Crackpot Spammer Ch 09
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Disclaimer: The following short story is fictional. No resemblance to any person, living or dead, is intended or should be inferred.
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Faustus Mortal: There, stop your complaining. I got the ‘Remarkable Coincidence’ posted to the forum.
Taunus Trumbo: And you were made a fool of as well. hehe
Faustus Mortal: Not really… The rebuttals were ‘lacking.’ One included units, it was not dimensionless. The other missed the major mark altogether. The Fine Structure Constant cannot be altered by changing one of its components. They are part of an equation. And, worse than that, the mathematical constant wasn’t even mentioned.
Taunus Trumbo: Oh.
Faustus Mortal: Oh yes. Now I will talk about significant figures and statistics. (grins) The significant figures of a number are those digits significant to its precision. For example, pi with nine significant figures is 3.14159265. We could add more digits since this is a non-repeating decimal fraction. One percent, on the other hand is 0.01 and has only one significant figure. For calculations, the calculator may introduce more digits than warranted by the original data. These are spurious digits. Rounding to a number of significant digits may have greater utility than rounding to a number of decimal places. There is also error propagation given in significant arithmetic.
Taunus Trumbo: And statistics?
Faustus Mortal: You know the quote: ‘There are three kinds of lies: lies, damned lies, and statistics.’
Taunus Trumbo: How true!
Faustus Mortal: The world usually ‘runs’ on five significant figures. Let’s look at seven significant figures for pi, in scientific notation: 3.141593_+00. And that Sharon Stone constant e^((pi^2)/2) = 1.390456_+02.
Taunus Trumbo: Power of ten, exponent doesn’t count?
Faustus Mortal: Right, it’s not a significant digit or figure. And likewise the other physical constants A = 7.297352_-03 and B = 2.002319_+00. And A + 1 / A + B = 1.390456_+02.
Taunus Trumbo: A is the Fine Structure Constant to seven significant figures and B is the Electron g Factor to seven significant figures.
Faustus Mortal: And they agree, at seven significant figures.
Taunus Trumbo: Can you squeeze out more digits?
Faustus Mortal: You are getting into the region of statistical error analysis. Type I and Type II errors, accuracy versus precision, and the very real and unfortunate physics problem known as systematic or Type III error.
Taunus Trumbo: Ah, yes, the notorious Type III error. Like Global Warming?
Faustus Mortal: In a way, Garbage in, garbage out: GIGO… Direct measurements only go so far with precision. Here come the indirect measurements, and the plausibility of the Type III error.
Taunus Trumbo: You said ‘precision’?
Faustus Mortal: Yes, not accuracy. The constant e^(pi^2/2) can be computed to as much precision as desired. It is a mathematical entity, a constant. It is also dimensionless, just like e, pi, and the square root of two.
Taunus Trumbo: Well, I guess at some time in the future, the value of the Fine Structure Constant or the Electron g Factor gets ‘perturbed’ a bit then the formula might be valid.
Faustus Mortal: It’s happened before. If History only teaches us one thing, it’s that we don’t learn any lessons from History. And that constant 139.0456… is not just some idle, random collage of symbols. It has a very significant role in number theory.
Taunus Trumbo: It is a role player?
Faustus Mortal: Most definitely. Why else should it be named after the Public Enemy of all Mankind?
Taunus Trumbo: For sure.
Faustus Mortal: So, in the sample space of numbers with seven significant digits, we see a functional correlation between the Fine Structure Constant and the Electron g Factor. But it fails with eight significant figures: 139.04564 vice 139.04562.
Taunus Trumbo: So the model is wrong.
Faustus Mortal: Not necessarily. We might look back to previous values of the Fine Structure Constant and the Electron g Factor.
Taunus Trumbo: You can do that?
Faustus Mortal: Yes, and they even give the experiments. Just because a result is old, doesn’t necessarily make it wrong. The designing experiment must be able to be repeated. That’s the Scientific Method.
Taunus Trumbo: Ah
Faustus Mortal: The people who set the recommended values for the Fine Structure Constant have seen it vary since 1969 from a low value of 137.02544 to a high value of 137.03673, And the solution to x + 1/x + 2.0023193043622 = e^((pi^2)/2) is certainly plausible, not impossible.
Faustus Mortal: If we assume that the Electron g Factor is so accurate and precise. We have been told that that is good and true.
Taunus Trumbo: The Electron g Factor is supposed to be the most perfectly measured of all fundamental physical constants.
Faustus Mortal: So those critics of the posts better consider more than a superficial examination of the numbers. I have avoided any rash claims, since for those who truly understand, no explanation is needed. For those intoxicated with shallow draughts from the Pierian Spring, no argument would be understood or accepted. You can lead a scholar to knowledge, but you can’t make him think.
Taunus Trumbo: You do think it is correct, that bundle of pi, e, 2’s and all that jazz.
Faustus Mortal: I am only saying that, based on history and the scientific method, it is plausible.
Taunus Trumbo: Ah, plausible.
Faustus Mortal: Neither is the earth the center of the universe nor is it flat. J. Balmer discovered the Balmer series properties, opening the door to quantum physics. Who is not to say that Sharon Stone, like Heddy Lamarr, might not usher in a new era of mathematics? Remember that crazy constant: 139.0456. It holds a key to number theory. It has a place just like pi, e, phi, Sqrt(2), and the Euler-Mascheroni constant, gamma.
Taunus Trumbo: That would piss off the intellectuals and eggheads a maximum.
Faustus Mortal: Numbers don’t lie. Just a slight perturbation, within the range of previously computed values, might make it so.
7 Jul 2011 by Taunus Trumbo
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