### Re: Prime numbers

```
John,

On 26 May 2013, at 00:54, John Mikes wrote:

Bruno and others:

the information about prof. Zhang's discovery (U of New Hampshire)?
It is still in the conjecture of mathematical proof and 'truth' with
a position of primes are greater
than 1 -  with the interesting conclusion that 'primes' are the
ATOMS of the number world.

Any thoughts?

Primes (1 is usually not considered as a prime number) are atoms of
the numbers when conceived multiplicatively, because all numbers can
be described uniquely as a product of primes. That is the existence
and unicity of decomposition of numbers into prime factors (without
taking the order of the multiplication into account). This is the so
called fundamental theorem of arithmetic. It is easy to prove the
existence of the decomposition into primes, but less easy to prove the
uniqueness.

For the twin conjecture, (it exists an infinity of pair of primes p
and q with p - q = 2) it looks like an important step has been proved,
(the case with p - q just bounded) but we are still far from proving
the twin one. Most mathematician believe that the twin conjecture is
true (like most believe that the Riemann conjecture is true). If they
were false, the distribution of primes would not be statistically
random, and that would mean something very special is at play, a bit
like a number conspiracy!  Why not, of course. We just don't know, but
a non random behavior of the primes is a bit like the UFO of number
theory. Well, except that for the UFO, there are (at least) some
evidences (from time to time, most are eventually explained in
general), but there is no evidence at all that the primes behave non-
randomly (in the statistical sense, not in Chaitin-Kolmogorov sense as
we can generate mechanically the distribution of primes).

Bruno

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

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### Re: Prime numbers

```
http://www.newscientist.com/article/dn23595-weinsteins-theory-of-everything-is-probably-nothing.html

Brent

On 5/25/2013 3:54 PM, John Mikes wrote:

Bruno and others:

the information about prof. Zhang's discovery (U of New Hampshire)?
It is still in the conjecture of mathematical proof and 'truth' with a position of
primes are greater

than 1 -  with the interesting conclusion that 'primes' are the ATOMS of the
number world.
Any thoughts?
JM
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### Re: Prime Numbers

```

On 27 Sep 2012, at 18:46, meekerdb wrote:

On 9/27/2012 1:19 AM, Bruno Marchal wrote:

On 26 Sep 2012, at 19:29, meekerdb wrote:

On 9/25/2012 9:51 PM, Jason Resch wrote:

On Sep 25, 2012, at 11:05 PM, meekerdb meeke...@verizon.net
wrote:

snip

So you mean if some mathematical object implies a contradiction
it doesn't exist, e.g. the largest prime number. But then of
course the proof of contradiction is relative to the axioms and
rules of inference.

Well there is always some theory we have to assume, some model we
operate under.  This is needed just to communicate or to think.

The contradiction proof is relevant to some theory, but so is the
existence proof.  You can't even define an object without using
some agreed upon theory.

Sure you can.  You point and say, That!  That's how you learned
the meaning of words, by abstracting from a lot of instances of
your mother pointing and saying, That.

But this uses implicit theories selected by evolution. A brain *is*
essentially a theory of the local universe already.

At least that's your theory.  :-)

Hmm... If by brain you mean the material object, then a brain is not a
theory, but the 3-I, the body description at the right comp-
substitution level, is the theory. It is a word (finite object)
interpreted by a universal system (physical forces, QM, bosons and
fermions).
The *material* brain, unfortunately perhaps, is not a word, it is an
infinity of words interpreted by an infinity of competing universal
numbers.

We have to explain, with comp, why little numbers seems to win,
because we can't prevent all the numbers to add their grains of salt,
hopefully not their buggy grains of sand generating noise and/or white
rabbits.

Bruno

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

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### Re: Prime Numbers

```

On 26 Sep 2012, at 19:29, meekerdb wrote:

On 9/25/2012 9:51 PM, Jason Resch wrote:

On Sep 25, 2012, at 11:05 PM, meekerdb meeke...@verizon.net wrote:

snip

So you mean if some mathematical object implies a contradiction it
doesn't exist, e.g. the largest prime number. But then of course
the proof of contradiction is relative to the axioms and rules of
inference.

Well there is always some theory we have to assume, some model we
operate under.  This is needed just to communicate or to think.

The contradiction proof is relevant to some theory, but so is the
existence proof.  You can't even define an object without using
some agreed upon theory.

Sure you can.  You point and say, That!  That's how you learned
the meaning of words, by abstracting from a lot of instances of your
mother pointing and saying, That.

But this uses implicit theories selected by evolution. A brain *is*
essentially a theory of the local universe already.

Bruno

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

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### Re: Prime Numbers

```
On 9/27/2012 1:19 AM, Bruno Marchal wrote:

On 26 Sep 2012, at 19:29, meekerdb wrote:

On 9/25/2012 9:51 PM, Jason Resch wrote:

On Sep 25, 2012, at 11:05 PM, meekerdb meeke...@verizon.net wrote:

snip

So you mean if some mathematical object implies a contradiction it doesn't exist,
e.g. the largest prime number. But then of course the proof of contradiction is
relative to the axioms and rules of inference.

Well there is always some theory we have to assume, some model we operate under.  This
is needed just to communicate or to think.

The contradiction proof is relevant to some theory, but so is the existence proof.
You can't even define an object without using some agreed upon theory.

Sure you can.  You point and say, That!  That's how you learned the meaning of words,
by abstracting from a lot of instances of your mother pointing and saying, That.

But this uses implicit theories selected by evolution. A brain *is* essentially a theory

At least that's your theory.  :-)

Brent

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### Re: Prime Numbers

```
On 9/25/2012 9:51 PM, Jason Resch wrote:

On Sep 25, 2012, at 11:05 PM, meekerdb meeke...@verizon.net wrote:

On 9/25/2012 8:54 PM, Jason Resch wrote:

On Sep 25, 2012, at 10:27 PM, meekerdb meeke...@verizon.net wrote:

On 9/25/2012 4:07 PM, Jason Resch wrote:

Yes. If we cannot prove that their existence is self-contradictory

Propositions can be self contradictory, but how can existence of something be

Brent

Brent, it was roger, not I, who wrote the above.  But in any case I interpreted his
statement to mean if some theoretical object is found to have contradictory
properties, then it does not exist.

Sorry.

No worries.

So you mean if some mathematical object implies a contradiction it doesn't exist, e.g.
the largest prime number. But then of course the proof of contradiction is relative to
the axioms and rules of inference.

Well there is always some theory we have to assume, some model we operate under.  This
is needed just to communicate or to think.

The contradiction proof is relevant to some theory, but so is the existence proof.  You
can't even define an object without using some agreed upon theory.

Sure you can.  You point and say, That!  That's how you learned the meaning of words, by
abstracting from a lot of instances of your mother pointing and saying, That.

Brent

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### Re: Prime Numbers

```

On Sep 26, 2012, at 12:29 PM, meekerdb meeke...@verizon.net wrote:

On 9/25/2012 9:51 PM, Jason Resch wrote:

On Sep 25, 2012, at 11:05 PM, meekerdb meeke...@verizon.net wrote:

On 9/25/2012 8:54 PM, Jason Resch wrote:

On Sep 25, 2012, at 10:27 PM, meekerdb meeke...@verizon.net
wrote:

On 9/25/2012 4:07 PM, Jason Resch wrote:
Yes. If we cannot prove that their existence is self-

Propositions can be self contradictory, but how can existence of

Brent

Brent, it was roger, not I, who wrote the above.  But in any case
I interpreted his statement to mean if some theoretical object is
found to have contradictory properties, then it does not exist.

Sorry.

No worries.

So you mean if some mathematical object implies a contradiction it
doesn't exist, e.g. the largest prime number. But then of course
the proof of contradiction is relative to the axioms and rules of
inference.

Well there is always some theory we have to assume, some model we
operate under.  This is needed just to communicate or to think.

The contradiction proof is relevant to some theory, but so is the
existence proof.  You can't even define an object without using
some agreed upon theory.

Sure you can.  You point and say, That!  That's how you learned
the meaning of words, by abstracting from a lot of instances of your
mother pointing and saying, That.

Brent

There is still an implicitly assumed model that the two people are
operating under (if they agree on what is meant by the chair they see).

Or they may use different models and define the chair differently.
For example, a solipist believes the chair is only his idea, a
physicalist thinks it is a collection of primitive matter, a
computationalist a dream of numbers.

Then while they might all agree on the existence of something, that
thing is different for each person because they are defining it under
different models.

Jason

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### Re: Prime Numbers

```
On 9/26/2012 12:11 PM, Jason Resch wrote:

On Sep 26, 2012, at 12:29 PM, meekerdb meeke...@verizon.net wrote:

On 9/25/2012 9:51 PM, Jason Resch wrote:

On Sep 25, 2012, at 11:05 PM, meekerdb meeke...@verizon.net wrote:

On 9/25/2012 8:54 PM, Jason Resch wrote:

On Sep 25, 2012, at 10:27 PM, meekerdb meeke...@verizon.net wrote:

On 9/25/2012 4:07 PM, Jason Resch wrote:

Yes. If we cannot prove that their existence is self-contradictory

Propositions can be self contradictory, but how can existence of something be

Brent

Brent, it was roger, not I, who wrote the above.  But in any case I interpreted his
statement to mean if some theoretical object is found to have contradictory
properties, then it does not exist.

Sorry.

No worries.

So you mean if some mathematical object implies a contradiction it doesn't exist,
e.g. the largest prime number. But then of course the proof of contradiction is
relative to the axioms and rules of inference.

Well there is always some theory we have to assume, some model we operate under.  This
is needed just to communicate or to think.

The contradiction proof is relevant to some theory, but so is the existence proof.
You can't even define an object without using some agreed upon theory.

Sure you can.  You point and say, That!  That's how you learned the meaning of words,
by abstracting from a lot of instances of your mother pointing and saying, That.

Brent

There is still an implicitly assumed model that the two people are operating under (if
they agree on what is meant by the chair they see).

Or they may use different models and define the chair differently.  For example, a
solipist believes the chair is only his idea, a physicalist thinks it is a collection of
primitive matter, a computationalist a dream of numbers.

Then while they might all agree on the existence of something, that thing is different
for each person because they are defining it under different models.

But if they are different then what sense does it make to say there is a contradiction in
*the* model and hence something doesn't exist.  That's why it makes no sense to talk about
a contradiction disproving the existence of something you can define ostensively.  It is
only in the Platonia of statements that you can derive contradictions from axioms and
rules of inference.  If you can point to the thing whose non-existence is proven, then it
just means you've made an error in translating between reality and Platonia.

Brent

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### Re: Prime Numbers

```On Wed, Sep 26, 2012 at 2:33 PM, meekerdb meeke...@verizon.net wrote:

On 9/26/2012 12:11 PM, Jason Resch wrote:

On Sep 26, 2012, at 12:29 PM, meekerdb meeke...@verizon.net wrote:

On 9/25/2012 9:51 PM, Jason Resch wrote:

On Sep 25, 2012, at 11:05 PM, meekerdb meeke...@verizon.net wrote:

On 9/25/2012 8:54 PM, Jason Resch wrote:

On Sep 25, 2012, at 10:27 PM, meekerdb meeke...@verizon.net wrote:

On 9/25/2012 4:07 PM, Jason Resch wrote:

Yes. If we cannot prove that their existence is self-contradictory

Propositions can be self contradictory, but how can existence of

Brent

Brent, it was roger, not I, who wrote the above.  But in any case I
interpreted his statement to mean if some theoretical object is found to
have contradictory properties, then it does not exist.

Sorry.

No worries.

So you mean if some mathematical object implies a contradiction it
doesn't exist, e.g. the largest prime number. But then of course the proof
of contradiction is relative to the axioms and rules of inference.

Well there is always some theory we have to assume, some model we
operate under.  This is needed just to communicate or to think.

The contradiction proof is relevant to some theory, but so is the
existence proof.  You can't even define an object without using some agreed
upon theory.

Sure you can.  You point and say, That!  That's how you learned the
meaning of words, by abstracting from a lot of instances of your mother
pointing and saying, That.

Brent

There is still an implicitly assumed model that the two people are
operating under (if they agree on what is meant by the chair they see).

Or they may use different models and define the chair differently.  For
example, a solipist believes the chair is only his idea, a physicalist
thinks it is a collection of primitive matter, a computationalist a dream
of numbers.

Then while they might all agree on the existence of something, that thing
is different for each person because they are defining it under different
models.

But if they are different then what sense does it make to say there is a
contradiction in *the* model and hence something doesn't exist.

It means a certain object (which is defined in a model) does not exist in
that model.  A model in one object is not the same as another object in a
different model, even if they might have the same name, symbol,
or appearance.  2 in a finite field, is a different thing from 2 in the
natural numbers.  The chair in the solipist model is different from the
chair in the materialist model.  A chair made out of primitively real
matter is non-existent in the solipist model.

I don't see how you can escape having to work within a model when you make
assertions, like X exists, or Y does not exist.  What is X or Y outside of
the model from which they are defined and exist within?

Jason

That's why it makes no sense to talk about a contradiction disproving the
existence of something you can define ostensively.  It is only in the
Platonia of statements that you can derive contradictions from axioms and
rules of inference.  If you can point to the thing whose non-existence is
proven, then it just means you've made an error in translating between
reality and Platonia.

Brent

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### Re: Prime Numbers

```
On 9/26/2012 2:53 PM, Jason Resch wrote:

On Wed, Sep 26, 2012 at 2:33 PM, meekerdb meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 9/26/2012 12:11 PM, Jason Resch wrote:

On Sep 26, 2012, at 12:29 PM, meekerdb meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 9/25/2012 9:51 PM, Jason Resch wrote:

On Sep 25, 2012, at 11:05 PM, meekerdb meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 9/25/2012 8:54 PM, Jason Resch wrote:

On Sep 25, 2012, at 10:27 PM, meekerdb
meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 9/25/2012 4:07 PM, Jason Resch wrote:

Yes. If we cannot prove that their existence is

Propositions can be self contradictory, but how can

Brent

Brent, it was roger, not I, who wrote the above.  But
in any
case I interpreted his statement to mean if some
theoretical
object is found to have contradictory properties, then
it does
not exist.

Sorry.

No worries.

So you mean if some mathematical object implies a
doesn't exist, e.g. the largest prime number. But then of
course the
proof of contradiction is relative to the axioms and rules
of inference.

Well there is always some theory we have to assume, some model
we
operate under.  This is needed just to communicate or to think.

The contradiction proof is relevant to some theory, but so is
the
existence proof.  You can't even define an object without using
some
agreed upon theory.

Sure you can.  You point and say, That!  That's how you learned
the
meaning of words, by abstracting from a lot of instances of your
mother
pointing and saying, That.

Brent

There is still an implicitly assumed model that the two people are
operating
under (if they agree on what is meant by the chair they see).

Or they may use different models and define the chair differently.  For
example,
a solipist believes the chair is only his idea, a physicalist thinks it
is a
collection of primitive matter, a computationalist a dream of numbers.

Then while they might all agree on the existence of something, that
thing is
different for each person because they are defining it under different
models.

But if they are different then what sense does it make to say there is a
contradiction in *the* model and hence something doesn't exist.

It means a certain object (which is defined in a model) does not exist in that model.  A
model in one object is not the same as another object in a different model, even if they
might have the same name, symbol, or appearance.  2 in a finite field, is a different
thing from 2 in the natural numbers.  The chair in the solipist model is different
from the chair in the materialist model.  A chair made out of primitively real matter
is non-existent in the solipist model.
I don't see how you can escape having to work within a model when you make assertions,
like X exists, or Y does not exist.

I don't try to escape that.

What is X or Y outside of the model from which they are defined and exist
within?

The whole point of having a model is that X and Y refer to something outside the model.
The model is a model *of* reality, not reality itself.  So when you prove X and ~X in
the model you may have proved X doesn't exist or you may have shown your model doesn't
correspond to reality.

Brent

Jason

That's why it makes no sense to talk about a contradiction disproving the
existence
of something you can define ostensively.  It is only in the Platonia of
statements
that you can derive contradictions from axioms and rules of inference.  If
you can
point to the thing whose non-existence is proven, then it just means you've
error in translating between reality and Platonia.

Brent

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### Re: Prime Numbers

```On Wed, Sep 26, 2012 at 5:01 PM, meekerdb meeke...@verizon.net wrote:

On 9/26/2012 2:53 PM, Jason Resch wrote:

On Wed, Sep 26, 2012 at 2:33 PM, meekerdb meeke...@verizon.net wrote:

On 9/26/2012 12:11 PM, Jason Resch wrote:

On Sep 26, 2012, at 12:29 PM, meekerdb meeke...@verizon.net wrote:

On 9/25/2012 9:51 PM, Jason Resch wrote:

On Sep 25, 2012, at 11:05 PM, meekerdb meeke...@verizon.net wrote:

On 9/25/2012 8:54 PM, Jason Resch wrote:

On Sep 25, 2012, at 10:27 PM, meekerdb meeke...@verizon.net wrote:

On 9/25/2012 4:07 PM, Jason Resch wrote:

Yes. If we cannot prove that their existence is self-contradictory

Propositions can be self contradictory, but how can existence of

Brent

Brent, it was roger, not I, who wrote the above.  But in any case I
interpreted his statement to mean if some theoretical object is found to
have contradictory properties, then it does not exist.

Sorry.

No worries.

So you mean if some mathematical object implies a contradiction it
doesn't exist, e.g. the largest prime number. But then of course the
proof
of contradiction is relative to the axioms and rules of inference.

Well there is always some theory we have to assume, some model we
operate under.  This is needed just to communicate or to think.

The contradiction proof is relevant to some theory, but so is the
existence proof.  You can't even define an object without using some
agreed
upon theory.

Sure you can.  You point and say, That!  That's how you learned the
meaning of words, by abstracting from a lot of instances of your mother
pointing and saying, That.

Brent

There is still an implicitly assumed model that the two people are
operating under (if they agree on what is meant by the chair they see).

Or they may use different models and define the chair differently.  For
example, a solipist believes the chair is only his idea, a physicalist
thinks it is a collection of primitive matter, a computationalist a dream
of numbers.

Then while they might all agree on the existence of something, that
thing is different for each person because they are defining it under
different models.

But if they are different then what sense does it make to say there is a
contradiction in *the* model and hence something doesn't exist.

It means a certain object (which is defined in a model) does not exist
in that model.  A model in one object is not the same as another object in
a different model, even if they might have the same name, symbol,
or appearance.  2 in a finite field, is a different thing from 2 in the
natural numbers.  The chair in the solipist model is different from the
chair in the materialist model.  A chair made out of primitively real
matter is non-existent in the solipist model.

I don't see how you can escape having to work within a model when you make
assertions, like X exists, or Y does not exist.

I don't try to escape that.

What is X or Y outside of the model from which they are defined and
exist within?

The whole point of having a model is that X and Y refer to something
outside the model.  The model is a model *of* reality, not reality itself.
So when you prove X and ~X in the model you may have proved X doesn't
exist or you may have shown your model doesn't correspond to reality.

Okay.  I think we are in agreement then.

The main idea is to make a model of reality and test it by seeing how well
the model's predictions for observations match our observations.

Jason

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### Re: Re: Prime Numbers

```Hi Stephen P. King

Yes, I think that the structures and
attributes of matter are provided
by a creator (the All, the supreme
monad, or God). Plato used the analogy
of geometrical shapes for his structures.

Roger Clough, rclo...@verizon.net
9/25/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Stephen P. King
Time: 2012-09-24, 10:42:12
Subject: Re: Prime Numbers

On 9/24/2012 9:46 AM, Roger Clough wrote:
God's ideas is fine. The numbers and arithmetic etc. can inhere in
some mind. The numbers are (idealistically) real, as I think
all arithmetic must be. For it is true whether known or
not. At least as you stay with common numbers and arithmetic.
Pretty sure.
Hi Roger,

One question I have to pose: How do the properties of entities
become discriminated from each other and collected together? Are the
properties on a object inherent or is there some other active system of
property attribution in Nature? Does God play a role in this?

--
Onward!

Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html

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### Re: Re: Prime Numbers

```On Tue, Sep 25, 2012 at 7:35 AM, Roger Clough rclo...@verizon.net wrote:

Hi Stephen P. King

Yes, I think that the structures and
attributes of matter are provided
by a creator (the All, the supreme
monad, or God). Plato used the analogy
of geometrical shapes for his structures.

But if you believe in the All do you also believe there are other types
of matter, other universes, other planets with intelligent beings, etc?

Jason

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### Re: Prime Numbers

```
On 9/25/2012 10:24 AM, Jason Resch wrote:

On Tue, Sep 25, 2012 at 7:35 AM, Roger Clough rclo...@verizon.net
mailto:rclo...@verizon.net wrote:

Hi Stephen P. King

Yes, I think that the structures and
attributes of matter are provided
by a creator (the All, the supreme
monad, or God). Plato used the analogy
of geometrical shapes for his structures.

But if you believe in the All do you also believe there are other
types of matter, other universes, other planets with intelligent
beings, etc?

Jason

Hi Jason,

Yes. If we cannot prove that their existence is self-contradictory
then we should consider them as possible. Just because I cannot
experience or imagine something is not a proof of impossibility.

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### Re: Prime Numbers

```On Tue, Sep 25, 2012 at 5:37 PM, Stephen P. King stephe...@charter.netwrote:

On 9/25/2012 10:24 AM, Jason Resch wrote:

On Tue, Sep 25, 2012 at 7:35 AM, Roger Clough rclo...@verizon.net wrote:

Hi Stephen P. King

Yes, I think that the structures and
attributes of matter are provided
by a creator (the All, the supreme
monad, or God). Plato used the analogy
of geometrical shapes for his structures.

But if you believe in the All do you also believe there are other types
of matter, other universes, other planets with intelligent beings, etc?

Jason

Hi Jason,

Yes. If we cannot prove that their existence is self-contradictory then
we should consider them as possible. Just because I cannot experience or
imagine something is not a proof of impossibility.

Roger,

I agree with you here.  But then this seems to contradict the notion that
*this* world is the best of all possible worlds, unless by this world you
mean the All.  After all Leibniz said Everything that is possible demands
to exist.

Jason

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### Re: Prime Numbers

```
On 9/25/2012 7:07 PM, Jason Resch wrote:

On Tue, Sep 25, 2012 at 5:37 PM, Stephen P. King
stephe...@charter.net mailto:stephe...@charter.net wrote:

On 9/25/2012 10:24 AM, Jason Resch wrote:

On Tue, Sep 25, 2012 at 7:35 AM, Roger Clough
rclo...@verizon.net mailto:rclo...@verizon.net wrote:

Hi Stephen P. King

Yes, I think that the structures and
attributes of matter are provided
by a creator (the All, the supreme
monad, or God). Plato used the analogy
of geometrical shapes for his structures.

But if you believe in the All do you also believe there are
other types of matter, other universes, other planets with
intelligent beings, etc?

Jason

Hi Jason,

Yes. If we cannot prove that their existence is
self-contradictory then we should consider them as possible.
Just because I cannot experience or imagine something is not a
proof of impossibility.

Roger,

I agree with you here.  But then this seems to contradict the notion
that *this* world is the best of all possible worlds, unless by this
world you mean the All.  After all Leibniz said Everything that is
possible demands to exist.

Jason

Hi Jason,

Well said! I think that Leibniz' idea that *this* world is the
best of all possible worlds has a stipulation that was not stated! It
only seems to make sense that Leibniz was defining  this world as the
world that we observe *and* communicate about with each other. It is
the best possible by necessity as it is impossible for us to experience
any other lesser version. We have  least action rules in physics that
are nice demonstration of this...

--
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Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html

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### Re: Prime Numbers

```
On 9/25/2012 4:07 PM, Jason Resch wrote:
Yes. If we cannot prove that their existence is self-contradictory

Propositions can be self contradictory, but how can existence of something be

Brent

then we should consider them as possible. Just because I cannot experience or imagine
something is not a proof of impossibility.

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### Re: Prime Numbers

```

On Sep 25, 2012, at 10:27 PM, meekerdb meeke...@verizon.net wrote:

On 9/25/2012 4:07 PM, Jason Resch wrote:

Yes. If we cannot prove that their existence is self-contradictory

Propositions can be self contradictory, but how can existence of

Brent

Brent, it was roger, not I, who wrote the above.  But in any case I
interpreted his statement to mean if some theoretical object is found
to have contradictory properties, then it does not exist.

Jason

then we should consider them as possible. Just because I cannot
experience or imagine something is not a proof of impossibility.

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### Re: Prime Numbers

```
On 9/25/2012 8:54 PM, Jason Resch wrote:

On Sep 25, 2012, at 10:27 PM, meekerdb meeke...@verizon.net wrote:

On 9/25/2012 4:07 PM, Jason Resch wrote:

Yes. If we cannot prove that their existence is self-contradictory

Propositions can be self contradictory, but how can existence of something be

Brent

Brent, it was roger, not I, who wrote the above.  But in any case I interpreted his
statement to mean if some theoretical object is found to have contradictory properties,
then it does not exist.

Sorry.

So you mean if some mathematical object implies a contradiction it doesn't exist, e.g. the
largest prime number. But then of course the proof of contradiction is relative to the
axioms and rules of inference.

Brent

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### Re: Prime Numbers

```

On Sep 25, 2012, at 11:05 PM, meekerdb meeke...@verizon.net wrote:

On 9/25/2012 8:54 PM, Jason Resch wrote:

On Sep 25, 2012, at 10:27 PM, meekerdb meeke...@verizon.net wrote:

On 9/25/2012 4:07 PM, Jason Resch wrote:

Yes. If we cannot prove that their existence is self-contradictory

Propositions can be self contradictory, but how can existence of

Brent

Brent, it was roger, not I, who wrote the above.  But in any case I
interpreted his statement to mean if some theoretical object is
found to have contradictory properties, then it does not exist.

Sorry.

No worries.

So you mean if some mathematical object implies a contradiction it
doesn't exist, e.g. the largest prime number. But then of course the
proof of contradiction is relative to the axioms and rules of
inference.

Well there is always some theory we have to assume, some model we
operate under.  This is needed just to communicate or to think.

The contradiction proof is relevant to some theory, but so is the
existence proof.  You can't even define an object without using some
agreed upon theory.

Jason

Brent

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### Re: Re: Prime Numbers

```Hi Bruno Marchal

Numbers are not in spacetime, that is, are not at location r at time t.
So they are ideas, they are not physical. To be physical you
have to have a specific location at a specific time. This is not
my view, it is that of Descartes.

The same with arithmetic. Numbers and arithmetic statements are not at (r,t).

Which is not to say that they are not real, if by real I mean true
or as is without an observer. Like in a textbook.

Roger Clough, rclo...@verizon.net
9/24/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Bruno Marchal
Time: 2012-09-23, 03:42:03
Subject: Re: Prime Numbers

On 22 Sep 2012, at 22:10, Stephen P. King wrote:

On 9/22/2012 7:32 AM, Roger Clough wrote:
How could mathematics be fiction ?
If so, then we could simply say that 2+2=5 because it's saturday.
How could we have a world we many minds can, on rare occasions, come
to complete agreement if that where the case? Perhaps it is true
that 2+2=4 because we all agree, at some level, that it is true. (I
am not just considering humans here with the word we!)

How will you define we without accepting 2+2=4, given that IF we
assume comp, we are defined by (L?ian) universal number and their
relations with other universal numbers?

Why do you keep an idealist conception of numbers, which contradicts
your references to papers which use, as most texts in science, the
independence and primitivity of elementary arithmetic?

Or you remark was ironic?

Bruno

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

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### Re: Re: Prime Numbers

```Hi Bruno Marchal

I believe that there are at least three attributes of numbers:

1) Are they true or false as in a numerical equation ? Does 2+ 2 = 4 ? True.

2) Do they physically exist or do they mentally inhere ?  They inhere. You
can't touch them.

3) Are they real or not ?  Numbers are always real (in the philosophical sense).

Roger Clough, rclo...@verizon.net
9/24/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Bruno Marchal
Time: 2012-09-23, 03:42:03
Subject: Re: Prime Numbers

On 22 Sep 2012, at 22:10, Stephen P. King wrote:

On 9/22/2012 7:32 AM, Roger Clough wrote:
How could mathematics be fiction ?
If so, then we could simply say that 2+2=5 because it's saturday.
How could we have a world we many minds can, on rare occasions, come
to complete agreement if that where the case? Perhaps it is true
that 2+2=4 because we all agree, at some level, that it is true. (I
am not just considering humans here with the word we!)

How will you define we without accepting 2+2=4, given that IF we
assume comp, we are defined by (L?ian) universal number and their
relations with other universal numbers?

Why do you keep an idealist conception of numbers, which contradicts
your references to papers which use, as most texts in science, the
independence and primitivity of elementary arithmetic?

Or you remark was ironic?

Bruno

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

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### Re: Re: Prime Numbers

```Hi Stephen P. King

That's what Peirce gave as a pragmatic definition of truth,
something that we would all agree to, given time enough.

But fiction can be true (as true fiction, a narrative woven about
actual events)  or not be true.  Arithmetic isn't, it's either
always true or always false.

Roger Clough, rclo...@verizon.net
9/24/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Stephen P. King
Time: 2012-09-22, 16:10:38
Subject: Re: Prime Numbers

On 9/22/2012 7:32 AM, Roger Clough wrote:
How could mathematics be fiction ?
If so, then we could simply say that 2+2=5 because it's saturday.
How could we have a world we many minds can, on rare occasions, come to
complete agreement if that where the case? Perhaps it is true that 2+2=4
because we all agree, at some level, that it is true. (I am not just
considering humans here with the word we!)

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Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html

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### Re: Prime Numbers

```

On 24 Sep 2012, at 12:39, Roger Clough wrote:

Hi Bruno Marchal

Numbers are not in spacetime, that is, are not at location r at time
t.

So they are ideas,

God's ideas? Then I am OK. The comp God is arithmetical truth, so this
works.

they are not physical.

OK.

To be physical you
have to have a specific location at a specific time.

I am OK with this, but note that it makes the Universe into a non
physical object. The Universe cannot belong to a location r at time t,
as it is the gauge making such position and time consistent in the
picture.

This is not
my view, it is that of Descartes.

The same with arithmetic. Numbers and arithmetic statements are not
at (r,t).

OK.

Which is not to say that they are not real, if by real I mean true
or as is without an observer. Like in a textbook.

OK. So you can understand how comp is interesting, as it explains
(partially but more than any other theory) how the physical beliefs
appears and why they come in two sort of shapes (quanta and qualia),
and this without assuming anything more than elementary arithmetic and
the invariance of consciousness for some digital transformations.
Then the big picture happens to be closer to the neoplatonists one
than the aristotelian one, which I think you should appreciate.

Bruno

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

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### Re: Re: Prime Numbers

```Hi Bruno Marchal

God's ideas is fine. The numbers and arithmetic etc. can inhere in
some mind.  The numbers are (idealistically) real, as I think
all arithmetic must be.  For it is true whether known or
not. At least as you stay with common numbers and arithmetic.
Pretty sure.

Roger Clough, rclo...@verizon.net
9/24/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Bruno Marchal
Time: 2012-09-24, 09:12:29
Subject: Re: Prime Numbers

On 24 Sep 2012, at 12:39, Roger Clough wrote:

Hi Bruno Marchal

Numbers are not in spacetime, that is, are not at location r at time
t.
So they are ideas,

God's ideas? Then I am OK. The comp God is arithmetical truth, so this
works.

they are not physical.

OK.

To be physical you
have to have a specific location at a specific time.

I am OK with this, but note that it makes the Universe into a non
physical object. The Universe cannot belong to a location r at time t,
as it is the gauge making such position and time consistent in the
picture.

This is not
my view, it is that of Descartes.

The same with arithmetic. Numbers and arithmetic statements are not
at (r,t).

OK.

Which is not to say that they are not real, if by real I mean true
or as is without an observer. Like in a textbook.

OK. So you can understand how comp is interesting, as it explains
(partially but more than any other theory) how the physical beliefs
appears and why they come in two sort of shapes (quanta and qualia),
and this without assuming anything more than elementary arithmetic and
the invariance of consciousness for some digital transformations.
Then the big picture happens to be closer to the neoplatonists one
than the aristotelian one, which I think you should appreciate.

Bruno

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

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### Re: Prime Numbers

```
On 9/24/2012 9:46 AM, Roger Clough wrote:

God's ideas is fine. The numbers and arithmetic etc. can inhere in
some mind.  The numbers are (idealistically) real, as I think
all arithmetic must be.  For it is true whether known or
not. At least as you stay with common numbers and arithmetic.
Pretty sure.

Hi Roger,

One question I have to pose: How do the properties of entities
become discriminated from each other and collected together? Are the
properties on a object inherent or is there some other active system of
property attribution in Nature? Does God play a role in this?

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Stephen

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### Re: Prime Numbers

```

On 22 Sep 2012, at 22:10, Stephen P. King wrote:

On 9/22/2012 7:32 AM, Roger Clough wrote:

How could mathematics be fiction ?
If so, then we could simply say that 2+2=5 because it's saturday.
How could we have a world we many minds can, on rare occasions, come
to complete agreement if that where the case? Perhaps it is true
that 2+2=4 because we all agree, at some level, that it is true. (I
am not just considering humans here with the word we!)

How will you define we without accepting 2+2=4, given that IF we
assume comp, we are defined by (Löbian) universal number and their
relations with other universal numbers?

Why do you keep an idealist conception of numbers, which contradicts
your references to papers which use, as most texts in science, the
independence and primitivity of elementary arithmetic?

Or you remark was ironic?

Bruno

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

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### Re: Prime Numbers

```
On 9/23/2012 3:42 AM, Bruno Marchal wrote:

On 22 Sep 2012, at 22:10, Stephen P. King wrote:

On 9/22/2012 7:32 AM, Roger Clough wrote:

How could mathematics be fiction ?
If so, then we could simply say that 2+2=5 because it's saturday.
How could we have a world we many minds can, on rare occasions, come
to complete agreement if that where the case? Perhaps it is true that
2+2=4 because we all agree, at some level, that it is true. (I am not
just considering humans here with the word we!)

How will you define we without accepting 2+2=4, given that IF we
assume comp, we are defined by (Löbian) universal number and their
relations with other universal numbers?

Why do you keep an idealist conception of numbers, which contradicts
your references to papers which use, as most texts in science, the
independence and primitivity of elementary arithmetic?

Or you remark was ironic?

Bruno

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

The continued confusion of the symbols and what they represent makes
this entire conversation an exercise in futility.

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Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html

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### Re: Re: Prime Numbers

```Hi Rex Allen

How could mathematics be fiction ?
If so, then we could simply say that 2+2=5 because it's saturday.

Roger Clough, rclo...@verizon.net
9/22/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Rex Allen
Time: 2012-09-21, 09:20:41
Subject: Re: Prime Numbers

Just to avoid confusion, this sentence:

I would say that mathematics is just very tightly plotted fiction where so many
details of the story are known up front that the plot can only progress in very
specific ways if it is to remain consistent and believable to the reader.?

Should probably be:

I would say that mathematics is just very tightly plotted fiction where so many
details of the back-story are known up front that the plot can only progress in
very specific ways if it is to remain consistent and believable to the

On Fri, Sep 21, 2012 at 8:40 AM, Rex Allen  wrote:

On Tue, Sep 18, 2012 at 11:50 PM, Terren Suydam  wrote:

On Tue, Sep 18, 2012 at 10:19 PM, Rex Allen  wrote:

On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam
wrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?

I find fictionalism to be the most plausible view of mathematics, with all
that implies for the Mandelbrot set.

I'm curious about what a plausible fictionalist account of the
Mandelbrot set could be. Is fictionalism the same as constructivism,
or the idea that knowledge doesn't exist outside of a mind?

I lean towards a strong form of fictionalism - which says that there are few
important differences between mathematics and literary fiction.

So - I could give a detailed answer - but I think I'd rather give a sketchy

I would say that mathematics is just very tightly plotted fiction where so many
details of the story are known up front that the plot can only progress in very
specific ways if it is to remain consistent and believable to the reader.

Mathematics is a kind of world building. ?n the?maginative?ense.

?

But ;et me turn the question around on you, if I can:

Do you have an explanation for how we discover mathematical objects and
otherwise interact with the Platonic realm?

How is it that we are able to reliably know things about Platonia?

I think just doing logic and math - starting from axioms and proving
things from them - is interacting with the Platonic realm.

But how is it that we humans do that? ?his is my main question. ?hat exactly
are we doing when we start from axioms and prove things from them? ?here does
this ability come from? ?hat does it consist of?

I would have thought that quarks and electrons from which we appear to be
constituted would be indifferent to truth.

Which would fit with the fact that I seem to make a lot of mistakes.

But you think otherwise?

I didn't understand the above... what do quarks and electrons have to
do with arithmetical platonism?

Are we not composed from quarks and electrons? ?f so - then how do mere
collections of quarks and electrons connect with platonic truths?

By chance? ?re we just fortunate that the initial conditions and causal laws of
the universe are such that our quarks and electrons take forms that mirror
Platonic Truths?

?

How can you make
sense of that in terms of the constructivist point of view that you
are (I think) compelled to take if you argue against arithmetical
platonism? ?t seems obvious that all possible intelligences would
discover the same forms of the Mandelbrot so long as they iterated on
z' = z^2 + c, but maybe I am missing the point of your argument.

I will agree with you that all intelligences that start from the same
premises as you, and follow the same rules as inference as you, will also
draw the same conclusions about the Mandelbrot set as you do.

However - I do not agree with you that this amenable group exhausts the set
of all *possible* intelligences.

I only meant that all possible intelligences that start from a
mathematics that includes addition, multiplication, and complex
numbers will find that if they iterate the function z' = z^2 + c, they
will find that some orbits become periodic or settle on a point, and
some escape to infinity. If they draw a graph of which orbits don't
escape, they will draw the Mandelbrot Set. All possible intelligences
that undertake that procedure will draw the same shape... and this
seems like discovery, not creation.

It seems like a tautology to me. ?f you do what I do and believe what I believe
then you will be a lot like me...?

Is there anything to mathematics other than belief?

What are beliefs? ?hy do we have the beliefs that we have? ?ow do we form
beliefs - what lies behind belief?

Can *our* mathematical abilities be reduced to something```

### Re: Re: Prime Numbers

```Hi Terren Suydam

I don't see that mathematics and fiction have anything in common.

With fiction, anything can happen.
A would of could be, or should be.

With mathematics you've got that nasty equals sign.
A world of is.

Hume pointed out that there's no way to get from is
to ought or vice versa.

Roger Clough, rclo...@verizon.net
9/22/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: Terren Suydam
Time: 2012-09-21, 12:29:56
Subject: Re: Prime Numbers

On Fri, Sep 21, 2012 at 8:40 AM, Rex Allen rexallen31...@gmail.com wrote:
On Tue, Sep 18, 2012 at 11:50 PM, Terren Suydam terren.suy...@gmail.com
wrote:

I'm curious about what a plausible fictionalist account of the
Mandelbrot set could be. Is fictionalism the same as constructivism,
or the idea that knowledge doesn't exist outside of a mind?

I lean towards a strong form of fictionalism - which says that there are few
important differences between mathematics and literary fiction.

Can you articulate any important differences between them?

So - I could give a detailed answer - but I think I'd rather give a sketchy

I would say that mathematics is just very tightly plotted fiction where so
many details of the story are known up front that the plot can only progress
in very specific ways if it is to remain consistent and believable to the

Mathematics is a kind of world building. In the imaginative sense.

I am not unsympathetic with this view, given the creativity that goes
into mathematical proofs. However, it falls apart for me when I
consider that an alien civilization is constrained to build the same
worlds if they start from the same logical axioms.

I think just doing logic and math - starting from axioms and proving
things from them - is interacting with the Platonic realm.

But how is it that we humans do that? This is my main question. What
exactly are we doing when we start from axioms and prove things from them?
Where does this ability come from? What does it consist of?

We're using our intelligence and creativity to search a space of
propositions (given a set of axioms) that are either provably true or
false. I would say our intelligence and creativity comes from our
animal nature, evolved as it is to make sense of the world (and each
other) and draw useful inferences that help us survive. I'm not sure
how to answer the question what does it consist of. Are you asking
how we can act intelligently, how creativity works?

I didn't understand the above... what do quarks and electrons have to
do with arithmetical platonism?

Are we not composed from quarks and electrons? If so - then how do mere
collections of quarks and electrons connect with platonic truths?

By chance? Are we just fortunate that the initial conditions and causal
laws of the universe are such that our quarks and electrons take forms that
mirror Platonic Truths?

I see. Assuming comp, we are some infinite subset of the trace of the
UD (universal dovetailer), which is a platonic entity. Quarks and
electrons are a part of the physics that emerges from that (the
numbers' dreams)... that's the reversal, where physics emerges from
computer science.

The question of how we, as mere collections of quarks etc. connect
back with Platonia, is answered by CT (Church-Turing Thesis). As we
are universal machines, we can emulate any computation, including the
universal dovetailer (for instance).

I only meant that all possible intelligences that start from a
mathematics that includes addition, multiplication, and complex
numbers will find that if they iterate the function z' = z^2 + c, they
will find that some orbits become periodic or settle on a point, and
some escape to infinity. If they draw a graph of which orbits don't
escape, they will draw the Mandelbrot Set. All possible intelligences
that undertake that procedure will draw the same shape... and this
seems like discovery, not creation.

It seems like a tautology to me. If you do what I do and believe what I
believe then you will be a lot like me...?

Is there anything to mathematics other than belief?

The point is that you are constrained in what you can prove starting
from a given set of axioms. You are not constrained in which axioms
you start with - that's where the belief comes in since there is no
way to prove that your axioms are True, except within a more
encompassing logical framework with its own axioms.

What are beliefs? Why do we have the beliefs that we have? How do we form
beliefs - what lies behind belief?

Beliefs in the everyday sense are inferences about our experience that
we hold to be true. They help us navigate the world as we experience
it, and make sense of it. Mostly our beliefs are formed by suggestion
from our parents and peers when we are young, and as we learn and grow
we complicate our worldview with new beliefs```

### Re: Re: Prime Numbers

```Hi meekerdb

Mathematical objects such as proofs ansd new theorems are found by intuition.
Penrose suggests that intuition is a peep into Platonia.
So these come from Platonia.

Roger Clough, rclo...@verizon.net
9/22/2012
Forever is a long time, especially near the end. -Woody Allen

- Receiving the following content -
From: meekerdb
Time: 2012-09-21, 13:30:03
Subject: Re: Prime Numbers

On 9/21/2012 5:40 AM, Rex Allen wrote:
On Tue, Sep 18, 2012 at 11:50 PM, Terren Suydam terren.suy...@gmail.com wrote:

On Tue, Sep 18, 2012 at 10:19 PM, Rex Allen rexallen31...@gmail.com wrote:

On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam terren.suy...@gmail.com
wrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?

I find fictionalism to be the most plausible view of mathematics, with all
that implies for the Mandelbrot set.

I'm curious about what a plausible fictionalist account of the
Mandelbrot set could be. Is fictionalism the same as constructivism,
or the idea that knowledge doesn't exist outside of a mind?

I lean towards a strong form of fictionalism - which says that there are few
important differences between mathematics and literary fiction.

So - I could give a detailed answer - but I think I'd rather give a sketchy

I would say that mathematics is just very tightly plotted fiction where so many
details of the story are known up front that the plot can only progress in very
specific ways if it is to remain consistent and believable to the reader.

Mathematics is a kind of world building.  In the imaginative sense.

But ;et me turn the question around on you, if I can:

Do you have an explanation for how we discover mathematical objects and
otherwise interact with the Platonic realm?

How is it that we are able to reliably know things about Platonia?

I think just doing logic and math - starting from axioms and proving
things from them - is interacting with the Platonic realm.

But how is it that we humans do that?  This is my main question.  What exactly
are we doing when we start from axioms and prove things from them?  Where does
this ability come from?  What does it consist of?

I would have thought that quarks and electrons from which we appear to be
constituted would be indifferent to truth.

Which would fit with the fact that I seem to make a lot of mistakes.

But you think otherwise?

I didn't understand the above... what do quarks and electrons have to
do with arithmetical platonism?

Are we not composed from quarks and electrons?  If so - then how do mere
collections of quarks and electrons connect with platonic truths?

By chance?  Are we just fortunate that the initial conditions and causal laws
of the universe are such that our quarks and electrons take forms that mirror
Platonic Truths?

How can you make
sense of that in terms of the constructivist point of view that you
are (I think) compelled to take if you argue against arithmetical
platonism?  It seems obvious that all possible intelligences would
discover the same forms of the Mandelbrot so long as they iterated on
z' = z^2 + c, but maybe I am missing the point of your argument.

I will agree with you that all intelligences that start from the same
premises as you, and follow the same rules as inference as you, will also
draw the same conclusions about the Mandelbrot set as you do.

However - I do not agree with you that this amenable group exhausts the set
of all *possible* intelligences.

I only meant that all possible intelligences that start from a
mathematics that includes addition, multiplication, and complex
numbers will find that if they iterate the function z' = z^2 + c, they
will find that some orbits become periodic or settle on a point, and
some escape to infinity. If they draw a graph of which orbits don't
escape, they will draw the Mandelbrot Set. All possible intelligences
that undertake that procedure will draw the same shape... and this
seems like discovery, not creation.

It seems like a tautology to me.  If you do what I do and believe what I
believe then you will be a lot like me...?

Is there anything to mathematics other than belief?

What are beliefs?  Why do we have the beliefs that we have?  How do we form
beliefs - what lies behind belief?

Can *our* mathematical abilities be reduced to something that is indifferent to
mathematical truth?

Could there be intelligences who start from vastly difference premises, and
use vastly different rules of inference, and draw vastly different
conclusions?

Of course, but then what they are doing doesn't relate to the Mandelbrot Set.

However - they might *believe* their creations to be just as significant and
universal as you consider the Mandelbrot Set to be - mightened they?

What would make them wrong in their belief but you right in yours```

### Re: Prime Numbers

```

On 21 Sep 2012, at 19:17, meekerdb wrote:

On 9/21/2012 1:22 AM, Bruno Marchal wrote:

On 20 Sep 2012, at 20:14, meekerdb wrote:

On 9/20/2012 10:31 AM, Bruno Marchal wrote:

On 20 Sep 2012, at 18:14, meekerdb wrote:

On 9/20/2012 2:05 AM, Bruno Marchal wrote:
A modal logic of probability is given by the behavior of the
probability one. In Kripke terms, P(x) = 1 in world alpha
means that x is realized in all worlds accessible from alpha,
and (key point) that we are not in a cul-de-sac world.

What does 'accessible' mean?

In modal logic semantic, it is a technical world for any element
in set + a binary relation on it.

A mapping of the set onto itself?

?

A relation is not a map. A world can access more than one world.
For example {a, b} with the relation {(a, a), (a, b)}, or aRa, aRb.

When applied to probability, the idea is to interpret the worlds
by the realization of some random experience, like throwing a
other with tail. In that modal (tail or head) is a certainty as
(tail or head) is realized everywhere in the accessible worlds.

Then accessible means nomologically possible.

Accessible means only that some binary relation exists on a set.
But in some concrete model of a multi-world or multi-situation
context, nomological possibility is not excluded.

Then I don't understand what other kinds of possibility are
allowed?  I don't see how logical possibility could be considered an
accessibility relation (at least not an interesting one) because it
would allow Rxy where y was anything except not-x.

But in the worlds of the UD there is no nomological constraint, so
there's no probability measure?

I am not sure why there is no nomological constraints in the UD.
UD* is a highly structured entity. You might elaborate on this.

A nomological constraint is one of physics.

Why? Define perhaps nomological.

But physics is derivative from part of the UD.  The UD is structured
only by arithmetic.

Why would this be not enough, given that physics will supervene on
arithmetical relations (computations)?

Bruno

Generally speaking a different world is defined as not
accessible.  If you can go there, it's part of your same world.

Yes. OK. Sorry. Logician used the term world in a technical
sense, and the worlds can be anything, depending of which modal
logic is used, for what purpose, etc. Kripke semantic main used
is in showing the independence of formula in different systems.

Bruno

Brent

This gives KD modal logics, with K:  = [](p - q)-([]p -
[]q), and D:  []p - p. Of course with [] for Gödel's
beweisbar we don't have that D is a theorem, so we ensure the D
property by defining a new box, Bp = []p  t.

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### Re: Prime Numbers

```
On 9/22/2012 7:32 AM, Roger Clough wrote:

How could mathematics be fiction ?
If so, then we could simply say that 2+2=5 because it's saturday.
How could we have a world we many minds can, on rare occasions, come to
complete agreement if that where the case? Perhaps it is true that 2+2=4
because we all agree, at some level, that it is true. (I am not just
considering humans here with the word we!)

--
Onward!

Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html

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### Re: Prime Numbers

```

On 20 Sep 2012, at 20:14, meekerdb wrote:

On 9/20/2012 10:31 AM, Bruno Marchal wrote:

On 20 Sep 2012, at 18:14, meekerdb wrote:

On 9/20/2012 2:05 AM, Bruno Marchal wrote:
A modal logic of probability is given by the behavior of the
probability one. In Kripke terms, P(x) = 1 in world alpha means
that x is realized in all worlds accessible from alpha, and (key
point) that we are not in a cul-de-sac world.

What does 'accessible' mean?

In modal logic semantic, it is a technical world for any element in
set + a binary relation on it.

When applied to probability, the idea is to interpret the worlds by
the realization of some random experience, like throwing a coin
would lead to two worlds accessible, one with head, the other with
tail. In that modal (tail or head) is a certainty as (tail or head)
is realized everywhere in the accessible worlds.

Then accessible means nomologically possible.

Accessible means only that some binary relation exists on a set. But
in some concrete model of a multi-world or multi-situation context,
nomological possibility is not excluded.

But in the worlds of the UD there is no nomological constraint, so
there's no probability measure?

I am not sure why there is no nomological constraints in the UD. UD*
is a highly structured entity. You might elaborate on this.

Bruno

Generally speaking a different world is defined as not
accessible.  If you can go there, it's part of your same world.

Yes. OK. Sorry. Logician used the term world in a technical sense,
and the worlds can be anything, depending of which modal logic is
used, for what purpose, etc. Kripke semantic main used is in
showing the independence of formula in different systems.

Bruno

Brent

This gives KD modal logics, with K:  = [](p - q)-([]p - []q),
and D:  []p - p. Of course with [] for Gödel's beweisbar we
don't have that D is a theorem, so we ensure the D property by
defining a new box, Bp = []p  t.

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### Re: Prime Numbers

```On Tue, Sep 18, 2012 at 11:50 PM, Terren Suydam terren.suy...@gmail.comwrote:

On Tue, Sep 18, 2012 at 10:19 PM, Rex Allen rexallen31...@gmail.com
wrote:

On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam terren.suy...@gmail.com
wrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?

I find fictionalism to be the most plausible view of mathematics, with
all
that implies for the Mandelbrot set.

I'm curious about what a plausible fictionalist account of the
Mandelbrot set could be. Is fictionalism the same as constructivism,
or the idea that knowledge doesn't exist outside of a mind?

I lean towards a strong form of fictionalism - which says that there are
few important differences between mathematics and literary fiction.

So - I could give a detailed answer - but I think I'd rather give a sketchy

I would say that mathematics is just very tightly plotted fiction where so
many details of the story are known up front that the plot can only
progress in very specific ways if it is to remain consistent and believable

Mathematics is a kind of world building.  In the imaginative sense.

But ;et me turn the question around on you, if I can:

Do you have an explanation for how we discover mathematical objects and
otherwise interact with the Platonic realm?

How is it that we are able to reliably know things about Platonia?

I think just doing logic and math - starting from axioms and proving
things from them - is interacting with the Platonic realm.

But how is it that we humans do that?  This is my main question.  What
exactly are we doing when we start from axioms and prove things from them?
Where does this ability come from?  What does it consist of?

I would have thought that quarks and electrons from which we appear to be
constituted would be indifferent to truth.

Which would fit with the fact that I seem to make a lot of mistakes.

But you think otherwise?

I didn't understand the above... what do quarks and electrons have to
do with arithmetical platonism?

Are we not composed from quarks and electrons?  If so - then how do mere
collections of quarks and electrons connect with platonic truths?

By chance?  Are we just fortunate that the initial conditions and causal
laws of the universe are such that our quarks and electrons take forms that
mirror Platonic Truths?

How can you make
sense of that in terms of the constructivist point of view that you
are (I think) compelled to take if you argue against arithmetical
platonism?  It seems obvious that all possible intelligences would
discover the same forms of the Mandelbrot so long as they iterated on
z' = z^2 + c, but maybe I am missing the point of your argument.

I will agree with you that all intelligences that start from the same
premises as you, and follow the same rules as inference as you, will also
draw the same conclusions about the Mandelbrot set as you do.

However - I do not agree with you that this amenable group exhausts the
set
of all *possible* intelligences.

I only meant that all possible intelligences that start from a
mathematics that includes addition, multiplication, and complex
numbers will find that if they iterate the function z' = z^2 + c, they
will find that some orbits become periodic or settle on a point, and
some escape to infinity. If they draw a graph of which orbits don't
escape, they will draw the Mandelbrot Set. All possible intelligences
that undertake that procedure will draw the same shape... and this
seems like discovery, not creation.

It seems like a tautology to me.  If you do what I do and believe what I
believe then you will be a lot like me...?

Is there anything to mathematics other than belief?

What are beliefs?  Why do we have the beliefs that we have?  How do we form
beliefs - what lies behind belief?

Can *our* mathematical abilities be reduced to something that is
indifferent to mathematical truth?

Could there be intelligences who start from vastly difference premises,
and
use vastly different rules of inference, and draw vastly different
conclusions?

Of course, but then what they are doing doesn't relate to the Mandelbrot
Set.

However - they might *believe* their creations to be just as significant
and universal as you consider the Mandelbrot Set to be - mightened they?

What would make them wrong in their belief but you right in yours?

What are the limits of belief, do you think?  Is there any belief that
is so
preposterous that even the maddest of the mad could not believe such a
thing?

I don't think so... based on my understanding of how mad maddest of

And if there is no such belief - then is it conceivable that quarks and
electrons could configure themselves in such a way as to *cause* a being
who
holds such beliefs to come into existence?

```

### Re: Prime Numbers

```On Wed, Sep 19, 2012 at 12:27 AM, Jason Resch jasonre...@gmail.com wrote:

On Sep 18, 2012, at 9:19 PM, Rex Allen rexallen31...@gmail.com wrote:

On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam  terren.suy...@gmail.com
terren.suy...@gmail.com wrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?

I find fictionalism to be the most plausible view of mathematics, with all
that implies for the Mandelbrot set.

But ;et me turn the question around on you, if I can:

Do you have an explanation for how we discover mathematical objects and
otherwise interact with the Platonic realm?

We study and create theories about objects in the mathematical realm just
as we study and create theories about objects in the physical realm.

So in the physical realm, we start from our senses - what we see, hear,
feel, etc.

From this, we infer the existence of electrons and wavefunctions and
strings and whatnot.  Or some of us do.  Others take a more instrumental
view of scientific theories.

So you're saying that thought is another kind of sense?  And that what
occurs to us in thought can also be used as a basis to infer the existence
of objects which help explain those thoughts?

But we believe that electrons interact causally with us because we are made
from similar stuff - and by doing so make themselves known to us...right?

How do Platonic objects interact causally with us?  Via a Platonic Field?
PFT - Platonic Field Theory?

It's not much different from how we develop theories about other things we
cannot interact with: the early universe, the cores of stars, the insides
of black holes, etc.

We test these theories by following their implications and seeing if they
lead to contridictions with other, more  established, facts.

Just as with physical theories, we ocasionally find that we need to throw
out the old set of theories (or axioms) for a new set which has greater
explanatory power.

So you think our current mathematical theories are not true in any
metaphysical sense - but rather are approximations of what exists in
Platonia?

Is there an equivalent of the idea of domains of validity that holds in
some circles in physics?

I'm not sure any of this counts as being evidence in favor of Platonism...

How is it that we are able to reliably know things about Platonia?

The very idea of knowing implies a differentiation between true and false.

Nearly any intelligent civilization that notices a partition between true
and false will eventyally get here.

True in what sense?  A coherentist conception of truth?  A correspondence
conception of truth?

How do we know truth?  Do we have an innate truth sense?

Does the ability to know truth require free will?

For instance:

If we say a statement is true because it is true, that is different than
saying it is true because our neurons fired in a way that determined our
response. If all our decisions were predetermined from the moment of the
big bang then rational discussion is meaningless. Whether or not anyone
agrees with you has nothing to do with the truth of your claim. Their
beliefs were hardwired from the beginning of time.

It follows then that your own beliefs are not based on their truth value.
You believe what you believe because your neurons have determined that you
will believe in this rather than that.

SO - what is this truth stuff, really?

I would have thought that quarks and electrons from which we appear to be
constituted would be indifferent to truth.

The unreasonable effectiveness of math in the physical sciences is yet
further support if Platonism.  If this, and seemingly infinite  physical
universes exist, and they are mathematical structures, why can't others
exist?

Which would fit with the fact that I seem to make a lot of mistakes.

But you think otherwise?

We are imperfect beings.

What is the source of imperfection?  Where does it come from?  What
explains it?

Objectively, intrinsically, absolutely imperfect?

Have you heard the term Works as coded, with respect to software
development?

So I can write a program that has a bug in it - and the computer will run
it perfectly.  The computer will do exactly what I told it to do.

The program works as coded.  When running my program, the computer is
perfectly imperfect.

I am the source of its imperfection.

However, in a functionalist theory of mind - I am actually just executing
my own program right?  Given the initial conditions of the universe and
the causal laws that govern it - I could not do other than I did when I
wrote that buggy code.

I also work as coded.  I also am perfectly imperfect.  And since in
this view I am not the source of my own imperfection - the universe's
initial conditions and causal laws must be that source.

But what explains that imperfection?

But - maybe there really is no such thing as imperfection?  It's all just

### Re: Prime Numbers

```

On Sep 21, 2012, at 8:13 AM, Rex Allen rexallen31...@gmail.com wrote:

On Wed, Sep 19, 2012 at 12:27 AM, Jason Resch jasonre...@gmail.com
wrote:
On Sep 18, 2012, at 9:19 PM, Rex Allen rexallen31...@gmail.com
wrote:
On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam terren.suy...@gmail.com
wrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?

I find fictionalism to be the most plausible view of mathematics,
with all that implies for the Mandelbrot set.

But ;et me turn the question around on you, if I can:

Do you have an explanation for how we discover mathematical
objects and otherwise interact with the Platonic realm?

We study and create theories about objects in the mathematical realm
just as we study and create theories about objects in the physical
realm.

So in the physical realm, we start from our senses - what we see,
hear, feel, etc.

From this, we infer the existence of electrons and wavefunctions and
strings and whatnot.  Or some of us do.  Others take a more
instrumental view of scientific theories.

Right, and we have similarly inferred the existence of primes,
fractals, non-computable functions, etc.

So you're saying that thought is another kind of sense?

Thought is needed for inference and building theories, equally in the
physical sciences and math.

And that what occurs to us in thought can also be used as a basis to
infer the existence of objects which help explain those thoughts?

Right, like you might think up genesis and dualism, or big bang and
materialism, or platonic truth and computationalism.  These are
ontological theories for what exists, and why we are here experiencing
it.

If you say math is fiction and only exists only as a story in our
brains, then obviously you can't use platonic truth and
computationalism as one if your theories of existence.

I think the fact that mathematics can serve as a theory for our
existence shows absolutely that mathematical theories and physical
theories are on equal footing.  We can gather evidence for them and
build cases for them, find out we were wrong about them, and so on.
Why do we believe in quarks, electrons, strings, etc.?  Because they
can explain our observations.  Why do I believe in the platonic
realm?  For the same reasons.

But we believe that electrons interact causally with us because we
are made from similar stuff - and by doing so make themselves known
to us...right?

How do Platonic objects interact causally with us?  Via a Platonic
Field?  PFT - Platonic Field Theory?

How did the warping of space and time cause Einsteins brain to figure
out relativity?

I think you are looking at it in the wrong way.  Our brains seek good
explanations.  They sometimes find one.  That's all that is going on.

Now you say our explainations when it comes to mathematics are
fiction, but if that is so, why not say the same of the physical
theories?  Why not say the big bang is fiction, or matter is fiction?
I think this leads to declaring everything but one's current thought
is fiction, which does not seem very useful.

It's not much different from how we develop theories about other
things we cannot interact with: the early universe, the cores of
stars, the insides of black holes, etc.

We test these theories by following their implications and seeing if
they lead to contridictions with other, more  established, facts.

Just as with physical theories, we ocasionally find that we need to
throw out the old set of theories (or axioms) for a new set which
has greater explanatory power.

So you think our current mathematical theories are not true in any
metaphysical sense - but rather are approximations of what exists in
Platonia?

They may or may not be true, but they are certainly incomplete.  Just
like our physical theories may or not be true descriptions of the
universe, and are certainly incomplete.

Is there an equivalent of the idea of domains of validity that
holds in some circles in physics?

I don't know what this concept means well enough to say.

I'm not sure any of this counts as being evidence in favor of
Platonism...

How is it that we are able to reliably know things about Platonia?

The very idea of knowing implies a differentiation between true and
false.

Nearly any intelligent civilization that notices a partition between
true and false will eventyally get here.

True in what sense?  A coherentist conception of truth?  A
correspondence conception of truth?

In the sense of the notion that a proposition is either true or false.

How do we know truth?  Do we have an innate truth sense?

How do we know anything?  Do we know anything?

Does the ability to know truth require free will?

Comparabalist or incompatibalist?

For instance:

If we say a statement is true because it is true,

What we say or ```

### Re: Prime Numbers

```On Fri, Sep 21, 2012 at 8:40 AM, Rex Allen rexallen31...@gmail.com wrote:
On Tue, Sep 18, 2012 at 11:50 PM, Terren Suydam terren.suy...@gmail.com
wrote:

I'm curious about what a plausible fictionalist account of the
Mandelbrot set could be. Is fictionalism the same as constructivism,
or the idea that knowledge doesn't exist outside of a mind?

I lean towards a strong form of fictionalism - which says that there are few
important differences between mathematics and literary fiction.

Can you articulate any important differences between them?

So - I could give a detailed answer - but I think I'd rather give a sketchy

I would say that mathematics is just very tightly plotted fiction where so
many details of the story are known up front that the plot can only progress
in very specific ways if it is to remain consistent and believable to the

Mathematics is a kind of world building.  In the imaginative sense.

I am not unsympathetic with this view, given the creativity that goes
into mathematical proofs. However, it falls apart for me when I
consider that an alien civilization is constrained to build the same
worlds if they start from the same logical axioms.

I think just doing logic and math - starting from axioms and proving
things from them - is interacting with the Platonic realm.

But how is it that we humans do that?  This is my main question.  What
exactly are we doing when we start from axioms and prove things from them?
Where does this ability come from?  What does it consist of?

We're using our intelligence and creativity to search a space of
propositions (given a set of axioms) that are either provably true or
false. I would say our intelligence and creativity comes from our
animal nature, evolved as it is to make sense of the world (and each
other) and draw useful inferences that help us survive. I'm not sure
how to answer the question what does it consist of. Are you asking
how we can act intelligently, how creativity works?

I didn't understand the above... what do quarks and electrons have to
do with arithmetical platonism?

Are we not composed from quarks and electrons?  If so - then how do mere
collections of quarks and electrons connect with platonic truths?

By chance?  Are we just fortunate that the initial conditions and causal
laws of the universe are such that our quarks and electrons take forms that
mirror Platonic Truths?

I see. Assuming comp, we are some infinite subset of the trace of the
UD (universal dovetailer), which is a platonic entity. Quarks and
electrons are a part of the physics that emerges from that (the
numbers' dreams)... that's the reversal, where physics emerges from
computer science.

The question of how we, as mere collections of quarks etc. connect
back with Platonia, is answered by CT (Church-Turing Thesis). As we
are universal machines, we can emulate any computation, including the
universal dovetailer (for instance).

I only meant that all possible intelligences that start from a
mathematics that includes addition, multiplication, and complex
numbers will find that if they iterate the function z' = z^2 + c, they
will find that some orbits become periodic or settle on a point, and
some escape to infinity. If they draw a graph of which orbits don't
escape, they will draw the Mandelbrot Set. All possible intelligences
that undertake that procedure will draw the same shape... and this
seems like discovery, not creation.

It seems like a tautology to me.  If you do what I do and believe what I
believe then you will be a lot like me...?

Is there anything to mathematics other than belief?

The point is that you are constrained in what you can prove starting
from a given set of axioms. You are not constrained in which axioms
you start with - that's where the belief comes in since there is no
way to prove that your axioms are True, except within a more
encompassing logical framework with its own axioms.

What are beliefs?  Why do we have the beliefs that we have?  How do we form
beliefs - what lies behind belief?

Beliefs in the everyday sense are inferences about our experience that
we hold to be true. They help us navigate the world as we experience
it, and make sense of it. Mostly our beliefs are formed by suggestion
from our parents and peers when we are young, and as we learn and grow
we complicate our worldview with new beliefs. There isn't much behind
belief except habituation. Certainly most of us hold onto some beliefs
that are contradicted by facts (particularly the beliefs we hold of
ourselves).

Can *our* mathematical abilities be reduced to something that is indifferent
to mathematical truth?

I think if you were doing math in a way that was indifferent to
mathematical truth, you wouldn't be very good at math.

Of course, but then what they are doing doesn't relate to the Mandelbrot
Set.

However - they might *believe* their creations to be just as significant and
universal ```

### Re: Prime Numbers

```
On 9/21/2012 1:22 AM, Bruno Marchal wrote:

On 20 Sep 2012, at 20:14, meekerdb wrote:

On 9/20/2012 10:31 AM, Bruno Marchal wrote:

On 20 Sep 2012, at 18:14, meekerdb wrote:

On 9/20/2012 2:05 AM, Bruno Marchal wrote:
A modal logic of probability is given by the behavior of the probability one. In
Kripke terms, P(x) = 1 in world alpha means that x is realized in all worlds
accessible from alpha, and (key point) that we are not in a cul-de-sac world.

What does 'accessible' mean?

In modal logic semantic, it is a technical world for any element in set + a binary
relation on it.

A mapping of the set onto itself?

When applied to probability, the idea is to interpret the worlds by the realization of
some random experience, like throwing a coin would lead to two worlds accessible, one
with head, the other with tail. In that modal (tail or head) is a certainty as (tail
or head) is realized everywhere in the accessible worlds.

Then accessible means nomologically possible.

Accessible means only that some binary relation exists on a set. But in some concrete
model of a multi-world or multi-situation context, nomological possibility is not excluded.

Then I don't understand what other kinds of possibility are allowed?  I don't see how
logical possibility could be considered an accessibility relation (at least not an
interesting one) because it would allow Rxy where y was anything except not-x.

But in the worlds of the UD there is no nomological constraint, so there's no
probability measure?

I am not sure why there is no nomological constraints in the UD. UD* is a highly
structured entity. You might elaborate on this.

A nomological constraint is one of physics.  But physics is derivative from part of the
UD.  The UD is structured only by arithmetic.

Brent

Bruno

Generally speaking a different world is defined as not accessible.  If you can go
there, it's part of your same world.

Yes. OK. Sorry. Logician used the term world in a technical sense, and the worlds can
be anything, depending of which modal logic is used, for what purpose, etc. Kripke
semantic main used is in showing the independence of formula in different systems.

Bruno

Brent

This gives KD modal logics, with K:  = [](p - q)-([]p - []q), and D:  []p - p.
Of course with [] for Gödel's beweisbar we don't have that D is a theorem, so we
ensure the D property by defining a new box, Bp = []p  t.

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### Re: Prime Numbers

```
On 9/21/2012 5:40 AM, Rex Allen wrote:
On Tue, Sep 18, 2012 at 11:50 PM, Terren Suydam terren.suy...@gmail.com
mailto:terren.suy...@gmail.com wrote:

On Tue, Sep 18, 2012 at 10:19 PM, Rex Allen rexallen31...@gmail.com
mailto:rexallen31...@gmail.com wrote:

On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam terren.suy...@gmail.com
mailto:terren.suy...@gmail.com
wrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?

I find fictionalism to be the most plausible view of mathematics, with all
that implies for the Mandelbrot set.

I'm curious about what a plausible fictionalist account of the
Mandelbrot set could be. Is fictionalism the same as constructivism,
or the idea that knowledge doesn't exist outside of a mind?

I lean towards a strong form of fictionalism - which says that there are few important
differences between mathematics and literary fiction.

So - I could give a detailed answer - but I think I'd rather give a sketchy answer at
this point.

I would say that mathematics is just very tightly plotted fiction where so many details
of the story are known up front that the plot can only progress in very specific ways if
it is to remain consistent and believable to the reader.

Mathematics is a kind of world building.  In the imaginative sense.

But ;et me turn the question around on you, if I can:

Do you have an explanation for how we discover mathematical objects and
otherwise interact with the Platonic realm?

How is it that we are able to reliably know things about Platonia?

I think just doing logic and math - starting from axioms and proving
things from them - is interacting with the Platonic realm.

But how is it that we humans do that?  This is my main question.  What exactly are we
doing when we start from axioms and prove things from them?  Where does this ability
come from?  What does it consist of?

I would have thought that quarks and electrons from which we appear to be
constituted would be indifferent to truth.

Which would fit with the fact that I seem to make a lot of mistakes.

But you think otherwise?

I didn't understand the above... what do quarks and electrons have to
do with arithmetical platonism?

Are we not composed from quarks and electrons?  If so - then how do mere collections
of quarks and electrons connect with platonic truths?

By chance?  Are we just fortunate that the initial conditions and causal laws of the
universe are such that our quarks and electrons take forms that mirror Platonic Truths?

How can you make
sense of that in terms of the constructivist point of view that you
are (I think) compelled to take if you argue against arithmetical
platonism?  It seems obvious that all possible intelligences would
discover the same forms of the Mandelbrot so long as they iterated on
z' = z^2 + c, but maybe I am missing the point of your argument.

I will agree with you that all intelligences that start from the same
premises as you, and follow the same rules as inference as you, will also
draw the same conclusions about the Mandelbrot set as you do.

However - I do not agree with you that this amenable group exhausts the
set
of all *possible* intelligences.

I only meant that all possible intelligences that start from a
mathematics that includes addition, multiplication, and complex
numbers will find that if they iterate the function z' = z^2 + c, they
will find that some orbits become periodic or settle on a point, and
some escape to infinity. If they draw a graph of which orbits don't
escape, they will draw the Mandelbrot Set. All possible intelligences
that undertake that procedure will draw the same shape... and this
seems like discovery, not creation.

It seems like a tautology to me.  If you do what I do and believe what I believe then
you will be a lot like me...?

Is there anything to mathematics other than belief?

What are beliefs?  Why do we have the beliefs that we have?  How do we form beliefs -
what lies behind belief?

Can *our* mathematical abilities be reduced to something that is indifferent to
mathematical truth?

Could there be intelligences who start from vastly difference premises,
and
use vastly different rules of inference, and draw vastly different
conclusions?

Of course, but then what they are doing doesn't relate to the Mandelbrot
Set.

However - they might *believe* their creations to be just as significant and universal
as you consider the Mandelbrot Set to be - mightened they?

What would make them wrong in their belief but you right in yours?

What are the limits of belief, do you think?  Is there any belief that is
so
preposterous that even the ```

### Re: Prime Numbers

```
On 9/21/2012 8:59 AM, Jason Resch wrote:

On Sep 21, 2012, at 8:13 AM, Rex Allen rexallen31...@gmail.com
mailto:rexallen31...@gmail.com wrote:

On Wed, Sep 19, 2012 at 12:27 AM, Jason Resch jasonre...@gmail.com
mailto:jasonre...@gmail.com wrote:

On Sep 18, 2012, at 9:19 PM, Rex Allen rexallen31...@gmail.com
mailto:rexallen31...@gmail.com wrote:

On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam terren.suy...@gmail.com
mailto:terren.suy...@gmail.com wrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?

I find fictionalism to be the most plausible view of mathematics, with all
that
implies for the Mandelbrot set.

But ;et me turn the question around on you, if I can:

Do you have an explanation for how we discover mathematical objects and
otherwise interact with the Platonic realm?

We study and create theories about objects in the mathematical realm just
as we
study and create theories about objects in the physical realm.

So in the physical realm, we start from our senses - what we see, hear, feel,
etc.

From this, we infer the existence of electrons and wavefunctions and strings and
whatnot.  Or some of us do.  Others take a more instrumental view of scientific theories.

Right, and we have similarly inferred the existence of primes, fractals, non-computable
functions, etc.

We invented counting, addition, etc and found it implied true propositions about primes,
fractals, etc.  To say they exist in the same way tables and chairs exist is going much
further.

So you're saying that thought is another kind of sense?

Thought is needed for inference and building theories, equally in the physical sciences
and math.

And that what occurs to us in thought can also be used as a basis to infer the
existence of objects which help explain those thoughts?

Right, like you might think up genesis and dualism, or big bang and materialism, or
platonic truth and computationalism.  These are ontological theories for what exists,
and why we are here experiencing it.

If you say math is fiction and only exists only as a story in our brains, then obviously
you can't use platonic truth and computationalism as one if your theories of existence.

I think the fact that mathematics can serve as a theory for our existence shows
absolutely that mathematical theories and physical theories are on equal footing.  We
can gather evidence for them and build cases for them, find out we were wrong about
them, and so on.  Why do we believe in quarks, electrons, strings, etc.?  Because they
can explain our observations.  Why do I believe in the platonic realm?  For the same
reasons.

But we believe that electrons interact causally with us because we are made from
similar stuff - and by doing so make themselves known to us...right?

How do Platonic objects interact causally with us?  Via a Platonic Field?  PFT -
Platonic Field Theory?

How did the warping of space and time cause Einsteins brain to figure out
relativity?

I think you are looking at it in the wrong way. Our brains seek good explanations.  They
sometimes find one.  That's all that is going on.

Now you say our explainations when it comes to mathematics are fiction, but if that is
so, why not say the same of the physical theories?  Why not say the big bang is fiction,
or matter is fiction?

They are stories which we intend to have referents independent of the stories
(theories).

Brent

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```

### Re: Prime Numbers

```Just to avoid confusion, this sentence:

*I would say that mathematics is just very tightly plotted fiction where so
many details of the story are known up front that the plot can only
progress in very specific ways if it is to remain consistent and believable

Should probably be:

*I would say that mathematics is just very tightly plotted fiction where so
many details of the back-story are known up front that the plot can only
progress in very specific ways if it is to remain consistent and believable

On Fri, Sep 21, 2012 at 8:40 AM, Rex Allen rexallen31...@gmail.com wrote:

On Tue, Sep 18, 2012 at 11:50 PM, Terren Suydam
terren.suy...@gmail.comwrote:

On Tue, Sep 18, 2012 at 10:19 PM, Rex Allen rexallen31...@gmail.com
wrote:

On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam terren.suy...@gmail.com

wrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?

I find fictionalism to be the most plausible view of mathematics, with
all
that implies for the Mandelbrot set.

I'm curious about what a plausible fictionalist account of the
Mandelbrot set could be. Is fictionalism the same as constructivism,
or the idea that knowledge doesn't exist outside of a mind?

I lean towards a strong form of fictionalism - which says that there are
few important differences between mathematics and literary fiction.

So - I could give a detailed answer - but I think I'd rather give a

I would say that mathematics is just very tightly plotted fiction where so
many details of the story are known up front that the plot can only
progress in very specific ways if it is to remain consistent and believable

Mathematics is a kind of world building.  In the imaginative sense.

But ;et me turn the question around on you, if I can:

Do you have an explanation for how we discover mathematical objects
and
otherwise interact with the Platonic realm?

How is it that we are able to reliably know things about Platonia?

I think just doing logic and math - starting from axioms and proving
things from them - is interacting with the Platonic realm.

But how is it that we humans do that?  This is my main question.  What
exactly are we doing when we start from axioms and prove things from them?
Where does this ability come from?  What does it consist of?

I would have thought that quarks and electrons from which we appear to be
constituted would be indifferent to truth.

Which would fit with the fact that I seem to make a lot of mistakes.

But you think otherwise?

I didn't understand the above... what do quarks and electrons have to
do with arithmetical platonism?

Are we not composed from quarks and electrons?  If so - then how do mere
collections of quarks and electrons connect with platonic truths?

By chance?  Are we just fortunate that the initial conditions and causal
laws of the universe are such that our quarks and electrons take forms that
mirror Platonic Truths?

How can you make
sense of that in terms of the constructivist point of view that you
are (I think) compelled to take if you argue against arithmetical
platonism?  It seems obvious that all possible intelligences would
discover the same forms of the Mandelbrot so long as they iterated on
z' = z^2 + c, but maybe I am missing the point of your argument.

I will agree with you that all intelligences that start from the same
premises as you, and follow the same rules as inference as you, will
also
draw the same conclusions about the Mandelbrot set as you do.

However - I do not agree with you that this amenable group exhausts the
set
of all *possible* intelligences.

I only meant that all possible intelligences that start from a
mathematics that includes addition, multiplication, and complex
numbers will find that if they iterate the function z' = z^2 + c, they
will find that some orbits become periodic or settle on a point, and
some escape to infinity. If they draw a graph of which orbits don't
escape, they will draw the Mandelbrot Set. All possible intelligences
that undertake that procedure will draw the same shape... and this
seems like discovery, not creation.

It seems like a tautology to me.  If you do what I do and believe what I
believe then you will be a lot like me...?

Is there anything to mathematics other than belief?

What are beliefs?  Why do we have the beliefs that we have?  How do we
form beliefs - what lies behind belief?

Can *our* mathematical abilities be reduced to something that is
indifferent to mathematical truth?

Could there be intelligences who start from vastly difference premises,
and
use vastly different rules of inference, and draw vastly different
conclusions?

Of course, but then what they are doing doesn't relate to the Mandelbrot
Set.

However - they ```

### Re: Prime Numbers

```On Fri, Sep 21, 2012 at 1:55 PM, meekerdb meeke...@verizon.net wrote:

On 9/21/2012 8:59 AM, Jason Resch wrote:

On Sep 21, 2012, at 8:13 AM, Rex Allen rexallen31...@gmail.com wrote:

On Wed, Sep 19, 2012 at 12:27 AM, Jason Resch jasonre...@gmail.comwrote:

On Sep 18, 2012, at 9:19 PM, Rex Allen rexallen31...@gmail.com wrote:

On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam
terren.suy...@gmail.comwrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?

I find fictionalism to be the most plausible view of mathematics, with
all that implies for the Mandelbrot set.

But ;et me turn the question around on you, if I can:

Do you have an explanation for how we discover mathematical objects
and otherwise interact with the Platonic realm?

We study and create theories about objects in the mathematical realm
just as we study and create theories about objects in the physical realm.

So in the physical realm, we start from our senses - what we see, hear,
feel, etc.

From this, we infer the existence of electrons and wavefunctions and
strings and whatnot.  Or some of us do.  Others take a more instrumental
view of scientific theories.

Right, and we have similarly inferred the existence of primes, fractals,
non-computable functions, etc.

We invented counting, addition, etc and found it implied true propositions
about primes, fractals, etc.  To say they exist in the same way tables and
chairs exist is going much further.

All of our scientific theories are inventions too.  We can only hope they
bear some resemblance to reality.

So you're saying that thought is another kind of sense?

Thought is needed for inference and building theories, equally in the
physical sciences and math.

And that what occurs to us in thought can also be used as a basis to
infer the existence of objects which help explain those thoughts?

Right, like you might think up genesis and dualism, or big bang and
materialism, or platonic truth and computationalism.  These are ontological
theories for what exists, and why we are here experiencing it.

If you say math is fiction and only exists only as a story in our
brains, then obviously you can't use platonic truth and computationalism as
one if your theories of existence.

I think the fact that mathematics can serve as a theory for our
existence shows absolutely that mathematical theories and physical theories
are on equal footing.  We can gather evidence for them and build cases for
them, find out we were wrong about them, and so on.  Why do we believe in
quarks, electrons, strings, etc.?  Because they can explain our
observations.  Why do I believe in the platonic realm?  For the same
reasons.

But we believe that electrons interact causally with us because we are
made from similar stuff - and by doing so make themselves known to
us...right?

How do Platonic objects interact causally with us?  Via a Platonic
Field?  PFT - Platonic Field Theory?

How did the warping of space and time cause Einsteins brain to figure
out relativity?

I think you are looking at it in the wrong way.  Our brains seek good
explanations.  They sometimes find one.  That's all that is going on.

Now you say our explainations when it comes to mathematics are fiction,
but if that is so, why not say the same of the physical theories?  Why not
say the big bang is fiction, or matter is fiction?

They are stories which we intend to have referents independent of the
stories (theories).

I don't see how this is any different from our mathematical theories though.

Jason

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```

### Re: Prime Numbers

```
On 9/21/2012 12:56 PM, Jason Resch wrote:

On Fri, Sep 21, 2012 at 1:55 PM, meekerdb meeke...@verizon.net
mailto:meeke...@verizon.net wrote:

On 9/21/2012 8:59 AM, Jason Resch wrote:

On Sep 21, 2012, at 8:13 AM, Rex Allen rexallen31...@gmail.com
mailto:rexallen31...@gmail.com wrote:

On Wed, Sep 19, 2012 at 12:27 AM, Jason Resch jasonre...@gmail.com
mailto:jasonre...@gmail.com wrote:

On Sep 18, 2012, at 9:19 PM, Rex Allen rexallen31...@gmail.com
mailto:rexallen31...@gmail.com wrote:

On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam terren.suy...@gmail.com
mailto:terren.suy...@gmail.com wrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?

I find fictionalism to be the most plausible view of mathematics, with
all
that implies for the Mandelbrot set.

But ;et me turn the question around on you, if I can:

Do you have an explanation for how we discover mathematical objects
and
otherwise interact with the Platonic realm?

We study and create theories about objects in the mathematical realm
just as
we study and create theories about objects in the physical realm.

So in the physical realm, we start from our senses - what we see, hear,
feel, etc.

From this, we infer the existence of electrons and wavefunctions and
strings and
whatnot.  Or some of us do.  Others take a more instrumental view of
scientific
theories.

Right, and we have similarly inferred the existence of primes, fractals,
non-computable functions, etc.

We invented counting, addition, etc and found it implied true propositions
primes, fractals, etc.  To say they exist in the same way tables and chairs
exist is
going much further.

All of our scientific theories are inventions too.  We can only hope they bear
some resemblance to reality.

So you're saying that thought is another kind of sense?

Thought is needed for inference and building theories, equally in the
physical
sciences and math.

And that what occurs to us in thought can also be used as a basis to infer
the
existence of objects which help explain those thoughts?

Right, like you might think up genesis and dualism, or big bang and
materialism, or
platonic truth and computationalism.  These are ontological theories for
what
exists, and why we are here experiencing it.

If you say math is fiction and only exists only as a story in our brains,
then
obviously you can't use platonic truth and computationalism as one if your
theories
of existence.

I think the fact that mathematics can serve as a theory for our existence
shows
absolutely that mathematical theories and physical theories are on equal
footing.
We can gather evidence for them and build cases for them, find out we were
wrong
about them, and so on.  Why do we believe in quarks, electrons, strings,
etc.?
Because they can explain our observations.  Why do I believe in the
platonic
realm?  For the same reasons.

But we believe that electrons interact causally with us because we are made
from
similar stuff - and by doing so make themselves known to us...right?

How do Platonic objects interact causally with us?  Via a Platonic Field?
PFT -
Platonic Field Theory?

How did the warping of space and time cause Einsteins brain to figure out
relativity?

I think you are looking at it in the wrong way. Our brains seek good
explanations.
They sometimes find one.  That's all that is going on.

Now you say our explainations when it comes to mathematics are fiction, but
if that
is so, why not say the same of the physical theories?  Why not say the big
bang is
fiction, or matter is fiction?

They are stories which we intend to have referents independent of the
stories
(theories).

I don't see how this is any different from our mathematical theories though.

It is different.  It's confusing because arithmetic (to take an example) is both a theory
about discrete objects, 1apple + 1apple = 2apples, which requires a correct interpretation
like any theory of physics,  1raindrop + 1raindrop = 1raindrop, but it's also a closed
story without any external referents, s(0)+s(0)=s(s(0)).  This is what makes mathematics
(and logic and language) useful; you can abstract from the physical world to the Platonia
story, manipulate it by some rules, and if you did it right interpret the result back in
the physical world.  But that doesn't mean language and logic and mathematics exist in the
same sense.

Brent

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### Re: Prime Numbers

```

On 19 Sep 2012, at 21:51, Stephen P. King wrote:

On 9/19/2012 2:39 PM, Bruno Marchal wrote:

Dear Bruno,

Your remarks raise an interesting question: Could it be that
both the object and the means to generate (or perceive) it are of
equal importance ontologically?

Yes. It comes from the embedding of the subject in the objects,
that any monist theory has to do somehow.

In computer science, the universal (in the sense of Turing)
association i - phi_i, transforms N into an applicative algebra.
The numbers are both perceivers and perceived  according of their
place x and y in the relation of phi_x(y).

You can define the applicative operation by x # y = phi_x(y). The
combinators are not far away from this, and provides intensional
and extensional models.

I remind you that phi_i represent the ith computable function in
some effective universal enumeration of the partial computable
functions. You can take LISP, or c++ to fix the things.

Bruno

Dear Bruno,

You are highlighting of the key property of a number, that it can
both represent itself and some other number.

It is a key property of anything finite, not just number. Lists and
strings do this even more easily and naturally.

My question becomes, how does one track the difference between these
representations?

By quotations, like when using Gödel number, or quoted list in LISP.
Those are computable operations.

You speak of measures, but I have never seen how relative measures
are discussed or defined in modal logic.

?

A modal logic of probability is given by the behavior of the
probability one. In Kripke terms, P(x) = 1 in world alpha means that
x is realized in all worlds accessible from alpha, and (key point)
that we are not in a cul-de-sac world. This gives KD modal logics,
with K:  = [](p - q)-([]p - []q), and D:  []p - p. Of course
with [] for Gödel's beweisbar we don't have that D is a theorem, so
we ensure the D property by defining a new box, Bp = []p  t.

It seems to me that if we have the possibility of a Godel numbering
scheme on the integers, then we lose the ability to define a global
index set on subsets of those integers

?

unless we can somehow call upon something that is not a number and
thus not directly representable by a number..

?
Not clear. We appeal to something non representable by adding the
p in the definition of the modal box, but this is for the qualia and
first person notion. The Dt (and variant like DDt, DDBDt, etc.) should
give the first person plural, normally. many possibility remains, as
the quantum p - []p appears in the three main material variants
of: S4Grz1, Z1*, and X1*, for p arithmetic sigma_1 proposition (the
arithmetical UD).

Bruno

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

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### Re: Prime Numbers

```
On 9/20/2012 2:05 AM, Bruno Marchal wrote:
A modal logic of probability is given by the behavior of the probability one. In
Kripke terms, P(x) = 1 in world alpha means that x is realized in all worlds accessible
from alpha, and (key point) that we are not in a cul-de-sac world.

What does 'accessible' mean?  Generally speaking a different world is defined as not
accessible.  If you can go there, it's part of your same world.

Brent

This gives KD modal logics, with K:  = [](p - q)-([]p - []q), and D:  []p - p. Of
course with [] for Gödel's beweisbar we don't have that D is a theorem, so we ensure
the D property by defining a new box, Bp = []p  t.

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### Re: Prime Numbers

```

On 20 Sep 2012, at 18:14, meekerdb wrote:

On 9/20/2012 2:05 AM, Bruno Marchal wrote:
A modal logic of probability is given by the behavior of the
probability one. In Kripke terms, P(x) = 1 in world alpha means
that x is realized in all worlds accessible from alpha, and (key
point) that we are not in a cul-de-sac world.

What does 'accessible' mean?

In modal logic semantic, it is a technical world for any element in
set + a binary relation on it.

When applied to probability, the idea is to interpret the worlds by
the realization of some random experience, like throwing a coin would
lead to two worlds accessible, one with head, the other with tail. In
that modal (tail or head) is a certainty as (tail or head) is realized
everywhere in the accessible worlds.

Generally speaking a different world is defined as not accessible.
If you can go there, it's part of your same world.

Yes. OK. Sorry. Logician used the term world in a technical sense, and
the worlds can be anything, depending of which modal logic is used,
for what purpose, etc. Kripke semantic main used is in showing the
independence of formula in different systems.

Bruno

Brent

This gives KD modal logics, with K:  = [](p - q)-([]p - []q),
and D:  []p - p. Of course with [] for Gödel's beweisbar we
don't have that D is a theorem, so we ensure the D property by
defining a new box, Bp = []p  t.

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### Re: Prime Numbers

```

On 18 Sep 2012, at 18:02, meekerdb wrote:

On 9/18/2012 8:13 AM, Bruno Marchal wrote:

On 17 Sep 2012, at 22:25, meekerdb wrote:

But did anybody think z' = z^2 + c was interesting before that?

Yes. This was known by people like Fatou and Julia, in the early
1900.

I knew they considered what are now called fractal sets, but not
that particular one.

I think Julia worked on the Mandelbrot's Julia sets, notably. The
Mandelbrot set is a classifier of the Julia sets. You can define the
Mandelbrot set by the the set of z such that z belongs to its Julia
J(z).

The point is that in math and physics such object are hard to miss,
even if you need a computer to figure out what they looks like.

Iterating analytical complex functions leads to the Mandelbrot
fractal sets, or similar.

The computer has made those objects famous, but the mathematicians
know them both from logic (counterexamples to theorem in analysis,
like finding a continuous function nowhere derivable), or from
dynamic system and iteration.

If you iterate the trigonometric cosec function on the Gauss plane
C, you can't miss the Mandelbrot set.

But this iteration is a tedious and impractical *construction* which
in practice depends on computers.

In practice, yes. But if I remember well, the point is that the M sets
and alike are discovered, not fictitious human's construction. To see
them, we need a computer, but to see a circle you need a compass, or a
very massive object, like the sun or the moon, ...

In nature too as the following video does not illustrate too much
seriously :)

In such beautiful imagery it is generally overlooked that it is not
the Mandelbrot set you are looking at, but rather regions colored
according how close they are to the set (which cannot be seen at all).

Hmm, the inside mandelbrot set has dimension 2, as you can extrapolate
from the big spot, and then the filament ar made of little mandelbrot
set. So you can always see something. You are correct, for the
filaments: usually we can see them, as the little Mandelbrot sets are
too small. The coloring only makes them less thin and more easily
observable, but you would see the same basic shape with a pure black
and white picture. for example, everywhere on the main (straight)
antenna, there is a little mandelbrot set, so even black and white
resolution will make a thin line (with always too big pixels, of
course). Of course, the line can become thinner and thinner, so with
deeper zoom, you will have to darken the picture, and then light it
up, etc. Of course this is true also for a circle, or a straight line,
which are too thin to be seen, too, but we don't worry to draw them
with chalks or pens, which approximates them quite well.

You can see that phenomenon here:

Bruno

Brent

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### Re: Prime Numbers

```
On 9/19/2012 8:39 AM, Bruno Marchal wrote:

On 18 Sep 2012, at 18:02, meekerdb wrote:

On 9/18/2012 8:13 AM, Bruno Marchal wrote:

On 17 Sep 2012, at 22:25, meekerdb wrote:

But did anybody think z' = z^2 + c was interesting before that?

Yes. This was known by people like Fatou and Julia, in the early 1900.

I knew they considered what are now called fractal sets, but not that
particular one.

I think Julia worked on the Mandelbrot's Julia sets, notably. The
Mandelbrot set is a classifier of the Julia sets. You can define the
Mandelbrot set by the the set of z such that z belongs to its Julia J(z).

The point is that in math and physics such object are hard to miss,
even if you need a computer to figure out what they looks like.

Iterating analytical complex functions leads to the Mandelbrot
fractal sets, or similar.

The computer has made those objects famous, but the mathematicians
know them both from logic (counterexamples to theorem in analysis,
like finding a continuous function nowhere derivable), or from
dynamic system and iteration.

If you iterate the trigonometric cosec function on the Gauss plane
C, you can't miss the Mandelbrot set.

But this iteration is a tedious and impractical *construction* which
in practice depends on computers.

In practice, yes. But if I remember well, the point is that the M sets
and alike are discovered, not fictitious human's construction. To see
them, we need a computer, but to see a circle you need a compass, or a
very massive object, like the sun or the moon, ...

In nature too as the following video does not illustrate too much
seriously :)

In such beautiful imagery it is generally overlooked that it is not
the Mandelbrot set you are looking at, but rather regions colored
according how close they are to the set (which cannot be seen at all).

Hmm, the inside mandelbrot set has dimension 2, as you can extrapolate
from the big spot, and then the filament ar made of little mandelbrot
set. So you can always see something. You are correct, for the
filaments: usually we can see them, as the little Mandelbrot sets are
too small. The coloring only makes them less thin and more easily
observable, but you would see the same basic shape with a pure black
and white picture. for example, everywhere on the main (straight)
antenna, there is a little mandelbrot set, so even black and white
resolution will make a thin line (with always too big pixels, of
course). Of course, the line can become thinner and thinner, so with
deeper zoom, you will have to darken the picture, and then light it
up, etc. Of course this is true also for a circle, or a straight line,
which are too thin to be seen, too, but we don't worry to draw them
with chalks or pens, which approximates them quite well.

You can see that phenomenon here:

Bruno

Dear Bruno,

Your remarks raise an interesting question: Could it be that both
the object and the means to generate (or perceive) it are of equal
importance ontologically?

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Stephen

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### Re: Prime Numbers

```

On 19 Sep 2012, at 17:03, Stephen P. King wrote:

On 9/19/2012 8:39 AM, Bruno Marchal wrote:

On 18 Sep 2012, at 18:02, meekerdb wrote:

On 9/18/2012 8:13 AM, Bruno Marchal wrote:

On 17 Sep 2012, at 22:25, meekerdb wrote:

But did anybody think z' = z^2 + c was interesting before that?

Yes. This was known by people like Fatou and Julia, in the early
1900.

I knew they considered what are now called fractal sets, but not
that particular one.

I think Julia worked on the Mandelbrot's Julia sets, notably. The
Mandelbrot set is a classifier of the Julia sets. You can define
the Mandelbrot set by the the set of z such that z belongs to its
Julia J(z).

The point is that in math and physics such object are hard to miss,
even if you need a computer to figure out what they looks like.

Iterating analytical complex functions leads to the Mandelbrot
fractal sets, or similar.

The computer has made those objects famous, but the
mathematicians know them both from logic (counterexamples to
theorem in analysis, like finding a continuous function nowhere
derivable), or from dynamic system and iteration.

If you iterate the trigonometric cosec function on the Gauss
plane C, you can't miss the Mandelbrot set.

But this iteration is a tedious and impractical *construction*
which in practice depends on computers.

In practice, yes. But if I remember well, the point is that the M
sets and alike are discovered, not fictitious human's construction.
To see them, we need a computer, but to see a circle you need a
compass, or a very massive object, like the sun or the moon, ...

In nature too as the following video does not illustrate too much
seriously :)

In such beautiful imagery it is generally overlooked that it is
not the Mandelbrot set you are looking at, but rather regions
colored according how close they are to the set (which cannot be
seen at all).

Hmm, the inside mandelbrot set has dimension 2, as you can
extrapolate from the big spot, and then the filament ar made of
little mandelbrot set. So you can always see something. You are
correct, for the filaments: usually we can see them, as the little
Mandelbrot sets are too small. The coloring only makes them less
thin and more easily observable, but you would see the same basic
shape with a pure black and white picture. for example, everywhere
on the main (straight) antenna, there is a little mandelbrot set,
so even black and white resolution will make a thin line (with
always too big pixels, of course). Of course, the line can become
thinner and thinner, so with deeper zoom, you will have to darken
the picture, and then light it up, etc. Of course this is true
also for a circle, or a straight line, which are too thin to be
seen, too, but we don't worry to draw them with chalks or pens,
which approximates them quite well.

You can see that phenomenon here:

Bruno

Dear Bruno,

Your remarks raise an interesting question: Could it be that both
the object and the means to generate (or perceive) it are of equal
importance ontologically?

Yes. It comes from the embedding of the subject in the objects, that
any monist theory has to do somehow.

In computer science, the universal (in the sense of Turing)
association i - phi_i, transforms N into an applicative algebra. The
numbers are both perceivers and perceived  according of their place x
and y in the relation of phi_x(y).

You can define the applicative operation by x # y = phi_x(y). The
combinators are not far away from this, and provides intensional and
extensional models.

I remind you that phi_i represent the ith computable function in some
effective universal enumeration of the partial computable functions.
You can take LISP, or c++ to fix the things.

Bruno

--
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Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html

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### Re: Prime Numbers

```
On 9/19/2012 2:39 PM, Bruno Marchal wrote:

Dear Bruno,

Your remarks raise an interesting question: Could it be that both
the object and the means to generate (or perceive) it are of equal
importance ontologically?

Yes. It comes from the embedding of the subject in the objects, that
any monist theory has to do somehow.

In computer science, the universal (in the sense of Turing)
association i - phi_i, transforms N into an applicative algebra. The
numbers are both perceivers and perceived  according of their place x
and y in the relation of phi_x(y).

You can define the applicative operation by x # y = phi_x(y). The
combinators are not far away from this, and provides intensional and
extensional models.

I remind you that phi_i represent the ith computable function in some
effective universal enumeration of the partial computable functions.
You can take LISP, or c++ to fix the things.

Bruno

Dear Bruno,

You are highlighting of the key property of a number, that it can
both represent itself and some other number. My question becomes, how
does one track the difference between these representations? You speak
of measures, but I have never seen how relative measures are discussed
or defined in modal logic. It seems to me that if we have the
possibility of a Godel numbering scheme on the integers, then we lose
the ability to define a global index set on subsets of those integers
unless we can somehow call upon something that is not a number and thus
not directly representable by a number..

--
Onward!

Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html

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### Re: Prime Numbers

```

On 17 Sep 2012, at 22:25, meekerdb wrote:

But did anybody think z' = z^2 + c was interesting before that?

Yes. This was known by people like Fatou and Julia, in the early 1900.
Iterating analytical complex functions leads to the Mandelbrot fractal
sets, or similar.

The computer has made those objects famous, but the mathematicians
know them both from logic (counterexamples to theorem in analysis,
like finding a continuous function nowhere derivable), or from dynamic
system and iteration.

If you iterate the trigonometric cosec function on the Gauss plane C,
you can't miss the Mandelbrot set.

In nature too as the following video does not illustrate too much
seriously :)

Bruno

Bretn

On 9/17/2012 1:17 PM, Terren Suydam wrote:

I would say computers were the tool that allowed us to see it, like a
microscope allowed us to see bacteria, and a telescope stars.

On Mon, Sep 17, 2012 at 3:14 PM, meekerdbmeeke...@verizon.net
wrote:

On 9/17/2012 10:36 AM, Terren Suydam wrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?  How can you
make

sense of that in terms of the constructivist point of view

How can you make sense of it otherwise.  The Mandelbrot set is only
interesting because it became possible to construct it by use of
computers.

Brent

that you
are (I think) compelled to take if you argue against arithmetical
platonism?  It seems obvious that all possible intelligences would
discover the same forms of the Mandelbrot so long as they iterated
on

z' = z^2 + c, but maybe I am missing the point of your argument.

Terren

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### Re: Prime Numbers

```
On 9/18/2012 8:13 AM, Bruno Marchal wrote:

On 17 Sep 2012, at 22:25, meekerdb wrote:

But did anybody think z' = z^2 + c was interesting before that?

Yes. This was known by people like Fatou and Julia, in the early 1900.

I knew they considered what are now called fractal sets, but not that
particular one.

Iterating analytical complex functions leads to the Mandelbrot fractal sets, or
similar.

The computer has made those objects famous, but the mathematicians know them both from
logic (counterexamples to theorem in analysis, like finding a continuous function
nowhere derivable), or from dynamic system and iteration.

If you iterate the trigonometric cosec function on the Gauss plane C, you can't miss the
Mandelbrot set.

But this iteration is a tedious and impractical *construction* which in practice depends
on computers.

In nature too as the following video does not illustrate too much seriously :)

In such beautiful imagery it is generally overlooked that it is not the Mandelbrot set you
are looking at, but rather regions colored according how close they are to the set (which
cannot be seen at all).

Brent

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### Re: Prime Numbers

```On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam terren.suy...@gmail.comwrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?

I find fictionalism to be the most plausible view of mathematics, with all
that implies for the Mandelbrot set.

But ;et me turn the question around on you, if I can:

Do you have an explanation for how we discover mathematical objects and
otherwise interact with the Platonic realm?

How is it that we are able to reliably know things about Platonia?

I would have thought that quarks and electrons from which we appear to be
constituted would be indifferent to truth.

Which would fit with the fact that I seem to make a lot of mistakes.

But you think otherwise?

How can you make
sense of that in terms of the constructivist point of view that you
are (I think) compelled to take if you argue against arithmetical
platonism?  It seems obvious that all possible intelligences would
discover the same forms of the Mandelbrot so long as they iterated on
z' = z^2 + c, but maybe I am missing the point of your argument.

I will agree with you that all intelligences that start from the same
premises as you, and follow the same rules as inference as you, will also
draw the same conclusions about the Mandelbrot set as you do.

However - I do not agree with you that this amenable group exhausts the set
of all *possible* intelligences.

Could there be intelligences who start from vastly difference premises, and
use vastly different rules of inference, and draw vastly different
conclusions?

If not - what makes them impossible intelligences?

=*=

What are the limits of belief, do you think?  Is there any belief that is
so preposterous that even the maddest of the mad could not believe such a
thing?

And if there is no such belief - then is it conceivable that quarks and
electrons could configure themselves in such a way as to *cause* a being
who holds such beliefs to come into existence?

And if this is beyond the capacity of quarks and electrons, does it seem
possible that there might be some other form of matter with more exotic
properties that might be up to the task?

And if not - why not?

Rex

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### Re: Prime Numbers

```On Tue, Sep 18, 2012 at 10:19 PM, Rex Allen rexallen31...@gmail.com wrote:

On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam terren.suy...@gmail.com
wrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?

I find fictionalism to be the most plausible view of mathematics, with all
that implies for the Mandelbrot set.

I'm curious about what a plausible fictionalist account of the
Mandelbrot set could be. Is fictionalism the same as constructivism,
or the idea that knowledge doesn't exist outside of a mind?

But ;et me turn the question around on you, if I can:

Do you have an explanation for how we discover mathematical objects and
otherwise interact with the Platonic realm?

How is it that we are able to reliably know things about Platonia?

I think just doing logic and math - starting from axioms and proving
things from them - is interacting with the Platonic realm. It is
reliable because such proofs are necessarily valid no matter what sort
of computational agent is computing them. Bruno really takes it to the
next level though when he talks of interviewing ideally correct
machines and treating them as entities (strictly platonic, of course)
that can talk about what they can prove (believe).

I would have thought that quarks and electrons from which we appear to be
constituted would be indifferent to truth.

Which would fit with the fact that I seem to make a lot of mistakes.

But you think otherwise?

I didn't understand the above... what do quarks and electrons have to
do with arithmetical platonism?

How can you make
sense of that in terms of the constructivist point of view that you
are (I think) compelled to take if you argue against arithmetical
platonism?  It seems obvious that all possible intelligences would
discover the same forms of the Mandelbrot so long as they iterated on
z' = z^2 + c, but maybe I am missing the point of your argument.

I will agree with you that all intelligences that start from the same
premises as you, and follow the same rules as inference as you, will also
draw the same conclusions about the Mandelbrot set as you do.

However - I do not agree with you that this amenable group exhausts the set
of all *possible* intelligences.

I only meant that all possible intelligences that start from a
mathematics that includes addition, multiplication, and complex
numbers will find that if they iterate the function z' = z^2 + c, they
will find that some orbits become periodic or settle on a point, and
some escape to infinity. If they draw a graph of which orbits don't
escape, they will draw the Mandelbrot Set. All possible intelligences
that undertake that procedure will draw the same shape... and this
seems like discovery, not creation.

Could there be intelligences who start from vastly difference premises, and
use vastly different rules of inference, and draw vastly different
conclusions?

Of course, but then what they are doing doesn't relate to the Mandelbrot Set.

If not - what makes them impossible intelligences?

=*=

What are the limits of belief, do you think?  Is there any belief that is so
preposterous that even the maddest of the mad could not believe such a
thing?

I don't think so... based on my understanding of how mad maddest of

And if there is no such belief - then is it conceivable that quarks and
electrons could configure themselves in such a way as to *cause* a being who
holds such beliefs to come into existence?

I'm guessing you meant to say and if there is such a belief  I'm
having a tough time understanding where you're going with this... it
seems like an interesting line of questions, but I have no idea how it
relates to what we were discussing.

Terren

And if this is beyond the capacity of quarks and electrons, does it seem
possible that there might be some other form of matter with more exotic
properties that might be up to the task?

And if not - why not?

Rex

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### Re: Prime Numbers

```

On Sep 18, 2012, at 9:19 PM, Rex Allen rexallen31...@gmail.com wrote:

On Mon, Sep 17, 2012 at 1:36 PM, Terren Suydam terren.suy...@gmail.com
wrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?

I find fictionalism to be the most plausible view of mathematics,
with all that implies for the Mandelbrot set.

But ;et me turn the question around on you, if I can:

Do you have an explanation for how we discover mathematical
objects and otherwise interact with the Platonic realm?

We study and create theories about objects in the mathematical realm
just as we study and create theories about objects in the physical
realm.

It's not much different from how we develop theories about other
things we cannot interact with: the early universe, the cores of
stars, the insides of black holes, etc.

We test these theories by following their implications and seeing if
they lead to contridictions with other, more  established, facts.

Just as with physical theories, we ocasionally find that we need to
throw out the old set of theories (or axioms) for a new set which has
greater explanatory power.

How is it that we are able to reliably know things about Platonia?

The very idea of knowing implies a differentiation between true and
false.

to concepts of numbers.  (e.g., even numbers of not operators cancel
out, so counting them becomes an issue). Once you get counting and
numbers, you get the uncapturable infinite truths concerning them, and
infinite hierarchies if ever more powerful consistent theories.

Nearly any intelligent civilization that notices a partition between
true and false will eventyally get here.

I would have thought that quarks and electrons from which we appear
to be constituted would be indifferent to truth.

The unreasonable effectiveness of math in the physical sciences is yet
further support if Platonism.  If this, and seemingly infinite
physical universes exist, and they are mathematical structures, why
can't others exist?

Which would fit with the fact that I seem to make a lot of mistakes.

But you think otherwise?

We are imperfect beings.

Jason

How can you make
sense of that in terms of the constructivist point of view that you
are (I think) compelled to take if you argue against arithmetical
platonism?  It seems obvious that all possible intelligences would
discover the same forms of the Mandelbrot so long as they iterated on
z' = z^2 + c, but maybe I am missing the point of your argument.

I will agree with you that all intelligences that start from the
same premises as you, and follow the same rules as inference as you,
will also draw the same conclusions about the Mandelbrot set as you
do.

However - I do not agree with you that this amenable group exhausts
the set of all *possible* intelligences.

Could there be intelligences who start from vastly difference
premises, and use vastly different rules of inference, and draw
vastly different conclusions?

If not - what makes them impossible intelligences?

=*=

What are the limits of belief, do you think?  Is there any belief
that is so preposterous that even the maddest of the mad could not
believe such a thing?

And if there is no such belief - then is it conceivable that quarks
and electrons could configure themselves in such a way as to *cause*
a being who holds such beliefs to come into existence?

And if this is beyond the capacity of quarks and electrons, does it
seem possible that there might be some other form of matter with
more exotic properties that might be up to the task?

And if not - why not?

Rex

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### Re: Prime Numbers

```
On 9/18/2012 9:27 PM, Jason Resch wrote:
The unreasonable effectiveness of math in the physical sciences is yet further support
if Platonism.

I don't see that this follows.  If we invent language, including mathematics, to describe
our theories of the world that explains their effectiveness.  But it doesn't imply that
every description refers.  The mathematics of Maxwell's equations was (and is) very
effective, but we now believe they only approximately describe what exists.

Brent

If this, and seemingly infinite  physical universes exist, and they are mathematical
structures, why can't others exist?

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### Re: Prime Numbers

```On Mon, Sep 17, 2012 at 12:27 AM, Rex Allen rexallen31...@gmail.com wrote:

On Sun, Sep 16, 2012 at 6:10 PM, Stephen P. King stephe...@charter.netwrote:

HI Rex,

Nice post! Could you riff a bit on what the number PHI tells us about
this characteristic. How is it that it seems that our perceptions of the
world find anything that is close to a PHI valued relationship to be
beautiful?

Thanks Stephen!

Actually my initial example of numeracy isn't quite right, but it's not
important to the rest of the argument.

My main point is that you can get to the concept of prime numbers just
using relative magnitudes that we have an innate sense of.

I think an easier way to intuit prime numbers that can't be represented as
rectangles, only a 1-wide lines.

While the concept of primes is straight forward, there is an unending set
of not-so-obvious facts that we continue to discover about the Primes.  For
example:

The average distance between primes of size N is approximately the natural
log of N, yet we know of no way to predict where the next prime will
exactly be. ( http://en.wikipedia.org/wiki/Prime_gap )

Between N and 2N, there will always be at least one prime. (
http://en.wikipedia.org/wiki/Bertrand's_postulate )

There is a one-to-one correspondence, and method to get one from the other,
between perfect numbers and primes of the form ((2^p) - 1) (
http://en.wikipedia.org/wiki/Perfect_number#Even_perfect_numbers )

For any prime p, and any integer i where 0  i  p, i^p divided by p has a
remainder of i.  This almost never works for composite numbers.  (
http://en.wikipedia.org/wiki/Fermat's_little_theorem )  the exception for
composite numbers where this does hold are known as Carmichael numbers (
http://en.wikipedia.org/wiki/Carmichael_number ) but they are rare.

And there are an infinite number of other such patterns waiting to be
discovered.

Jason

As for the significance of PHI - well - I guess there's probably some
plausible sounding evolutionary story that could be told about that.

Though how satisfying or useful an explanation like that is just depends
on what you're after and what your interests are.

An explanation that might be useful in one context might be useless in
some other context.

Explanations are observer dependent.

Probably.

Rex

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### Re: Prime Numbers

```On Mon, Sep 17, 2012 at 2:05 AM, Jason Resch jasonre...@gmail.com wrote:

I think an easier way to intuit prime numbers that can't be represented as
rectangles, only a 1-wide lines.

While the concept of primes is straight forward, there is an unending set
of not-so-obvious facts that we continue to discover about the Primes.

Right.  My proposal is that this entire infinite edifice is built on top of
our innate sense of more, less, and equal.

Which I am tentatively advancing as the basis of an argument against
Platonism.

Rex

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### Re: Prime Numbers

```Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?  How can you make
sense of that in terms of the constructivist point of view that you
are (I think) compelled to take if you argue against arithmetical
platonism?  It seems obvious that all possible intelligences would
discover the same forms of the Mandelbrot so long as they iterated on
z' = z^2 + c, but maybe I am missing the point of your argument.

Terren

On Mon, Sep 17, 2012 at 12:32 PM, Rex Allen rexallen31...@gmail.com wrote:
On Mon, Sep 17, 2012 at 2:05 AM, Jason Resch jasonre...@gmail.com wrote:

I think an easier way to intuit prime numbers that can't be represented as
rectangles, only a 1-wide lines.

While the concept of primes is straight forward, there is an unending set
of not-so-obvious facts that we continue to discover about the Primes.

Right.  My proposal is that this entire infinite edifice is built on top of
our innate sense of more, less, and equal.

Which I am tentatively advancing as the basis of an argument against
Platonism.

Rex

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### Re: Prime Numbers

```
On 9/17/2012 10:36 AM, Terren Suydam wrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?  How can you make
sense of that in terms of the constructivist point of view

How can you make sense of it otherwise.  The Mandelbrot set is only interesting because it
became possible to construct it by use of computers.

Brent

that you
are (I think) compelled to take if you argue against arithmetical
platonism?  It seems obvious that all possible intelligences would
discover the same forms of the Mandelbrot so long as they iterated on
z' = z^2  + c, but maybe I am missing the point of your argument.

Terren

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### Re: Prime Numbers

```I would say computers were the tool that allowed us to see it, like a
microscope allowed us to see bacteria, and a telescope stars.

On Mon, Sep 17, 2012 at 3:14 PM, meekerdb meeke...@verizon.net wrote:
On 9/17/2012 10:36 AM, Terren Suydam wrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?  How can you make
sense of that in terms of the constructivist point of view

How can you make sense of it otherwise.  The Mandelbrot set is only
interesting because it became possible to construct it by use of computers.

Brent

that you
are (I think) compelled to take if you argue against arithmetical
platonism?  It seems obvious that all possible intelligences would
discover the same forms of the Mandelbrot so long as they iterated on
z' = z^2 + c, but maybe I am missing the point of your argument.

Terren

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### Re: Prime Numbers

```
But did anybody think z' = z^2 + c was interesting before that?

Bretn

On 9/17/2012 1:17 PM, Terren Suydam wrote:

I would say computers were the tool that allowed us to see it, like a
microscope allowed us to see bacteria, and a telescope stars.

On Mon, Sep 17, 2012 at 3:14 PM, meekerdbmeeke...@verizon.net  wrote:

On 9/17/2012 10:36 AM, Terren Suydam wrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?  How can you make
sense of that in terms of the constructivist point of view

How can you make sense of it otherwise.  The Mandelbrot set is only
interesting because it became possible to construct it by use of computers.

Brent

that you
are (I think) compelled to take if you argue against arithmetical
platonism?  It seems obvious that all possible intelligences would
discover the same forms of the Mandelbrot so long as they iterated on
z' = z^2 + c, but maybe I am missing the point of your argument.

Terren

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### Re: Prime Numbers

```Benoit Mandelbrot did. But what does interesting have to do with it?
Did anyone think that empty patch of sky was interesting before
Hubble turned it into one of the most amazing photos ever taken?

On Mon, Sep 17, 2012 at 4:25 PM, meekerdb meeke...@verizon.net wrote:
But did anybody think z' = z^2 + c was interesting before that?

Bretn

On 9/17/2012 1:17 PM, Terren Suydam wrote:

I would say computers were the tool that allowed us to see it, like a
microscope allowed us to see bacteria, and a telescope stars.

On Mon, Sep 17, 2012 at 3:14 PM, meekerdbmeeke...@verizon.net  wrote:

On 9/17/2012 10:36 AM, Terren Suydam wrote:

Rex,

Do you have a non-platonist explanation for the discovery of the
Mandelbrot set and the infinite complexity therein?  How can you make
sense of that in terms of the constructivist point of view

How can you make sense of it otherwise.  The Mandelbrot set is only
interesting because it became possible to construct it by use of
computers.

Brent

that you
are (I think) compelled to take if you argue against arithmetical
platonism?  It seems obvious that all possible intelligences would
discover the same forms of the Mandelbrot so long as they iterated on
z' = z^2 + c, but maybe I am missing the point of your argument.

Terren

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### Re: Prime Numbers

```
On 9/17/2012 2:45 PM, Terren Suydam wrote:

Benoit Mandelbrot did.

I wasn't aware of that.  Did he have a proof of the fractal nature of the set before he
calculated it?

Brent

But what does interesting have to do with it?
Did anyone think that empty patch of sky was interesting before
Hubble turned it into one of the most amazing photos ever taken?

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### Re: Prime Numbers

```On Mon, Sep 17, 2012 at 6:52 PM, meekerdb meeke...@verizon.net wrote:
On 9/17/2012 2:45 PM, Terren Suydam wrote:

Benoit Mandelbrot did.

I wasn't aware of that.  Did he have a proof of the fractal nature of the
set before he calculated it?

Brent

I don't know. I doubt it, I'm not even sure he had even coined the
term 'fractal' yet. I would be willing to bet though that what made
plotting z' = z^2 + c interesting to him was the same basic curiosity
that led astronomers to point Hubble at an empty patch of space
(despite the considerable cost of doing so): is there anything there
to be discovered?

Terren

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### Re: Prime Numbers

```
On 9/16/2012 3:43 PM, Rex Allen wrote:

It seems to me that numbers are based on our ability to judge relative
magnitudes:

Which is bigger, which is closer, which is heavier, etc.

Many animals have this ability - called numeracy.  Humans differ only
in the degree to which it is developed, and in our ability to build
higher level abstractions on top of this fundamental skill.

SO - prime numbers, I think, emerge from a peculiar characteristic of
our ability to judge relative magnitudes, and the way this feeds into
the abstractions we build on top of that ability.

=*=

Let’s say you take a board and divide it into 3 sections of equal
length (say, by drawing a line on it at the section boundaries).

Having done so – is there a way that you could have divided the board
into fewer sections of equal length so that every endpoint of a long
section can be matched to the end of a shorter section?

In other words – take two boards of equal length.  Divide one into 3
sections.  Divide the other into two sections.  The dividing point of
the two-section-board will fall right into the middle of the middle
section of the three-section-board.  There is no way to divide the
second board into fewer sections so that all of its dividing points
are matched against a dividing point on the longer board.

Because of this – three is a prime.  (Notice that I do not say:  “this
is because 3 is prime” – instead I reverse the causal arrow).

=*=

Let’s take two boards and divide the first one into 10 equally sized sections.

Now – there are two ways that we can divide the second board into a
smaller number of equally sized sections so that the end-points of
every section on this second board are matched to a sectional dividing
point on the first board (though the opposite will not be true):

We can divide the second board into either 2 sections (in which case
the dividing point will align with the end of the 5th section on the
first board),

OR

We can divide the second board into 5 sections – each of which is the
same size as two sections on the first board.

Because of this, the number 10 is not prime.

=*=

The entire field of Number Theory grows out of this peculiar
characteristic of how we judge relative magnitudes.

Do you think?

HI Rex,

Nice post! Could you riff a bit on what the number PHI tells us
of the world find anything that is close to a PHI valued relationship to
be beautiful?

--
Onward!

Stephen

http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html

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### Re: Prime Numbers

```On Sun, Sep 16, 2012 at 6:10 PM, Stephen P. King stephe...@charter.netwrote:

HI Rex,

Nice post! Could you riff a bit on what the number PHI tells us about
this characteristic. How is it that it seems that our perceptions of the
world find anything that is close to a PHI valued relationship to be
beautiful?

Thanks Stephen!

Actually my initial example of numeracy isn't quite right, but it's not
important to the rest of the argument.

My main point is that you can get to the concept of prime numbers just
using relative magnitudes that we have an innate sense of.

As for the significance of PHI - well - I guess there's probably some
plausible sounding evolutionary story that could be told about that.

Though how satisfying or useful an explanation like that is just depends on
what you're after and what your interests are.

An explanation that might be useful in one context might be useless in some
other context.

Explanations are observer dependent.

Probably.

Rex

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### Re: prime numbers etc

```Touche.
But I don't believe (in?) it - I am agnostic. Nonbeliever.
(SONG: I lost my turf in San Francisco)
J

On Thu, Sep 6, 2012 at 10:36 PM, Stathis Papaioannou stath...@gmail.comwrote:

On Fri, Sep 7, 2012 at 8:07 AM, John Mikes jami...@gmail.com wrote:
Stathis wrote (to Craig):

But you believe that the neurochemicals do things contrary to what
chemists would predict, for example an ion channel opening or closing
without any cause such as a change in transmembrane potential or
consistent with any scientific evidence. You interpret the existence
spontaneous neural activity as meaning that something magical like
this happens, but it doesn't mean that at all.

Stathis, you know ... whatever we state as 'knowledge about mind etc.'
is an
explanation for the little we think we learned - with lots we have no
idea
Like: chemicals ... potentials ... scientific evidence ... even cause
(meaning the
part we alredy know about) and mauch much more.
It is your turf, you must know about more we don't know only think we do.

It's your turf too - you're a chemist.

--
Stathis Papaioannou

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### Re: prime numbers etc

```On Fri, Sep 7, 2012 at 8:07 AM, John Mikes jami...@gmail.com wrote:
Stathis wrote (to Craig):

But you believe that the neurochemicals do things contrary to what
chemists would predict, for example an ion channel opening or closing
without any cause such as a change in transmembrane potential or
consistent with any scientific evidence. You interpret the existence
spontaneous neural activity as meaning that something magical like
this happens, but it doesn't mean that at all.

Stathis, you know ... whatever we state as 'knowledge about mind etc.' is an
explanation for the little we think we learned - with lots we have no idea
Like: chemicals ... potentials ... scientific evidence ... even cause
(meaning the
part we alredy know about) and mauch much more.
It is your turf, you must know about more we don't know only think we do.

It's your turf too - you're a chemist.

--
Stathis Papaioannou

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