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December 2008Is 0 / 0 "undefined"?I read in a recent forum post recently that zero divided by zero is "undefined". This got me thinking once again about the human element and cultural considerations that pervade maths and have nothing to do with the actual Universe we live in. Nature does not have the luxury of "undefined". It doesn't suddenly get confused when it encounters a zero and it doesn't produce unpredictable results. In mathematician-speak "undefined" means "I don't know, so I'll blame the mathematics". If a mathematician tells you that the maths are undefined or unpredictable - it often means there's a problem with his "rules" that doesn't match reality. Don't be afraid to dig a little deeper and ask "Why"? Note once again that the taboo here involves zero. We are not arguing whether 2/2 is undefined nor 100/100. The conventional { 0 } view of zero is simply flawed and falls apart when you apply it to Physics. Using the null { } view of zero, 0/0 = null (i.e. 0). Always.
Mathematicians and PhysicsIt is the purpose of these pages to highlight the successes and failures of mathematics in Physics. To comfort the afflicted and to afflict the comfortable... The 0/0 example demonstrates again the gap between mathematicians and physics and the cultures in which they operate. In Planck's Constant and Zero and Relativity I point out that there are sometimes better interpretations of the results, but the physicists involved followed the mathematical conventions of the day (which were established well prior to, and independently of, the Physics of the time). From the time of Max Planck we have had an equation that almost begged us to contemplate h=0/0, yet we skipped over it, because it didn't fit our conventions. It went into the "undefined" basket.
Consider this:
...are all based on division by zero. Each of the predictions uses the { 0 } view of zero.
Regards, AJ Corcoran
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