TheHermit <firstname.lastname@example.org> writes:
Well done, and thank-you, ERiC!!! As you figured out, and have subsequently had confirmed, I left them in odd dimensions and unitless in order to make the point that they are intrinsically recognizeable. And that the actual measurement and units are far less significant than the ratios that they represent. I hoped somebody would do this as it made the point far more completely than any words I could use.
Actually, I refuted your point -- I provided the context ("frame of reference") in which your "truths" hold. Tim also demonstrated their inherent context by providing the wrong one -- in which your "truth" is no longer true.
It is becuase of our similar education (the common framework of our society) that I was able to recgonize those numbers at all -- and I pointed that out with my first-century Roman Soldier reference.
One blooper on your part. All of the sequences I chose were selected because they can be expressed ratiometrically - or why primes were excluded - I think that is all you missed.
I don't think all of the examples you included can be expressed ratiometrically. Specifically, The Perfect Squares have no common ratio...
Being an amateur historian with a special interest in mathematics and science (I grew up on Mathematics for the Million and Science for the Citizen so I have a head full of "totally useless mathematical trivia") I agree that as they are represented here (due to the limitations of the media) they are very context specific. If this were not email, I could have drawn each and everyone of these relationships graphically - and there, the troubles with units and bases does not arise. Think about it for a bit and you will see that I am right. Oh sure, Plank's Constant would be a little tricky to decipher if there were no clue as to what it relates to, but even there, there are ways to draw it so that somebody getting the context can figure it out. A series of color swatches (filters) would be the most obvious way to depict it, but I am sure that a little thought would generate many more.
Any medium you choose to represent them with (pictures, numbers, sounds, whatever) is a system of symbols -- and as such, it requires a "frame of reference" in order to *communicate* it's truth to the reader (looker/listener/toucher/etc). Truth *encodes* properties of the universe in a system of symbols (in the most general sense of that word) -- and those symbols carry with them a "frame of reference". Indeed, for trancendentals, most symbol systems cannot even encode the entire property -- this is the source of the "..."'s after the numbers you wrote above. (for formal symbol systems, Godel *proved* that either the system is incorrect or incomplete)