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In general; if one creates an ad-hoc relationship of constants, can we use it to solve equations OR is it just an abstract/artificial math construct?

I'm a grad student and as we all know, these ad-hoc constants are very easy to make, but are they useful?

Sometimes I think that I'm chasing my own tail...

R0^73*w0^73*e0^2/(c0^68*h0^74*A0^2*G0*N0^73)=23/10390 http://www.sendspace.com/pro/dl/rbvvix

Granted that the example is an artificial relationship, and has an error of a few parts per billion; still this type of ratio seems both unit and Prius invariant. The constants aren't going to change, hence the ratio should stay the same in all units.

maple sheet http://www.sendspace.com/pro/dl/7chckl

In summary, if one creates an artificial ad-hoc relationship; then it is abusing dimensional analysis by definition?

user56162
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1 Answers1

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A clear case of "abusing dimensional analysis". Perhaps not the first time that a physics stack-exchange question is answered by xkcd:

abusing dimensional analysis

Johannes
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