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John Kennison

Intro

Hi,

My name is John Kennison and I am glad to be welcomed to the Friam group. I am a retired Math professor and have been a friend and colleague of Nick Thompson's for many years. My field is category theory and I am interested in all kinds of applications of categories to other areas of math, including dynamical systems. I have been reading Rosen's "Life Itself" which seems half-baked, pretentious and badly written, but which also seems to be asking some deep and important questions. So I enjoy trying to puzzle my way through it.

I like listening to discussions about the nature of math. While I have practical experience as a mathematician and am not afraid to voice my opinions, I have done almost no philosophical reading on this subject.

---John

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

Tom Johnson

Re: Intro

Welcome, John. I hope you can visit Santa Fe and give us a rich briefing on category theory.

All the best,
Tom Johnson

On Mon, Aug 11, 2008 at 8:11 PM, John F. Kennison <[hidden email]> wrote:

Hi,

My name is John Kennison and I am glad to be welcomed to the Friam group. I am a retired Math professor and have been a friend and colleague of Nick Thompson's for many years. My field is category theory and I am interested in all kinds of applications of categories to other areas of math, including dynamical systems. I have been reading Rosen's "Life Itself" which seems half-baked, pretentious and badly written, but which also seems to be asking some deep and important questions. So I enjoy trying to puzzle my way through it.

I like listening to discussions about the nature of math. While I have practical experience as a mathematician and am not afraid to voice my opinions, I have done almost no philosophical reading on this subject.

---John

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

--
==========================================
J. T. Johnson
Institute for Analytic Journalism -- Santa Fe, NM USA
www.analyticjournalism.com
505.577.6482(c) 505.473.9646(h)
http://www.jtjohnson.com [hidden email]

"You never change things by fighting the existing reality.
To change something, build a new model that makes the
existing model obsolete."
-- Buckminster Fuller
==========================================

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

Owen Densmore

Re: Intro

Administrator

In reply to this post by John Kennison

Hi John, welcome to the warm pile of puppies!

Just curious: is there a book or paper(s) you'd recommend for folks
interested in category theory? Maybe two, considering the FRIAM
audience: one for folks with a good undergrad math background, and one
for generalists?

I ask because several conversations here have mentioned it and I've
yet to hear a conversation that could not have simply used basic
"modern algebraic" notions of sets and operations on them: groups,
rings, fields, integer domains, and so on.

-- Owen

On Aug 11, 2008, at 8:11 PM, John F. Kennison wrote:

> Hi,
>
> My name is John Kennison and I am glad to be welcomed to the Friam
> group. I am a retired Math professor and have been a friend and
> colleague of Nick Thompson's for many years. My field is category
> theory and I am interested in all kinds of applications of
> categories to other areas of math, including dynamical systems. I
> have been reading Rosen's "Life Itself" which seems half-baked,
> pretentious and badly written, but which also seems to be asking
> some deep and important questions. So I enjoy trying to puzzle my
> way through it.
>
> I like listening to discussions about the nature of math. While I
> have practical experience as a mathematician and am not afraid to
> voice my opinions, I have done almost no philosophical reading on
> this subject.
>
> ---John
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org

Jochen Fromm-4

Applications of category theory

I wonder if category theory can be applied
to model metaphors and analogies? Or perhaps
gene regulatory networks?

The following slides seem to be suitable for folks
with a good undergrad math background:
"Category Theory for Beginners"
http://www.cs.toronto.edu/~sme/presentations/cat101.pdf

-J.

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

Carl Tollander

Re: Applications of category theory

Thought about this quite a bit over the last few,
though not much traction on this list. Among other things I'm interested
in the functor category between GRNs and Metabolic Networks
and how they might mutually select (one really needs N-cats and NTs).
Though since I have little official background in the area I have some
fears about being over-glib.

I can refer you to some SFI associated folks who might indulge the
notion if you are really interested.

C.

Jochen Fromm wrote:

> I wonder if category theory can be applied
> to model metaphors and analogies? Or perhaps
> gene regulatory networks?
>
> The following slides seem to be suitable for folks
> with a good undergrad math background:
> "Category Theory for Beginners"
> http://www.cs.toronto.edu/~sme/presentations/cat101.pdf
>
> -J.
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org
>
>

John Kennison

Re: Applications of category theory

In reply to this post by Jochen Fromm-4

Re: [FRIAM] Applications of category theory Further thoughts on categories and their applications.

References: Toposes. Theories and Triples can be found at Michael Barr’s home page, www.math.mcgill.ca/barr/. The notes suggested by Jochen, below, are a good starting point.

Applications: There are a lot of different types of categories and categorical constructions. So there are, potentially, lots of possible applications. It is probably best to have a team approach, with at least one expert in the area of the intended application and at least one expert in category theory. But all experts have to learn something of the language, basic results, concepts of both fields, then they can see if one set of ideas can map onto another.

This sort of provides an answer to Nick’s question. One can benefit (or perhaps enjoy) a field of abstract mathematics if the underlying concepts can be made intuitively clear with a minimum of technical complexity.

Specifically can categories relate to questions of metaphor and analogy? Rosen in “Life Itself” belabors an approach to metaphor which strikes me as heavy-handed yet not comprehensive enough. Is there a better connection? --I think that’s a good question.

--John

On 8/12/08 3:39 PM, "Jochen Fromm" <[hidden email]> wrote:

I wonder if category theory can be applied
to model metaphors and analogies? Or perhaps
gene regulatory networks?

The following slides seem to be suitable for folks
with a good undergrad math background:
"Category Theory for Beginners"
http://www.cs.toronto.edu/~sme/presentations/cat101.pdf

-J.

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

Carl Tollander

Re: Applications of category theory

John,

How do you feel about Goldblatt's book on Topoi? I've been working
through it slooowly and like it so far, but I'm not sure whether it is
leaving important things out. In particular, if you need something to
understand the exposition, say, sheaves, then he goes back and tells you
just enough about sheaves instead of referring you elsewhere.

Like this:
http://www.amazon.com/Topoi-Categorial-Analysis-Logic-Mathematics/dp/0486450260/ref=pd_bbs_2?ie=UTF8&s=books&qid=1218653851&sr=8-2

When I try to talk to non-math-centric folks about Category Theory, I
usually start off with Derek Wise's "Stuff with Structure, having
certain Properties" based explanation, but usually people think its such
an advanced topic that such a starting point couldn't possibly be that
straightforward. If they do buy into that, however, you can give them a
feel for n-Cats and natural transformations. At that point they start
thinking what they could do with them and there's (maybe) enough
motivation to backfill in with the formal definitions. It's harder I
think to go with the formal stuff first (I know it is for me) if there
isn't much formal math background to relate to.

I think category theory (particularly for us as it relates to
complexity) represents a cultural change and so the initial explanations
we seek have to resonate broadly at that level if we are going to set a
foundation for not fooling ourselves (and our clients) when things get
more formal.

And I always liked the idea of using "stuff" as a technical term.

Carl

John F. Kennison wrote:

> Further thoughts on categories and their applications.
>
> References: Toposes. Theories and Triples can be found at Michael
> Barr’s home page, www.math.mcgill.ca/barr/. The notes suggested by
> Jochen, below, are a good starting point.
>
> Applications: There are a lot of different types of categories and
> categorical constructions. So there are, potentially, lots of possible
> applications. It is probably best to have a team approach, with at
> least one expert in the area of the intended application and at least
> one expert in category theory. But all experts have to learn something
> of the language, basic results, concepts of both fields, then they can
> see if one set of ideas can map onto another.
>
> This sort of provides an answer to Nick’s question. One can benefit
> (or perhaps enjoy) a field of abstract mathematics if the underlying
> concepts can be made intuitively clear with a minimum of technical
> complexity.
>
> Specifically can categories relate to questions of metaphor and
> analogy? Rosen in “Life Itself” belabors an approach to metaphor which
> strikes me as heavy-handed yet not comprehensive enough. Is there a
> better connection? --I think that’s a good question.
>
> --John
>
> On 8/12/08 3:39 PM, "Jochen Fromm" <[hidden email]> wrote:
>
> I wonder if category theory can be applied
> to model metaphors and analogies? Or perhaps
> gene regulatory networks?
>
> The following slides seem to be suitable for folks
> with a good undergrad math background:
> "Category Theory for Beginners"
> http://www.cs.toronto.edu/~sme/presentations/cat101.pdf
> <http://www.cs.toronto.edu/%7Esme/presentations/cat101.pdf>
>
> -J.
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org
>
>
> ------------------------------------------------------------------------
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org

John Kennison

Re: Applications of category theory

Re: [FRIAM] Applications of category theory Carl,

I have only skimmed parts of Goldblatt’s book. It did look like it was trying to do the hard job of giving the important concepts of topos theory, along with the basic technical details. (it is easier to assume that the readers know category theory and also know how to digest a book that only gives a formal approach to a subject.)

Probably the best way to digest a new topic is to see how it applies to a particular problem, that is of interest. When I get organized (right now I am, teaching an intensive two-week course for incoming students who need a brushing up on pre-calculus, or pre-pre-calculus—and I also have a 12-year old granddaughter, who likes math, suduko and monopoly visiting until Tues.) --I might try to explain how I use topos theory to break a dynamic system into its cyclic parts.

John

On 8/13/08 3:36 PM, "Carl Tollander" <[hidden email]> wrote:

John,

How do you feel about Goldblatt's book on Topoi? I've been working
through it slooowly and like it so far, but I'm not sure whether it is
leaving important things out. In particular, if you need something to
understand the exposition, say, sheaves, then he goes back and tells you
just enough about sheaves instead of referring you elsewhere.

Like this:
http://www.amazon.com/Topoi-Categorial-Analysis-Logic-Mathematics/dp/0486450260/ref=pd_bbs_2?ie=UTF8=books=1218653851=8-2 <http://www.amazon.com/Topoi-Categorial-Analysis-Logic-Mathematics/dp/0486450260/ref=pd_bbs_2?ie=UTF8&s=books&qid=1218653851&sr=8-2>

When I try to talk to non-math-centric folks about Category Theory, I
usually start off with Derek Wise's "Stuff with Structure, having
certain Properties" based explanation, but usually people think its such
an advanced topic that such a starting point couldn't possibly be that
straightforward. If they do buy into that, however, you can give them a
feel for n-Cats and natural transformations. At that point they start
thinking what they could do with them and there's (maybe) enough
motivation to backfill in with the formal definitions. It's harder I
think to go with the formal stuff first (I know it is for me) if there
isn't much formal math background to relate to.

I think category theory (particularly for us as it relates to
complexity) represents a cultural change and so the initial explanations
we seek have to resonate broadly at that level if we are going to set a
foundation for not fooling ourselves (and our clients) when things get
more formal.

And I always liked the idea of using "stuff" as a technical term.

Carl

John F. Kennison wrote:
> Further thoughts on categories and their applications.
>
> References: Toposes. Theories and Triples can be found at Michael
> Barr’s home page, www.math.mcgill.ca/barr/. The notes suggested by
> Jochen, below, are a good starting point.
>
> Applications: There are a lot of different types of categories and
> categorical constructions. So there are, potentially, lots of possible
> applications. It is probably best to have a team approach, with at
> least one expert in the area of the intended application and at least
> one expert in category theory. But all experts have to learn something
> of the language, basic results, concepts of both fields, then they can
> see if one set of ideas can map onto another.
>
> This sort of provides an answer to Nick’s question. One can benefit
> (or perhaps enjoy) a field of abstract mathematics if the underlying
> concepts can be made intuitively clear with a minimum of technical
> complexity.
>
> Specifically can categories relate to questions of metaphor and
> analogy? Rosen in “Life Itself” belabors an approach to metaphor which
> strikes me as heavy-handed yet not comprehensive enough. Is there a
> better connection? --I think that’s a good question.
>
> --John
>
> On 8/12/08 3:39 PM, "Jochen Fromm" <[hidden email]> wrote:
>
>     I wonder if category theory can be applied
>     to model metaphors and analogies? Or perhaps
>     gene regulatory networks?
>
>     The following slides seem to be suitable for folks
>     with a good undergrad math background:
>     "Category Theory for Beginners"
>     http://www.cs.toronto.edu/~sme/presentations/cat101.pdf
>     <http://www.cs.toronto.edu/%7Esme/presentations/cat101.pdf>
>
>     -J.
>
>     ============================================================
>     FRIAM Applied Complexity Group listserv
>     Meets Fridays 9a-11:30 at cafe at St. John's College
>     lectures, archives, unsubscribe, maps at http://www.friam.org
>
>
> ------------------------------------------------------------------------
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

Owen Densmore

Re: Applications of category theory

Administrator

Catching up on my mail, I found this saved.

John: care to chat a bit more how you use topos theory?

We've tried to get someone to chat about category theory, either at
wedtech or in the complex, but thus far no one has felt up to the
task. Not sure why. Possibly just too elusive? Or possibly evolving
too quickly?

-- Owen

On Aug 13, 2008, at 1:58 PM, John F. Kennison wrote:

> Carl,
>
> I have only skimmed parts of Goldblatt's book. It did look like it
> was trying to do the hard job of giving the important concepts of
> topos theory, along with the basic technical details. (it is easier
> to assume that the readers know category theory and also know how to
> digest a book that only gives a formal approach to a subject.)
>
> Probably the best way to digest a new topic is to see how it applies
> to a particular problem, that is of interest. When I get organized
> (right now I am, teaching an intensive two-week course for incoming
> students who need a brushing up on pre-calculus, or pre-pre-calculus-
> and I also have a 12-year old granddaughter, who likes math, suduko
> and monopoly visiting until Tues.) --I might try to explain how I
> use topos theory to break a dynamic system into its cyclic parts.
>
> John
>
>
> On 8/13/08 3:36 PM, "Carl Tollander" <[hidden email]> wrote:
>
> John,
>
> How do you feel about Goldblatt's book on Topoi? I've been working
> through it slooowly and like it so far, but I'm not sure whether it is
> leaving important things out. In particular, if you need something to
> understand the exposition, say, sheaves, then he goes back and tells
> you
> just enough about sheaves instead of referring you elsewhere.
>
> Like this:
> http://www.amazon.com/Topoi-Categorial-Analysis-Logic-Mathematics/dp/0486450260/ref=pd_bbs_2?ie=UTF8=books=1218653851=8-2
> <http://www.amazon.com/Topoi-Categorial-Analysis-Logic-Mathematics/dp/0486450260/ref=pd_bbs_2?ie=UTF8&s=books&qid=1218653851&sr=8-2
> ><http://www.amazon.com/Topoi-Categorial-Analysis-Logic-Mathematics/dp/0486450260/ref=pd_bbs_2?ie=UTF8&s=books&qid=1218653851&sr=8-2
> >
>
> When I try to talk to non-math-centric folks about Category Theory, I
> usually start off with Derek Wise's "Stuff with Structure, having
> certain Properties" based explanation, but usually people think its
> such
> an advanced topic that such a starting point couldn't possibly be that
> straightforward. If they do buy into that, however, you can give
> them a
> feel for n-Cats and natural transformations. At that point they start
> thinking what they could do with them and there's (maybe) enough
> motivation to backfill in with the formal definitions. It's harder I
> think to go with the formal stuff first (I know it is for me) if there
> isn't much formal math background to relate to.
>
> I think category theory (particularly for us as it relates to
> complexity) represents a cultural change and so the initial
> explanations
> we seek have to resonate broadly at that level if we are going to
> set a
> foundation for not fooling ourselves (and our clients) when things get
> more formal.
>
> And I always liked the idea of using "stuff" as a technical term.
>
> Carl
>
> John F. Kennison wrote:
>> Further thoughts on categories and their applications.
>>
>> References: Toposes. Theories and Triples can be found at Michael
>> Barr's home page, www.math.mcgill.ca/barr/. The notes suggested by
>> Jochen, below, are a good starting point.
>>
>> Applications: There are a lot of different types of categories and
>> categorical constructions. So there are, potentially, lots of
>> possible
>> applications. It is probably best to have a team approach, with at
>> least one expert in the area of the intended application and at least
>> one expert in category theory. But all experts have to learn
>> something
>> of the language, basic results, concepts of both fields, then they
>> can
>> see if one set of ideas can map onto another.
>>
>> This sort of provides an answer to Nick's question. One can benefit
>> (or perhaps enjoy) a field of abstract mathematics if the underlying
>> concepts can be made intuitively clear with a minimum of technical
>> complexity.
>>
>> Specifically can categories relate to questions of metaphor and
>> analogy? Rosen in "Life Itself" belabors an approach to metaphor
>> which
>> strikes me as heavy-handed yet not comprehensive enough. Is there a
>> better connection? --I think that's a good question.
>>
>> --John
>>
>> On 8/12/08 3:39 PM, "Jochen Fromm" <[hidden email]> wrote:
>>
>> I wonder if category theory can be applied
>> to model metaphors and analogies? Or perhaps
>> gene regulatory networks?
>>
>> The following slides seem to be suitable for folks
>> with a good undergrad math background:
>> "Category Theory for Beginners"
>> http://www.cs.toronto.edu/~sme/presentations/cat101.pdf
>> <http://www.cs.toronto.edu/%7Esme/presentations/cat101.pdf><http://www.cs.toronto.edu/%7Esme/presentations/cat101.pdf
>> >
>>
>> -J.
>>
>> ============================================================
>> FRIAM Applied Complexity Group listserv
>> Meets Fridays 9a-11:30 at cafe at St. John's College
>> lectures, archives, unsubscribe, maps at http://www.friam.org
>>
>>
>> ------------------------------------------------------------------------
>>
>> ============================================================
>> FRIAM Applied Complexity Group listserv
>> Meets Fridays 9a-11:30 at cafe at St. John's College
>> lectures, archives, unsubscribe, maps at http://www.friam.org
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org