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StarLab
2004-Oct-22, 05:23 PM
OK, you guys know all about those Planck constants....time, mass, length, temp, etc.

He gets these numbers by mulitplying or dividing h, G, and c (with powers). If I were to use only these three constants in an equation, what combination would I need to get a numerical result of ONE? (Even if it's dimensionless)

StarLab
2004-Oct-23, 05:22 AM
Is there nothing? Is this such a stumper that it belongs in the Mind Trap string?

gavwvin
2004-Oct-23, 08:36 AM
If you really want to know... its very contrived:

((hc)^0.41194500914170876131159117264751) / G = 1

where 0.41194500914170876131159117264751 is ln(G)/ln(hc)
(if you know a little about maths you will see why this is a bit stupid!)

There is a really cool (non-contrived) one in maths: you know what pi is, e is another of these natural irrational numbers, and theres a crazy number called j which doesn't exist. (its the square root of minus 1)
Anyway...

e^(j times pi) + 1 = 0

StarLab
2004-Oct-23, 05:45 PM
Hm...well, there's gotta be another way...

And about that second equation, yes I have seen it before, I wonder if any of those - e, pi, or i - have any correlation with phi?

wstevenbrown
2004-Oct-24, 09:01 PM
Starlab--
I think what you're looking for is the "natural units" which arise whenever mutually consistent sets of universal constants are chosen to be unitary-- (c, h, k) is not the only such set. The definitive early work in this line, still in print and very accessible, is Dimensional Analysis, by P. W. Bridgman.
As to the connections among numbers, which flavor of answer are you looking for? My own area of interest and expertise is phi. What kind of connections I make to other numbers is the subject of a book now being written-- this isn't a plug, it will be pseudonymous. Regards, Steve