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Re: 1. Is the Equal Sign Overrated? Mathematicians Hash It Out | WIRED (Tom Johnson)

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jon zingale

Re: 1. Is the Equal Sign Overrated? Mathematicians Hash It Out | WIRED (Tom Johnson)

Thanks Tom.

It is exciting to see topos theory finding a place in the sun.

When I was participating in Dan Freed's TQFT seminars at

the University of Texas, we worked through one of Jacob's papers.

Despite the seemingly all-pervasive mistrust of category theory

(let alone topos theory), these seminars highlighted how this

wondrous branch of mathematics can elucidate the importance

of considering structural equivalence when there cannot be

a notion of strict equality.

============================================================
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Frank Wimberly-2

Re: 1. Is the Equal Sign Overrated? Mathematicians Hash It Out | WIRED (Tom Johnson)

In the work I did at CMU on statistical causal reasoning, we made heavy use of equivalence classes. Our algorithms would find equivalence classes of causal models (generalizations of acyclic digraphs). If any edge occurred in all elements of a class then it represented a cause between the variables (nodes) associated with the edge. As I recall.

-----------------------------------
Frank Wimberly

My memoir:
https://www.amazon.com/author/frankwimberly

My scientific publications:
https://www.researchgate.net/profile/Frank_Wimberly2

Phone (505) 670-9918

On Mon, Oct 14, 2019, 11:32 AM Jon Zingale <[hidden email]> wrote:

Thanks Tom.

It is exciting to see topos theory finding a place in the sun.
When I was participating in Dan Freed's TQFT seminars at
the University of Texas, we worked through one of Jacob's papers.
Despite the seemingly all-pervasive mistrust of category theory
(let alone topos theory), these seminars highlighted how this
wondrous branch of mathematics can elucidate the importance
of considering structural equivalence when there cannot be
a notion of strict equality.

============================================================
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
archives back to 2003: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove

Carl Tollander

Re: 1. Is the Equal Sign Overrated? Mathematicians Hash It Out | WIRED (Tom Johnson)

I first became aware of the equality issue from a Barry Mazur paper http://www.math.harvard.edu/~mazur/preprints/when_is_one.pdf .

The Robert Goldblatt book "Topoi The Categorical Analysis of Logic" has an honored place on my bookshelf but is mostly beyond me. I keep it because it covers a lot of stuff I encountered in my youth but never had sufficient time to explore. And because I like the pictures.

Carl

On Mon, Oct 14, 2019 at 11:39 AM Frank Wimberly <[hidden email]> wrote:

In the work I did at CMU on statistical causal reasoning, we made heavy use of equivalence classes. Our algorithms would find equivalence classes of causal models (generalizations of acyclic digraphs). If any edge occurred in all elements of a class then it represented a cause between the variables (nodes) associated with the edge. As I recall.

-----------------------------------
Frank Wimberly

My memoir:
https://www.amazon.com/author/frankwimberly

My scientific publications:
https://www.researchgate.net/profile/Frank_Wimberly2

Phone (505) 670-9918

On Mon, Oct 14, 2019, 11:32 AM Jon Zingale <[hidden email]> wrote:
Thanks Tom.

It is exciting to see topos theory finding a place in the sun.
When I was participating in Dan Freed's TQFT seminars at
the University of Texas, we worked through one of Jacob's papers.
Despite the seemingly all-pervasive mistrust of category theory
(let alone topos theory), these seminars highlighted how this
wondrous branch of mathematics can elucidate the importance
of considering structural equivalence when there cannot be
a notion of strict equality.

============================================================
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
archives back to 2003: http://friam.471366.n2.nabble.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
archives back to 2003: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove