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.
I'll tackle the rest in-line.
> -----Original Message-----
> From: firstname.lastname@example.org
> [mailto:email@example.com]On Behalf
> Of Eric Boyd
> Sent: Wednesday, May 12, 1999 10:51 PM
> To: firstname.lastname@example.org
> Subject: Re: virus: maxims and ground rules and suppositions
> Plank's constant ??? I thought that was at 10^-34 ??? The smallest
> unit of energy. Depends on unit definitions.
You are correct - I use the MJ as my basic unit as almost all the energy we play with here would have an overwhelming number of 0s else.
> e -- useful in calculus; equals
> lim (1+x)^(1/x) = lim (1+ 1/x)^x
> x -->0 x --> infinity
> and (here's the kicker...) diff(e^x, x) = e^x
Yes. Where Plank defines the universe (without doubt, Plank defined the seminal concept, insight and number in Quantum Physics when he defined h), this one does about the same for the nature of numbers and areas.
> 1/sqrt(2) -- useful as a design coefficient (ideal damping ratio)
As an engineer I could not omit it :-) And of course, the reciprocal is also required.
> The Golden Ratio = [1+sqrt(5)]/2. Creates aesthetically pleasing
> rectangles. May be cultural or species dependent. It also turns up
> as part of the solution to a problem I talk about below... one of the
> many "small miracles" involved.
It seems to be interspecies, interorder, even intertype. Dogs "prefer" baskets with these ratios too... Bees use it all over their hives. Dolphin and whale songs are based on it. And plants grow stems by it....
> The Universal Gas Constant -- in metric (this number depends on unit
> definitions). Useless itself, but can be converted for use with
> specific gases via molecular weight, and *then* used in the Ideal Gas
> Law (itself only an approximation to reality)
Actually it works "perfectly" for an ideal gas and almost perfectly for Hydrogen (we are not sure about whether it applies during the triple state under pressures close to those which will create metallic Hydrogen) but it seems to work for every other temperature pressure combination.
> Any "constants" which depend on units would be unrecgonizable to
> anybody without the context of our current system. (and our current
> system is mere historical/cultural accident, really)
Of course. But the numbers are just symbols on a piece of paper anyway. I was trying to get past that to the fact that the ratios themselves are what is relevant. And that because they are ratiometric and appear all over that their actual "message" is true to the universe.
> Counting (Arithmetic Sequence with a=1 d=1)
> The Fibonacci Sequence
> Exponential Growth (Geometic Sequence with a=1 r=2)
> (also the place values in base two (*very* familiar))
> The Perfect Squares
> On sequence which should definitely be included:
> The Primes:
> 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, ...
> (of course, they carry much more of a "frame of reference" then the
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.
> So, if you agree with me that these digit sequences (numbers and
> progressions) are "useful truths" in that they denote certain
> "special" values tied into the fabric of the universe or the nature of
> numbers, and that they remain "useful truths" without a particular
> "frame of reference", then we need to look again at the postulated
> TheHermit: Every single one of those numbers and sequences has a
> context; or "frame of reference" (some even have a culturally defined
> context, rather than a naturally defined one) -- and most are utterly
> useless unless you happen to be doing something special. One does not
> escape "frames of reference" merely by making that frame reality --
> becuase we still have to choose how to describe that reality, if only
> the trivial choice of base and representation system (see _Number: The
> Language of Science_ to learn that our number system itself is a vast
> collection of implicit knowledge (read: a frame of reference), or
> prove it to yourself by thinking what a first century Roman would see
> in the above -- nothing but scribbles on a page).
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.
>  Much talked about -- it seems these numbers, amoung many other
> things, specify the differing groups into which flowers can be
> sorted -- via the number of petals they possess. (it also explains
> the apparent rareness of four leaf clovers...) My math professor says
> that an excellent intelligence test is asking for the general (nth)
> term of this sequence -- one will not stumble upon it by chance. It
> is just the type of thing an intelligent group of aliens might require
> of a species before "first contact"...
Well done again anyway...
Hermit <Thinking - "When he that speaks, and he to whom he speaks, neither of them understand what is meant, that is metaphysics." ~Voltaire :-) >
"I refuse to prove that I exist" says God, "for proof denies faith, and without faith, I am nothing." "Oh," says man, "but the Babel Fish is a dead give-away, isn't it? It proves You exist, and so therefore You don't. Q.E.D." "Oh, I hadn't thought of that," says God, who promptly vanishes in a puff of logic. ~Douglas Adams, Hitchhiker's Guide to the Galaxy