(urth) barrington interview

[Jeffery Wilson clueland.com]

On 10/10/2014 8:09 AM, Lee wrote:
>> Gerry Quinn: All mathematics can be encoded entirely inside the standard arithmetic
>
>> of the natural numbers, or simple geometry on a plane.
>
>
> A nice summation of my point. Math requires numbers. Numbers describe the
>
> universe in terms of discrete, countable units. I find it quite possible that there
>
> are places/times in geography and history of the universe in which the concept of
>
> numbers was meaningless.

Er, no, because the concept does not depend on the actuality. The 
numbers necessary for math can be entirely notional, and in fact the 
numbers are *always* notional and abstract. There is no place you can 
touch the number two, for instance.

However, that also does not prevent mathematics from being used to 
speculate on what happens *if* the number two can be touched, and other 
"impossible" things. The best we can do is to show it makes a 
contradiction, but that could mean only that the premise is flawed.

You might be interested to explore the history of David Hilbert and Kurt 
Goedel. Godel discovered the inherently incomplete nature of math, which 
made him somehting of a Voltairean figure: a devil set on destroying 
mathemtical science as completists like Hilbert may have felt, but also 
a figure of grace and liberty freeing it from the need to be complete 
and all encompassing and eventually finite.

-- 
Jeff Wilson - < jwilson at clueland.com >
A&M Texarkana Computational Intelligence Lab
< http://www.tamut.edu/cil >