**From:** Brian Harper (*harper.10@osu.edu*)

**Date:** Wed Sep 03 2003 - 15:59:25 EDT

**Previous message:**Debbie Mann: "RE: Van Till's Ultimate Gap"**In reply to:**Debbie Mann: "RE: Van Till's Ultimate Gap"**Next in thread:**George Murphy: "math (was Re: Van Till's Ultimate Gap)"**Next in thread:**Jim Armstrong: "Re: Van Till's Ultimate Gap"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

At 02:15 PM 9/3/2003 -0500, Debbie Mann wrote:

DFS said:

One line, the one commonly

noted, goes from integers to rationals to irrationals and imaginaries.

And each set of numbers, including the modular numbers you mentioned later,

represents a real part of our universe. One cannot count the flow of water

in the same way one counts apples. Imaginary numbers seem totally ridiculous

unless you are in the other dimension which they represent, in which case

they are indispensible. Any electrical engineer uses irrational numbers

daily, in practice if not in theory. The waves of electricity, which most of

us have seen graphed, are heavily based on both irrational and imaginary

numbers. This is a case where I argue that they are based - not modeled in

an abstract sense. The rotation of a magnetic field near electrical

conductors produces electricity which is very precisely represented by these

imaginary and irrational numbers. Tell me that isn't real? I'll admit you

can't see it, smell it, taste it or hear it - but the calculations will tell

you what will happen if you try to get in its way.

Euclid described the two 'party trick' geometries. And Einstein demonstrated

how they represent reality when one gets beyond our 'normal' limits of size.

The Romans used Roman Numerals successfully for years. They had no zero.

Does zero exist - certainly! Our need for math increases with our realm of

knowledge. If we had no need for the microscopic or macroscopic - we would

have no need for these two 'non-Euclidean' geometries.

This reminds me of some thing Pascal wrote

that I thought was clever:

"I know some who cannot understand that to take four

from nothing leaves nothing" Pascal,

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