On 25 Sep 2011, at 04:20, Pierz wrote:
OK, so I've read the UDA and I 'get' it,
Wow. Nice!
but at the moment I simply
can't accept that it is anything like a 'proof'.
Hmm... (Then you should not say "I get it", but "I don't get it"). A
proof is only something presented as a proof. You can only say: here
is the flaw, (in case you have found one). I guess that is what you
did, or thought you did.
I keep reading Bruno
making statements like "If we are machine-emulable, then physics is
necessarily reducible to number psychology", but to me there remain
serious flaws, not in the logic per se, but in the assumptions.
Bruno says that "no science fiction devices are necessary, other than
the robust physical universe".
To get the step-7. But that robust universe assumption is discharged
in the step 8. Which I have explained with more details (than in
sane04) on this very list:
http://www.nabble.com/MGA-1-td20566948.html#a20566948
He also claims that to argue that the
universe may not be large or robust enough (by robust I assume he
means stable over time) to support his Universal Dovetailer is "ad
hoc and disgraceful". I think it is anything but.
By robust I mean expanding enough to run the UD.
It is disgraceful with respect to the reasoning. But if for some
reason, you believe that there are evidence that the physical universe
does develop the infinite running of a UD, then you can skip the last
(and most difficult) step 8. Physics is already a branch of computer
science/number theory, in that case.
This is funny: if we have evidence that the physical universe has a
never ending running UD, then we can from step 7 alone conclude that
physics is a branch of number theory. And by Occam, we don't need to
assume the primitive physical universe.
But we don't, and I doubt we can, have such an evidence. The UD
running is very demanding. Not only the universe must expand
infinitely, but in a way which connect solidly all its parts. Better
to grasp the step 8 (the movie graph argument).
To describe such an
argument as "disgraceful" is to dismiss with a wave of the hand the
entirety of modern cosmology and physics, disciplines which after all
have managed to produce a great deal more results in the way of
prediction, explanation and tangible benefits than Bruno's theory (I
insist it is a theory and not a 'result').
Yes, it is the theory known as "mechanism". The theory that the brain
is a natural machine. The result is that physics emerges from
numbers, or combinators, or from any first order specification of a
universal machine, in the sense of theoretical computer science
(branch of math).
As a computer science
expert, I assume Bruno is aware of modern computational approaches to
physics. Such approaches explicitly forbid any kind of 'infinite
informational resolution' as is required by Bruno's theory.
Where is this required?
Note that as a corollary of UDA we can show that the physical universe
is not a computable object, a priori.
The computational approach to physics can have many interesting
application, but it can't tackle the mind body problem. But to get
this, it is better to grasp UDA first.
The
information content of the universe is seen as being a fundamental
quantity much like energy, constantly transforming but conserved over
the whole system in the same way energy is.
There is no assumption about the universe in the theory. We assume
only that the brain (or the generalized brain, that is the portion of
observable things needed to be emulated for my consciousness to be
preserved) is Turing emulable.
UDA assumes the existence of brains and doctors, and thus on some
physical reality, but not on a primitive physical reality. At the
start of the UDA, we are neutral on the nature of both mind and
universes.
This computational
approach indeed seems to be the *basis* for much of Bruno talks about
(computability, emulability and so on are all fundamental ideas), but
then he flies in the face of it by proposing some kind of automated,
Platonic computation devoid of any constraints in terms of state
memory or time.
Computation is a mathematical notion, discovered by Post, Turing, etc.
It is based on the notion of state memory, time steps, etc. It is not
base on physical implementation of those notion (unlike engineering).
Let's take a look at the UD. Obviously this is not an 'intelligent'
device,
You are right. It is very dumb. It is not even Turing universal, and
it computes in the most complex possible way the empty function (it
has no input, it has no output).
beyond the intelligence implicit in the very simple base
algorithm. It just runs every possible computer program.
Yes.
Random
computer programs are made of and produce *static*, they are a random
arrangement of bits.
There is no randomness in the work of the UD.
Now clearly, we know that if you look at a large
enough field of static, you will find pictures in it, assemblies of
dots that happen to form structured, intelligible images.
OK. But they are not related by computations. Neither in the first
person views, nor in the third person views.
Likewise in
the field of random computed algorithms, very very occasionally one
will make some kind of 'sense', although the sense will naturally be
entirely accidental and in the vast, vast majority of cases will give
way a moment later to nonsense again.
The only randomness which might appear comes from the first person
indterminacy, and the fact that we acnnot know in which computation we
are. This leads to the "white rabbit" problem, but the computation
themselves are not random at all, and the WR problem is basically the
problem to which physics is reduced too, at the conclusion of the
reasoning.
So when the UD runs through its
current sequence of programs, what it is really doing is just
generating a vast random field of bits.
I have not the slightest clue why you say that. It is provably false.
No program can generate randomness in this third person way. The
randomness ¨possible* can only appear from the first person (emulated
in the UD) perspective.
The UD generates, to give an example, the program emulating the
Heisenberg matrix of the Milky Way, at the level of string theory, and
this with 10^(10^(10^(10^(10^9999999))))) digits. Notably. Actually it
does it also with 10^(10^(10^(10^(10^9999999))))) + 1 digits, and
10^(10^(10^(10^(10^9999999))))) + 2 digits, etc.
The point here is that all those running are not random structures. In
fact, there is no randomness at all.
Nonetheless, each of these
individual programs needs to have potentially infinite state memory
available to it (the Turing machine tape). Now the list of of programs
run by the machine continues to grow with each iteration as it adds
new algorithms, so it takes longer and longer to return to program 0
to run the next operation.
Right. Note that such delays are not perceptible for the emulated
observers.
As it needs to run *all* programs, a
necessarily infinite number, it requires infinite time, but for some
reason Bruno thinks this is not important.
It is utterly important.
This why the first person indeterminacy bears on a continuum, despite
the digitalness of all present factors.
You attribute me things which I never say, here. n the contrary, the
fact that the UD never stops is crucial.
Either it has infinite
processing speed as well as memory, or it has infinite time on its
hands.
The UD* (the infinite trace or running of the UD) is part of a tiny
part of arithmetical truth (the sigma_1 arithmetical truth).
Step 8 makes the physical running of the UD irrelevant.
UD and UD* are mathematical notion (indeed arithmetical relations).
Fine. But then we can simply dispense with the UD altogether and just
gather up its final results,
This does not make any sense. A non stopping program does not output
anything.
which is an infinite field of static, a
giant digital manuscript typed by infinite monkeys. Everything capable
of being represented by information will exist in this field, which
means it is capable of "explaining" everything. And nothing.
I think you miss the step 3: the first person indeterminacy. I think
you miss also the arithmetical non random dynamic of the UD. You are
confusing an infinite set of information, with an infinite non random
and well defined particular computation.
We have to deconstruct the notion of "computation" here. Computation
is the orderly transformation of information.
I can agree, although information is more an emerging notion. It is
not used in the definition of computation.
But the UD's orderliness
is the orderliness of the typing monkey.
Not at all. It is the orderliness of the computations. Or the
orderliness of the sigma_1 sentences and the logic of their
probability/consistency (as it is made completely transparent in the
AUDA: the translation of the UDA in arithmetic, or in the language of
the Löbian machine).
If it is orderly at all, it
is by mistake.
It is 100% orderly.
By talking about it the UD as performing computation
more intelligence is implicitly imputed than this hypothetical device
possesses.
Where? The existence of the UD is already a theorem of Peano
Arithmetic. Robinson arithmetic *is* a UD. You need only the
intelligence for grasping addition and multiplication. The UD has been
implemented:
http://iridia.ulb.ac.be/~marchal/bxlthesis/Volume4CC/4%20GEN%20%26%20DU.pdf
And besides, the physical and psychological (theological,
biological,..) order are brought by the machines from inside the
running of the UD. The UD's intelligence is not needed.
Yes, it would generate every possible information state,
and would therefore create me and all my possible futures, but these
'pictures' would have no coherence, would immediately dissolve back
into the static they emerged from.
The point is that IF we are machine, then we have no choice other than
extracting the physical laws from the UD. This is done in the
mathematical part, where, contrary to all expectations (at least by
some of my colleagues at the time) we get already quantum logics.
The UD, as a generator of static,
cannot explain coherence in my experience.
You need a theory of knowledge. I use the most classical theory of
knowledge (the one by Theaetetus), and it is enough to cut any easy
conclusion against mechanism.
There is a fundamental circularity here. Something must explain the
coherence of 1p and 3p accounts (laws of physics).
This is explained by the non triviality of the Theaetetus theory of
knowledge, once we take the incompleteness phenomenon into account to
the study of the first person indeterminacy. You might read the second
part of the sane04 paper. But you have to grasp the UDA first.
Because the UD must
exist (someone please explain this to me!),
Step 8 shows that the UD does not need to exist physically. It needs
the same time of existence than the sequence of prime numbers.
the explanation must lie
in the UD. Because the UD is pure computation, the laws of physics
(the coherence) must be reducible to principles of computation.
Right. The explanation is provided by the UD and its internal
observers generated by the computations.
But
why no earth must the UD exist?
It does not need to exist physically. You have fail to grasp step 3,
5, 6, 7, and/or 8. I think.
It exist mathematically, and by step 8, this means we have to live
with it.
And if it did exist, the reduction of
the UD to an infinite static field shows that it is devoid of such
explanatory power.
I guess you mean UD*. It is better to keep in mind the difference
between the UD (a finite little program), and UD* the infinite
running, or trace, of the UD.
UD* is NOT an infinite static field. It is a highly structured
mathematical object, and, and this is a key point, it get additional
structure when seen from inside by machines (taking the first person
indeterminacy into account). Indeed, it leads to non trivial notion of
truth, belief, knowledge, observation, feeling, and all this, divided
by two (the communicable/provable part, by the machine), and the non
communicable (non provable by the machine) part. This gives quanta and
qualia. (accepting reasonable axiomatic or near axiomatic definition
of those terms). All this is justified in all detail. tell me
precisely what you miss.
Only if there is something about the UDA that
confines it to meaningful, orderly algorithms (whatever that might
mean), can Bruno's argument follow. But the UD's algorithm is a few
lines of code, there is no hidden magic to allow it to select such
algorithms. We have to throw out the UD, not the laws of physics.
We can't no more throw out the UD than we can throw out the prime
numbers.
The whole notion of the 'teleporting consciousness' is obviously
fundamental to the argument. It is assumed by 'yes doctor' (and argued
for in step 8) that consciousness is not bound to any physical
substrate, but is a function of certain computational states - ie
arrangements of bits. What again is deeply unclear is how a boundary
is formed around such arrangements to give them coherence in the
overall field.
That is the result. I am not defending mechanism. Just showing that it
is incompatible with physicalism or even with very weak form of
materialism. I reduce the mind body problem to a purely body problem
in computer science/arithmetic. Then in the second part, I do show a
partial solution; based on the logic of provability by Löbian machine.
I extract the logic of stable observation.
In an infinite field of transforming information - the
output of the UD -
What output? The UD has no outputs.
there will be areas of apparent coherence, but the
coherence is apparent, not real.
What do you mean by "real"?. Such a notion is preposterous in such a
field. When studying a reasoning, you have to stick on the assumption
in the reasoning.
Such a coherent region could only be
identified by a mind (or computer) capable of recognizing coherence or
pattern. The UD does not possess such intelligence, or only as yet
another algorithm which is on the same level as the other algorithms,
and not capable of accessing the states of all other computational
threads.
By the first person indeterminacy, this is is more subtle than what
you say in that paragraph.
You'd need to posit some new level of meta-computation
picking out the coherent results of the UD from the incoherent ones,
but how does *it* recognise coherence? It's an infinite regress.
No. The observers are any self-aware program run by the UD. They build
the coherence. For physics and feeling, this is studied by adding
explicitly the consistency assumption in the machine beliefs, by using
the modal variant of the logic of self-reference, obtained from
provability (Bp), together with the consistency assumption:
Bp & Dt (observation with probability one)
Bp a Dt & p (feeling).
Dt = consistency = ~Bf (f = "0=1").
It works pretty well. We can do that because G* proves Bp equivalent
to them, but G (the machine) cannot see this, and this is how the set
of all computations get structured by the machines.
This is explained in the second part of the sane04 (and is the main
object of my thesis in computer science).
And how do these coherent areas of the field which we call
consciousnesses (or 1p) connect with their self-similar regions in the
UD output?
I guess you mean UD*. The answer of this is given by the first person
statistics.
But you must not see the UD Argument as an attempt to explain the
physical (and psychological) reality, but as an attempt to get a
precise formulation of the mind body problem.
The UDA point is only that IF we are machine, then we HAVE TO derived
the physical laws by a relative statistics on the computations, as
seen by first person machine points of view.
AUDA, the interview of the löbian machines, gives the hint needed to
see that it makes sense, and that it is a "real mathematical problem".
And it gives a partial solution, also (which also provides a
transparent arithmetical interpretation of Plotinus theology, but this
has come well after the defense of the thesis). This has been
published if you want to look at the technics. See my url.
There may be pictures of me in all possible states within
this field, but they will be completely disconnected from one another.
You must understand that most version of "you" will be generated by
many (long) computations. All I say, if that if we are machine, then
the laws of physics are given by the relative statistics on those
computations going through your state. Then I succeeded in isolating
the logic of the "probability one", and it already gives a quantum
logic close to the Birkhoff von Neumann one.
How does the consciousness apparently implicit in the picture of me
'join the dots' between these random images to make a timeline which
defines my history?
It is your brain, which makes this. But there are no random images in
UD*.
The argument that it is 'machine psychology' or
'laws of arithmetic' merely begs the question - or obfuscates it.
Not at all. Once you grasp step 8, you have no other choice than using
'machine's theology' (that is the 8 logics described in the
arithmetical version of the UDA). And that theology is defined in
arithmetical terms.
In the end, the UDA merely asserts the results of its own assumptions,
but the assumptions are profoundly doubtful.
That might be. But they are not mine. It is the very common assumption
that the brain functions like a machine. It is as old as humanity, I
think. It appears in some old indian and chinese text, in the greek
one, and reappear with Descartes, and then is believed, in his modern
digital form, by virtually all scientists today, with some notable
exception (like Penrose).
I am neutral on this.
You can dress the
emperor's nakedness up in a lot of fancy mathematical formulism and
obscure verbal manoeuvres,
*That* is a verbal manoeuvre. Indeed: this is called an insult.
Please, try to really take the time to study the work, and if you have
any doubt on the validity, ask question. That is what a discussion
list is for.
but he is still naked. Infinite randomness
is a 'powerful' explanation because you can find anything you like
inside it.
I don't use the notion of randomness, and there is no randomness in
the UD*.
But when you see how vast the sea of surrounding
meaninglessness is,
I beg your pardon?
you realise the bankruptcy of that mode of
explanation.
I expose a problem.
I think you have read the work too much quickly, and your tone makes
me suspect some prejudice at the start.
If you want I can explain the UD proof step by step, so that you
might, who knows, find a real flaw. I think you are confusing the
counting algorithm, with the universal dovetailing algorithm. In term
of theories, you are confusion the theory of succession, with the
theory of succession+addition+multiplication. The second one have rich
notion of internal observers, and of internal logics. But even without
those logics, you should be able to grasp the body problem of the
mechanist theory.
You might also try to avoid the use of authoritative arguments, please.
You seem also to confuse the assumption (digital mechanism: a much
weaker form of computationalism than the one discussed in the
literature) and the conclusion: the *necessity* that physics arise
from addition and multiplication.
Bruno
http://iridia.ulb.ac.be/~marchal/
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