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Dawning of the age of stochasticity

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Grant Holland

Dawning of the age of stochasticity

http://www.stat.uchicago.edu/~lekheng/courses/191f09/mumford-AMS.pdf

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glen ep ropella

Re: Dawning of the age of stochasticity

Very cool article, Grant! Thanks. I started to get lost on page 11 with the meta-axioms that give the Bernoulli random variables. *8^( It's interesting that the wikipedia page (https://en.wikipedia.org/wiki/Continuum_hypothesis#Arguments_for_and_against_CH) mentions Feferman's semi-intuitionistic ideas in the same context as Freiling's argument against the CH.

But I was irritated by his maps from the traditional subdivisions of math to the primitive elements of human experience. The geometry one seems right to me. But either he didn't finish explaining the referents of analysis, or I disagree. Analysis (to me, of course) is all about _proximity_, the closeness of any bunch of things. Differentiation being about the determination of a locality and integration being about establishing totalities. Although it's obvious (hindsight is 20/20) how to get to analysis from the calculus and from forces. It doesn't strike me that forces (and acceleration and oscillation) are the primitive human experiences referred to by analysis, as a domain.

Also, I don't really agree with the map from algebra to recipes of action. To me algebra is about the preservation of some ... "substance" _through_ transformation. So, like with forces giving us (well, Newton and Leibniz) a path into the calculus, the composition of actions in algebra is a kind of side effect. The core of it (to me, a non-mathematician!) is about the preservation of some quality through equivalence (and equivalence classes).

Obviously, it would be silly for me to argue with Mumford on this sort of thing. But I'm wondering whether you (or anyone on the list) see these experience correlations more as he sees them?

As usual, I have no comment on the actual topic of the paper. 8^)

On 11/13/2016 10:21 AM, Grant Holland wrote:
> http://www.stat.uchicago.edu/~lekheng/courses/191f09/mumford-AMS.pdf

--
glen ep ropella ⊥ 971-280-5699

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Meets Fridays 9a-11:30 at cafe at St. John's College
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Grant Holland

Re: Dawning of the age of stochasticity

Thanks, Glenn. I appreciate your persistence in reading the whole article.

I think this is an important and timely article, mainly, I must admit,
because it is in my current area of research. I'm working on a different
thread than Mumford but my intention is very sympathetic to his. And I
think you might agree that his main points are that we are now in the
"age of stochasticity" and that we should now integrate "probability
thinking" into the foundations of mathematics.

To address your questions about the article, let me just suggest to
concentrate on his section 1, "Introduction", section 5, "Putting random
variables into the foundations" and section 7, "Thinking as Bayesian
inference". I think that unless one is a mathematician, etc. the other
sections can be skipped without too much loss. And even within those
sections, Mumford has pretty much segregated math/logic-speak from plain
English; and that one can usually skip the insider stuff when you want
to, and still get the significance of the article.

Grant

On 11/15/16 1:11 PM, glen ep ropella wrote:

>
> Very cool article, Grant! Thanks. I started to get lost on page 11
> with the meta-axioms that give the Bernoulli random variables. *8^(
> It's interesting that the wikipedia page
> (https://en.wikipedia.org/wiki/Continuum_hypothesis#Arguments_for_and_against_CH)
> mentions Feferman's semi-intuitionistic ideas in the same context as
> Freiling's argument against the CH.
>
> But I was irritated by his maps from the traditional subdivisions of
> math to the primitive elements of human experience. The geometry one
> seems right to me. But either he didn't finish explaining the
> referents of analysis, or I disagree. Analysis (to me, of course) is
> all about _proximity_, the closeness of any bunch of things.
> Differentiation being about the determination of a locality and
> integration being about establishing totalities. Although it's obvious
> (hindsight is 20/20) how to get to analysis from the calculus and from
> forces. It doesn't strike me that forces (and acceleration and
> oscillation) are the primitive human experiences referred to by
> analysis, as a domain.
>
> Also, I don't really agree with the map from algebra to recipes of
> action. To me algebra is about the preservation of some ...
> "substance" _through_ transformation. So, like with forces giving us
> (well, Newton and Leibniz) a path into the calculus, the composition
> of actions in algebra is a kind of side effect. The core of it (to
> me, a non-mathematician!) is about the preservation of some quality
> through equivalence (and equivalence classes).
>
> Obviously, it would be silly for me to argue with Mumford on this sort
> of thing. But I'm wondering whether you (or anyone on the list) see
> these experience correlations more as he sees them?
>
> As usual, I have no comment on the actual topic of the paper. 8^)
>
> On 11/13/2016 10:21 AM, Grant Holland wrote:
>> http://www.stat.uchicago.edu/~lekheng/courses/191f09/mumford-AMS.pdf
>

Frank Wimberly-2

Re: Dawning of the age of stochasticity

Have you sent this to Reuben Hersh? I just did so. Sine he is the first mathematician referenced that seems appropriate.

Frank

Frank Wimberly
Phone (505) 670-9918

On Nov 15, 2016 4:12 PM, "Grant Holland" <[hidden email]> wrote:

Thanks, Glenn. I appreciate your persistence in reading the whole article.

I think this is an important and timely article, mainly, I must admit, because it is in my current area of research. I'm working on a different thread than Mumford but my intention is very sympathetic to his. And I think you might agree that his main points are that we are now in the "age of stochasticity" and that we should now integrate "probability thinking" into the foundations of mathematics.

To address your questions about the article, let me just suggest to concentrate on his section 1, "Introduction", section 5, "Putting random variables into the foundations" and section 7, "Thinking as Bayesian inference". I think that unless one is a mathematician, etc. the other sections can be skipped without too much loss. And even within those sections, Mumford has pretty much segregated math/logic-speak from plain English; and that one can usually skip the insider stuff when you want to, and still get the significance of the article.

Grant

On 11/15/16 1:11 PM, glen ep ropella wrote:

Very cool article, Grant! Thanks. I started to get lost on page 11 with the meta-axioms that give the Bernoulli random variables. *8^( It's interesting that the wikipedia page (https://en.wikipedia.org/wiki/Continuum_hypothesis#Arguments_for_and_against_CH) mentions Feferman's semi-intuitionistic ideas in the same context as Freiling's argument against the CH.

But I was irritated by his maps from the traditional subdivisions of math to the primitive elements of human experience. The geometry one seems right to me. But either he didn't finish explaining the referents of analysis, or I disagree. Analysis (to me, of course) is all about _proximity_, the closeness of any bunch of things. Differentiation being about the determination of a locality and integration being about establishing totalities. Although it's obvious (hindsight is 20/20) how to get to analysis from the calculus and from forces. It doesn't strike me that forces (and acceleration and oscillation) are the primitive human experiences referred to by analysis, as a domain.

Also, I don't really agree with the map from algebra to recipes of action. To me algebra is about the preservation of some ... "substance" _through_ transformation. So, like with forces giving us (well, Newton and Leibniz) a path into the calculus, the composition of actions in algebra is a kind of side effect. The core of it (to me, a non-mathematician!) is about the preservation of some quality through equivalence (and equivalence classes).

Obviously, it would be silly for me to argue with Mumford on this sort of thing. But I'm wondering whether you (or anyone on the list) see these experience correlations more as he sees them?

As usual, I have no comment on the actual topic of the paper. 8^)

On 11/13/2016 10:21 AM, Grant Holland wrote:

http://www.stat.uchicago.edu/~lekheng/courses/191f09/mumford-AMS.pdf

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove

Grant Holland

Re: Dawning of the age of stochasticity

Frank,

Thanks for pointing that out. I had not noticed that. I'm afraid that I only know Reuben by reputation - mainly from you and Dean; so, no, I did not send it to him; and I'm glad that you did.

Thx,

Grant

On 11/15/16 4:24 PM, Frank Wimberly wrote:

Have you sent this to Reuben Hersh? I just did so. Sine he is the first mathematician referenced that seems appropriate.

Frank

Frank Wimberly
Phone (505) 670-9918

On Nov 15, 2016 4:12 PM, "Grant Holland" <[hidden email]> wrote:

Thanks, Glenn. I appreciate your persistence in reading the whole article.

I think this is an important and timely article, mainly, I must admit, because it is in my current area of research. I'm working on a different thread than Mumford but my intention is very sympathetic to his. And I think you might agree that his main points are that we are now in the "age of stochasticity" and that we should now integrate "probability thinking" into the foundations of mathematics.

To address your questions about the article, let me just suggest to concentrate on his section 1, "Introduction", section 5, "Putting random variables into the foundations" and section 7, "Thinking as Bayesian inference". I think that unless one is a mathematician, etc. the other sections can be skipped without too much loss. And even within those sections, Mumford has pretty much segregated math/logic-speak from plain English; and that one can usually skip the insider stuff when you want to, and still get the significance of the article.

Grant

On 11/15/16 1:11 PM, glen ep ropella wrote:

Very cool article, Grant! Thanks. I started to get lost on page 11 with the meta-axioms that give the Bernoulli random variables. *8^( It's interesting that the wikipedia page (https://en.wikipedia.org/wiki/Continuum_hypothesis#Arguments_for_and_against_CH) mentions Feferman's semi-intuitionistic ideas in the same context as Freiling's argument against the CH.

But I was irritated by his maps from the traditional subdivisions of math to the primitive elements of human experience. The geometry one seems right to me. But either he didn't finish explaining the referents of analysis, or I disagree. Analysis (to me, of course) is all about _proximity_, the closeness of any bunch of things. Differentiation being about the determination of a locality and integration being about establishing totalities. Although it's obvious (hindsight is 20/20) how to get to analysis from the calculus and from forces. It doesn't strike me that forces (and acceleration and oscillation) are the primitive human experiences referred to by analysis, as a domain.

Also, I don't really agree with the map from algebra to recipes of action. To me algebra is about the preservation of some ... "substance" _through_ transformation. So, like with forces giving us (well, Newton and Leibniz) a path into the calculus, the composition of actions in algebra is a kind of side effect. The core of it (to me, a non-mathematician!) is about the preservation of some quality through equivalence (and equivalence classes).

Obviously, it would be silly for me to argue with Mumford on this sort of thing. But I'm wondering whether you (or anyone on the list) see these experience correlations more as he sees them?

As usual, I have no comment on the actual topic of the paper. 8^)

On 11/13/2016 10:21 AM, Grant Holland wrote:

http://www.stat.uchicago.edu/~lekheng/courses/191f09/mumford-AMS.pdf

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove