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Go Figure Go Figure
by Jan Sand
2008-01-13 10:22:02
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Like the average guy I shop for various items in a store and try to keep the prices in my head so that when I approach the cash register I have a vague idea about how badly I am about to be hit. But living in the real world is like being under bombardment with sounds and colors and the occasional very pretty girl strolling through the shop and all those numbers spin clockwise north of the equator and counter-clockwise in South Africa and disappear down the drain. Which leaves me with the unnerving suspicion that some of my money is slipping sidewise into an undeserved pocket.

As someone delighted with the possibilities of understanding the world as precisely as possible and frustrated by the lack of a gut feel of how to deal with algebraic intricacy when confronted with the compact information in the typical mathematical equation I have tried to work my intestinal instincts into better relationships with the numbing associations of numbers.

After all, mathematics is not a science. It is a language and with that language one can describe, not only this world as we perceive it but also many alternate worlds, one of which we may eventually discover is a bit more like the way it really is. Einstein demonstrated that when he showed that a modification of Newton's laws of motion which are fundamental to the understanding of the structure of the universe was essential at extreme speeds that approach that of light. He required a new mathematics and discovered that these new maths had been worked out some decades before as purely mathematical exercises.

As example, when I was in high school physics I was given the rather simple equation for conversion between the temperature systems of Celsius and Fahrenheit. It is Tc = (5/9)x(Tf-32) where Tc is the temperature in Celsius and Tf is the temperature in Fahrenheit. It is an easy linear equation but to work it mentally I must first mentally subtract 32 from the Fahrenheit measurement and then mentally multiply that by five and mentally divide that by nine. Each of those operations are not particularly difficult but my memory is not so hot with numbers and somewhere in the process one or two of the digits frequently gets switched around and the mechanically obtained result naturally gets screwed up.

As simple as it is, a mathematical equation is essentially conceived along the lines of a slot machine. It has a number of variables and an unknown variable and, in the method of a slot machine, by dropping a constant or two into the proper unknowns there is an automatic system which can be performed by a human or a machine and the final unknown becomes known and drops out like a candy bar from a slot machine. But the human does not have to think about the relationships shifting around inside as the process goes to completion and that is where I have my battle with the standard approach to mathematics.

My mind does not work like a slot machine. I have to understand the way the variables are inter-related and feel that if I push this one in one direction the others will move in directions that make sense. I have to see all the levers and how they are connected and operate and the levers have to be constructed inside my mind to do their work.

Going back to the temperature conversion equation, my mind prefers to see the process in this way. A Fahrenheit degree is 1.7 times the size of a Celsius degree or a bit over one and a half times. Fahrenheit freezing point of water is 32 degrees. The same point in Celsius is zero. To convert a measurement in Fahrenheit to Celsius I must first wipe away the difference in freezing points by subtracting 32 and then approximate the temperature in Celsius by making the result something over half. The boiling point of water in Fahrenheit is 212. Minus 32 makes it 180 and something over half of that becomes 100, the boiling point in Celsius. These are the precise numbers but "something over half "is very sloppy math but good enough for a general feel of how the numbers relate and a much more mentally satisfying participation in the process. Not good enough for an engineer or a scientist but fine for me on a cold day to figure what the temperature in New York might be while I'm freezing my ass off in Helsinki.

   
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