Skip to comments.One of the most abstract fields in math finds application in the 'real' world
Posted on 05/23/2013 11:23:14 AM PDT by neverdem
Every pure mathematician has experienced that awkward moment when asked, So whats 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 ...
Why do I find this so unsurprising? It seems rather obvious. Hence, I must be missing something.
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.
I wish I had gone to college then maybe I could understand what this article is all about......
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.
I was a math major in school and in this particular case, you aren't missing much.
But where does that leave Haskell?
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.
“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”
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Hanging out with the Beaver and schmoozing his parents?
Bump. (That is the extent of my understanding of the article).
Feynman diagrams would be analogous.