Posted on **05/23/2013 11:23:14 AM PDT** by **neverdem**

Every pure mathematician has experienced that awkward moment when asked, “So what’s your research good for?” There are standard responses: a proud “Nothing!”; an explanation that mathematical research is an art form like, say, Olympic gymnastics (with a much smaller audience); or a stammered response that so much of pure math has ended up finding application that maybe, perhaps, someday, it will turn out to be useful.

That last possibility is now proving itself to be dramatically true in the case of category theory, perhaps the most abstract area in all of mathematics. Where math is an abstraction of the real world, category theory is an abstraction of mathematics: It describes the architectural structure of any mathematical field, independent of the specific kind of mathematical object being considered. Yet somehow, what is in a sense the purest of all pure math is now being used to describe areas throughout the sciences and beyond, in computer science, quantum physics, biology, music, linguistics and philosophy.

Samuel Eilenberg of Columbia University and Saunders Mac Lane of the University of Chicago developed category theory in the 1940s to build a bridge between abstract algebra (the generalization of high school algebra) and topology (the qualitative study of shapes, including those in very high dimensions). Very similar arguments repeatedly cropped up in the two fields in different contexts, so the mathematicians reasoned that some deeper structure must unite these situations.

They created an organizing framework that any field of mathematics could be put in. A “category” is a collection of mathematical objects together with arrows connecting them. So, for example, the natural numbers are the objects of a category, and one particular arrow in that category would connect each number to its double. Eilenberg and Mac Lane could then analyze maps between entire categories, and maps...

(Excerpt) Read more at sciencenews.org ...

To: **neverdem**

Why do I find this so unsurprising? It seems rather obvious. Hence, I must be missing something.

To: **neverdem**

I will put this in plain terms for the less enlightened Freepers:

Free Republic and Democrat Underground are really just two sides of the same coin. C++ is the other side.

It’s really quite simple.

3
posted on **05/23/2013 11:35:00 AM PDT**
by InterceptPoint
(If I had a tag line this is where you would find it)

To: **neverdem**

I wish I had gone to college then maybe I could understand what this article is all about......

To: **Hot Tabasco**

Don't wring your hands over that. Going to college wouldn't have helped. You are safe to assume that there are more Green Bay Packers than people who really understand this stuff.

5
posted on **05/23/2013 11:41:58 AM PDT**
by InterceptPoint
(If I had a tag line this is where you would find it)

To: **Hot Tabasco**

I was a math major in school and in this particular case, you aren't missing much.

To: **InterceptPoint**

But where does that leave Haskell?

To: **cynwoody**

The nice thing about mathematical disciplines that can handle more than three dimensions is that they allow an answer to your question:

Haskell is on the other, other side of the coin.

8
posted on **05/23/2013 11:49:52 AM PDT**
by InterceptPoint
(If I had a tag line this is where you would find it)

To: **neverdem**

“Category theory has found broad and deep use in the world of statically-typed functional programming languages since as early as 1991, and Haskell has been using category-theoretic formalisms to structure programs since the late ‘90s. While I’d not yet classify this sort of usage as being mainstream, it’s hardly a new thing. Nonetheless, I think that the notion of using category theory to formalize the scientific method makes perfect sense; indeed, as my colleague @alissapajer’s talk at the Strange Loop 2013 programming conference indicates, category theory is “An Abstraction For Everything.” nuttycom May. 20, 2013 at 1:13pm”

To: **varmintman**

John Derbyshire touches on Category Theory in his excellent book *Unknown Quantity*. I've read the chapter and, though it's written for the *layman :)*, I don't think I'll ever understand the subject. My kudos to anyone who can!

To: **El Gato; Ernest_at_the_Beach; Robert A. Cook, PE; lepton; LadyDoc; jb6; tiamat; PGalt; Dianna; ...**

The big fat truth - More and more studies show that being overweight does not always shorten life — but some public-health researchers would rather not talk about them.

DNA-guided assembly yields novel ribbon-like nanostructures

'Universal' flu vaccine effective in animals

UPDATE 1-Regeneron, Sanofi asthma drug seen as potential game changer. Comment# 10 is an example of how to use PubMed for the relation between asthma and magnesium deficiency. There are also two FReebies in comment# 1 for those with an interest in asthma and this new monoclonal antibody.

**FReepmail** me if you want on or off my health and science ping list.

To: **cynwoody**

Hanging out with the Beaver and schmoozing his parents?

To: **neverdem**

Bump. (That is the extent of my understanding of the article).

13
posted on **05/23/2013 4:19:47 PM PDT**
by conservatism_IS_compassion
(Liberalism is a conspiracy against the public by wire-service journalism.)

To: **6SJ7; AdmSmith; AFPhys; Arkinsaw; allmost; aristotleman; autumnraine; Beowulf; Bones75; BroJoeK; ...**

Thanks neverdem. Completely unrelated:

· View or Post in 'blog · post a topic · subscribe ·

14
posted on **05/24/2013 8:38:44 PM PDT**
by SunkenCiv
(Romney would have been worse, if you're a dumb ass.)

To: **neverdem**

Feynman diagrams would be analogous.

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