to result in conscious computations such
as ours than the case where the computation supporting your brain
experiencing this moment is some initial condition of a very specific
program. Certainly, those programs exist too, but they are much rarer.

RIght, but how fast do they get rarer?

It's hard to say. We would have to develop some model for estimating the
Kolmogorov complexity (and maybe also incorporate frequency) of different
programs and their relation to a given mind.

They appear in the UD much less frequently than say the program
corresponding to the approximate laws of physics of this universe.

It takes far more data to describe your brain than it does to describe
the physical system on which it is based.

How do you estimate this?

The UDA is a comparatively short program, and provably contains the
program that is identical to your mind.  Similarly, all of the known laws
of physics could fit on a couple sheets of paper.  QM seems to suggest that
all possible solutions to certain equations exist, and so there is no need
to specify the initial conditions of the universe (which would require much

Are you assuming that a lot of data can be compressed using symmetries
and redundancies. This looks like a Kolmogorov complexity/entropy...

Somewhat. I think how frequently a program is referenced / instantiated
by other non-halting programs may play a role.

So we are (mostly) still in the same universe, and so we can interact
with and affect the consciousness of other people.

From my reasoning, the appearance that we are in the same universe
is a by product of bisimilarities in the infinity of computations that are
each of us. In other words, there  are many computations that are running
Stephen that are identical to and thus are the same ```

### Re: Bruno's mathematical reality

```What I think Jason is saying is that the TRACE of the UD (knowns as UD* - I
previous post for an elaboration.

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### Re: Bruno's mathematical reality

```Hi Jason,

Could you discuss the trace of the UD that LizR mentioned? How is it
computed? Could you write an explicit example? I have never been able to
grok it.

On Fri, Dec 27, 2013 at 9:29 PM, LizR lizj...@gmail.com wrote:

What I think Jason is saying is that the TRACE of the UD (knowns as UD* -
I made the same mistake!) will *eventually* contain your mind. See my
previous post for an elaboration.

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Stephen Paul King

Senior Researcher

Mobile: (864) 567-3099

stephe...@provensecure.com

http://www.provensecure.us/

“This message (including any attachments) is intended only for the use of
the individual or entity to which it is addressed, and may contain
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exempt from disclosure under applicable law or may be constituted as
attorney work product. If you are not the intended recipient, you are
hereby notified that any use, dissemination, distribution, or copying of
this communication is strictly prohibited. If you have received this
message in error, notify sender immediately and delete this message
immediately.”

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### Re: Bruno's mathematical reality

```On 28 December 2013 15:31, Stephen Paul King stephe...@provensecure.comwrote:

Hi Jason,

Could you discuss the trace of the UD that LizR mentioned? How is it
computed? Could you write an explicit example? I have never been able to
grok it.

This is something that I also find it rather hard to get my head around. I
think the argument goes that the trace of the UD exists in arithmetic,
along with all other computations, and indeed everything else (infinity is
a big place, I guess...!)

The hard bit is understanding how one state of UD* can know that it is
part of a computation when it's just there (a bit like a slice thru a
block universe, perhaps). Perhaps this involves something like Fred Hoyle's
pigeon hole idea from October the first is too late - a fab book, by the
way, as I imagine everyone here already knows.

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### Re: Bruno's mathematical reality

```I think friending is something to do with facebook, or similar social
media, so I think SPK is saying that programmes which reference other
programmes give them more reality. (Or something like that! :-)

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### Re: Bruno's mathematical reality

```On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King
stephe...@provensecure.com wrote:

Hi Jason,

Could you discuss the trace of the UD that LizR mentioned? How is it
computed? Could you write an explicit example? I have never been able to
grok it.

Bruno has written an actual UD in the LISP programming language.  I will
write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the integer i
Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far

# For each program we have generated that has not halted, execute one
instruction of it
for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next time
through
i = i + 1;
}

Any program, and whether or not it ever terminates can be translated to a
statement concerning numbers in arithmetic. Thus mathematical truth
captures the facts concerning whether or not any program executes forever,
and what all of its intermediate states are. If these statements are true
independently of you and me, then the executions of these programs are
embedded in arithmetical truth and have a platonic existence.  The first,
second, 10th, 1,000,000th, and 10^100th, and 10^100^100th state of the UD's
execution are mathematical facts which have definite values, and all the
conscious beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part of the
execution of the UD are there, in the math.

Jason

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### Re: Bruno's mathematical reality

```There is one point to add which I think you've missed, Jason (apologies if
I've misunderstood). The UD generates the first instruction of the first
programme, then the first instruction of the second programme, and so on.
Once it has generated the first instruction of every possible programme, it
then adds the second instruction of the first programme, the
second instruction of the second programme, and so on. This is why it's
called a dovetailer, I believe, and stops it running into problems with
non-halting programmes, or programmes that would crash, or various other
contingencies...

This isn't intrinsic to the UD, which could in principle write the first
programme before it moves on to the next one - but it allows it to avoid
certain problems caused by having a programme that writes other programmes.

...I think. I'm sure Bruno will let me know if that's wrong.

:)

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### Re: Bruno's mathematical reality

```PS I like the while (true) statement. What would Pontius Pilate have made
of that? :-)

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### Re: Bruno's mathematical reality

```Dear Jason,

ISTM that the line  For each program we have generated that has not
halted, execute one instruction of it for each (Program p in
listOfPrograms) is buggy.

It assumes that the space of programs that do not halt is accessible. How?

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch jasonre...@gmail.com wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King
stephe...@provensecure.com wrote:

Hi Jason,

Could you discuss the trace of the UD that LizR mentioned? How is it
computed? Could you write an explicit example? I have never been able to
grok it.

Bruno has written an actual UD in the LISP programming language.  I will
write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the integer
i
Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far

# For each program we have generated that has not halted, execute one
instruction of it
for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next time
through
i = i + 1;
}

Any program, and whether or not it ever terminates can be translated to a
statement concerning numbers in arithmetic. Thus mathematical truth
captures the facts concerning whether or not any program executes forever,
and what all of its intermediate states are. If these statements are true
independently of you and me, then the executions of these programs are
embedded in arithmetical truth and have a platonic existence.  The first,
second, 10th, 1,000,000th, and 10^100th, and 10^100^100th state of the UD's
execution are mathematical facts which have definite values, and all the
conscious beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part of the
execution of the UD are there, in the math.

Jason

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Stephen Paul King

Senior Researcher

Mobile: (864) 567-3099

stephe...@provensecure.com

http://www.provensecure.us/

“This message (including any attachments) is intended only for the use of
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hereby notified that any use, dissemination, distribution, or copying of
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### Re: Bruno's mathematical reality

```On Fri, Dec 27, 2013 at 10:20 PM, LizR lizj...@gmail.com wrote:

There is one point to add which I think you've missed, Jason (apologies if
I've misunderstood). The UD generates the first instruction of the first
programme, then the first instruction of the second programme, and so on.
Once it has generated the first instruction of every possible programme, it
then adds the second instruction of the first programme, the
second instruction of the second programme, and so on.

If it did work like this, it would never get to run the second instruction
of any program, since there is a countable infinity of possible programs.

This is why it's called a dovetailer, I believe, and stops it running
into problems with non-halting programmes, or programmes that would crash,
or various other contingencies...

This is addressed by not trying to run any one program to its completion,
instead it gives each program it has generated up to that point some time
on the CPU.

This isn't intrinsic to the UD, which could in principle write the first
programme before it moves on to the next one - but it allows it to avoid
certain problems caused by having a programme that writes other programmes.

There is no program with the UD encountering programs that themselves
instantiate other programs.  Indeed, the UD encounters itself, infinitely
often.

...I think. I'm sure Bruno will let me know if that's wrong.

:)

PS I like the while (true) statement. What would Pontius Pilate have made
of that? :-)

:-)  Good question, I haven't the faintest idea.  I could have used while
(i == i) but then if someday Brent's paralogic takes over, it might fail.

Jason

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### Re: Bruno's mathematical reality

```Hi Jason,

Any program, and whether or not it ever terminates can be translated to a
statement concerning numbers in arithmetic. Thus mathematical truth
captures the facts concerning whether or not any program executes forever,
and what all of its intermediate states are.

this also captures every instance of random numbers as well. What method is
deployed to ensure that a program is not just a regular random number
and not some random number prefixed on a real halting program?

Truth is not a measure zero set, or is it?

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch jasonre...@gmail.com wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King
stephe...@provensecure.com wrote:

Hi Jason,

Could you discuss the trace of the UD that LizR mentioned? How is it
computed? Could you write an explicit example? I have never been able to
grok it.

Bruno has written an actual UD in the LISP programming language.  I will
write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the integer
i
Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far

# For each program we have generated that has not halted, execute one
instruction of it
for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next time
through
i = i + 1;
}

Any program, and whether or not it ever terminates can be translated to a
statement concerning numbers in arithmetic. Thus mathematical truth
captures the facts concerning whether or not any program executes forever,
and what all of its intermediate states are. If these statements are true
independently of you and me, then the executions of these programs are
embedded in arithmetical truth and have a platonic existence.  The first,
second, 10th, 1,000,000th, and 10^100th, and 10^100^100th state of the UD's
execution are mathematical facts which have definite values, and all the
conscious beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part of the
execution of the UD are there, in the math.

Jason

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To unsubscribe from this group and all its topics, send an email to
To post to this group, send email to everything-list@googlegroups.com.

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Kindest Regards,

Stephen Paul King

Senior Researcher

Mobile: (864) 567-3099

stephe...@provensecure.com

http://www.provensecure.us/

“This message (including any attachments) is intended only for the use of
the individual or entity to which it is addressed, and may contain
information that is non-public, proprietary, privileged, confidential and
exempt from disclosure under applicable law or may be constituted as
attorney work product. If you are not the intended recipient, you are
hereby notified that any use, dissemination, distribution, or copying of
this communication is strictly prohibited. If you have received this
message in error, notify sender immediately and delete this message
immediately.”

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```

### Re: Bruno's mathematical reality

```On Fri, Dec 27, 2013 at 10:41 PM, Jason Resch jasonre...@gmail.com wrote:

On Fri, Dec 27, 2013 at 10:20 PM, LizR lizj...@gmail.com wrote:

There is one point to add which I think you've missed, Jason (apologies
if I've misunderstood). The UD generates the first instruction of the first
programme, then the first instruction of the second programme, and so on.
Once it has generated the first instruction of every possible programme, it
then adds the second instruction of the first programme, the
second instruction of the second programme, and so on.

If it did work like this, it would never get to run the second instruction
of any program, since there is a countable infinity of possible programs.

This is why it's called a dovetailer, I believe, and stops it running
into problems with non-halting programmes, or programmes that would crash,
or various other contingencies...

This is addressed by not trying to run any one program to its completion,
instead it gives each program it has generated up to that point some time
on the CPU.

This isn't intrinsic to the UD, which could in principle write the first
programme before it moves on to the next one - but it allows it to avoid
certain problems caused by having a programme that writes other programmes.

There is no program with the UD encountering programs that themselves
instantiate other programs.  Indeed, the UD encounters itself, infinitely
often.

I meant There is no *problem*

Jason

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### Re: Bruno's mathematical reality

```Hi Jason,

The first, second, 10th, 1,000,000th, and 10^100th, and 10^100^100th state
of the UD's execution are mathematical facts ... Umm, how? Godel and
Matiyasevich would disagree! If there does not exist a program that can
evaluate whether or not a UD substring is a faithful representation of a
true theorem, then how is it a fact?

On Fri, Dec 27, 2013 at 10:09 PM, Jason Resch jasonre...@gmail.com wrote:

On Fri, Dec 27, 2013 at 9:31 PM, Stephen Paul King
stephe...@provensecure.com wrote:

Hi Jason,

Could you discuss the trace of the UD that LizR mentioned? How is it
computed? Could you write an explicit example? I have never been able to
grok it.

Bruno has written an actual UD in the LISP programming language.  I will
write a simple one in pseudo-code below:

List listOfPrograms = new List[]; # Empty list
int i = 0;
while (true)
{
# Create a program corresponding to the binary expansion of the integer
i
Program P = createProgramFromInteger(i);

# Add the program to a list of programs we have generated so far

# For each program we have generated that has not halted, execute one
instruction of it
for each (Program p in listOfPrograms)
{
if (p.hasHalted() == false)
{
executeOneInstruction(p);
}
}

# Finally, increment i so a new program is generated the next time
through
i = i + 1;
}

Any program, and whether or not it ever terminates can be translated to a
statement concerning numbers in arithmetic. Thus mathematical truth
captures the facts concerning whether or not any program executes forever,
and what all of its intermediate states are. If these statements are true
independently of you and me, then the executions of these programs are
embedded in arithmetical truth and have a platonic existence.  The first,
second, 10th, 1,000,000th, and 10^100th, and 10^100^100th state of the UD's
execution are mathematical facts which have definite values, and all the
conscious beings that are instantiated and evolve and write books on
consciousness, and talk about the UD on their Internet, etc. as part of the
execution of the UD are there, in the math.

Jason

--
You received this message because you are subscribed to a topic in the
To unsubscribe from this topic, visit
To unsubscribe from this group and all its topics, send an email to
To post to this group, send email to everything-list@googlegroups.com.

--

Kindest Regards,

Stephen Paul King

Senior Researcher

Mobile: (864) 567-3099

stephe...@provensecure.com

http://www.provensecure.us/

“This message (including any attachments) is intended only for the use of
the individual or entity to which it is addressed, and may contain
information that is non-public, proprietary, privileged, confidential and
exempt from disclosure under applicable law or may be constituted as
attorney work product. If you are not the intended recipient, you are
hereby notified that any use, dissemination, distribution, or copying of
this communication is strictly prohibited. If you have received this
message in error, notify sender immediately and delete this message
immediately.”

--
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