Saturday, 12 May 2007

Solution to 0.999...

For those of you wondering about the .999... (repeating) puzzle, here it is.

Take the number 1, and divide it into three equal pieces, represented as fractions. You get three 1/3s. Add them together and you get one again, right? Right.

Take the number 1, and divide it into three equal pieces, represented as decimals. You get three portions of 0.333... (repeating). Add them together and you get 0.999... (repeating) Uh Oh. That's not 1!

Except it is. 0.999... and 1 are the same number.

There are many more complex proofs for this concept, using calculus and other methods. I must admit, many of these explanations are beyond me, but I do get the take-home-point: numbers are bad-ass, and although we (non-mathematicians) all pretty much assume we understand numbers, we really do not.

That's why I think statistics are cool (shock-horror!) and I enjoy helping to teach classes about them. They can illustrate our reality in ways that elude our normal perceptions. When I say "statistics," I'm not talking about "86% of people think BrandyBrand products are GREAT!" No, I'm not even talking about Analysis of Variance or Regression, though those are the workhorses of most statistically-based research. I'm talking about multi-dimensional scaling (MDS), cluster analysis, path analysis, and similar ilk. Stuff that allows us to create physical, geometric representations of abstract mental constructs by analyzing their numerical relationships. I realize this may be sounding a bit fuzzy or ivory-tower, but I hope to explain more in future posts - it's stuff I'm still learning about, and think is absolutely fascinating - but I should be posting ocassional numbers-are-fun posts over the next few months. It's great fun, and not as scary as it sounds.

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