Kevin wrote
> Now there's a thought! Let's start a thread about what Brin-Lers are
> reading!
Cannot resist! Though I should. These books are affecting how I
think about the world.
Two books:
Where Mathematics Comes From:
How the Embodied Mind Brings Mathematics into Being
by George Lakoff, Rafael E. Nunez 2000, ISBN: 0-465-03770-4
and
Moral Politics: What Conservatives Know That Liberals Don't
by George Lakoff 1997, ISBN: 022-646-8054
Both are about cognitive linguistics, how Lakoff thinks that language
works.
The `Moral Politics' book argues that in US politics both
conservatives and liberals (in the contemporary, conventional
definitions) base their political programs on reasoning that derives
from metaphors about how a family should be organized. However, the
conservatives understand what they are doing and how they are thinking
and the liberals do not. I have not read enough of this book to tell
you much about it -- I was inspired to buy it by reading the beginning
of the mathematics book.
In `Where Mathematics Comes From', Lakoff and Nunez argue that
mathematics is based on `conceptual metaphors' that are
... a cognitive mechanism for allowing us to reason about one kind
of thing as if it were another.
A `conceptual metaphor' is an
... inference-preserving cross-domain mapping
The authors argue that mathematics consists of metaphor piled on
metaphor, blended and transformed, so people often do not realize the
basis of it all.
Lakoff and Nunez provide evidence that infants can see the sizes of
groups of up to four objects and recognize substraction and addition
prior to the development of language. They contend that arithmetic
comes from an inference-preserving extension of this ability to larger
numbers.
Moreover, they argue that there are actually four `grounding'
metaphors (metaphors based on experiences many of us have had as
children); these are
* adding and taking away objects from a collection (playing with pebbles)
* construction of a larger whole from smaller objects (playing with blocks)
* measuring the width or height of something (by stretching our
hands to the ends of the object or standing up to see how high it is)
* moving from one place to another (by crawling or walking)
These experiences provide us with four metaphors that work with
arithmetic: four inference-preserving cross-domain mapping mechanisms
that work consistently with each other and the world.
Measuring provides us with zero and moving provides us with negative
numbers. By blending these metaphors, and insisting on consistency,
we get zero and negative numbers for collections, too. And then by
adding new metaphors based on existing arithmetic metaphors onto
existing ones, we get the `empty set' and set theory....
--
Robert J. Chassell [EMAIL PROTECTED]
Rattlesnake Enterprises http://www.rattlesnake.com
