### unabstracting math

This is related to what some people posted for last week, I think....

An implication of Chapter 2 is that one fundamental mistake of Western thinking is the common assumption that mathematical structures (the coordinate plane, angular proportions, even numbers) are abstract entities. They aren’t (necessarily) abstract, but are, rather, representational tools that have often been mistaken for basic computational descriptions/structures.... Hutchins posits a universal computational structure/theory/description behind navigation that precedes/is more basic than the representation of the problem in mathematical (algebraic and analytic-geometric) structures. His “computational account” (50) gives a mathematical math (as compared to a mathematcal physics or mathematical biology), or is a mathematics of math under the domain of navigation.

This may not be interesting to people who didn't waste 7/8 of their higher education studying math and struggling with its supposed abstractness. Or it might be. I've come to accept that, (oh how I hate this phrase:) "in this day and age," people don't necessarily see math as having some access to some fundamental and absolute truth. (Do they?) But I do think people still take math to be about something very basic and abstract, that almost any phenomena can be modeled in terms of. But Hutchins is not disproving this, claiming that some phenomena that we might like to think of as "ideally mathematical" cannot be represented in such terms. But he is saying that math is less a "step back" (an abstraction) from phenomena than a step aside (to different terms). This suggests trouble for the idea of math as something basic/fundamental/boring...

An implication of Chapter 2 is that one fundamental mistake of Western thinking is the common assumption that mathematical structures (the coordinate plane, angular proportions, even numbers) are abstract entities. They aren’t (necessarily) abstract, but are, rather, representational tools that have often been mistaken for basic computational descriptions/structures.... Hutchins posits a universal computational structure/theory/description behind navigation that precedes/is more basic than the representation of the problem in mathematical (algebraic and analytic-geometric) structures. His “computational account” (50) gives a mathematical math (as compared to a mathematcal physics or mathematical biology), or is a mathematics of math under the domain of navigation.

This may not be interesting to people who didn't waste 7/8 of their higher education studying math and struggling with its supposed abstractness. Or it might be. I've come to accept that, (oh how I hate this phrase:) "in this day and age," people don't necessarily see math as having some access to some fundamental and absolute truth. (Do they?) But I do think people still take math to be about something very basic and abstract, that almost any phenomena can be modeled in terms of. But Hutchins is not disproving this, claiming that some phenomena that we might like to think of as "ideally mathematical" cannot be represented in such terms. But he is saying that math is less a "step back" (an abstraction) from phenomena than a step aside (to different terms). This suggests trouble for the idea of math as something basic/fundamental/boring...

## 1 Comments:

Anthony,

Could you go back in time with me and teach my math classes? I don't understand everything you said, but I'm starting to buy the idea that math could be relevant to settings other than the classrooms from which I couldn't escape fast enough!

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