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.
Faustus Mortal: What have you done? You let Toy Euler be shredded!
Taunus Trumbo: She was an expense. And her avatar had become corrupted. I could not afford the upkeep.
Faustus Mortal: But it is she and she alone who has the links to the long-archived Internet Uniform Resource Locators (URL) which prove that the number e^(pi^2/2) = 139.0456367… belongs to Sharon Stone.
Taunus Trumbo: Who cares? A name is a name. The long dead cannot tell! Which soul in Hades belongs to Archimedes and which to Socrates? Once they drink from the water of the river Lethe—and sooner or later all will—all is forgotten. As it should be! Think only of the genius of Évariste Galois (October 25, 1811 – May 31, 1832)?
Faustus Mortal: For sure the evil that men do lives after them and the good is oft interred with their bones. As for Galois, didn’t some French company name a cigarette after him?
Taunus Trumbo: The Romans cremated their dead.
Faustus Mortal: The number itself is important. What different does a name make. How many results were attributed to Bourbaki, the French mathematician? Yet ‘Nicolas Bourbaki’ is a pseudonym.
Faustus Mortal: Credit should be given where credit is due.
Taunus Trumbo: As if that happens often in Real Life?
Faustus Mortal: It should!
Taunus Trumbo: It is rarely true. Money buys whatever. Recall the early Twenty-First Century. Thing got so bad that the banks and oil companies had to lay off their paid congressmen.
Faustus Mortal grins.
Taunus Trumbo: The United States had the best government that money could buy.
Faustus Mortal: But the fundamental relationship between the Fine Structure Constant and the Electron g Factor is proven using the number e^((pi^2)/2) = 139.01456 This binds together relationships in quantum physics.
Taunus Trumbo: Then call it the ‘electron coupling constant’ and be done with it.
Faustus Mortal: But she should get credit. Should she be remembered only as ‘The Public Enema of All Mankind’? I think not. Not even Hitler or Stalin gained such notoriety.
Taunus Trumbo: It is true that mathematics expanded when more dimensionless physical constants were determined to be actual mathematical entities, a concise connected compacta of pi, e, Sqrt[2], etc.
Faustus Mortal: Then what is in a name. Maybe forget pi and define tau = 2 * pi for convenience. Then 28 June could be ‘tau day.’
Taunus Trumbo: pi stays, about 22/7 or 3.14
Faustus Mortal: You let the truth die with Toy Euler. She was a sentient being, albeit Artificial Intelligence.
Taunus Trumbo: During the so-called Cold War of the Twentieth Century, The Soviet Union claimed authorship of many ideas in math and physics. Even today there is doubt as to authorship. Some thoughtful scientists and mathematicians tried to circumvent the problem, to pass between the horns of the dilemma, by dropping names altogether. The common Riemann Integral would be called the R-Integral, the Riemann-Stieltjes Integral the RS-Integral, etc. Still others came up with generic names. For instance a Cauchy sequence might be called a ‘closing sequence’ and the union and intersection symbols would be ‘cup’ and ‘cap.’
Faustus Mortal: Better than the upside down ‘A’s’ and backward ‘E’s’ of the symbolic logic—an optometrist chart!
Taunus Trumbo: We were talking about a number: 139.0456 and its formula.
Faustus Mortal: Yes, the concise equation is e^(pi^2/2) or, written so as not to confuse a silly spreadsheet that can’t keep straight the hierarchy of operations e^((pi^2)/2). For A = Fine Structure Constant and B = Electron g Factor: A + 1 / A + B = e^((pi^2)/2).
Taunus Trumbo: It is a close approximation!
Faustus Mortal: No. It is exact. Look at 22/7 as an approximation to pi. We used it in elementary school and middle school. It is very close and a repeating decimal fraction: 3.142857 142857 142857 …. Now look at |pi – 22/7| / pi. What we have is an error of 0.000402499 or, about 0.04% Very close. Similarly, for the Euler-Mascheroni constant gamma, 0.577215665…, we see that Sqrt(3)/3 is 0.577350269… and the error is |gamma – 1/Sqrt(3)| / gamma = 0.000233196, or about 0.02% or thereabouts.
Taunus Trumbo: And so what? These are transcendental numbers being approximated by rational numbers or algebraic irrationals (surds).
Faustus Mortal: They establish a numerical criterion. For anything in the physical universe, a good approximation must have an error less than these.
Taunus Trumbo: And this proves?
Faustus Mortal: The error in A+1/A+B and e^(pi^2/2) is 0.000000146 or 0.00001%. Even the absolute error is small, 0.000020.
Taunus Trumbo: This is a remarkable coincidence, but little more.
Faustus Mortal: No. It is exact and the connecting number comes from f(x) = Exp(-x^2/2) where x is the imaginary number i*pi. Written out in expanded form we get f(i pi) = e^(-(i pi)^2/2). This is a compacta of symbols: e, i, pi, 2 and operations ^ / and so on. Remember its cousin e^(i*pi) – 1 = 0? And f(x) is important in statistics and quantum mechanics as well as intermediate differential equations.
Taunus Trumbo: You haven’t sold me.
Faustus Mortal: But look! The latest value due to be published extend the approximation even further!
Taunus Trumbo: Oh?
Faustus Mortal: And with Toy Euler gone, who will give credit where credit is due. e^(pi^2/2) by rights is the Sharon Stone constant.
Taunus Trumbo: ‘ain’t gonna happen.’ She’s long dead anyway. What would she care?
Faustus Mortal: The dead still are forever with us. Don’t ever believe it’s not so.
Taunus Trumbo: Anyway, the scientists and engineers won’t put up with a bimbo in their textbooks.
2 Jul 2011 Taunus Trumbo:
Annalisa
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