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Thanks again Marcus

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jon zingale

Thanks again Marcus

https://link.springer.com/article/10.1007/s10670-019-00165-8#Sec6

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thompnickson2

FW: Thanks again Marcus

Hi,

This is directed mostly to steve and frank and anybody else who attended the SFI summer course at St. Johns all those years ago. There was always a set of lectures in which a bunch of old guys went crazy about how discontinuity was the crux of complexity. Sorry to put it so ham-handedly, but I never quite understood. It was something like, “because we treat our parameter spaces as continuous, when they are actually discontinuous, that we misunderstand all sorts of natural phenomena, including high tails.” My intuition was that the lecturers were on trick ponies who never figured out what their trick was actually worth.

So, is this paper the same thing? And should I have been paying better attention to those lecturers?

Nick

Nicholas Thompson

Emeritus Professor of Ethology and Psychology

Clark University

[hidden email]

https://wordpress.clarku.edu/nthompson/

-----Original Message-----
From: Friam <[hidden email]> On Behalf Of Jon Zingale
Sent: Friday, June 19, 2020 1:21 PM
To: [hidden email]
Subject: [FRIAM] Thanks again Marcus

https://link.springer.com/article/10.1007/s10670-019-00165-8#Sec6

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jon zingale

Re: Thanks again Marcus

In reply to this post by jon zingale

Relatedly,

A lecture by Chris Isham, whose topos is discussed a bit in Smolin's
book 'Three roads to quantum gravity', lectures on results from his
paper on Toposes, Heidegger, and the foundations of physics.

jon zingale

Re: Thanks again Marcus

Also, for a non-general public but otherwise gentle technical
introduction to toposes, here is a set of lectures with Andre Joyal.
Presently, I am finishing up part 1 of 4 and would love to chat
with any other interested parties.

https://www.youtube.com/watch?v=Ro8KoFFdtS4

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thompnickson2

Re: Thanks again Marcus

In reply to this post by jon zingale

Oh, Jon,

In sofaras I am able I read this paper. I don't see how it relates to the
Peircian principle that most sequences of events are random, but that
organisms (including physicists) should be tuned to the ones that aren't.

I am still wondering if there is any relation between this paper and those
endless lectures on the relation between discontinuity and complexity in the
SFI summer school. Here is how I get there. Every real number has an
infinity of information, which I read as, every real number has an infinite
number of digits. So the numbers that physicists use, which are necessarily
truncated, aren't real numbers. Did I get anywhere close?

Nick

Nicholas Thompson
Emeritus Professor of Ethology and Psychology
Clark University
[hidden email]
https://wordpress.clarku.edu/nthompson/

-----Original Message-----
From: Friam <[hidden email]> On Behalf Of Jon Zingale
Sent: Friday, June 19, 2020 1:21 PM
To: [hidden email]
Subject: [FRIAM] Thanks again Marcus

https://link.springer.com/article/10.1007/s10670-019-00165-8#Sec6

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jon zingale

Re: Thanks again Marcus

This post was updated on .

The numbers most physicists use are finitely specifiable. π, for instance,
has an infinite and non-repeating representation and yet there exist
algorithms to get whatever nth digit you desire. Numbers like π are said to
be computable and so are expressible in a finite way. Physicists get to keep
π. There are other numbers, like Chaitin's constant, which have no such
algorithm. What is worse, there are so many more of these numbers that the
numbers physicists use may as well not exist, they are so few. The paper
goes on to speak of these non-computable numbers as being, in essence, what
we mean by a random number. To my mind, this is akin to Peirce's statement
that nearly everything is random. Gisin continues by pointing out that these
numbers, as they would take an infinite amount of energy to store in a
finite space, are decidedly non-physical. Chaitin points out that we cannot
even really get to know them as there is nothing we can say about them. It
seems if Pierce accepted such a thing that he might too consider them to be
non-meaningful.

So now, left with only those numbers which behave nicely in that they are
finitely storable and can be computed, we are left with numbers that can be
compared or related. Because everywhere the word number appeared above you
can substitute some physical thing (energy-matter), we have a situation
where we can speak about what is real through relations even though anything
that can be considered real is vanishingly small wrt what is random.

The last detail, which seems relevant is that some dynamics (really most
dynamics) are notoriously badly behaved. That is, long term prediction in
classical physics is notoriously sensitive to initial conditions. The fact
that information in our model universe is finite, as understood above, those
initial conditions will march towards randomness despite the fact that the
dynamics are determined. I don't know Pierce's work outside of things you
have told me, but it seems that there might be similarities worth pursuing.

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Frank Wimberly-2

Re: Thanks again Marcus

In reply to this post by thompnickson2

I have a different answer from Jon's which is my understanding and which I hope is helpful. Every rational number (the ones physicists use, like 2.0)

is also a real number. They also use truncated irrational numbers like pi and sqrt(2) in their calculations--that is, 3.14159265 (a rational number) instead of pi. They use pi in theoretical derivations. As Jon says, there are uncountably many non-rational numbers.

As for sensitivity to initial conditions, physicists or engineers calculate the trajectory of a probe to Pluto and they launch with an initial impulses or set of impulses which won't result in an exact arrival at Pluto. The saving grace is that they can apply small impulses (f*deltat) later in the trip to make corrections.

Frank

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Fri, Jun 19, 2020, 9:36 PM <[hidden email]> wrote:

Oh, Jon,

In sofaras I am able I read this paper. I don't see how it relates to the
Peircian principle that most sequences of events are random, but that
organisms (including physicists) should be tuned to the ones that aren't.

I am still wondering if there is any relation between this paper and those
endless lectures on the relation between discontinuity and complexity in the
SFI summer school. Here is how I get there. Every real number has an
infinity of information, which I read as, every real number has an infinite
number of digits. So the numbers that physicists use, which are necessarily
truncated, aren't real numbers. Did I get anywhere close?

Nick

Nicholas Thompson
Emeritus Professor of Ethology and Psychology
Clark University
[hidden email]
https://wordpress.clarku.edu/nthompson/

-----Original Message-----
From: Friam <[hidden email]> On Behalf Of Jon Zingale
Sent: Friday, June 19, 2020 1:21 PM
To: [hidden email]
Subject: [FRIAM] Thanks again Marcus

https://link.springer.com/article/10.1007/s10670-019-00165-8#Sec6

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jon zingale

Re: Thanks again Marcus

In reply to this post by jon zingale

I think that reinterpreting computability in terms of truncation
obfuscates the philosophical content that may be of interest to Nick.
As a thought experiment, consider the collection of all computable
sequences. Each sequence will in general have many possible algorithms
that produce the given sequence up to the nth digit. Those algorithms
which produce the same sequence for all n can be considered the same.
Others that diverge at some digit are simply approximations. Now, if I
am given a number like π, I can stably select from the collection of
possible algorithms.

Now we can play a game. To begin, the dealer produces n digits of a
sequence and the players all choose some algorithm which they think
produce the dealer's sequence. Next, the dealer proceeds to expose
more and more digits beginning with the n+1th digit and continuing until
all but one player, say, is shown to have chosen an incorrect algorithm.
In the case of π, one can exactly choose a winning algorithm. If the
dealer had chosen a random number, a player cannot win without
cheating by forever changing their algorithm.

This seems to be a point of Gisin's argument, there is meaningful
philosophical content in the computability claim. He is not saying
that the rationals are real, he is saying that the reals are not.
π is a special kind of non-algebraic number in that it is computable,
and not just a matter of measurement. It is this switch away from

measurement that distinguishes it (possibly frees it) from the kinds

of pitfalls we see in quantum interpretations, the subjectivity with

which we choose our truncations is irrelevant. A similar argument is

made by Chris Isham.

Frank Wimberly-2

Re: Thanks again Marcus

I understand, Jon. Do you Nick? I think (hope) he understands my explanation.

A clarification between me and you, Jon. A rational number isn't literally a real number but the field of rational numbers is isomorphic to a subfield of the field of real numbers so it makes sense to identify a rational number with its image under that isomorphism.

Can you explain the assertion that real numbers aren't real? Obviously the scientists and engineers who compute the trajectory of a probe to the outer reaches of the Solar System don't choose among algorithms to compute the nth digit of pi and other real numbers.

Frank

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Sat, Jun 20, 2020, 9:12 AM Jon Zingale <[hidden email]> wrote:

I think that reinterpreting computability in terms of truncation
obfuscates the philosophical content that may be of interest to Nick.
As a thought experiment, consider the collection of all computable
sequences. Each sequence will in general have many possible algorithms
that produce the given sequence up to the nth digit. Those algorithms
which produce the same sequence for all n can be considered the same.
Others that diverge at some digit are simply approximations. Now, if I
am given a number like π, I can stably select from the collection of
possible algorithms.

Now we can play a game. To begin, the dealer produces n digits of a
sequence and the players all choose some algorithm which they think
produce the dealer's sequence. Next, the dealer proceeds to expose
more and more digits beginning with the n+1th digit and continuing until
all but one player, say, is shown to have chosen an incorrect algorithm.
In the case of π, one can exactly choose a winning algorithm. If the
dealer had chosen a random number, a player cannot win without
cheating by forever changing their algorithm.

This seems to be a point of Gisin's argument, there is meaningful
philosophical content in the computability claim. He is not saying
that the rationals are real, he is saying that the reals are not.
π is a special kind of non-algebraic number in that it is computable,
and not just a matter of measurement. It is this switch away from
measurement that distinguishes it (possibly frees it) from the kinds
of pitfalls we see in quantum interpretations, the subjectivity with
which we choose our truncations is irrelevant. A similar argument is
made by Chris Isham.
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Frank Wimberly-2

Re: Thanks again Marcus

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679...

is enough.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Sat, Jun 20, 2020, 10:01 AM Frank Wimberly <[hidden email]> wrote:

I understand, Jon. Do you Nick? I think (hope) he understands my explanation.

A clarification between me and you, Jon. A rational number isn't literally a real number but the field of rational numbers is isomorphic to a subfield of the field of real numbers so it makes sense to identify a rational number with its image under that isomorphism.

Can you explain the assertion that real numbers aren't real? Obviously the scientists and engineers who compute the trajectory of a probe to the outer reaches of the Solar System don't choose among algorithms to compute the nth digit of pi and other real numbers.

Frank

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Sat, Jun 20, 2020, 9:12 AM Jon Zingale <[hidden email]> wrote:
I think that reinterpreting computability in terms of truncation
obfuscates the philosophical content that may be of interest to Nick.
As a thought experiment, consider the collection of all computable
sequences. Each sequence will in general have many possible algorithms
that produce the given sequence up to the nth digit. Those algorithms
which produce the same sequence for all n can be considered the same.
Others that diverge at some digit are simply approximations. Now, if I
am given a number like π, I can stably select from the collection of
possible algorithms.

Now we can play a game. To begin, the dealer produces n digits of a
sequence and the players all choose some algorithm which they think
produce the dealer's sequence. Next, the dealer proceeds to expose
more and more digits beginning with the n+1th digit and continuing until
all but one player, say, is shown to have chosen an incorrect algorithm.
In the case of π, one can exactly choose a winning algorithm. If the
dealer had chosen a random number, a player cannot win without
cheating by forever changing their algorithm.

This seems to be a point of Gisin's argument, there is meaningful
philosophical content in the computability claim. He is not saying
that the rationals are real, he is saying that the reals are not.
π is a special kind of non-algebraic number in that it is computable,
and not just a matter of measurement. It is this switch away from
measurement that distinguishes it (possibly frees it) from the kinds
of pitfalls we see in quantum interpretations, the subjectivity with
which we choose our truncations is irrelevant. A similar argument is
made by Chris Isham.
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jon zingale

Re: Thanks again Marcus

This post was updated on .

In reply to this post by Frank Wimberly-2

The isomorphism *isn't*, in some sense, enough. For instance, the rationals
can be philosophically different than the integers. Sure we can identify
them via diagonal argument, but when we want a field we don't reach for the
integers. I claim that something similar is happening here and that the
point of the article is missed when we jump to the isomorphism. Gisin would
have just talked about the rationals if he meant the rationals, instead, he
invokes Chaitin and computability on purpose. The truncation simplification
obfuscates the deeper point. He is making an ontological claim about the
universe and one that theoreticians of quantum theory may appreciate but
applied mathematicians will not. The subjectivity of an observer is forced
on us by classical logic. Here he constructs a physics over a completely
different topos and what follows is not needing to make the observer
interpretation. This point is significant enough to think about as being
*more* than just truncation, it establishes what can be meant by randomness
and the possibility that determinism may be an illusion, even in macroscopic
physics.

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Marcus G. Daniels

Re: Thanks again Marcus

In reply to this post by Frank Wimberly-2

If one is talking about objects within a cutoff of a millimeter, then 8 digits might suffice to talk about the locations of things. If one is talking about objects within Pluto, that’s another 15 digits or so. It’s certainly not surprising that there are computational approximations to real numbers that are inadequate for some things. That doesn’t mean that given a particular context, that there isn’t a sufficient approximation.

From: Friam <[hidden email]> on behalf of Frank Wimberly <[hidden email]>
Reply-To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
Date: Saturday, June 20, 2020 at 9:04 AM
To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
Subject: Re: [FRIAM] Thanks again Marcus

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679...

is enough.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Sat, Jun 20, 2020, 10:01 AM Frank Wimberly <[hidden email]> wrote:

I understand, Jon. Do you Nick? I think (hope) he understands my explanation.

A clarification between me and you, Jon. A rational number isn't literally a real number but the field of rational numbers is isomorphic to a subfield of the field of real numbers so it makes sense to identify a rational number with its image under that isomorphism.

Can you explain the assertion that real numbers aren't real? Obviously the scientists and engineers who compute the trajectory of a probe to the outer reaches of the Solar System don't choose among algorithms to compute the nth digit of pi and other real numbers.

Frank

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Sat, Jun 20, 2020, 9:12 AM Jon Zingale <[hidden email]> wrote:

I think that reinterpreting computability in terms of truncation
obfuscates the philosophical content that may be of interest to Nick.
As a thought experiment, consider the collection of all computable
sequences. Each sequence will in general have many possible algorithms
that produce the given sequence up to the nth digit. Those algorithms
which produce the same sequence for all n can be considered the same.
Others that diverge at some digit are simply approximations. Now, if I
am given a number like π, I can stably select from the collection of
possible algorithms.

Now we can play a game. To begin, the dealer produces n digits of a
sequence and the players all choose some algorithm which they think
produce the dealer's sequence. Next, the dealer proceeds to expose
more and more digits beginning with the n+1th digit and continuing until
all but one player, say, is shown to have chosen an incorrect algorithm.
In the case of π, one can exactly choose a winning algorithm. If the
dealer had chosen a random number, a player cannot win without
cheating by forever changing their algorithm.

This seems to be a point of Gisin's argument, there is meaningful
philosophical content in the computability claim. He is not saying
that the rationals are real, he is saying that the reals are not.
π is a special kind of non-algebraic number in that it is computable,
and not just a matter of measurement. It is this switch away from

measurement that distinguishes it (possibly frees it) from the kinds

of pitfalls we see in quantum interpretations, the subjectivity with

which we choose our truncations is irrelevant. A similar argument is

made by Chris Isham.

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Frank Wimberly-2

Re: Thanks again Marcus

In reply to this post by jon zingale

Philosophically different. Give the axioms of the rational numbers we can construct, using ZF set theory, a set of equivalence classes of ordered pairs of integers which satisies those axioms. We can also construct a set of equivalence classes of Cauchy sequences of rational numbers which satisfy the axioms for real numbers, including algebraic and transcendental numbers.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Sat, Jun 20, 2020, 10:45 AM Jon Zingale <[hidden email]> wrote:

The isomorphism *isn't*, in some sense, enough. For instance, the rationals
can be philosophically different than the integers. Sure we can identify
them via diagonal argument, but when we want a field we don't reach for the
integers. I claim that something similar is happening here and that the
point of the article is missed when we jump to the isomorphism. Gisin would
have just talked about the rationals if he meant the rationals, instead, he
invokes Chaitin and computability on purpose. The truncation simplification
obfuscates the deeper point. He is making an ontological claim about the
universe and one that theoreticians of quantum theory may appreciate but
applied mathematicians will not. The subjectivity of an observer is forced
on us by classical logic. Here he constructs a physics over a completely
different topos and what follows is not needing to make the observer
interpretation. This point is significant enough to think about as being
*more* than just truncation, it establishes what can be meant by randomness
and the possibility that determinacy may be an illusion, even in macroscopic
physics.

--
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Frank Wimberly-2

Re: Thanks again Marcus

In reply to this post by jon zingale

Excellent, as Glen would say. My explanation for Nick assumes applied mathematicians.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Sat, Jun 20, 2020, 10:45 AM Jon Zingale <[hidden email]> wrote:

The isomorphism *isn't*, in some sense, enough. For instance, the rationals
can be philosophically different than the integers. Sure we can identify
them via diagonal argument, but when we want a field we don't reach for the
integers. I claim that something similar is happening here and that the
point of the article is missed when we jump to the isomorphism. Gisin would
have just talked about the rationals if he meant the rationals, instead, he
invokes Chaitin and computability on purpose. The truncation simplification
obfuscates the deeper point. He is making an ontological claim about the
universe and one that theoreticians of quantum theory may appreciate but
applied mathematicians will not. The subjectivity of an observer is forced
on us by classical logic. Here he constructs a physics over a completely
different topos and what follows is not needing to make the observer
interpretation. This point is significant enough to think about as being
*more* than just truncation, it establishes what can be meant by randomness
and the possibility that determinacy may be an illusion, even in macroscopic
physics.

--
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thompnickson2

Re: Thanks again Marcus

Frank and Jon,

I am touched by your attempts to bring me on board with respect to the “marcus” paper, but I have to confess that I don’t quite get it. Recall that the story of my life is that I never did understand my brother, the mathematician. Because he was my older brother, I may have confused adulthood with being a mathematician, and so assumed that understanding mathematics is something I would just “grow in to”. But now he is dead, and I am older than he was when he died, I think I have to give up on that assumption.

I guess I understand what a rational number is and that rational numbers are a subset of computable numbers. And I guess I understand that a number which is computable to the Nth digit can be uncomputable to the nth plus one. And I guess I understand that a number that is uncomputable, is PRACTICALLY SPEAKING, random. (This last step worries me because it seems to confuse our inability to establish a fact with the existence of a fact to be established. ) But what I never could get my mind around was the relation of all of this to the notion of a “real” number. And why it matters. I suspect that for you, two, that is the easiest point to understand.

Thanks for your kind indulgence. I no doubt will have to leave this topic to you wizards, but perhaps I could take one more step with you before I send you on your way.

Nick

Nicholas Thompson

Emeritus Professor of Ethology and Psychology

Clark University

[hidden email]

https://wordpress.clarku.edu/nthompson/

From: Friam <[hidden email]> On Behalf Of Frank Wimberly
Sent: Saturday, June 20, 2020 10:56 AM
To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
Subject: Re: [FRIAM] Thanks again Marcus

Excellent, as Glen would say. My explanation for Nick assumes applied mathematicians.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Sat, Jun 20, 2020, 10:45 AM Jon Zingale <[hidden email]> wrote:

The isomorphism *isn't*, in some sense, enough. For instance, the rationals
can be philosophically different than the integers. Sure we can identify
them via diagonal argument, but when we want a field we don't reach for the
integers. I claim that something similar is happening here and that the
point of the article is missed when we jump to the isomorphism. Gisin would
have just talked about the rationals if he meant the rationals, instead, he
invokes Chaitin and computability on purpose. The truncation simplification
obfuscates the deeper point. He is making an ontological claim about the
universe and one that theoreticians of quantum theory may appreciate but
applied mathematicians will not. The subjectivity of an observer is forced
on us by classical logic. Here he constructs a physics over a completely
different topos and what follows is not needing to make the observer
interpretation. This point is significant enough to think about as being
*more* than just truncation, it establishes what can be meant by randomness
and the possibility that determinacy may be an illusion, even in macroscopic
physics.

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