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I find Kaprekar's operation totally uninteresting because it is (or at least seems to me) totally linked to base ten representation of numbers. If at least you

I find Kaprekar's operation totally uninteresting because it is (or at least seems to me) totally linked to base ten representation of numbers. If at least you had a result like "in any base, the analogue of Kaprekar's operation in that base has a fixed point for digits of length 3 or 4 only", it would be mildly interesting. But as it is it's not math, just senseless symbol manipulation.

JoachimSchipper 15y ago
"Recreational mathematics". Don't take it too seriously, the practitioners don't either. But yes, the fact that this is bound to a decimal system suggests that there are no deep wisdoms here.
- alphaBetaGamma 15y ago
  I don't have anything against recreational math; I rather like it myself. But, IMHO, the fact that something is tied to the representation of numbers removes it from the realm of "math".
  - william42 15y ago
    I'd say that the representation of numbers is an important part of math. That said, I'd agree that decimal is not a particularly interesting part of math. For reals, continued fractions are probably the most interesting representation, and have nicer mathematical properties, at that.
    - _delirium 15y ago
      To the extent that 'regular' mathematicians pay attention to these things (which a good number do), I don't think it's because decimal representations are inherently that interesting, but more because some of the number-theoretic and meta-mathematical questions are interesting and yet a bit puzzling. We don't yet really have a great handle on proof techniques and understanding of these kinds of problems: why should some simple-to-state claims about integers and iterated operations on them be true, and others false, and why are some seemingly true ones so hard to prove (like the Collatz conjecture)? The fact that this one is about rearranging digits in base-10 integers is just an intuitively-appealing way of stating simple properties, but the interesting thing isn't really about the base-10-ness imo.
Martijn 15y ago
This reminds me of a beautiful and appropriate comic by Cowbirds in Love: http://cowbirdsinlove.com/43 http://cowbirdsinlove.com/43
lurker19 15y ago
Perhaps you should set out to prove or disprove that conjecture, instead of writing an uninteresting post that is just senseless symbol manipulation linked to the base-26 representation of English.

JoachimSchipper 15y ago

"Recreational mathematics". Don't take it too seriously, the practitioners don't either. But yes, the fact that this is bound to a decimal system suggests that there are no deep wisdoms here.

alphaBetaGamma 15y ago
I don't have anything against recreational math; I rather like it myself. But, IMHO, the fact that something is tied to the representation of numbers removes it from the realm of "math".
- william42 15y ago
  I'd say that the representation of numbers is an important part of math. That said, I'd agree that decimal is not a particularly interesting part of math. For reals, continued fractions are probably the most interesting representation, and have nicer mathematical properties, at that.
  - _delirium 15y ago
    To the extent that 'regular' mathematicians pay attention to these things (which a good number do), I don't think it's because decimal representations are inherently that interesting, but more because some of the number-theoretic and meta-mathematical questions are interesting and yet a bit puzzling. We don't yet really have a great handle on proof techniques and understanding of these kinds of problems: why should some simple-to-state claims about integers and iterated operations on them be true, and others false, and why are some seemingly true ones so hard to prove (like the Collatz conjecture)? The fact that this one is about rearranging digits in base-10 integers is just an intuitively-appealing way of stating simple properties, but the interesting thing isn't really about the base-10-ness imo.

Martijn 15y ago

This reminds me of a beautiful and appropriate comic by Cowbirds in Love: http://cowbirdsinlove.com/43 http://cowbirdsinlove.com/43

lurker19 15y ago

Perhaps you should set out to prove or disprove that conjecture, instead of writing an uninteresting post that is just senseless symbol manipulation linked to the base-26 representation of English.