Insomnia and math…Call it “amateur numerology”.
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December 6, 2009 at 3:04 pm |
I feel dizzy…..
December 7, 2009 at 11:11 am |
It is a little mesmerizing, isn’t it?
December 8, 2009 at 6:55 am |
Intrigued, I decided to try to establish the general case and then prove it using mathematical induction. As it turns out, the general case is so incredibly trivial that constructing a proof would be absurd. (Indeed, it resolves to an algebraic tautology).
BUT – this exercise didn’t satisfy me because it didn’t capture the idea of “adding the numbers represented by the individual numerals composing a number”. It occurred to me that in order to do this, one would have to construct a model (c.f. Gödel) of Peano arithmetic that gives you a metalanguage to mobilize the distinction between “numeral” (or digit) and “number”. Too long and too hard for me (I’m not very good at logic nor math).
If you did make such a model, then I suspect you could also generalize THAT case to all possible base-10 positional notation systems (other than the Hindu-Arabic numeral system).
December 8, 2009 at 11:22 am |
Finn: As a historian of science I’m sadly pretty lackluster in the math department…But I do find it interesting that the “model” to “capture the idea of ‘adding the numbers represented by individual numeral composing a number’” would be a little complex. It’s an axiom of numerology to employ that process (until you pare down to a “pure” single digit). Demystifying it would be fascinating…And terribly bothersome to devoted numerologists…
December 8, 2009 at 11:55 am |
I suppose building a nuclear reactor and then irradiating mercury to synthesize gold would be terribly tiring to alchemists as well.
I suppose double-blind clinical trials would be terribly tiring to homeopaths as well.
I suppose explaining planetary motion using special relativity would be tiresome to astrologists as well.
See a pattern? (hehehe, pun intended).
If we want to demystify, then reasoned argument from logical axioms or well-measured empirical data is what we need. Everything else is just poetry.
December 8, 2009 at 12:08 pm |
This doesn’t necessarily demystify, but it certainly clarifies.