Mathematical Universe Hypothesis

[kujawski...@gmail.com]

Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:

- applicability of mathematic, to natural sciences

- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.

- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.

What are your thoughts.

Regards

[Philip Thrift]

A well-written response is by Jeremy Butterfield [ https://en.wikipedia.org/wiki/Jeremy_Butterfield ]:

https://plus.maths.org/content/world-made-maths

extended arXiv version: https://arxiv.org/abs/1406.4348

(though I always chuckle at the Britishism "maths").

-pt

 

[Bruno Marchal]

On 28 Sep 2018, at 00:34, kujawski...@gmail.com wrote:

Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:

Yes, it was proved as a consequence of the Mechanist Hypothesis (well before Tegmark introduced it as an hypothesis).

- applicability of mathematic, to natural sciences

- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.

What Tegmark missed is the first person indeterminacy, which makes the physical reality into a sort of statistics on *all* mathematical structures. The physical reality is not a mathematical structure among others, but a precise mathematical phenomenon, occurring in arithmetic.

- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.

What are your thoughts.

If mechanism is false, both substantial physicalism and non substantial physicalism are wrong. Mechanism, in the cognitive science, makes the physical reality not Turing emulbale (“digital physics” is incoherent). Physics becomes reducible to machine’s psychology, or better, machine or number theology. Unfortunately a giant gap remain between physicists (who have the right question, but an inadequate metaphysics) and logician (who have the right tool but run away from theology and metaphysics).

The main advantage in using Mechanism (properly) is that incompleteness justified all the modes of the self, and this makes possible to get a precise theory of quanta and qualia.

In this list, we are a bit in advance on this, to be short. I can give references if asked. Actually I just gave them in some preceding posts.

What some people missed, is that there has never been any evidence for Aristotelian Primary Matter. Materialism will be abandoned as a lasting supersitition.

Bruno

Regards

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[Bruno Marchal]

That is still physicalism in disguise, and an implicit elimination of the first person.

Some critics there are valid, and have been presented here a long time ago. But other critic can be done. Maybe later … 

Bruno

-pt

 

[agrays...@gmail.com]

On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com wrote:

Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:

f

- applicability of mathematic, to natural sciences

- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.

- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.

What are your thoughts.

If it's what I think it is, it's demonstrably wrong. One counter example suffices; there are plane wave solutions to Maxwell's equations, but if you know what plane waves are, they clearly do NOT exist in physical reality. If this is correct, other models also fall by the wayside. AG

Regards

[Philip Thrift]

On Friday, September 28, 2018 at 2:44:18 AM UTC-5, Bruno Marchal wrote:

On 28 Sep 2018, at 00:34, kujawski...@gmail.com wrote:

Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:

Yes, it was proved as a consequence of the Mechanist Hypothesis (well before Tegmark introduced it as an hypothesis).

- applicability of mathematic, to natural sciences

- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.

What Tegmark missed is the first person indeterminacy, which makes the physical reality into a sort of statistics on *all* mathematical structures. The physical reality is not a mathematical structure among others, but a precise mathematical phenomenon, occurring in arithmetic.

- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.

What are your thoughts.

If mechanism is false, both substantial physicalism and non substantial physicalism are wrong. Mechanism, in the cognitive science, makes the physical reality not Turing emulbale (“digital physics” is incoherent). Physics becomes reducible to machine’s psychology, or better, machine or number theology. Unfortunately a giant gap remain between physicists (who have the right question, but an inadequate metaphysics) and logician (who have the right tool but run away from theology and metaphysics).

The main advantage in using Mechanism (properly) is that incompleteness justified all the modes of the self, and this makes possible to get a precise theory of quanta and qualia.

In this list, we are a bit in advance on this, to be short. I can give references if asked. Actually I just gave them in some preceding posts.

What some people missed, is that there has never been any evidence for Aristotelian Primary Matter. Materialism will be abandoned as a lasting supersitition.

Bruno

On the other side it is held that numbers - universal numbers - actually exist (arithmeticalism) is superstition. 

Even the texts in which the definition of the universal numbers appear are material: They are seen as electronic dots on a screen in a PDF viewer, or ink glyphs on paper in a printout, etc. But there is nothing more than that . 

There is nothing outside matter.

(Materialism is not physicalism.)

- pt

[agrays...@gmail.com]

Space is outside matter. Why can't you guys admit you're wrong about the MUH? I gave a solid counter-example that puts it in the trash heap of erroneous theories. AG

[smitra]

I've written up my thoughts here:

https://fqxi.org/data/essay-contest-files/Mitra_without.pdf

Whether or not there exists a mathematical multiverse is, of course,
debatable. However, a multiverse of any sort that's large enough to
give rise of identical copies of observers, will affect the laws of
physics. Since the laws of physics are what we observe them to be, this
means that what we observe already includes the effects of the
multiverse, i.e. the laws of physics actually describe some sector of
the multiverse rather than a particular universe.

This then means that if the mathematical multiverse hypothesis is
correct, the laws of quantum mechanics should be considered to give an
effective description of that multiverse. The set of all your copies
considered as algorithms that are in the same state (your state simply
refers to what algorithm is running including what information is being
processed), are distributed over the entire multiverse, they are not all
in the same universe. To derive the effective laws of physics, one needs
to do statistics over the ensemble of identical observers. This involves
performing summations over the multiverse, but these summations are with
a constraint that says that some given observer is present.
Mathematically it is more convenient to perform unrestricted summations,
a convenient way to take into account constraints is by including them
using phase factors.

For example, if we want to compute a summation over a function f(n1, n2,
n3, n4,....) where the nj are integers, we can just sum over n1,
n2,...etc., independently. But suppose that we need to sum over f(n1,
n2, n3, n4,....), such that some other function g(n1,n2,n3,...) is kept
fixed to some constant value M. The way one handles that is by summing
over the function f(n1, n2, n3, n4,....) Exp[i t g (n1,n2,...)] without
any restrictions. This summation then becomes a function of the
parameter t. By taking the Fourier transform of this function, one can
extract the component of Exp[i t M] of that function, obviously only
terms of the original summation such that g(n1,n2,...) takes the value
M, contribute to that.

In case of keeping track of a given observer, one needs to include a
vast number of constraints, one can then get to a something similar to
the path integral formulation of QM. But I have no rigorous arguments at
this moment that one can really reproduce QM this way.


Saibal

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[Philip Thrift]

I don't know. I think physicists say that there is no place in space where there is actually nothing at all (and everything is somewhere).

- pt 

[Bruno Marchal]

On 28 Sep 2018, at 14:42, Philip Thrift <cloud...@gmail.com> wrote:

On Friday, September 28, 2018 at 2:44:18 AM UTC-5, Bruno Marchal wrote:

On 28 Sep 2018, at 00:34, kujawski...@gmail.com wrote:

Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:

Yes, it was proved as a consequence of the Mechanist Hypothesis (well before Tegmark introduced it as an hypothesis).

- applicability of mathematic, to natural sciences

- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.

What Tegmark missed is the first person indeterminacy, which makes the physical reality into a sort of statistics on *all* mathematical structures. The physical reality is not a mathematical structure among others, but a precise mathematical phenomenon, occurring in arithmetic.

- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.

What are your thoughts.

If mechanism is false, both substantial physicalism and non substantial physicalism are wrong. Mechanism, in the cognitive science, makes the physical reality not Turing emulbale (“digital physics” is incoherent). Physics becomes reducible to machine’s psychology, or better, machine or number theology. Unfortunately a giant gap remain between physicists (who have the right question, but an inadequate metaphysics) and logician (who have the right tool but run away from theology and metaphysics).

The main advantage in using Mechanism (properly) is that incompleteness justified all the modes of the self, and this makes possible to get a precise theory of quanta and qualia.

In this list, we are a bit in advance on this, to be short. I can give references if asked. Actually I just gave them in some preceding posts.

What some people missed, is that there has never been any evidence for Aristotelian Primary Matter. Materialism will be abandoned as a lasting supersitition.

Bruno

On the other side it is held that numbers - universal numbers - actually exist (arithmeticalism) is superstition. 

With Turing’s definition (or any equivalent one (Church, Kleene, Post, …), the existence of universal number is a theorem of Peano Arithmetic. Robinson arithmetic is itself a universal number, but has not the cognitive ability to prove it. But Peano can, without any problem. 

It is has nothing to do with arithmeticalism. Most logicians are materialist (without necessarily vindicating it), but none doubt that the universal numbers exist in the same sense (of existence) than the prime numbers.

Even the texts in which the definition of the universal numbers appear are material:

Yes, but that does not make it existing ontologically. Keep in mind that Plato and Aristotle differs on the very criterion of existence. To see, touch, observe, measure is not a criterion of existence, as we can dream this things, and then with mechanism we have a model where number existence is enough to have the dreams.

Observing and touching matter is not an argument of existence, unless you assume materialism at the start. But when we do metaphysics seriously, we cannot assume any ontology other that what we need to develop the discourse.

They are seen as electronic dots on a screen in a PDF viewer, or ink glyphs on paper in a printout, etc. But there is nothing more than that . 

There is nothing outside matter.

That is strong materialism.

That is a quite strong metaphysical assumption. It is incompatible with Mechanism in cognitive science.

In fact, even weak materialism (matter exists ontologically and is not reducible to anything else) is incompatible with Mechanism.

(Materialism is not physicalism.)

Physicalism does not imply materialism. OK.

Yet, I define matter by “the object of study of physics”, or the study of the observable mode, making strong materialism implying physicalism.

Bruno

- pt

[Bruno Marchal]

With mathematicalism, we don’t assume that there is a (primitive/irreducible) physical reality.

You are begging the question.

Since the antic dream argument, we know that observation cannot be used to prove that anything exist, but an observer.

Bruno

If this is correct, other models also fall by the wayside. AG

Regards

[Bruno Marchal]

> On 28 Sep 2018, at 17:09, smitra <smi...@zonnet.nl> wrote:
>
> On 28-09-2018 00:34, kujawski...@gmail.com wrote:
>> Hello I think this good forum for this topic - what do you think about
>> Mathematical Universe, there are very big arguments for that
>> hypothesis:
>> - applicability of mathematic, to natural sciences
>> - all we discovere are structures and I didnt find explanation of the
>> diference beetwen physical structures and mathematical structures.
>> - scientists and philosophers of science tend to affirm belive in
>> diverse structure and homogeneous substance (neutral monism) or
>> mathematicism vide Ladyman, Ross, French, Tegmark etc.
>> What are your thoughts.
>> Regards
>
> I've written up my thoughts here:
>
> https://fqxi.org/data/essay-contest-files/Mitra_without.pdf
>
> Whether or not there exists a mathematical multiverse is, of course, debatable.

Lawyere has tried, with CAT, the category of all categories, but this did not work, and he discover the toposes, independently of Grothendieck who discovered them in abstract geometry.

The notion of the whole of mathematics is not definable in mathematics, and I am not sure it makes any sense.

Fortunately, with mechanism; we can limit ourselves to the arithmetical truth, and eventually to the sigma_1 arithmetical truth, which is related to the universal dovetailer (which is sigma_1 provability). G* proves them equivalent, but G does not, so the equivalence of sigma_1 truth and sigma_1 provability is known only by “God".

> However, a multiverse of any sort that's large enough to give rise of identical copies of observers, will affect the laws of physics.

Assuming mechanism, or wekemening of it. Yes.

> Since the laws of physics are what we observe them to be, this means that what we observe already includes the effects of the multiverse, i.e. the laws of physics actually describe some sector of the multiverse rather than a particular universe.
>
> This then means that if the mathematical multiverse hypothesis is correct, the laws of quantum mechanics should be considered to give an effective description of that multiverse. The set of all your copies considered as algorithms that are in the same state (your state simply refers to what algorithm is running including what information is being processed), are distributed over the entire multiverse, they are not all in the same universe. To derive the effective laws of physics, one needs to do statistics over the ensemble of identical observers. This involves performing summations over the multiverse, but these summations are with a constraint that says that some given observer is present. Mathematically it is more convenient to perform unrestricted summations, a convenient way to take into account constraints is by including them using phase factors.
>
> For example, if we want to compute a summation over a function f(n1, n2, n3, n4,....) where the nj are integers, we can just sum over n1, n2,...etc., independently. But suppose that we need to sum over f(n1, n2, n3, n4,....), such that some other function g(n1,n2,n3,...) is kept fixed to some constant value M. The way one handles that is by summing over the function f(n1, n2, n3, n4,....) Exp[i t g (n1,n2,...)] without any restrictions. This summation then becomes a function of the parameter t. By taking the Fourier transform of this function, one can extract the component of Exp[i t M] of that function, obviously only terms of the original summation such that g(n1,n2,...) takes the value M, contribute to that.
>
> In case of keeping track of a given observer, one needs to include a vast number of constraints, one can then get to a something similar to the path integral formulation of QM. But I have no rigorous arguments at this moment that one can really reproduce QM this way.

The universal machine have been proved to say this, but in a more “arithmeticalist setting”.

The physical reality becomes the border of the Turing universal machine's mindscape.

Bruno

>
>
> Saibal
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[Bruno Marchal]

Everting physical is somewhere, except the physical universe, if that exists.

But with mechanism, there is no physical universe. The physical reality is entirely phenomenological. 

A persistent illusion of numbers, living in deep and linear histories…

Bruno

- pt 

[agrays...@gmail.com]

On Friday, September 28, 2018 at 4:04:41 PM UTC, Bruno Marchal wrote:

On 28 Sep 2018, at 11:32, agrays...@gmail.com wrote:

On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com wrote:

Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:

f

- applicability of mathematic, to natural sciences

- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.

- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.

What are your thoughts.

If it's what I think it is, it's demonstrably wrong. One counter example suffices; there are plane wave solutions to Maxwell's equations, but if you know what plane waves are, they clearly do NOT exist in physical reality.

With mathematicalism, we don’t assume that there is a (primitive/irreducible) physical reality.

You are begging the question.

In what way?  The MUH says, for example, that for every mathematical solution or equation, there is a (perceived) physical universe mapped identically from, or into that solution or equation. I gave a simple counter example. AG

[Philip Thrift]

On Friday, September 28, 2018 at 11:00:58 AM UTC-5, Bruno Marchal wrote:

Yet, I define matter by “the object of study of physics”, or the study of the observable mode, making strong materialism implying physicalism.

Bruno

I think (along with Philip Goff*) that physics is not complete in its study of matter. Either a new physics is needed, of there is a theoretical gap between physics and brains.

* https://twitter.com/philipthrift/status/1045666843304890368

- pt

[kujawski...@gmail.com]

 

Thank you everybody for your responses.

Bruno Marchal I looked at your statement, they are very interesting but some very good neruoscientists argue that brain is not like computer

Here for example (4min video) Edelman:

https://www.youtube.com/watch?v=qmyfQY4TaVc

Please give me your thought on that.

[agrays...@gmail.com]

On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com wrote:

 

Thank you everybody for your responses.

Bruno Marchal I looked at your statement, they are very interesting but some very good neruoscientists argue that brain is not like computer

Here for example (4min video) Edelman:

https://www.youtube.com/watch?v=qmyfQY4TaVc

The question can be turned around. Why would anyone think a brain is strongly comparable or identical to a computer? It has some superficial similarities such as being able to store memory and logical functions (which are simulated by a computer), but its cells are not two state systems like computer transistors. AG

[agrays...@gmail.com]

On Friday, September 28, 2018 at 4:37:17 PM UTC, agrays...@gmail.com wrote:

On Friday, September 28, 2018 at 4:04:41 PM UTC, Bruno Marchal wrote:

On 28 Sep 2018, at 11:32, agrays...@gmail.com wrote:

On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com wrote:

Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:

f

- applicability of mathematic, to natural sciences

- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.

- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.

What are your thoughts.

If it's what I think it is, it's demonstrably wrong. One counter example suffices; there are plane wave solutions to Maxwell's equations, but if you know what plane waves are, they clearly do NOT exist in physical reality.

With mathematicalism, we don’t assume that there is a (primitive/irreducible) physical reality.

You are begging the question.

In what way?  The MUH says, for example, that for every mathematical solution or equation, there is a (perceived) physical universe mapped identically from, or into that solution or equation. I gave a simple counter example. AG

I used "perceived" to indicate no bias for or against a material universe. We are always dealing with observations, so if the MUH were correct, it would mean we could observe plane waves (or for that matter, advanced waves). But the former can never be observed in any universe unless you want to posit instantaneous propagation initially, at their creation, and on-going as the amplitude changes immediately in all directions to infinity as the wave propagates. As for advanced waves, they have never been observed and their existence likely trashes causality. So IMO, the MUH is easily falsified. AG

[Bruno Marchal]

On 28 Sep 2018, at 18:37, agrays...@gmail.com wrote:

On Friday, September 28, 2018 at 4:04:41 PM UTC, Bruno Marchal wrote:

On 28 Sep 2018, at 11:32, agrays...@gmail.com wrote:

On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com wrote:

Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:

f

- applicability of mathematic, to natural sciences

- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.

- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.

What are your thoughts.

If it's what I think it is, it's demonstrably wrong. One counter example suffices; there are plane wave solutions to Maxwell's equations, but if you know what plane waves are, they clearly do NOT exist in physical reality.

With mathematicalism, we don’t assume that there is a (primitive/irreducible) physical reality.

You are begging the question.

In what way?  The MUH says, for example, that for every mathematical solution or equation, there is a (perceived) physical universe mapped identically from, or into that solution or equation. I gave a simple counter example. AG

If that is the MUH, then that it is plainly ridiculous, indeed. To have a perceived universe, you need a measure on the computation/sigma-sentences. The physical emerges from an arithmetical phenomenon (assuming mechanism in cognitive science). 

The version of mathematicalism implied by mechanism does not lead any choice for the “physical reality”, it has to be a statistic on computations structured by the “observable” mode of self-reference. That indeed predicts quantum logic, and the many “histories” interpretation of arithmetic. Oracle are not impossible, but there are no evidence for them, and should be invoked in last resort (a bit like the “Alien” in cosmology).

The empirical evidence is that there is no physical universe at all.

Bruno

[Bruno Marchal]

On 28 Sep 2018, at 20:26, Philip Thrift <cloud...@gmail.com> wrote:

On Friday, September 28, 2018 at 11:00:58 AM UTC-5, Bruno Marchal wrote:

Yet, I define matter by “the object of study of physics”, or the study of the observable mode, making strong materialism implying physicalism.

Bruno

I think (along with Philip Goff*) that physics is not complete in its study of matter.

I agree. Physics can predict an eclipse, but is unable to predict why we feel to see an eclipse when we can predict it.

It uses to that effect an identity thesis linking “my mind” to “my brain”, but with mechanism, we all have an infinity of brain in arithmetic. 

Either a new physics is needed, of there is a theoretical gap between physics and brains.

With mechanism, it is easy to understand that there is a theoretical gap between brains, mind, and physics.

But Mechanism solves that problem, although probably not like the Aristotelians (weak materialist) would like.

Bruno

* https://twitter.com/philipthrift/status/1045666843304890368

- pt

[Bruno Marchal]

I don’t like to be negative on people. Edelman makes a lot of good points, but he seems to have no idea what a computer is. He has, like many, a reductionist conception of machine, which is totally impossible to maintain after Gödel’s discovery of Incompleteness in 1930 (transformed by Turing, Kleene, and some others). 

Before Gödel, mathematicians hoped to reduced the mathematics of the infinite by the mathematics of finite system having discourse on the infinite. But Gödel found that this is not only impossible, but that even by using the mathematics of the infinite, we can control the mathematics of the *finite*. 

The responsible of incompleteness has been found, by Tarski (somehow), and is the (Turing) universal machine. We know today that we know nothing about them, and if the Church Turing thesis is true, we will never know them completely, we can only scratch the surface. Those negative result are constructive. Today we know that the universal machine, once “rich enough cognitively” (which does not ask for much) is aware that it has a soul that this soul is not a machine, and that this can be verified empirically, because the theory of matter becomes a sub-theory of that soul theory. Here soul is basically the representational body (the relative code) in conjunction with a notion of truth. 

Bruno

[agrays...@gmail.com]

On Saturday, September 29, 2018 at 6:40:05 AM UTC, Bruno Marchal wrote:

On 28 Sep 2018, at 18:37, agrays...@gmail.com wrote:

On Friday, September 28, 2018 at 4:04:41 PM UTC, Bruno Marchal wrote:

On 28 Sep 2018, at 11:32, agrays...@gmail.com wrote:

On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com wrote:

Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:

f

- applicability of mathematic, to natural sciences

- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.

- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.

What are your thoughts.

If it's what I think it is, it's demonstrably wrong. One counter example suffices; there are plane wave solutions to Maxwell's equations, but if you know what plane waves are, they clearly do NOT exist in physical reality.

With mathematicalism, we don’t assume that there is a (primitive/irreducible) physical reality.

You are begging the question.

In what way?  The MUH says, for example, that for every mathematical solution or equation, there is a (perceived) physical universe mapped identically from, or into that solution or equation. I gave a simple counter example. AG

If that is the MUH, then that it is plainly ridiculous, indeed. To have a perceived universe, you need a measure on the computation/sigma-sentences. The physical emerges from an arithmetical phenomenon (assuming mechanism in cognitive science). 

The version of mathematicalism implied by mechanism does not lead any choice for the “physical reality”, it has to be a statistic on computations structured by the “observable” mode of self-reference. That indeed predicts quantum logic, and the many “histories” interpretation of arithmetic. Oracle are not impossible, but there are no evidence for them, and should be invoked in last resort (a bit like the “Alien” in cosmology).

The empirical evidence is that there is no physical universe at all.

Bruno

This double-talk nonsense IMO. I clearly gave a counter-example to the MUH, falsifying it. Moreover, I explained clearly why I used "perceived". I just meant that plane waves can never be observed, and since they are solutions to Maxwell's equations, the MUH is false. Deal with that directly and stop with the double talk about the non-existence of the physical universe. That's not even an issue, since I am only dealing with what can be observed. AG

[Bruno Marchal]

A bacteria is already a computer (at least), and a neurone is already a rather sophisticated society of bacteria and viruses, plausibly enough. So, a society of billions of neurons should not be compared to transistors. The substitution level is plausibly much lower than the level of neurons.

But we don’t know in Nature anything which at some level is not emulable by a computer, except for controversial notion like

A) primary matter (if that exists, it is not emulable by a computer)

B) the reduction of the wave packet (if that exists, it is provably not emulable by a computer).

But there are no evidence neither for A) nor for B).

Bruno

Please give me your thought on that.

[Bruno Marchal]

On 29 Sep 2018, at 09:16, agrays...@gmail.com wrote:

On Saturday, September 29, 2018 at 6:40:05 AM UTC, Bruno Marchal wrote:

On 28 Sep 2018, at 18:37, agrays...@gmail.com wrote:

On Friday, September 28, 2018 at 4:04:41 PM UTC, Bruno Marchal wrote:

On 28 Sep 2018, at 11:32, agrays...@gmail.com wrote:

On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com wrote:

Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:

f

- applicability of mathematic, to natural sciences

- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.

- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.

What are your thoughts.

If it's what I think it is, it's demonstrably wrong. One counter example suffices; there are plane wave solutions to Maxwell's equations, but if you know what plane waves are, they clearly do NOT exist in physical reality.

With mathematicalism, we don’t assume that there is a (primitive/irreducible) physical reality.

You are begging the question.

In what way?  The MUH says, for example, that for every mathematical solution or equation, there is a (perceived) physical universe mapped identically from, or into that solution or equation. I gave a simple counter example. AG

If that is the MUH, then that it is plainly ridiculous, indeed. To have a perceived universe, you need a measure on the computation/sigma-sentences. The physical emerges from an arithmetical phenomenon (assuming mechanism in cognitive science). 

The version of mathematicalism implied by mechanism does not lead any choice for the “physical reality”, it has to be a statistic on computations structured by the “observable” mode of self-reference. That indeed predicts quantum logic, and the many “histories” interpretation of arithmetic. Oracle are not impossible, but there are no evidence for them, and should be invoked in last resort (a bit like the “Alien” in cosmology).

The empirical evidence is that there is no physical universe at all.

Bruno

This double-talk nonsense IMO. I clearly gave a counter-example to the MUH,

You want make some mathematical object physical real. That assume some physical reality, which cannot be done.

To say that a mathematical object  exist physically, does not make sense. It starts with a category error.

No mathematical object can be a physical object. But what remains possible is that a physical object belongs to the dream of a person supported by (infinity) of computation (which are arithmetical object a priori).

falsifying it. Moreover, I explained clearly why I used "perceived". I just meant that plane waves can never be observed,

You don’t need to go that far. The numbers 0, 1, 2, … cannot be observed. No mathematical object can be observed. They do not belong to the category of what can be observed.

Now, an observation might be explained by a sort of arithmetical prestidigitation. Some numbers can make some numbers believing in a lot of things.

and since they are solutions to Maxwell's equations, the MUH is false.

The MUH is only the idea that the physical might be a part of the mathematical. Not that mathematical things have to exist physically. 

Tp put it simply, mathematicalism is the idea that there is no physical universe at all.

There is no time, no space, no energy, those are just Löbian machine's elaborate fiction to figure out our indexical local geography.

Look at a experimental physicist. He measured numbers, and infer relation between numbers, and then avoid the qualia:consciousness question, which indeed is only “physical” in string version of materialism, which requires the brain and body to be infinite entities.

To refute mathematicalism, you need a theory of matter giving an observable role to some infinite entities, having secondary observable consequence. Mechanism is a bit like that: if the physics deducible from mechanism is different from what we observe, that might be used to infer such infinite entities, but the preliminary results, and QM, does not go in that direction.

Deal with that directly and stop with the double talk about the non-existence of the physical universe. That's not even an issue, since I am only dealing with what can be observed. AG

If you take “observation” as a criteria of reality, you assume right at the start the theology of Aristotle.

I just say that this is incompatible with the idea that a brain is Turing emulable. 

Study the sane04 paper, which explain all this, and ask question if something is unclear.

Bruno

[agrays...@gmail.com]

On Saturday, September 29, 2018 at 8:57:54 AM UTC, Bruno Marchal wrote:

On 29 Sep 2018, at 09:16, agrays...@gmail.com wrote:

On Saturday, September 29, 2018 at 6:40:05 AM UTC, Bruno Marchal wrote:

On 28 Sep 2018, at 18:37, agrays...@gmail.com wrote:

On Friday, September 28, 2018 at 4:04:41 PM UTC, Bruno Marchal wrote:

On 28 Sep 2018, at 11:32, agrays...@gmail.com wrote:

On Friday, September 28, 2018 at 1:02:36 AM UTC, kujawski...@gmail.com wrote:

Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:

f

- applicability of mathematic, to natural sciences

- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.

- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.

What are your thoughts.

If it's what I think it is, it's demonstrably wrong. One counter example suffices; there are plane wave solutions to Maxwell's equations, but if you know what plane waves are, they clearly do NOT exist in physical reality.

With mathematicalism, we don’t assume that there is a (primitive/irreducible) physical reality.

You are begging the question.

In what way?  The MUH says, for example, that for every mathematical solution or equation, there is a (perceived) physical universe mapped identically from, or into that solution or equation. I gave a simple counter example. AG

If that is the MUH, then that it is plainly ridiculous, indeed. To have a perceived universe, you need a measure on the computation/sigma-sentences. The physical emerges from an arithmetical phenomenon (assuming mechanism in cognitive science). 

The version of mathematicalism implied by mechanism does not lead any choice for the “physical reality”, it has to be a statistic on computations structured by the “observable” mode of self-reference. That indeed predicts quantum logic, and the many “histories” interpretation of arithmetic. Oracle are not impossible, but there are no evidence for them, and should be invoked in last resort (a bit like the “Alien” in cosmology).

The empirical evidence is that there is no physical universe at all.

Bruno

This double-talk nonsense IMO. I clearly gave a counter-example to the MUH,

You want make some mathematical object physical real. That assume some physical reality, which cannot be done.

This is the MUH, not what I want or believe. AG

https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis

Tegmark's MUH is: Our external physical reality is a mathematical structure.^[3] That is, the physical universe is not merely described by mathematics, but is mathematics (specifically, a mathematical structure). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Observers, including humans, are "self-aware substructures (SASs)". In any mathematical structure complex enough to contain such substructures, they "will subjectively perceive themselves as existing in a physically 'real' world".^[4]

To say that a mathematical object  exist physically, does not make sense. It starts with a category error.

I don't think you know what the MUH is. I have falsified it. AG

[Philip Thrift]

The arithmeticalist thinks matter is fiction.

The materialist thinks arithmetic is fiction.

That's all I know. :)

- pt

[agrays...@gmail.com]

You can't understand how I falsified the MUH because you don't know what it is. It claims that all mathematical objects exist in "physical" reality, which is sort-of isomorphic or in some sense identical to these objects. That is, no dichotomy between "physical" and mathematical objects, and all the latter including plane waves exist in this reality. But you will never observe a plane wave, so the MUH is falsified. AG

[Philip Thrift]

On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com wrote:

 It claims that all mathematical objects exist in "physical" reality, which is sort-of isomorphic or in some sense identical to these objects. That is, no dichotomy between "physical" and mathematical objects, and all the latter including plane waves exist in this reality. But you will never observe a plane wave, so the MUH is falsified. AG 

1. Tegmark claims everything in the universe is mathematical - that is, the universe consists of mathematical objects.

2. Tegmark also says that infinities should be eliminated from physics - in fact, infinities are ruining physics.

[ http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/ ]

So then via Tegmark there can be no real continuous (infinitely divisible) objects like (mathematical) waves, putting 1 and 2 together. Only particular mathematical objects exist.

 - pt

[agrays...@gmail.com]

On Saturday, September 29, 2018 at 10:41:42 AM UTC, Philip Thrift wrote:

On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com wrote:

 It claims that all mathematical objects exist in "physical" reality, which is sort-of isomorphic or in some sense identical to these objects. That is, no dichotomy between "physical" and mathematical objects, and all the latter including plane waves exist in this reality. But you will never observe a plane wave, so the MUH is falsified. AG 

1. Tegmark claims everything in the universe is mathematical - that is, the universe consists of mathematical objects.

2. Tegmark also says that infinities should be eliminated from physics - in fact, infinities are ruining physics.

[ http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/ ]ac

Bruno wrote 1 & 2.  AG

So then via Tegmark there can be no real continuous (infinitely divisible) objects like (mathematical) waves, putting 1 and 2 together. Only particular mathematical objects exist.

According to Wiki, and what I've heard from its adherents, the MUH posits that ALL mathematical object or entities exist in nature. But plane waves do not exist in nature. (Do you know what they are?) So the MUH as claimed by Wiki and its adherents is falsified. AG

 - pt

[agrays...@gmail.com]

On Saturday, September 29, 2018 at 7:16:41 AM UTC, Bruno Marchal wrote:

On 28 Sep 2018, at 21:00, agrays...@gmail.com wrote:

On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com wrote:

 

Thank you everybody for your responses.

Bruno Marchal I looked at your statement, they are very interesting but some very good neruoscientists argue that brain is not like computer

Here for example (4min video) Edelman:

https://www.youtube.com/watch?v=qmyfQY4TaVc

The question can be turned around. Why would anyone think a brain is strongly comparable or identical to a computer? It has some superficial similarities such as being able to store memory and logical functions (which are simulated by a computer), but its cells are not two state systems like computer transistors. AG

A bacteria is already a computer (at least),

Really? Then you should be able to identify the entities that store binary information. And where is the clock which pulses and advances the instruction pointer? And where is the instruction pointer located? AG

[Philip Thrift]

In his original arXiv  [ https://arxiv.org/abs/0704.0646 ] and in other places he presents MUH as different "levels", so a level-one MUH would have different mathematics than a level-four MUH, etc.

To be honest, I find MUH to be both boring, adding nothing to science, and somewhat (or maybe a lot) confused.

- pt

[Philip Thrift]

On Saturday, September 29, 2018 at 6:34:15 AM UTC-5, agrays...@gmail.com wrote:

On Saturday, September 29, 2018 at 7:16:41 AM UTC, Bruno Marchal wrote:

A bacteria is already a computer (at least),

Really? Then you should be able to identify the entities that store binary information. And where is the clock which pulses and advances the instruction pointer? And where is the instruction pointer located? AG

 

There is the famous tic-tac-toe playing enzymes [ https://en.wikipedia.org/wiki/DNA_computing#Tic-tac-toe_game ] created in 2002. Maybe the first synbio life forms to compute things. (More recent little biocomputers are in the news all the time.)

- pt

[Brent Meeker]

On 9/29/2018 12:16 AM, Bruno Marchal wrote:

On 28 Sep 2018, at 21:00, agrays...@gmail.com wrote:

On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com wrote:

 

Thank you everybody for your responses.

Bruno Marchal I looked at your statement, they are very interesting but some very good neruoscientists argue that brain is not like computer

Here for example (4min video) Edelman:

https://www.youtube.com/watch?v=qmyfQY4TaVc

The question can be turned around. Why would anyone think a brain is strongly comparable or identical to a computer? It has some superficial similarities such as being able to store memory and logical functions (which are simulated by a computer), but its cells are not two state systems like computer transistors. AG

A bacteria is already a computer (at least), and a neurone is already a rather sophisticated society of bacteria and viruses, plausibly enough. So, a society of billions of neurons should not be compared to transistors. The substitution level is plausibly much lower than the level of neurons.

It has been estimated that simulating a single neuron requires a micro-controller like an AVR, which contains 80,000 transistors.



Brent

[Brent Meeker]

On 9/29/2018 4:34 AM, agrays...@gmail.com wrote:

A bacteria is already a computer (at least),

Really? Then you should be able to identify the entities that store binary information. And where is the clock which pulses and advances the instruction pointer? And where is the instruction pointer located? AG

Not all computers are von Neumann computers.

Brent

[agrays...@gmail.com]

Maybe he means a parallel processor, but whatever he means should be spelled out explicitly. One can't just assert, as if it's obvious, that a bacteria is already a computer. One thing for sure; he doesn't know what the MUH is, and therefore cannot understand my simple falsification of the hypothesis. AG

[Brent Meeker]

On 9/29/2018 1:45 PM, agrays...@gmail.com wrote:

On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote:

On 9/29/2018 4:34 AM, agrays...@gmail.com wrote:

A bacteria is already a computer (at least),

Really? Then you should be able to identify the entities that store binary information. And where is the clock which pulses and advances the instruction pointer? And where is the instruction pointer located? AG

Not all computers are von Neumann computers.

Brent

Maybe he means a parallel processor, but whatever he means should be spelled out explicitly. One can't just assert, as if it's obvious, that a bacteria is already a computer.

Of course it is obvious that a bacterium computes things...like swimming toward nutrients and how to make another bacterium.

Brent

One thing for sure; he doesn't know what the MUH is, and therefore cannot understand my simple falsification of the hypothesis. AG

[Philip Thrift]

On Saturday, September 29, 2018 at 3:53:04 PM UTC-5, Brent wrote:

On 9/29/2018 1:45 PM, agrays...@gmail.com wrote:

On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote:

On 9/29/2018 4:34 AM, agrays...@gmail.com wrote:

A bacteria is already a computer (at least),

Really? Then you should be able to identify the entities that store binary information. And where is the clock which pulses and advances the instruction pointer? And where is the instruction pointer located? AG

Not all computers are von Neumann computers.

Brent

Maybe he means a parallel processor, but whatever he means should be spelled out explicitly. One can't just assert, as if it's obvious, that a bacteria is already a computer.

Of course it is obvious that a bacterium computes things...like swimming toward nutrients and how to make another bacterium.

Brent

 

Bacterial computing: a form of natural computing and its applications

- https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3971165/

Bacteria make computers look like pocket calculators

- https://www.theguardian.com/science/blog/2009/jul/24/bacteria-computer

Bacteria Can Now Be Programmed Like a Computer

- https://tonic.vice.com/en_us/article/43d9en/bacteria-can-now-be-programmed-like-a-computer

 

- pt

 

[agrays...@gmail.com]

- ptIs

What is a computer -- what is it -- that bacteria can be seen as being like? Why bother to define it. Nothing obvious here except sloppy use of analogies. AG

 

[Philip Thrift]

On Sunday, September 30, 2018 at 12:30:33 AM UTC-5, agrays...@gmail.com wrote:

On Saturday, September 29, 2018 at 9:28:34 PM UTC, Philip Thrift wrote:

On Saturday, September 29, 2018 at 3:53:04 PM UTC-5, Brent wrote:

On 9/29/2018 1:45 PM, agrays...@gmail.com wrote:

On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote:

On 9/29/2018 4:34 AM, agrays...@gmail.com wrote:

A bacteria is already a computer (at least),

Really? Then you should be able to identify the entities that store binary information. And where is the clock which pulses and advances the instruction pointer? And where is the instruction pointer located? AG

Not all computers are von Neumann computers.

Brent

Maybe he means a parallel processor, but whatever he means should be spelled out explicitly. One can't just assert, as if it's obvious, that a bacteria is already a computer.

Of course it is obvious that a bacterium computes things...like swimming toward nutrients and how to make another bacterium.

Brent

 

Bacterial computing: a form of natural computing and its applications

- https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3971165/

Bacteria make computers look like pocket calculators

- https://www.theguardian.com/science/blog/2009/jul/24/bacteria-computer

Bacteria Can Now Be Programmed Like a Computer

- https://tonic.vice.com/en_us/article/43d9en/bacteria-can-now-be-programmed-like-a-computer

 

- pt

What is a computer -- what is it -- that bacteria can be seen as being like? Why bother to define it. Nothing obvious here except sloppy use of analogies. AG

 

What is a computer?

A computer is a device that executes programs.

If we can synthesize bacteria that execute programs (which we can do), then these bacteria are computers.

- pt

 

[agrays...@gmail.com]

On Saturday, September 29, 2018 at 8:53:04 PM UTC, Brent wrote:

On 9/29/2018 1:45 PM, agrays...@gmail.com wrote:

On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote:

On 9/29/2018 4:34 AM, agrays...@gmail.com wrote:

A bacteria is already a computer (at least),

Really? Then you should be able to identify the entities that store binary information. And where is the clock which pulses and advances the instruction pointer? And where is the instruction pointer located? AG

Not all computers are von Neumann computers.

Brent

Maybe he means a parallel processor, but whatever he means should be spelled out explicitly. One can't just assert, as if it's obvious, that a bacteria is already a computer.

Of course it is obvious that a bacterium computes things...like swimming toward nutrients and how to make another bacterium.

Brent

So anything that shows intentional behavior you're going to call a computer? A comet which misses the Sun, or one that doesn't, can be imagined as having intentional behavior. AG

[Philip Thrift]

Scientists have built the most complex biomolecular computer yet and stored a movie

https://spectrum.ieee.org/biomedical/devices/biocomputer-and-memory-built-inside-living-bacteria 

- pt 

[kujawski...@gmail.com]

Bruno Marchal thank you for your anwser.

Physicist Paul Benioff make interesting idea https://arxiv.org/abs/quant-ph/0201093
that mathematics and laws of physics coemerged somehow randomly.

[agrays...@gmail.com]

You wanted an answer to a question; whether the MUH is valid. I falsified it. Did you understand and appreciate my answer? AG

[agrays...@gmail.com]

I don't see how Bruno answered your question when he misstated and doesn't understand the MUH. Yet you thank him and not me. AG

[Philip Thrift]

Thanks for this reference! Much of it jibes with my codicalist-materialist view.

The essential point to make here is that language is physical.  

Gödel maps can also be used in physical theories. However, for these theories, they have some different properties. For a coherent theory of mathematics and physics, or for any physical theory that is universally applicable, a G¨odel map does not extend the domain of applicability of the theory. The reason is that, since language is physical, all expressions of any language are already in the theory domain as states of physical systems. 

Finally it should be noted that it may be worthwhile to replace validity in the basic requirement with consistency.

- pt

[Bruno Marchal]

That is refuted by the mechanist hypothesis and its consequence, although it is less wrong that materialism, it fails to see that the physical is phenomenological. I have developed this with more details a long time ago in this list. The shorter way to understand this is to study my papers. To equate mathematical existence with physical existence does not make any sense, and might be unfair to Tegmark (but his view have evolved, so I am not sure).

That wiki entry is bad, but I would prefer people argue instead of relying on links, which distracts and add obscurity more than adding light. I have not the time, but I could criticised each line of that entry.

Perhaps the main critics is that the “mathematical universe hypothesis” is not an hypothesis, nor a speculation. It is the material hypothesis which is the speculation here, as no-one has ever found the slightest experimental evidence for matter, in the ontological sense. Nothing makes sense in that wiki page.

To say that a mathematical object  exist physically, does not make sense. It starts with a category error.

I don't think you know what the MUH is. I have falsified it. AG

Good me too. But with mechanism, the material hypothesis, and/or physicalism,  is/are  falsified too.

Bruno

[Bruno Marchal]

Good summary. My result is that Mechanism (the idea that my body is Turing emulable at a level of description relevant to my consciousness) entails arithmeticalism.

Arithmeticalism is not assumed. That materialism is false is the conclusion, and the proof is constructive, showing exactly how to recover the physical appearances, and it works, at least as far as it has been verified until now. Physicalism has never worked (indeed, that explains the rise of most contemporary religion). Physicalism is tucked on the mind-body problem, which is traditionally put under the rug.

Bruno

- pt

[Bruno Marchal]

No problem with this. As explained in the wiki, the MUH does not make any sense.

Bruno

[Bruno Marchal]

On 29 Sep 2018, at 12:41, Philip Thrift <cloud...@gmail.com> wrote:

On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com wrote:

 It claims that all mathematical objects exist in "physical" reality, which is sort-of isomorphic or in some sense identical to these objects. That is, no dichotomy between "physical" and mathematical objects, and all the latter including plane waves exist in this reality. But you will never observe a plane wave, so the MUH is falsified. AG 

1. Tegmark claims everything in the universe is mathematical - that is, the universe consists of mathematical objects.

2. Tegmark also says that infinities should be eliminated from physics - in fact, infinities are ruining physics.

[ http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/ ]

But that is correct, as I urge Tegmark to avoid the axiom of infinity, or to propose clearly a non-computationalist hypothesis. He agreed. 

Bruno

So then via Tegmark there can be no real continuous (infinitely divisible) objects like (mathematical) waves, putting 1 and 2 together. Only particular mathematical objects exist.

 - pt

[Bruno Marchal]

There is no nature that you can invoke. Once mechanism is assumed, a term like nature needs to be (re-defined, or explained, without physicalist assumption, implicit or explicit.

(Do you know what they are?) So the MUH as claimed by Wiki and its adherents is falsified. AG

I agree with your conclusion, but you assume some nature or matter, which cannot work in the mechanist context.

Bruno

 - pt

[Bruno Marchal]

On 29 Sep 2018, at 13:34, agrays...@gmail.com wrote:

On Saturday, September 29, 2018 at 7:16:41 AM UTC, Bruno Marchal wrote:

On 28 Sep 2018, at 21:00, agrays...@gmail.com wrote:

On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com wrote:

 

Thank you everybody for your responses.

Bruno Marchal I looked at your statement, they are very interesting but some very good neruoscientists argue that brain is not like computer

Here for example (4min video) Edelman:

https://www.youtube.com/watch?v=qmyfQY4TaVc

The question can be turned around. Why would anyone think a brain is strongly comparable or identical to a computer? It has some superficial similarities such as being able to store memory and logical functions (which are simulated by a computer), but its cells are not two state systems like computer transistors. AG

A bacteria is already a computer (at least),

Really? Then you should be able to identify the entities that store binary information.

By computer I mean a number u such that phi_u(<x,y>) = phi_x(y), for some enumeration phi_i of the partial computable function. No need of binary information. But it needs digitally coded information, and that is given by the genome (the sequence of adenine, thymine, cytosine, guanine (French spelling, sorry).

And where is the clock which pulses and advances the instruction pointer? And where is the instruction pointer located? AG

Dont confuse a computer (universal number, universal Turing machine, …)  and a von Neumann physical computer. Reread my explanation in the thread “why is Church’s thesis a miracle). Ask me question from there.

Bruno

[Bruno Marchal]

Intersting. I have myself work with the geneticist René Thomas on how far we can program a bacteria to do some typical elementary calculation. He succeeded in implementing the if then else, and some infinite loop, like adding a plasmid (a little circular DNA strand) back in and out the main bacterial “chromosome”. 

Unfortunately, the mathematicians refuse that I continue this cooperation (which was my master thesis) and ask me to work on forcing theory in set theories with classes. 

We did biocomputing 40 years ago. I planned a concentration of bacteria and bacteriophages allowing a vey huge parallel processing. I have kept contact with biologist and biochemist all my life. I really discovered the universal machine in biology book, before discovering that all this was already implement in the numbers, which makes me decide to study mathematical logic instead. My goal has always been philosophical or theological, but those field are sick since long (since 529, precisely albeit symbolically).

Bruno

- pt

[agrays...@gmail.com]

On Sunday, September 30, 2018 at 9:35:18 AM UTC, Bruno Marchal wrote:

On 29 Sep 2018, at 13:16, agrays...@gmail.com wrote:

On Saturday, September 29, 2018 at 10:41:42 AM UTC, Philip Thrift wrote:

On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com wrote:

 It claims that all mathematical objects exist in "physical" reality, which is sort-of isomorphic or in some sense identical to these objects. That is, no dichotomy between "physical" and mathematical objects, and all the latter including plane waves exist in this reality. But you will never observe a plane wave, so the MUH is falsified. AG 

1. Tegmark claims everything in the universe is mathematical - that is, the universe consists of mathematical objects.

2. Tegmark also says that infinities should be eliminated from physics - in fact, infinities are ruining physics.

[ http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/ ]ac

Bruno wrote 1 & 2.  AG

So then via Tegmark there can be no real continuous (infinitely divisible) objects like (mathematical) waves, putting 1 and 2 together. Only particular mathematical objects exist.

According to Wiki, and what I've heard from its adherents, the MUH posits that ALL mathematical object or entities exist in nature. But plane waves do not exist in nature.

There is no nature that you can invoke. Once mechanism is assumed, a term like nature needs to be (re-defined, or explained, without physicalist assumption, implicit or explicit.

(Do you know what they are?) So the MUH as claimed by Wiki and its adherents is falsified. AG

I agree with your conclusion, but you assume some nature or matter, which cannot work in the mechanist context.

I didn't assume anything, except that plane waves will never be observed (regardless of your model of external reality) unless you agree to instantaneous action at a distance, and on steroids (!), since as time evolves, the amplitude of a plane wave changes instantaneously in all infinite directions. So I am just asserting that Tegmark's MUH has been falsified since plane waves mathematically exist, but are never reified by whatever is out there -- matter, or nothing but restrictions on motion giving rise the illusion of matter or something solid existing. Incidentally, I don't think the Wiki article refutes Tegmark as you claim; rather it just describes it. AG

[Bruno Marchal]

On 29 Sep 2018, at 20:59, Brent Meeker <meek...@verizon.net> wrote:

On 9/29/2018 12:16 AM, Bruno Marchal wrote:

On 28 Sep 2018, at 21:00, agrays...@gmail.com wrote:

On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com wrote:

 

Thank you everybody for your responses.

Bruno Marchal I looked at your statement, they are very interesting but some very good neruoscientists argue that brain is not like computer

Here for example (4min video) Edelman:

https://www.youtube.com/watch?v=qmyfQY4TaVc

The question can be turned around. Why would anyone think a brain is strongly comparable or identical to a computer? It has some superficial similarities such as being able to store memory and logical functions (which are simulated by a computer), but its cells are not two state systems like computer transistors. AG

A bacteria is already a computer (at least), and a neurone is already a rather sophisticated society of bacteria and viruses, plausibly enough. So, a society of billions of neurons should not be compared to transistors. The substitution level is plausibly much lower than the level of neurons.

It has been estimated that simulating a single neuron requires a micro-controller like an AVR, which contains 80,000 transistors.

<blicjehabnofhiib.png>

Nice illustration. Yes, a neurone is already an incredibly complex machinery. I bet that it would need even much more than 80.000 transistors.  Today we know that the glial cells do participate in the information treatment. They don’t use axons, but communicate through chemical wave. Our substitution level, assuming mechanism, might be the atomic level, in fact the electronically level, near the Heisenberg uncertainty position treshold. At least if we want to survive integrally, with our precise memory and character.

Bruno

[agrays...@gmail.com]

On Sunday, September 30, 2018 at 9:40:07 AM UTC, Bruno Marchal wrote:

On 29 Sep 2018, at 13:34, agrays...@gmail.com wrote:

On Saturday, September 29, 2018 at 7:16:41 AM UTC, Bruno Marchal wrote:

On 28 Sep 2018, at 21:00, agrays...@gmail.com wrote:

On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com wrote:

 

Thank you everybody for your responses.

Bruno Marchal I looked at your statement, they are very interesting but some very good neruoscientists argue that brain is not like computer

Here for example (4min video) Edelman:

https://www.youtube.com/watch?v=qmyfQY4TaVc

The question can be turned around. Why would anyone think a brain is strongly comparable or identical to a computer? It has some superficial similarities such as being able to store memory and logical functions (which are simulated by a computer), but its cells are not two state systems like computer transistors. AG

A bacteria is already a computer (at least),

Really? Then you should be able to identify the entities that store binary information.

By computer I mean a number u such that phi_u(<x,y>) = phi_x(y), for some enumeration phi_i of the partial computable function. No need of binary information. But it needs digitally coded information, and that is given by the genome (the sequence of adenine, thymine, cytosine, guanine (French spelling, sorry).

So now a computer isn't some device that executes programs, but a number? Please elaborate on your mathematics. I have no idea what it is supposed to mean. AG

[Bruno Marchal]

On 29 Sep 2018, at 22:52, Brent Meeker <meek...@verizon.net> wrote:

On 9/29/2018 1:45 PM, agrays...@gmail.com wrote:

On Saturday, September 29, 2018 at 8:07:12 PM UTC, Brent wrote:

On 9/29/2018 4:34 AM, agrays...@gmail.com wrote:

A bacteria is already a computer (at least),

Really? Then you should be able to identify the entities that store binary information. And where is the clock which pulses and advances the instruction pointer? And where is the instruction pointer located? AG

Not all computers are von Neumann computers.

Brent

Maybe he means a parallel processor, but whatever he means should be spelled out explicitly. One can't just assert, as if it's obvious, that a bacteria is already a computer.

Of course it is obvious that a bacterium computes things...like swimming toward nutrients and how to make another bacterium.

Sure. But that would not be enough to be a “creative set” (a universal number). Typically, self-reproduction is not Turing universal (Royer wrote a nice book on when a control structure is Turing universal, and very powerful recursion are shown to be not Turing universal, this leads to interesting subset of the partial computable functions, known as the sub creative hierarchies). They verify the SMN theorem, but not the enumeration (universality) theorem.

But a bacteria can emulate a full universal machine. The hard part is the read and write interface, which requires handling well some phages (virus). Might say that it is only bacteria + phage which are operationally Turing universal. 

Bruno

[Bruno Marchal]

If phi_i is an enumeration of the partial computable function, the one closed to diagonalisation as I explained in the thread “why Church thesis is a miracle”.  Reread that post, I wrote it for you.

Bruno

[Bruno Marchal]

OK. You might add “… that can execute all programs”. In any programming language. All universal number (mathematical computer, universal Turing machine, …) can imitate any other universal numbers. Either by Rogers compilation theorem, or by the usual interpretation theorems.

Bruno

- pt

 

[Bruno Marchal]

I will take a look, but probably this is old stuff, still missing the “mind-body” issue, which I illustrate has a deep impact on this, and where incompleteness plays the key role in deducing physics from arithmetic.

Bruno

[agrays...@gmail.com]

On Sunday, September 30, 2018 at 9:53:06 AM UTC, agrays...@gmail.com wrote:

On Sunday, September 30, 2018 at 9:35:18 AM UTC, Bruno Marchal wrote:

On 29 Sep 2018, at 13:16, agrays...@gmail.com wrote:

On Saturday, September 29, 2018 at 10:41:42 AM UTC, Philip Thrift wrote:

On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com wrote:

 It claims that all mathematical objects exist in "physical" reality, which is sort-of isomorphic or in some sense identical to these objects. That is, no dichotomy between "physical" and mathematical objects, and all the latter including plane waves exist in this reality. But you will never observe a plane wave, so the MUH is falsified. AG 

1. Tegmark claims everything in the universe is mathematical - that is, the universe consists of mathematical objects.

2. Tegmark also says that infinities should be eliminated from physics - in fact, infinities are ruining physics.

[ http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/ ]ac

Bruno wrote 1 & 2.  AG

So then via Tegmark there can be no real continuous (infinitely divisible) objects like (mathematical) waves, putting 1 and 2 together. Only particular mathematical objects exist.

According to Wiki, and what I've heard from its adherents, the MUH posits that ALL mathematical object or entities exist in nature. But plane waves do not exist in nature.

There is no nature that you can invoke. Once mechanism is assumed, a term like nature needs to be (re-defined, or explained, without physicalist assumption, implicit or explicit.

(Do you know what they are?) So the MUH as claimed by Wiki and its adherents is falsified. AG

I agree with your conclusion, but you assume some nature or matter, which cannot work in the mechanist context.

I didn't assume anything, except that plane waves will never be observed (regardless of your model of external reality) unless you agree to instantaneous action at a distance, and on steroids (!), since as time evolves, the amplitude of a plane wave changes instantaneously in all infinite directions. So I am just asserting that Tegmark's MUH has been falsified since plane waves mathematically exist, but are never reified by whatever is out there -- matter, or nothing but restrictions on motion giving rise the illusion of matter or something solid existing. Incidentally, I don't think the Wiki article refutes Tegmark as you claim; rather it just describes it. AG

Last sentence above is factually wrong. The Wiki article does contain some interesting criticisms of Tegmark's MUH. AG

[Bruno Marchal]

On 30 Sep 2018, at 11:53, agrays...@gmail.com wrote:

On Sunday, September 30, 2018 at 9:35:18 AM UTC, Bruno Marchal wrote:

On 29 Sep 2018, at 13:16, agrays...@gmail.com wrote:

On Saturday, September 29, 2018 at 10:41:42 AM UTC, Philip Thrift wrote:

On Saturday, September 29, 2018 at 4:48:44 AM UTC-5, agrays...@gmail.com wrote:

 It claims that all mathematical objects exist in "physical" reality, which is sort-of isomorphic or in some sense identical to these objects. That is, no dichotomy between "physical" and mathematical objects, and all the latter including plane waves exist in this reality. But you will never observe a plane wave, so the MUH is falsified. AG 

1. Tegmark claims everything in the universe is mathematical - that is, the universe consists of mathematical objects.

2. Tegmark also says that infinities should be eliminated from physics - in fact, infinities are ruining physics.

[ http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/ ]ac

Bruno wrote 1 & 2.  AG

So then via Tegmark there can be no real continuous (infinitely divisible) objects like (mathematical) waves, putting 1 and 2 together. Only particular mathematical objects exist.

According to Wiki, and what I've heard from its adherents, the MUH posits that ALL mathematical object or entities exist in nature. But plane waves do not exist in nature.

There is no nature that you can invoke. Once mechanism is assumed, a term like nature needs to be (re-defined, or explained, without physicalist assumption, implicit or explicit.

(Do you know what they are?) So the MUH as claimed by Wiki and its adherents is falsified. AG

I agree with your conclusion, but you assume some nature or matter, which cannot work in the mechanist context.

I didn't assume anything, except that plane waves will never be observed (regardless of your model of external reality)

That is a too general statement. I can agree with some definition of observation. But then we never observe anything mathematical, still less infinite.

Anyway, you seem to use “observation” as a criteria of reality. Then I just did an observation of a plane wave, in my waking dream ...

unless you agree to instantaneous action at a distance, and on steroids (!), since as time evolves, the amplitude of a plane wave changes instantaneously in all infinite directions. So I am just asserting that Tegmark's MUH has been falsified since plane waves mathematically exist,

In which theory. With mechanism what exist is only the numbers (or only the combinators, …).

but are never reified by whatever is out there -- matter, or nothing but restrictions on motion giving rise the illusion of matter or something solid existing.

OK. That is where we will be led, in the computationalist frame.

Incidentally, I don't think the Wiki article refutes Tegmark as you claim; rather it just describes it.

Read more carefully. I have refuted Tegmark in this list. Then I say that that wiki entry is very bad. Those are independent statements.

Bruno

[Bruno Marchal]

On 30 Sep 2018, at 11:58, agrays...@gmail.com wrote:

On Sunday, September 30, 2018 at 9:40:07 AM UTC, Bruno Marchal wrote:

On 29 Sep 2018, at 13:34, agrays...@gmail.com wrote:

On Saturday, September 29, 2018 at 7:16:41 AM UTC, Bruno Marchal wrote:

On 28 Sep 2018, at 21:00, agrays...@gmail.com wrote:

On Friday, September 28, 2018 at 6:49:37 PM UTC, kujawski...@gmail.com wrote:

 

Thank you everybody for your responses.

Bruno Marchal I looked at your statement, they are very interesting but some very good neruoscientists argue that brain is not like computer

Here for example (4min video) Edelman:

https://www.youtube.com/watch?v=qmyfQY4TaVc

The question can be turned around. Why would anyone think a brain is strongly comparable or identical to a computer? It has some superficial similarities such as being able to store memory and logical functions (which are simulated by a computer), but its cells are not two state systems like computer transistors. AG

A bacteria is already a computer (at least),

Really? Then you should be able to identify the entities that store binary information.

By computer I mean a number u such that phi_u(<x,y>) = phi_x(y), for some enumeration phi_i of the partial computable function. No need of binary information. But it needs digitally coded information, and that is given by the genome (the sequence of adenine, thymine, cytosine, guanine (French spelling, sorry).

So now a computer isn't some device that executes programs, but a number? Please elaborate on your mathematics. I have no idea what it is supposed to mean. AG

I already did. See the thread “why is Church’s thesis a miracle”. I can explain again, but right now I have some work to finish. In a nutshell, choose your favorite Turing universal formalism, enumerate in that formalisme the code of the partial computable functions, and thus (with repetition) the partial computable functions themselves  phi_i, fix a bijection between NxN and N <x, y>, then a number u is universal if phi_u(<x,y>) = phi_x(y). u is the computer, x the program, and y the data. We say that u emulates x on y.

Bruno

[Lawrence Crowell]

On Thursday, September 27, 2018 at 8:02:36 PM UTC-5, kujawski...@gmail.com wrote:

Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:

- applicability of mathematic, to natural sciences

- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.

- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.

What are your thoughts.

Regards

 I think it is best to assume pragmatic stance with respect to this. The idea the physical universe is ultimately mathematics is a huge category mixing that suffers from problems. Physics is an empirical subject that tests the workings of a theory by performing observations and measurements. Mathematics is a subject concerned with abstract structures and objects and their logical relationships. Physical objects move through space or are an aspect of geometrodynamics in relativity and they obey conservation rules. As such mathematics is used to describe physical systems and to compute things. This is different than saying the two subjects are equivalent. Mathematics is not an empirical subject, though with computers some areas of math have started to take one a sort of synthetic empiricism. Physics is also not something that is determined entirely by logical relationships and just pure theory. We have some issues of course with quantum gravitation and whether that can ever be empirically brought to tests. 

Quantum mechanics is close to being a sort of physical logic. Quantum mechanics is close to being a case of MUH, though I would not go so far as to actually make that pronouncement. For  those who take the trouble to learn about the bosonic string, say by reading Polchinski's vol 1 String Theory will see this is really pure quantum mechanics according to a more complete understanding of the complex plane. This may go further with modular forms. Vol 2 of Polchinski's book works with supersymmetry. This might be ultimately a deeper description of quantum mechanics. Maybe quantum mechanics is just a modular system of automorphisms over the Fischer-Griess Monster Group that maintains a conservation of this as the fundamental vacuum state. So this all sounds highly mathematical, but I would still hesitate to say physics is mathematics.

The relationship between physics and mathematics is maybe unknowable. I think of Garrison Keillor with his Guy Noir skits that start with, "One man on the tenth floor of the Acme Building searches for answers to life's persistent questions; Guy Noir private eye."

LC

[Philip Thrift]

On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:

[Re:] forcing theory in set theories with classes. 

Bruno

Do you follow the work of Joel David Hamkins (forcing applied to set-theoretic "multiverse", etc.)

(I have a basic idea of a type-theoretic parallel to this.)

The set-theoretic multiverse

https://arxiv.org/abs/1108.4223

Joel David Hamkins

@JDHamkins

Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow in Philosophy, University College Oxford. Formerly of New York.

http://jdh.hamkins.org

- pt

[Philip Thrift]

On Sunday, September 30, 2018 at 5:05:27 AM UTC-5, Bruno Marchal wrote:

On 30 Sep 2018, at 08:03, Philip Thrift <cloud...@gmail.com> wrote:

What is a computer?

A computer is a device that executes programs.

If we can synthesize bacteria that execute programs (which we can do), then these bacteria are computers.

OK. You might add “… that can execute all programs”. In any programming language. All universal number (mathematical computer, universal Turing machine, …) can imitate any other universal numbers. Either by Rogers compilation theorem, or by the usual interpretation theorems.

Bruno

I now have a next version of 

Real computationalism

     https://codicalist.wordpress.com/2018/09/30/real-computationalism/

=  my "pragmatic" definition of computing.

0.1. PTLOS configurations

A configuration PTLOS(π,λ,τ,ο,Σ) — lower case Greek letters π, λ, τ, ο, and capital Greek letter Σ are variables that take on concrete (particular) values — is defined:

PLTOS(π,λ,τ,ο,Σ) designates a program π that is written in a language λ that is transformed via a compiler/assembler τ into an output object ο that executes in a computing substrate Σ.

(Turing-completeness is included.)

But I want to meet therein the "consciousness challenge" of Philip Golff and Gaylen Strawson in the PLTOS framework (the output object would be a conscious agent):

6.5. A programming language including experiential modalities (experiential modal logic, experiential modal operators or qualifiers) is needed to extend the picture we have of matter [Goff] to include consciousness.

(Modal logic historically covers modalities such as possibility/necessity, belief, time, morality, knowability [ML1], but also self-reference [SR1],[SR2],[SR3].)

Selves: An Essay in Revisionary Metaphysics
Galen Strawson
[Selves]

The Subject of Experience
Galen Strawson
[SubjExp]

- pt

 

[Brent Meeker]

Are you trying to define consciousness into existence by assuming modal operators for it?  Or are you just trying to provide a language for talking about it?  Where is the subconscious in this theory?

Brent

Selves: An Essay in Revisionary Metaphysics
Galen Strawson
[Selves]

The Subject of Experience
Galen Strawson
[SubjExp]

- pt

 

[Philip Thrift]

On Sunday, September 30, 2018 at 6:14:22 PM UTC-5, Brent wrote:

On 9/30/2018 7:58 AM, Philip Thrift wrote:

On Sunday, September 30, 2018 at 5:05:27 AM UTC-5, Bruno Marchal wrote:

On 30 Sep 2018, at 08:03, Philip Thrift <cloud...@gmail.com> wrote:

What is a computer?

A computer is a device that executes programs.

If we can synthesize bacteria that execute programs (which we can do), then these bacteria are computers.

OK. You might add “… that can execute all programs”. In any programming language. All universal number (mathematical computer, universal Turing machine, …) can imitate any other universal numbers. Either by Rogers compilation theorem, or by the usual interpretation theorems.

Bruno

I now have a next version of 

Real computationalism

     https://codicalist.wordpress.com/2018/09/30/real-computationalism/

=  my "pragmatic" definition of computing.

0.1. PTLOS configurations

A configuration PTLOS(π,λ,τ,ο,Σ) — lower case Greek letters π, λ, τ, ο, and capital Greek letter Σ are variables that take on concrete (particular) values — is defined:

PLTOS(π,λ,τ,ο,Σ) designates a program π that is written in a language λ that is transformed via a compiler/assembler τ into an output object ο that executes in a computing substrate Σ.

(Turing-completeness is included.)

But I want to meet therein the "consciousness challenge" of Philip Golff and Gaylen Strawson in the PLTOS framework (the output object would be a conscious agent):

6.5. A programming language including experiential modalities (experiential modal logic, experiential modal operators or qualifiers) is needed to extend the picture we have of matter [Goff] to include consciousness.

(Modal logic historically covers modalities such as possibility/necessity, belief, time, morality, knowability [ML1], but also self-reference [SR1],[SR2],[SR3].)

Are you trying to define consciousness into existence by assuming modal operators for it?  Or are you just trying to provide a language for talking about it?  Where is the subconscious in this theory?

Brent

The proposal is in terms of the the PLTOS(π,λ,τ,ο,Σ) framework:

π would be a program in a λ with experiential modalities (modal operators).

A compiler τ (presumably a biocompiler [ https://en.wiktionary.org/wiki/biocompiler ]) would produce a conscious agent ο executing in some substate Σ.

The subconscious of ο would be whatever else is going on in ο's runtime not having to do with the conscious stuff, I guess. (What else would it be?)

- pt

[Bruno Marchal]

On 30 Sep 2018, at 13:42, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Thursday, September 27, 2018 at 8:02:36 PM UTC-5, kujawski...@gmail.com wrote:

Hello I think this good forum for this topic - what do you think about Mathematical Universe, there are very big arguments for that hypothesis:

- applicability of mathematic, to natural sciences

- all we discovere are structures and I didnt find explanation of the diference beetwen physical structures and mathematical structures.

- scientists and philosophers of science tend to affirm belive in diverse structure and homogeneous substance (neutral monism) or mathematicism vide Ladyman, Ross, French, Tegmark etc.

What are your thoughts.

Regards

 I think it is best to assume pragmatic stance with respect to this.

I am not sure of this. I would have said that only a theoretical view can be given, where we make clear the metaphysical theological or psychological hypotheses. 

The idea the physical universe is ultimately mathematics is a huge category mixing that suffers from problems.

I agree with this, and that is why it is important to state the hypothesis, notably in the cognitive science.

Physics is an empirical subject that tests the workings of a theory by performing observations and measurements. Mathematics is a subject concerned with abstract structures and objects and their logical relationships. Physical objects move through space or are an aspect of geometrodynamics in relativity and they obey conservation rules. As such mathematics is used to describe physical systems and to compute things. This is different than saying the two subjects are equivalent. Mathematics is not an empirical subject, though with computers some areas of math have started to take one a sort of synthetic empiricism. Physics is also not something that is determined entirely by logical relationships and just pure theory. We have some issues of course with quantum gravitation and whether that can ever be empirically brought to tests. 

As I explain in my papers, once we assume the “indexical digital mechanist hypothesis”,(hereafter called simply Mechanism) physicalism does not work, and physics do not explain why the physical prediction fit with the psychological (first person) predictions. It uses implicitly a very strong induction axioms which can be shown inconsistent.

With Mechanism, there is no more a “physical universe” at the ontological level, and physics is reduced to the theology, or psychology if you prefer, intrinsic to the numbers and their arithmetical relations.

This makes the physical reality into pure arithmetic, with respect to psychology/theology.

The propositional logic of the observable, for example, is given by the logic of some variants of the logic of provability. This works in the sense that we get a quantum logic where it should be expected. 

Quantum mechanics is close to being a sort of physical logic. Quantum mechanics is close to being a case of MUH, though I would not go so far as to actually make that pronouncement. For  those who take the trouble to learn about the bosonic string, say by reading Polchinski's vol 1 String Theory will see this is really pure quantum mechanics according to a more complete understanding of the complex plane. This may go further with modular forms. Vol 2 of Polchinski's book works with supersymmetry. This might be ultimately a deeper description of quantum mechanics. Maybe quantum mechanics is just a modular system of automorphisms over the Fischer-Griess Monster Group that maintains a conservation of this as the fundamental vacuum state. So this all sounds highly mathematical, but I would still hesitate to say physics is mathematics.

Physics is not mathematics. That would be the category error you allude to above. 

With mechanism, all this is rather well clarified. The physical reality emerges from a very special mathematical phenomenon: the way the "dreams by numbers" (the computations seen in the self-referential modes) get structured by the incompleteness phenomenon.

The relationship between physics and mathematics is maybe unknowable.

It is indeed, as Mechanism is unknowable too, but we can hope, prey, fear … it could be true.

Bruno

I think of Garrison Keillor with his Guy Noir skits that start with, "One man on the tenth floor of the Acme Building searches for answers to life's persistent questions; Guy Noir private eye."

LC

[Bruno Marchal]

The math is interesting, and could be of some use, but it is a priori far too much Aristotelian to be coherent with the mechanist hypothesis. That should follow “easily” from the result described in most of my papers on this subject. The author does not seem aware of the mind-body problem, which put extreme constraints on what the physical reality can come from. Even Peano arithmetic, although integral part of the notion of observer, is too much rich for the ontology, where not only the axiom of infinity is too strong, but even the induction axioms are too strong. 

Pragmatically, sets and typed lambda terms or typed combinators can indeed be very useful. 

[agrays...@gmail.com]

On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:

On 30 Sep 2018, at 16:30, Philip Thrift <cloud...@gmail.com> wrote:

On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:

[Re:] forcing theory in set theories with classes. 

Bruno

Do you follow the work of Joel David Hamkins (forcing applied to set-theoretic "multiverse", etc.)

(I have a basic idea of a type-theoretic parallel to this.)

The set-theoretic multiverse

https://arxiv.org/abs/1108.4223

Joel David Hamkins

@JDHamkins

Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow in Philosophy, University College Oxford. Formerly of New York.

http://jdh.hamkins.org

The math is interesting, and could be of some use, but it is a priori far too much Aristotelian to be coherent with the mechanist hypothesis. That should follow “easily” from the result described in most of my papers on this subject. The author does not seem aware of the mind-body problem, which put extreme constraints on what the physical reality can come from. Even Peano arithmetic, although integral part of the notion of observer, is too much rich for the ontology, where not only the axiom of infinity is too strong,

Since you want to banish the concept of infinity from mathematics, how would you define, say, the limit of an "infinite" series? How would you even discuss this series in the context of finite mathematics? AG

[John Clark]

On Fri, Sep 28, 2018 at 2:26 PM Philip Thrift <cloud...@gmail.com> wrote:

> I think (along with Philip Goff*) that physics is not complete in its study of matter.

That is very true, today physics has no idea what Dark Energy or Dark Matter is and they make up 95% of the matter/energy in the universe. And physics doesn't know what will happen when 2 incompatible theories, General Relativity and Quantum Mechanics, collide head on at the center of a Black Hole. Hell we don't even have a very good theory about why friction works the way it does, and the same goes for high temperature superconductors.  

 John K Clark

 

[John Clark]

On Sat, Sep 29, 2018 at 2:59 PM Brent Meeker <meek...@verizon.net> wrote:

>It has been estimated that simulating a single neuron requires a micro-controller like an AVR, which contains 80,000 transistors.

And 4 years ago in 2014 the human race manufactured 2.5 * 10^20 transistors, that works out to 8 trillion transistors a second 24/7 for an entire year. I don't know how many transistors are made in 2018 but I'm sure it's several times as large.

John K Clark

 

[kujawski...@gmail.com]

 Agrays:

I don't see how Bruno answered your question when he misstated and doesn't understand the MUH. Yet you thank him and not me. AG

No, I thanked everybody in this topic in my earlier message, and here I thanked Bruno not for answer about MUH but about Gerald Edelman movie.

[agrays...@gmail.com]

OK.

Now we can think about this; the idea that I've falsified in the MUH  is that every mathematical form is reified in what we observe, or imagine, as an external reality. For me this idea is awfully close to another idea I find to be false, but not easily demonstrated; namely, the seminal idea of the MWI, that every possible outcome of a quantum experiment must be realized or measured, if not in this universe, then in another, and simultaneously. AG

[Brent Meeker]

In human terms the subconscious is thinking that is not conscious but controls action and becomes or produces conscious thoughts.  It doesn't include bodily housekeeping and transduction of signals.

Brent

[Philip Thrift]

I guess then in the case of the output object ο above, the part not implementing the experiential modalities of λ minus its the part implementing its "bodily house keeping" would be its subconscious.

- pt

[Bruno Marchal]

On 1 Oct 2018, at 14:20, agrays...@gmail.com wrote:

On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:

On 30 Sep 2018, at 16:30, Philip Thrift <cloud...@gmail.com> wrote:

On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:

[Re:] forcing theory in set theories with classes. 

Bruno

Do you follow the work of Joel David Hamkins (forcing applied to set-theoretic "multiverse", etc.)

(I have a basic idea of a type-theoretic parallel to this.)

The set-theoretic multiverse

https://arxiv.org/abs/1108.4223

Joel David Hamkins

@JDHamkins

Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow in Philosophy, University College Oxford. Formerly of New York.

http://jdh.hamkins.org

The math is interesting, and could be of some use, but it is a priori far too much Aristotelian to be coherent with the mechanist hypothesis. That should follow “easily” from the result described in most of my papers on this subject. The author does not seem aware of the mind-body problem, which put extreme constraints on what the physical reality can come from. Even Peano arithmetic, although integral part of the notion of observer, is too much rich for the ontology, where not only the axiom of infinity is too strong,

Since you want to banish the concept of infinity from mathematics, how would you define, say, the limit of an "infinite" series? How would you even discuss this series in the context of finite mathematics? AG

Good question.

The answer is not simple technically. The point is that using only the theory Q (Robinson Arithmetic) or SK (the combinators), I can define the universal (Turing, Church) machine, and the concept of infinity will be a tool used by them in their mathematics.

I do not ban anything from mathematics, nor from physics. I ban only infinity from the ontological terms. I ban only infinity in the metaphysics/theology. (Even God is not ontological, like in Proclus or Plotinus theology).

Have you understand the post on Church’s thesis. You might tell me as this will help me to see how to proceed to make you grasp all this.

Bruno

[Philip Thrift]

On Tuesday, October 2, 2018 at 2:20:10 AM UTC-5, Bruno Marchal wrote:

On 1 Oct 2018, at 14:20, agrays...@gmail.com wrote:

On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:

On 30 Sep 2018, at 16:30, Philip Thrift <cloud...@gmail.com> wrote:

On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:

[Re:] forcing theory in set theories with classes. 

Bruno

Do you follow the work of Joel David Hamkins (forcing applied to set-theoretic "multiverse", etc.)

(I have a basic idea of a type-theoretic parallel to this.)

The set-theoretic multiverse

https://arxiv.org/abs/1108.4223

Joel David Hamkins

@JDHamkins

Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow in Philosophy, University College Oxford. Formerly of New York.

http://jdh.hamkins.org

The math is interesting, and could be of some use, but it is a priori far too much Aristotelian to be coherent with the mechanist hypothesis. That should follow “easily” from the result described in most of my papers on this subject. The author does not seem aware of the mind-body problem, which put extreme constraints on what the physical reality can come from. Even Peano arithmetic, although integral part of the notion of observer, is too much rich for the ontology, where not only the axiom of infinity is too strong,

Since you want to banish the concept of infinity from mathematics, how would you define, say, the limit of an "infinite" series? How would you even discuss this series in the context of finite mathematics? AG

Good question.

The answer is not simple technically. The point is that using only the theory Q (Robinson Arithmetic) or SK (the combinators), I can define the universal (Turing, Church) machine, and the concept of infinity will be a tool used by them in their mathematics.

I do not ban anything from mathematics, nor from physics. I ban only infinity from the ontological terms. I ban only infinity in the metaphysics/theology. (Even God is not ontological, like in Proclus or Plotinus theology).

Have you understand the post on Church’s thesis. You might tell me as this will help me to see how to proceed to make you grasp all this.

Bruno

What do you think of bounded arithmetic and other "finitist" approaches?

https://en.wikipedia.org/wiki/Bounded_arithmetic

see bibliography: http://jeanpaulvanbendegem.be/home/papers/strict-finitism/

Computable real analysis (one can teach computable calculus instead of "conventional" calculus) is essentially finitist:

https://en.wikipedia.org/wiki/Computable_analysis

One can formulate the Axiom of Infinity [ https://en.wikipedia.org/wiki/Axiom_of_infinity ] in a type of bounded set theory (Jan Mycielski [ https://en.wikipedia.org/wiki/Jan_Mycielski ], described in https://books.google.com/books/about/Understanding_the_Infinite.html?id=GvGqRYifGpMC ]. What results is an "ontology" of bigger and bigger finite sets of numbers with gaps in them.

 - pt

[agrays...@gmail.com]

On Tuesday, October 2, 2018 at 7:20:10 AM UTC, Bruno Marchal wrote:

On 1 Oct 2018, at 14:20, agrays...@gmail.com wrote:

On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:

On 30 Sep 2018, at 16:30, Philip Thrift <cloud...@gmail.com> wrote:

On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:

[Re:] forcing theory in set theories with classes. 

Bruno

Do you follow the work of Joel David Hamkins (forcing applied to set-theoretic "multiverse", etc.)

(I have a basic idea of a type-theoretic parallel to this.)

The set-theoretic multiverse

https://arxiv.org/abs/1108.4223

Joel David Hamkins

@JDHamkins

Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow in Philosophy, University College Oxford. Formerly of New York.

http://jdh.hamkins.org

The math is interesting, and could be of some use, but it is a priori far too much Aristotelian to be coherent with the mechanist hypothesis. That should follow “easily” from the result described in most of my papers on this subject. The author does not seem aware of the mind-body problem, which put extreme constraints on what the physical reality can come from. Even Peano arithmetic, although integral part of the notion of observer, is too much rich for the ontology, where not only the axiom of infinity is too strong,

Since you want to banish the concept of infinity from mathematics, how would you define, say, the limit of an "infinite" series? How would you even discuss this series in the context of finite mathematics? AG

Good question.

The answer is not simple technically. The point is that using only the theory Q (Robinson Arithmetic) or SK (the combinators), I can define the universal (Turing, Church) machine, and the concept of infinity will be a tool used by them in their mathematics.

I do not ban anything from mathematics, nor from physics. I ban only infinity from the ontological terms. I ban only infinity in the metaphysics/theology. (Even God is not ontological, like in Proclus or Plotinus theology).

Have you understand the post on Church’s thesis. You might tell me as this will help me to see how to proceed to make you grasp all this.

Bruno

You only ban infinity from ontological terms? I have no idea what this means. I do know you start with the natural numbers, presumably an infinite set and existing in some Platonic realm. So I have no idea about your aversion or denial of infinity. As for the Church's thesis, I have set aside a copy of Chrome with several relevant topics which I see as prerequisites to that understanding including, for example, Cantor's theorem, but have yet to get into it seriously due to personal issues and computer problems in Russia and Ukraine (the latter now solved). But when I do, I'll get back to you. AG

[Bruno Marchal]

I wrote a paper on this, in a book in honour to Jean-paul Vanbendegem. But its approach is more than finitist, and a bit less than ultra-finitism. It does not fit the study of the “theology” of the machine, and is thus useless for deriving physics. That does not mean it is not interesting pragmatically, on the contrary, it is well fitted with the goal to make usable programs. I do think that mathematically, it is also a restriction of Post creativity (Turing universality in set theoretical terms) to sub creativity. There is no possible universal machine there.

Computable real analysis (one can teach computable calculus instead of "conventional" calculus) is essentially finitist:

https://en.wikipedia.org/wiki/Computable_analysis

One can formulate the Axiom of Infinity [ https://en.wikipedia.org/wiki/Axiom_of_infinity ] in a type of bounded set theory (Jan Mycielski [ https://en.wikipedia.org/wiki/Jan_Mycielski ], described in https://books.google.com/books/about/Understanding_the_Infinite.html?id=GvGqRYifGpMC ]. What results is an "ontology" of bigger and bigger finite sets of numbers with gaps in them.

Yes, and that is interesting. But not so much for the mind-body problem, where we cannot bound anything, except by omega. 

The weaker theory known from which my approach can work, is the delta_0-induction based on Q + the axioms for the exponential, known as Delta_0Exp. That is Q:

1) 0 ≠ s(x)
2) x ≠ y -> s(x) ≠ s(y)
3) x ≠ 0 -> Ey(x = s(y)) 
4) x+0 = x
5) x+s(y) = s(x+y)
6) x*0=0
7) x*s(y)=(x*y)+x

+ 

8) x^0 = 1

9) x^s(y) = x * (x^y)

+ the scheme of induction axioms:

P(0) & [For all n (P(n) -> P(s(n)))] ->. For all n P(n),

with P restricted to the delta_0 (= sigma_0 = pi_0 = recursive, decidable, …) formula.

That is the weaker Löbian machine known today.

In between Q and Delta_0Exp, you have all the bounded arithmetics.

An excellent book on this is (without the many accent for the names):

Hajek, P. & Pudlak P., 1993, Metamathematics of First-Order Arithmetic, Springer-Verlag.

But no need of this for the mind body problem, which needs at least Delta_0Exp (Löbianity), for the observer. Of course I use the fact that Q can mimic Delta_0Exp. But Q does not believe what Delta_0Exp is saying, and the theology is for Delta_0Exp and all its consistent extensions, like PA, ZF, and you, and me …

I need the sigma_1 completeness. It is not for practical computational application, but only for guessing what is fundamental to assume, to understand where the appearances come from. It might have application in the foundations of physics, though, and is the best way to figure out the structure of the afterlife or parallel life, etc.

[Bruno Marchal]

On 2 Oct 2018, at 10:14, agrays...@gmail.com wrote:

On Tuesday, October 2, 2018 at 7:20:10 AM UTC, Bruno Marchal wrote:

On 1 Oct 2018, at 14:20, agrays...@gmail.com wrote:

On Monday, October 1, 2018 at 11:47:47 AM UTC, Bruno Marchal wrote:

On 30 Sep 2018, at 16:30, Philip Thrift <cloud...@gmail.com> wrote:

On Sunday, September 30, 2018 at 4:50:01 AM UTC-5, Bruno Marchal wrote:

[Re:] forcing theory in set theories with classes. 

Bruno

Do you follow the work of Joel David Hamkins (forcing applied to set-theoretic "multiverse", etc.)

(I have a basic idea of a type-theoretic parallel to this.)

The set-theoretic multiverse

https://arxiv.org/abs/1108.4223

Joel David Hamkins

@JDHamkins

Professor of Logic, University of Oxford, and Sir Peter Strawson Fellow in Philosophy, University College Oxford. Formerly of New York.

http://jdh.hamkins.org

The math is interesting, and could be of some use, but it is a priori far too much Aristotelian to be coherent with the mechanist hypothesis. That should follow “easily” from the result described in most of my papers on this subject. The author does not seem aware of the mind-body problem, which put extreme constraints on what the physical reality can come from. Even Peano arithmetic, although integral part of the notion of observer, is too much rich for the ontology, where not only the axiom of infinity is too strong,

Since you want to banish the concept of infinity from mathematics, how would you define, say, the limit of an "infinite" series? How would you even discuss this series in the context of finite mathematics? AG

Good question.

The answer is not simple technically. The point is that using only the theory Q (Robinson Arithmetic) or SK (the combinators), I can define the universal (Turing, Church) machine, and the concept of infinity will be a tool used by them in their mathematics.

I do not ban anything from mathematics, nor from physics. I ban only infinity from the ontological terms. I ban only infinity in the metaphysics/theology. (Even God is not ontological, like in Proclus or Plotinus theology).

Have you understand the post on Church’s thesis. You might tell me as this will help me to see how to proceed to make you grasp all this.

Bruno

You only ban infinity from ontological terms? I have no idea what this means.

It means that 0 exist, 1, exists, 2 exists, etc.

I do know you start with the natural numbers, presumably an infinite set and existing in some Platonic realm.

Not really. Only 0, 1, 2, …

But not {0, 1, 2, 3 …}, which is not a natural number.

It means that my axioms, for the whole theory of everything including consciousness is literally just classical logic + the axioms of Q:

1) 0 ≠ s(x)
2) x ≠ y -> s(x) ≠ s(y)
3) x ≠ 0 -> Ey(x = s(y)) 
4) x+0 = x
5) x+s(y) = s(x+y)
6) x*0=0
7) x*s(y)=(x*y)+x

There is no infinity axiom, nor any infinite object in the intended model. What is proved from Q is true in all models (interpretations) of Q.

I don’t even allow the induction axioms, despite the phenomenology use them, as Q is rich enough to mimic the believer in the induction axioms, and indeed the believer in infinity (like the ZF machine).

To grasp this it is important to understand the difference between compute and proof.

Keep in mind that Q can mimic ZF proving the consistence of Q; but that cannot convince Q of its consistency (by the second incompleteness theorem of Gödel).

So I have no idea about your aversion or denial of infinity.

No aversion at all. It is just part of the phenomenology, and if I put it in the ontology, the “white rabbits” becomes to numerous, and the physics predicts too many things.

As for the Church's thesis, I have set aside a copy of Chrome with several relevant topics which I see as prerequisites to that understanding including, for example, Cantor's theorem, but have yet to get into it seriously due to personal issues and computer problems in Russia and Ukraine (the latter now solved). But when I do, I'll get back to you. AG

OK. Normally my post was self contained. (Except for the notion of function). Ask any question.

Bruno 

[Philip Thrift]

When if comes to just physics, what is there in the application of any theory of physics (QM, GR, The Standard Model, ...) to experiments can't be done in replacing the theory with a Python program, of a Go program or whatever. 

Physicists take a theory T and replace it with a program P that then is used to match with data D. The theory T is completely dispensable. Only P matters, because it is only P that us used to say whether a theory T matches D in the results sections of papers.

- pt

[Bruno Marchal]

Reality, even just the arithmetical reality is beyond what can accomplish a program.

The partial computable is the tiny sigma_1 reality (the true proposition having the shape ExP(x) with P decidable). The arithmetical reality is the union of all sigma_i reality (i =  0, 1, 2, …). It contains the truth of proposition like (x)(Ey)(z)(Eu)P(x,y,z,u), which might be decidable or not. 

To apply a theory for a prediction in the physical reality, you need also an identity brain/mind, which cannot been afforded in the arithmetical reality, a priori.

Physicists take a theory T and replace it with a program P that then is used to match with data D.

How? You first person state of mind is realised by an infinity of computations in the arithmetical reality, so the identity used by the physicalist does not work. A vague consciousness of this is reflected in the Boltzman brain problem, which is a very particular case in the universal dovetailing that is isomorphic (for computability) with the sigma_1 arithmetical reality.

The theory T is completely dispensable. Only P matters, because it is only P that us used to say whether a theory T matches D in the results sections of papers.

The theory will corresponds to the observer. To say that the theory is dispensable, is like to say that both a brain and a telescope is dispensable for the existence of the far away galaxy. But brain, telescope are also natural process that we have to explain. Proving, knowing, observing, … are different from computing, even if they are definable in term of computations and their relation with truth. Eventually, the physical reality is a non computable things emerging from all computation. 

I assume Digital Mechanism all along, to be sure.

[Philip Thrift]

Suppose one starts with the PLTOS template:

PLTOS(π,λ,τ,ο,Σ) designates a program π that is written in a language λ that is transformed via a compiler/assembler τ into an output object ο that executes in a computing substrate Σ.

Suppose Σ = UniversalNumbers 

That is, the computing substrate is the actual Universal Numbers (arithmetic reality).

What would be the programs and languages (π,λ) that could be defined?

- pt

 

 

[Bruno Marchal]

You need a universal machinery. Very elementary arithmetic (like Peano without induction) determines such a universal machinery (the phi_i), then, you get all the universal number u (such that phi_u(x,y) = phi_x(y), and each u defines its own universal machinerery: phi_u(0, _), phi_u(0, _), phi_u(1, _), phi_u(2, _), …

All universal “thing” mimic all universal “thing”, but they have special statistical relation, and different personal beliefs. They determine (in the arithmetical reality) the “consciousness flux”, which determine the (unique!) physical reality, which is a sort of multiverse/multi-dreams.

What would be the programs and languages (π,λ) that could be defined?

All of them, but with their different relative measure. They are mathematically determined by the G* logic (self-referential truth).

[Philip Thrift]

Approaching this with a PLTOS template identifies the parts  π,λ,τ,ο,Σ. What is the compiler/assembler τ for example?

(PLTOS is a bit of a play-on-words: It looks like PLT Operating System.)

In PLT (programming language theory), one part of comprehending the whole shebang is in terms of semantics, specifically its denotational vs operational semantics [ http://courses.cs.vt.edu/~cs3304/Spring04/notes/Chapter-3b ].

In the case of "real" hardware Σ (is there a CPU or a GPU or a TPU - Google's NN chip?) then the operational semantics are significant.

In the case of Σ = UniversalNumbers/UniversalMachine it is a bit difficult to see what the operational semantics would be.

- pt

[Brent Meeker]

On 10/4/2018 12:06 AM, Bruno Marchal wrote:

You need a universal machinery. Very elementary arithmetic (like Peano without induction) determines such a universal machinery (the phi_i), then, you get all the universal number u (such that phi_u(x,y) = phi_x(y), and each u defines its own universal machinerery: phi_u(0, _), phi_u(0, _), phi_u(1, _), phi_u(2, _), …

All universal “thing” mimic all universal “thing”, but they have special statistical relation, and different personal beliefs. They determine (in the arithmetical reality) the “consciousness flux”, which determine the (unique!) physical reality, which is a sort of multiverse/multi-dreams.

What would be the programs and languages (π,λ) that could be defined?

All of them, but with their different relative measure. They are mathematically determined by the G* logic (self-referential truth).

What is the measure on universal machines in arithmetic?

Brent

[Bruno Marchal]

It is the association i ==> phi_i, that is of a function (seen as infinite set of input/ouput) to its code, or anything recursively equivalent. Some caution is needed here, but they are not so important, because the main semantics will be brought by the machine/code themselves, by the numbers bring to figure out what happens, like we do now. The theology (including the physics) is independent of the choice of the initial universal system. I use elementary arithmetic (which has a simple familiar semantics), or the combinators (which are operationally easy, even if the usual extensional semantics is not obvious, but eventually clarified by the denotational work of Dana Scott). The hardware and software distinction is locally relative, but eventually, the hardware get absolute by being a first person statistics on all software possible below our substitution level. This follows simply from the first person/third person distinction.

[Bruno Marchal]

It is given by the “Gleason-like” unique measure on the proposition entailed by the variants of the logic of self-reference: mainly, with p sigma_1-arithmetical (or combinatorical) sentences, the variants are given by []p & p, []p & <>t and []p & <>t & p. The facts that we obtain quantum logics there is a good sign, but much more work need to be done to get the mathematical form and uniqueness of it.If there is no such measure, which is still possible, Mechanism would be refuted. Up to now, the three quantum logic does not depart from the minimal quantum logic, part of all quantum logic inferred from the observation.

Bruno

Brent

[Tomas Pales]

I am generally sympathetic to Tegmark's mathematical multiverse idea, but I have two comments/criticisms to it:

1) I am not sure whether Tegmark is aware of the so-called "instantiation" relation. In philosophy, the instantiation relation is the relation between a general and a particular object, where the particular object is an instance of the general object. In other words, the general object is a property of the particular object. Example: general triangle (or triangle "in general") is the property of any particular triangle, and any particular triangle is an instance of general triangle. Another example: number 2 is a general relation that is instantiated in the particular relation between any two objects. I am not sure whether Tegmark realizes the difference between general objects and their instances, because he said something like: when we probe matter we only find numbers (and hence reality is just mathematics). But numbers cannot be found in our world; you cannot find number 2 sitting on a tree or in the atomic nucleus. You can only find instances of number 2, as relations between particular objects. Mathematical objects are usually thought to be general objects, but in that case there is more in reality than mathematical objects: there are general objects and their instances. And in our physical world there are no general objects, only their instances. If we want to say that there are mathematical objects in our physical world, we should include among mathematical objects also non-general objects, that is, objects that have no instances. (By the way, there is a hierarchy of generality: more general objects are instantiated in less general objects and those are ultimately instantiated in non-general objects. Non-general objects are often called "concrete", while general objects are also called "abstract".)

2) While I agree with Tegmark that reality contains all mathematical objects (both general and non-general), I think there is also a non-mathematical aspect of reality. That's because mathematical objects are relations or structures of relations, but relations cannot exist without objects between which they hold. While it is true that relations can hold between other relations, there should also be objects that are non-relations, which ultimately make sense of all relations. These non-relations are the non-mathematical objects and they (or at least some of them) may be the qualities of consciousness (qualia) - because (1) they have an unanalyzable/unstructured nature, and (2) they stand in relations to other objects (relations or non-relations) that we call "correlates of consciousness".

Tomas

[Philip Thrift]

Ironically, Tegmark doesn't believe that at all. He says infinite mathematical entities are "ruining physics".

- http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/

The only thing to conclude is that Mad Max published his mathematical universe hypothesis as a joke!

- https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis

- pt 

[Philip Thrift]

BTW,  on "non-relations [which] are the non-mathematical objects and they (or at least some of them) may be the qualities of consciousness (qualia)", that is what I try to address in 

        https://codicalist.wordpress.com/2018/10/14/experience-processing/

where there is information processing (which is all mathematical processing) and something else: experience processing.

- pt

[Tomas Pales]

On Sunday, October 21, 2018 at 4:28:21 PM UTC+2, Philip Thrift wrote:

      "reality contains all mathematical objects"

Ironically, Tegmark doesn't believe that at all. He says infinite mathematical entities are "ruining physics".

- http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/

The only thing to conclude is that Mad Max published his mathematical universe hypothesis as a joke!

- https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis

Already in his Mathematical Universe paper on arxiv, Tegmark discussed a restricted version of MUH called CUH (computable universe hypothesis). He mentioned that the attractive feature of CUH would be the disappearance of the measure problem and also the exclusion of structures of which we may never know whether they are consistent (due to Godel's second incompleteness theorem) and thus whether they exist. On the other hand, the fact that we cannot calculate probabilities (the measure problem) or find whether a structure is consistent seems like an epistemic problem, not an ontological one. The infinities may exist in reality, we just can't extract useful statistics from them or confirm their existence. But reality doesn't depend on whether we find it useful or whether we can confirm its existence.

The universe in which we live, or even the inflationary multiverse, may be a finite/computable structure but there may also be infinite structures in the larger mathematical multiverse. 

[Philip Thrift]

If our universe does not have infinitely-computing objects but there are other universes that do, that would seem strange.

Why would our universe be left out? :)

- pt 

[Tomas Pales]

On Sunday, October 21, 2018 at 5:52:13 PM UTC+2, Philip Thrift wrote:

If our universe does not have infinitely-computing objects but there are other universes that do, that would seem strange.

Why would our universe be left out? :)

The mathematical multiverse would contain all possible (consistently defined) mathematical structures, both finite and infinite. We would live in a finite one. Why? I don't know. Maybe just by accident. Or maybe only finite structures can contain conscious entities. 

[Tomas Pales]

On Sunday, October 21, 2018 at 5:22:20 PM UTC+2, Philip Thrift wrote:

BTW,  on "non-relations [which] are the non-mathematical objects and they (or at least some of them) may be the qualities of consciousness (qualia)", that is what I try to address in 

        https://codicalist.wordpress.com/2018/10/14/experience-processing/

where there is information processing (which is all mathematical processing) and something else: experience processing.

- pt

I would say that any description is relational and therefore mathematical/logical. When you describe an object you always define/present it in relations to other objects - in relations to its parts or properties. You can't describe the object itself, only give it a label. So you can't describe qualities of consciousness themselves either. Not sure how you would "process" them then.

Is there really a fundamental difference between hardware and software? I mean, software can be seen as part of hardware: software is a particular configuration of electron flows in hardware.

[Philip Thrift]

Mathematics is genre of fiction [ https://plato.stanford.edu/entries/fictionalism-mathematics/ ], so relations are fictional. "Processing" relations/mathematics has no real meaning.

The difference between hardware and software today is somewhat blurred with synthetic biology, programmable matter, reconfigurable hardware.

- pt

[Brent Meeker]

On 10/21/2018 7:11 AM, Tomas Pales wrote:

I am generally sympathetic to Tegmark's mathematical multiverse idea, but I have two comments/criticisms to it:

1) I am not sure whether Tegmark is aware of the so-called "instantiation" relation. In philosophy, the instantiation relation is the relation between a general and a particular object, where the particular object is an instance of the general object. In other words, the general object is a property of the particular object. Example: general triangle (or triangle "in general") is the property of any particular triangle, and any particular triangle is an instance of general triangle. Another example: number 2 is a general relation that is instantiated in the particular relation between any two objects. I am not sure whether Tegmark realizes the difference between general objects and their instances, because he said something like: when we probe matter we only find numbers (and hence reality is just mathematics). But numbers cannot be found in our world; you cannot find number 2 sitting on a tree or in the atomic nucleus. You can only find instances of number 2, as relations between particular objects. Mathematical objects are usually thought to be general objects, but in that case there is more in reality than mathematical objects: there are general objects and their instances. And in our physical world there are no general objects, only their instances. If we want to say that there are mathematical objects in our physical world, we should include among mathematical objects also non-general objects, that is, objects that have no instances. (By the way, there is a hierarchy of generality: more general objects are instantiated in less general objects and those are ultimately instantiated in non-general objects. Non-general objects are often called "concrete", while general objects are also called "abstract".)

This appears not to be a well-order hierarchy.  The thing I am sitting on is an instance of a chair, and it's concrete.  But it's also an instance of a matter, i.e. a collection of particles of the Standard Model (which may or may not be the most general category).  It's also an instance of things I own.

2) While I agree with Tegmark that reality contains all mathematical objects (both general and non-general), I think there is also a non-mathematical aspect of reality. That's because mathematical objects are relations or structures of relations, but relations cannot exist without objects between which they hold. While it is true that relations can hold between other relations, there should also be objects that are non-relations, which ultimately make sense of all relations. These non-relations are the non-mathematical objects and they (or at least some of them) may be the qualities of consciousness (qualia) - because (1) they have an unanalyzable/unstructured nature, and (2) they stand in relations to other objects (relations or non-relations) that we call "correlates of consciousness".

Can  you clarify with some examples?

Brent

[Tomas Pales]

On Sunday, October 21, 2018 at 11:16:29 PM UTC+2, Brent wrote:

On 10/21/2018 7:11 AM, Tomas Pales wrote:

I am generally sympathetic to Tegmark's mathematical multiverse idea, but I have two comments/criticisms to it:

1) I am not sure whether Tegmark is aware of the so-called "instantiation" relation. In philosophy, the instantiation relation is the relation between a general and a particular object, where the particular object is an instance of the general object. In other words, the general object is a property of the particular object. Example: general triangle (or triangle "in general") is the property of any particular triangle, and any particular triangle is an instance of general triangle. Another example: number 2 is a general relation that is instantiated in the particular relation between any two objects. I am not sure whether Tegmark realizes the difference between general objects and their instances, because he said something like: when we probe matter we only find numbers (and hence reality is just mathematics). But numbers cannot be found in our world; you cannot find number 2 sitting on a tree or in the atomic nucleus. You can only find instances of number 2, as relations between particular objects. Mathematical objects are usually thought to be general objects, but in that case there is more in reality than mathematical objects: there are general objects and their instances. And in our physical world there are no general objects, only their instances. If we want to say that there are mathematical objects in our physical world, we should include among mathematical objects also non-general objects, that is, objects that have no instances. (By the way, there is a hierarchy of generality: more general objects are instantiated in less general objects and those are ultimately instantiated in non-general objects. Non-general objects are often called "concrete", while general objects are also called "abstract".)

This appears not to be a well-order hierarchy.  The thing I am sitting on is an instance of a chair, and it's concrete.  But it's also an instance of a matter, i.e. a collection of particles of the Standard Model (which may or may not be the most general category).  It's also an instance of things I own.

Yes, it is not always possible to say that one object is more general than another. Matter (the property of being a material object) is more general than chair (the property of being a chair) because the set of chairs is a subset of the set of material objects. But the property of being a chair is not necessarily more or less general than the property of being a thing you own.

 

2) While I agree with Tegmark that reality contains all mathematical objects (both general and non-general), I think there is also a non-mathematical aspect of reality. That's because mathematical objects are relations or structures of relations, but relations cannot exist without objects between which they hold. While it is true that relations can hold between other relations, there should also be objects that are non-relations, which ultimately make sense of all relations. These non-relations are the non-mathematical objects and they (or at least some of them) may be the qualities of consciousness (qualia) - because (1) they have an unanalyzable/unstructured nature, and (2) they stand in relations to other objects (relations or non-relations) that we call "correlates of consciousness".

Can  you clarify with some examples?

Relation is an object that holds between other objects. (By the way, all relations are instances of the similarity relation, which means that the objects between which a similarity relation holds have some same property and some different property.) But how could there only be relations between other relations that are relations between other relations etc., just relations? It seems that the definition of all those relations would be infinitely postponed; they would never be defined. And if you wanted to make a finite structure of relations that is ultimately cyclical, where relations are defined in relation to each other, every relation in that structure would end up being defined as a relation between itself and other relations. Which is another nonsense, because a relation holds between other objects than itself.