2 comments/ 5907 views/ 0 favorites Crackpot Spammer By: Taunus Faustus Mortal is a fictional character. So is Sari Stone, for that matter. This is not to say that they were not inspired by living human beings; however, any resemblance to persons living or dead is purely coincidental and none should be inferred. * The day begins early with Faustus Mortal in the Basilica Cardinale. He is there each and every day as a religious. Today, however, is different from all others. He is greeted outside the Basilica by Sari Stone, a young college coed majoring in physics. She has heard of Faustus's latest discovery and is curious about it. Faustus is not used to having a great deal of social contact. Sari Stone: Greetings Faustus! Faustus Mortal: Whatever brings you to cyberspace, Sari? Faustus Mortal: I thought that you were cured of your Internet addiction! Sari Stone: Tell me of the formula for the isospin of the proton-neutron. Sari Stone: You should publish it! Faustus Mortal: I tried to post it in Physics Forum. Sari Stone: And? (Mn-Mp)/Me = ln(4pi) Faustus Mortal: They deleted my post and banned me forever. Faustus Mortal: They said that I was a "Crackpot spammer." Faustus Mortal pouts. Sari Stone: Was the number wrong? Faustus Mortal: It was 99.9985% correct. Faustus Mortal: Not to worry. Some tenured professor will use it. Faustus Mortal: They will take it as their own discovery. Faustus Mortal: Why should I care? After all... Faustus Mortal: I am a "Crackpot Spammer." Sari Stone: You come here every day and beseech the almighty for a solution to the energy dilemma. That is "crackpot"? And you received an answer once. It was a trick from Printz Darkness. But how would anyone know otherwise? The safe thing to do is to follow blindly the tenured teachers and their doings. How did you once express it? "They follow well-worn ways and pluck low-hanging fruit from the much-decayed tree of obsolete technology." Faustus Mortal: Those were the words of an angry young man. Faustus Mortal: I have changed. I come here every day. Sari Stone: I don't go much for all those ancient rituals. Faustus Mortal: The church is, after all, on my side. Faustus Mortal: They want clean, cheap, copious energy! Sari Stone: Doesn't everyone want that? Faustus Mortal guffaws. Faustus Mortal: I wish! Sari Stone: So, you studied energy, what about wind energy? Sari Stone: It's being hyped so much in the media. Faustus Mortal: Great theory, but it has problems. Sari Stone: Do tell. Faustus Mortal: Conventional energy production has a generating facility. It uses some source, coal, falling water, nuclear fuel, or the like. But wind is spread out and needs to be collected up via transmission lines. This is a problem, both of installation expense and maintenance. Clearly, the best fuel would be hydrogen produced by electrolysis of water. But hydrogen is a light gas, not easily compressed. Consider carbon dioxide. You can get a tiny cylinder to make your sparkling water. Ditto for nitrogen. There are nitrogen cylinders. But helium? That's another story. You get a large metal container. Helium is not easily compressed into a tiny cylinder. Natural gas can be compressed easily. But hydrogen cannot. If it could, then one could compress the gas and collect it for storage and transport. But this won't happen. Perhaps technology someday will come up with a way to encapsulate or incarcerate hydrogen and retrieve it. But that is off in the future. The problem is here and now. Sari Stone: Why not transmission lines for wind energy turbines? Faustus Mortal: Great idea, but very expensive. And each wind turbine needs a connecting line. Not only that, wind is unpredictable and intermittent. Doldrums come along from time to time and then there is no power. What then? Sari Stone: You do have a point. And what about solar power? Faustus Mortal: Great idea, but expensive. It needs places with lots of sunshine. That eliminates vast regions of the country. Especially during the winter months when electricity demand is greatest. The energy needed to produce the solar cells isn't small either. We are looking at decades for either wind or solar. We can't wait that long. Sari Stone: It looks so bleak for environmentally safe energy. Faustus Mortal: Of course there is nuclear energy. But, IMHO, it's about the dumbest way to boil water that is conceivable. And it scares people with all that media hype about melt downs and radioactivity. Chernobyl did a lot to frighten the whole world, even the religious with their mystic interpretation of the star "Wormwood." Sari Stone: What might you suggest for nuclear fission energy? Faustus Mortal: Moi? Well, one could burn the Uranium-238 if it didn't have such a long half-life. Of course the Fundamental Law of Radioactive Decay states that no physical process can alter the half-life. But I think it is possible. After all, special relativity can extend, prolong, or dilate it. Maybe on the quantum end there is some way to energize an intrinsic property and shorten the half-life. That would give ninety-nine times the energy that is available now!! Sari Stone is intrigued. "Have you mentioned this to others?" Faustus Mortal: No. They would only consider it some crackpot idea. Faustus Mortal: They called my derivation of the mass ratios of fundamental particles "numerology." But not to fear, they are well-funded by those selling crude oil, natural gas, and coal. I call that trio the Fossil Fuel Fellowship under the titular head of Old King Coal. They own the Congress, btw, lock, (preferred) stock, and (oil) barrel. You can remember the child's poem? "Old King Coal was a dirty old soul and a dirty old soul was he. He called for his pipe(line) and called for his bowl and called for his lobbyists three! Sari Stone smiles. The isospin equation is the natural logarithm of four times pi. The formula in my TI-30X is ln(4pi). (Check it out.) Sari Stone: So you want fission? One time you told of "burning" protons directly to energy and powering interstellar travel via a constantly accelerating reference plane. For a while you concept of "cold fission" had a small, albeit elite, following. Faustus Mortal: The Fossil Fuel Fellowship has won the war. Soon coal powered generators will be the norm. They are already over 51%. It's simple economics. No matter how much capital is pumped into the so-called "green energy" sources, coal is cheap, coal is plentiful, and coal is dirty. Crackpot Spammer Ch. 02 Disclaimer: The following short story is fictional. No resemblance to any person, living or dead, is intended or should be inferred. Faustus begins his lecture on the newly revealed knowledge in quantum physics. The two transcendental irrational numbers most occurring in mathematics are pi and e. "pi" being approximately 3.1415926535... and e being approximately 2.718281828.... On these two numbers hang most of the mysteries of mathematics. The first equation to consider is e^(i*t) = cos(t) + i*sin(t), where i = Sqrt(-1) = (-1)^(1/2) "i" is the so-called "imaginary number, where i*i = -1. And we blissfully set t in the above equation to pi to get e^(i*pi) = -1 ...or... e^(i*pi) + 1 = 0 Here pi, e, and i each make their cameo appearance. The parsimony of symbols and numbers is remarkable. Then of course, come the Gaussian distribution: e^(-x^2/2), which is normalized to be f(x) = e^(-x^2/2) / Sqrt(2*pi), which is also remarkable. It manages to include the irrational number Sqrt(2); it lacks the imaginary number. But consider the hybrid by inserting x = i*pi into e^(-x^2/2). This yields a number e^(pi^2/2) = 139.0456367... [Eqn_1] Now this number does crop up here and there in abstract number theory, but until 30 May 2011 it did not have an application in applied math or physics. Now let A = Fine Structure Constant and B = Electron g Factor. Then we observe the remarkable coincidence, to seven significant figures: A + 1/A + B = e^(pi^2/2) [Eqn_2] This gives an equation relating the Fine Structure Constant and the Electron g Factor. If we assume that "B" is both accurately and precisely known, then "A" is found from a quadratic equation. x^2 + (B-e^(pi^2/2))*x + 1 = 0, something soluble by high school math. -------------------------- Your assignment is to look up the best values for the Fine Structure Constant and the Electron g Factor and plug them into the equation [Eqn_2]. Given the Electron g Factor, determine the Fine Structure Constant. Assume [Eqn_2] is correct. What would be an accurate value for A? ------------------------ The value of the measure of a particular physical constant may be accurate, or precise, or neither, or both. Let's see what these terms really mean. We start with a measurement system. If the measurement is close to the actual (or true) value of the constant, then the measurement system is said to be accurate or to accurately measure the constant's value. The precision of a measurement system is a measure of the reproducibility of the measurement system. So, let's look back in history. The number pi was originally conceived of as about three; it was then more precisely approximated as a variety of rational numbers including 22/7, a common approximation in High School mathematics. A rational number is always precise---it is a mathematical entity. But it may fail to accurately determine the value of pi. The number 22/7, for example, is a repeating decimal fraction: 3.142857 142857 142857.... We have that |pi – 22/7| is 0.00126, or thereabouts. For centuries, millennia even, pi was considered as a dimensionless physical constant, the ratio of the circumference of a circle to its diameter. Various rational numbers were given as approximate values of pi. It wasn't until the Seventeenth Century that science and mathematics realized that pi was a transcendental irrational number and that its value could be determined by infinite series or infinite products. Now the value of pi is known both accurately and precisely. It is undeniably a mathematical and not a physical constant. Measurements of dimensionless physical constants may be precise but not accurate. In statistics, a Type I error is a false positive, a Type II error is a false negative, and a Type III is the error of measuring the incorrect entity with the measurement system. Precision is important; however, accuracy is essential. ------------------------ Let's try values of the Electron g Factor in [Eqn_2] and solve for A. We have a good approximation for A = Fine Structure Constant as well as 1/A. B = 2.00 A = 0.007297227944674 1/A = 137.0383394327 B = 2.002 A = 0.007297334450971 1/A = 137.0363393262 B = 2.0023 A = 0.007297350427184 1/A = 137.0360393102 B = 2.00231 A = 0.007297350959725 1/A = 137.0360293097 B = 2.002319 A = 0.007297351439013 1/A = 137.0360203092 B = 2.00231930 A = 0.007297351454989 1/A = 137.0360200092 B = 2.002319304 A = 0.007297351455202 1/A = 137.0360200052 B = 2.0023193043622 A = 0.007297351455221 1/A = 137.0360200048 Recommended Values A = 0.0072973525376 1/A = 137.035999679 From B = 2.0023 on, we have A = 0.00729735 and 1/A = 137.0360. These numbers are sufficient for most calculations. It wouldn't take much perturbation to nudge these constants into a perfect fit. The CODATA values move about from time to time as technology changes and new systematic errors are discovered. It will be History that eventually makes the final decision. ------------------------ The driving constant behind this equation is e^(pi^2/2) = 139.0456365056... [Eqn_3] This constant has no name. It should be named after the Muse who inspired it: Sharon Stone, the actor. This constant has a particular mystery about it. It is related to e^(-pi^2/2), a value in the function g(x) = e^(-x^2/2), where x = i*pi, i being such that i*i=-1. ------------------------ Your next assignment is to find where e^(pi^2/2) appears in abstract number theory and, from there, make an educated guess as to how it might relate the Fine Structure Constant to the Electron g Factor. ----------------------- 6 June 2011 Taunus Trumbo Crackpot Spammer Ch. 03 Disclaimer: The following short story is fictional. No resemblance to any person, living or dead, is intended or should be inferred. * Faustus begins his lecture with some miscellaneous facts about the mystery of complex variables. "We first think of Infinity as a symbol. It is often thought of as the 'end of the line of integers,' 1, 2, 3, and so on. And for the real number line there is a positive Infinity to the right and a negative Infinity to the left. The Texan would call the Infinity symbol a 'lazy eight,' which is the number eight turned on its side. The medieval scholar would call it a lemniscate, now called the Lemniscate of Bernoulli." "Jump from the real line to the complex plane and many marvels occur. The complex plane may be viewed as a stereographic projection. This may be visualized as a ball on a flat table. The point of contact is zero. The 'top' of the ball would be complex Infinity. Pass a line from the top of the ball through any point on the surface of the ball, the sphere, and it uniquely determines a point on the complex plane. Shortly we will see that the table could be round or square, there is but one complex Infinity. A mathematician would say that the Riemann Sphere is the complex plane with an added symbol." "In classical geometry, the stereographic projection is a mapping that projects each point on a sphere onto a point in the complex number plane. The projection is defined on the entire sphere, except at one point---the Infinity point. The stereographic projection is a way of depicting the sphere as the plane plus an Infinity symbol." "So, suppose we are on a complex plane and decide to march along the x-axis say. Recall from high school algebra that a complex number z is given as x + i y. Here the symbol i is the square root of minus one and each of x and y is a real number. So march on and approach Infinity. March to the left and approach Infinity again, not negative real Infinity, but complex Infinity. Take a long, deep breath. This is a real quantum jump. There is but one complex Infinity, regardless of the path taken towards it." "I will now consider time as a complex number. Call it 't.' The part we dwell in, in our 3D reality, is the real component. But wait, the imaginary component may explain something very fundamental. As Re[t] approaches zero, we experience the 'Big Bang.' What if the imaginary component Im[t] maps to Infinity as it approaches zero? That is complex Infinity, a pole. So only in a infinitesimal neighborhood of zero need we be concerned about the value Im[t] maps to. At any time Re[t] > 0 we have 'time' defined in the usual manner." "Take a region in space itself. The Schrödinger wave equation and Maxwell's equations assume that their underlying solutions are analytic or, at worst, 'Real Analytic.' In the physical world solutions are bounded. If space were infinite, then by Louisville's Theorem 'bounded entire functions are constant.' This is undesirable. Space must be finite." "The Big Bang theory is very well accepted. There are other theories of creation, but the Big Bang theory is well-substantiated and consistent with reality as we understand it. For convenience, let 'u' stand for the real component of time Re[t] and let 'v' stand for the imaginary component of time Im[t]. I am assuming that time 't' is a complex number. Then t = u + i v. The Big Bang starts at u = zero. Let's suppose that when u = 1, the fundamental particles---protons, electrons, and photons---are formed. Then in the time half plane we might say that for all u > 1 that the universe is analytic out to its boundary. It is like some expanding region. So matter exists and photons and all that we experience for Re[t] and so that Im[t] is finite for all values of v in the half plane u > 1. But in the half plane u "Now I present the major result. From the Schrödinger wave equation and the use of complex time, I derive Maxwell's equations. This will apply to quantum regions and does not take into account relativity considerations. But that will follow." 29 Jun 2011 Taunus Trumbo Crackpot Spammer Ch. 04 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: Crackpot Spammer Ch. 05 Disclaimer: The following short story is fictional. No resemblance to any person, living or dead, is intended or should be inferred. * 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 Crackpot Spammer Ch. 06 Disclaimer: The following short story is fictional. No resemblance to any person, living or dead, is intended or should be inferred. Faustus begins his lecture by discussing significant figures: "Consider a number of the form '1.234567,' or thereabouts. Such a number clearly has seven significant digits. Such a number might arise from rounding the transcendental irrational number pi, for example. The number pi is given by 3.1415926535898.... Rounded to seven significant figures it is 3.141593. For almost any imaginable scientific or engineering endeavor this is a suitable approximation to pi. Likewise the number 'e' may be approximated by 2.718282 and the square roots of two and three are 1.4142134 and 1.732051. Many scientific calculators, e.g., the TI-30XIIS, display ten significant digits. For purely mathematical constants, as those just mentioned, this is both accurate and precise." Faustus pauses a minute to contemplate accuracy versus precision and then continues: "But for the real world there may be lurking (or exogenous) variables influencing the numerical display. These may affect the accuracy of the displayed number. There may also be spurious digits arising from less significant input values. Let's investigate for a moment with the square root of three, rounded to seven significant figures. (George Washington was born in 1732.) 1.732051^2 = 3.000000667. This is rounded to 3.000000. This is the integer number three, more or less, mostly more. Notice how accurate the square of 1.732051 actually is!" "We will look at two physical constants and one mathematical constant. The mathematical constant is e^((pi^2)/2) = 139.0456366605..., which rounds at seven significant digits to 139.0456. This is a 'bad news' number for physicists, increasing the scope of pure mathematics at the expense of the pedants pushing extra digits to obtain advanced degrees. No small wonder that it is named after the actress known as 'The Public Enemy of All Mankind.'" "The two physical constants are the Electron g Factor and the Fine Structure Constant. Let's first consider the Electron g Factor, since it is easier to discuss and has measurement considered more precise and accurate than the Fine Structure Constant (and its inverse). The most recent recommended value for the Electron g Factor is 1.0023193043622. Physicists claim this is a very good approximation, both accurate and precise. For the moment, let's take them at their word. After all, it is a single, simple measurement, not an artifact constructed from several other constants as is the Fine Structure Constant and its inverse." "Let us list the eleven values of the inverse Fine Structure Constant from learned bibliographies from 1969 to 2006, in increasing order: 137.03544, 137.03545, 137.03591, 137.03597, 137.0359895, 137.03599883, 137.0359997, 137.0360017, 137.0360017, 137.0360119, 137.036073. Now we have a range of values to look at. Let x denote the value obtained from the equation x + 1/x + 2.0023193043622 = e^(pi^2/2). It is 137.036020005 and 1/x = 0.0729735145521. It lies between the seventh and eighth estimate. Clearly this is a candidate, assuming that the Electron g Factor is correct. What can be done to 'sharpen' this estimate? It has been stated in several textbooks and mentioned in the physics forum that the Fine Structure Constant and the Electron g Factor are interdependent or somehow entangled. This could be one such functional relationship. Could this be 'the' functional relationship? If so, the Ansatz e^(pi^2/2) is a pure mathematical constant with physical significance." "What remains to be done to firm up this theory? The Electron g Factor needs to have a pure mathematical formulation. This would require some special knowledge of the structure of the electron. The dimensionless physical constant needs some elementary formulation in terms of pi, e, the square root of an integer, and the imaginary number i." "If History teaches us anything about the Fine Structure Constant, it's that its value moves around, but its inverse is always near 137.0360. This matches with our estimate in seven significant digits. Now the challenge is to find a closed-form expression for the Electron g Factor. Accomplish this and the Fine Structure Constant will be proven to be a mathematical constant. Then one can 'back engineer' the value to the correct geometric model of fundamental physical particles. But this is a very difficult feat to accomplish." Faustus concludes: "It was the Seventeenth Century before the number pi entered into the domain of mathematics instead of physical measurement. And the scope of mathematics was expanded as irrational numbers were understood to be either algebraic or transcendental. While rational numbers and algebraic irrational numbers are countable, the transcendental irrational numbers are uncountable. And our understanding of the mysteries of mathematics was expanded." Summing up, Faustus says: "Likewise, should the Electron g Factor and the Fine Structure constant be found to be mathematical constants, Physics will lose one of its prized joys and mathematics will find new foundations. In fact, the understanding of the geometry of fundamental particles will be expanded. Rather than just tossing out some recipe or formula, like the Schrödinger wave equation, working models may be constructed. The present powers-that-be are diametrically opposed to such a situation. Having become aware of the constant e^(pi^2/2), it is time to determine the basis for the Electron g Factor." 25 Jul 2011 Taunus Trumbo Crackpot Spammer Ch. 07 Disclaimer: The following simulated dialogue is fictional. No resemblance to any person, living or dead, is neither intended nor should be inferred. * Taunus Trumbo: You keep preaching about pi once being a physical and not a mathematical constant. What human difference does that make? Faustus Mortal: Well, suppose you carefully construct a circle one meter in diameter, as well as humanly possible. Then stretch a string tightly around it. Remove a measure the string with a metric ruler. To the finest tick mark on the ruler it is 3,142 millimeters. This is assuming no error in the construction of the circle or in the measuring of the string. To add another digit we would have to have a circle ten meters in diameter. This would give an approximation to the value of pi to be 3.1415. For another decimal place an impractically giant circle one hundred meters in diameter would have to be constructed. Even doing everything correct, the error would be plus-or-minus 0.0001, the "true value" being between 3.1414 and 3.1416. Taunus Trumbo: At that rate to get five decimal-place accuracy, you would need a circle with a diameter of an Egyptian pyramid. Faustus Mortal: Yes; all sorts of errors can creep in then. Taunus Trumbo: Say you measure the value of pi many times; can't you get a statistical mean and variance? So we can be accurate and precise? Faustus Mortal: String stretches and the surfaces vary. There are systemic as well as statistical errors. Taunus Trumbo: So how to do it mathematically? Faustus Mortal: Use a "limiting process." Construct geometric figures whose circumference is known and which converge to a circle. Then the ratio should converge to pi. Taunus Trumbo: Sounds like Calculus to me. Faustus Mortal: It is partially Calculus. It is a true statement that the history of mathematics was, up until recently, the history of pi and its influences. Now we have number crunching digital computers. Taunus Trumbo: Most students don't even know how to compute the square root of two by hand and almost none know how to compute the cube root of two by hand. Faustus Mortal: This is very true. But pi is not a root of some rational number or algebraic equation. It is transcendental. Taunus Trumbo: Something to do with a dentist? Faustus Mortal: Not that! The point that I'm trying to make is that if pi were still considered to be a physical constant then there would no doubt be a "recommended" value and a Standard Error (SE). And, I wouldn't be surprised if it didn't disagree with the true theoretical number. But for seven significant figures or less, who would care? Taunus Trumbo: Well, I for one wouldn't care. We used 22/7ths in grade school and 3.14 in High School and everyone seemed pleased with the results. Faustus Mortal: If you have a calculator, press the "pi" key. If you get the expected number, you are 95% certain that the calculator is working property. To double check, try Exp(1) = 2.718281828. Taunus Trumbo: So you think some of your approximations are correct? Faustus Mortal: Possibly. One philosophically correct point is mass defect and mass excess. I base mine on the particle-to-electron mass ratio. Physicists base theirs on the atomic weight-to-atomic mass unit ratio of the constituents. It's the nucleus and not the electrons involved here. Taunus Trumbo: Who cares? Faustus Mortal: Well, it generates some nifty formulas. Taunus Trumbo: Why don't you research them? What would you like to gain? Faustus Mortal: I claim that the decomposition of the proton is the quintessential and penultimate energy source. Protons are found in interstellar space. Taunus Trumbo: And you can do this? Faustus Mortal: I was booted out of graduate school in physics. Taunus Trumbo: Go back. Now with energy a problem the fossil fuel fellowship no longer has hegemony over the universities and government. Faustus Mortal: No can do: too old, too poor, I and have Parkinson's disease. Besides, being over seventy years old means that even if I were given a PhD Honoris Causa, it wouldn't be worth the paper it was printed on, unless the paper is made of one hundred dollar bills. Taunus Trumbo: Ha ha... Faustus Mortal: Come up with something else in interstellar space to fuel you with. Is there an Arco(tm) station lurking there? Taunus Trumbo: I don't think so. =) Faustus Mortal: So that's that. Taunus Trumbo: You know Faustus, you are just a bluff. Faustus Mortal: That may or may not be true. Suppose that the probability that I'm right is one in ten thousand, like Pascal's Wager, only more realistic. P[X] = 0.0001, where X is event that I'm right. Taunus Trumbo: OK Faustus Mortal: What is the probability that some tenured teacher will come up with a solution better than: walk, ride a bicycle, use natural sunlight, be a vegetarian, hug a tree, and so on ad infinitum, ad nauseum... Solar, wind, geothermal, bio-fuel are too iffy, too expensive, and too unreliable... P[Y] =?, where Y is the event that a solution for the energy quagmire would come from academia. Taunus Trumbo: You have a point. Faustus Mortal: Remember: "Old King Coal was a dirty old soul and a dirty old soul was he. He called for his pipe(line) and he called for his bowl and he called for his lobbyists three." Taunus Trumbo: Kinda like an oxymoron: jumbo shrimp, military intelligence, Microsoft works, and "Clean Coal." Faustus Mortal: Sad but true. 9 Aug 2011 Taunus Trumbo Crackpot Spammer Ch. 08 Disclaimer: The following simulated dialogue is fictional. No resemblance to any person, living or dead, is neither intended nor should be inferred. * Taunus Trumbo is on line. Faustus Mortal is on line. Taunus Trumbo: I saw a TV show on "Science". They explained the formation of the elements. From Hydrogen at the Big Band, to the elements Helium through Iron from stars, to all the heavy elements via super novae. Their theory is different from yours. Faustus Mortal: Believe what you will. I have a model. Start with nothing and experience pair production: a positron with energy and an electron. The positron's standing wave flattens out and is tangent to the positron at a single point. From that point there are three degrees of freedom created via inversion of the spheres, of lengths 4pi, (4pi-1/pi), and (4pi-2/pi), whose product just happens to be 1836.15... Taunus Trumbo: Convenient numerology. Faustus Mortal: These then become one "Ur-atom": protons, electrons, and the two fusing to from neutrons. It's like the periodic table, only bigger and bigger, expanding many times. Like Sharp, Principal, Diffuse, and Fine (SPDF). ((And "g," whatever that is.)) Taunus Trumbo: What's to prevent it from expanding forever? Faustus Mortal: I'm glad that you asked. The Fermat primes don't go on forever. The sporadic groups don't either, but "why" is a monster of a problem. And we have no idea whether the Mersenne primes stop after some point or not. Taunus Trumbo: You are implying that the periodic table might expand into some huge atom and stop? Faustus Mortal: Yes, and then "Big Bang." Taunus Trumbo: Preposterous. How does this explain heavy elements? Faustus Mortal: Better than that, how do the super novae explain the fact that ores aren't all alloys? If all of the elements heavier than Iron were fused at once, then why aren't there mixtures of metals? Taunus Trumbo: I don't know. Faustus Mortal: I see one huge Ur-atom with separate decay sequences, symmetrically producing metals and isotopes. Witness that Iron's isotopes are constant throughout the universe. This should not happen from a super novae creation theory. Taunus Trumbo: hmm... Faustus Mortal: Look at the number of atoms in each period of the periodic table: 2, 8, 8, 18, 18, 32, 32, 50, 50,... The totals are: 2, 10, 18, 36, 54, 86, 118, 168, 218,... Taunus Trumbo: The sequence stops with stable elements in period 7. Faustus Mortal: But at the instant of the Big Bang there is no time, no radioactive decay. What's to limit the number of periods? Perhaps some mathematics? Some "less well" understood math! It is claimed that the number of possible elements is limited by the velocity of light on electrons or the so-called proton-neutron drip lines. But what is velocity without time? (grins) Taunus Trumbo blinks. Faustus Mortal: Imagine some complicated set of mathematical rules that eventually terminate pair-production. The final period. At that moment the Ur-Atom may just disintegrate as the Big Bang. Taunus Trumbo: And you have such a limiting value? Faustus Mortal: If I did, I would certainly not tell you. Three times I advanced to a candidate for a PhD in physics. Three times I was an All But Dissertation (ABD). Nineteen years, yes NINETEEN years and three worthless master's degrees. Working jobs while going to school, enduring hard lessons, and gaining nothing. Taunus Trumbo: That's tough. But energy? What does all this theory have to do with energy? Faustus Mortal: Decompose the proton. Taunus Trumbo:? Faustus Mortal: Fire an electron accelerated with precisely 48*pi -- 8/pi times the electron mass. Taunus Trumbo: So that decomposes the proton into energy plus positron. But how to harness such stuff? Faustus Mortal: Do I look like the Shell(R) Answer Man? Taunus Trumbo: It looks too complicated. What's wrong with wind, geo-thermal, bio-fuels, and solar? Faustus Mortal: too erratic, too inaccessible, too expensive, and only good on sunlit days. Besides, some of these "sources" will not function at 60 cycles. That Hertz (hurts). We need to redo all our electric appliances. Taunus Trumbo: That would be very expensive. Faustus Mortal: For sure. But it's windy. Taunus Trumbo: It seems as though the Fossil Fuel Fellowship is funding known failures. Faustus Mortal: You must be a genius to figure that out. Finally there is "Old King Coal" who will come as the messiah to save the day. Taunus Trumbo: That's so nice to know: Clean Coal at last. Faustus Mortal: But it's affordable. * 9 Aug 2011 Taunus Trumbo Crackpot Spammer Ch. 09 Disclaimer: The following simulated dialogue is fictional. No resemblance to any person, living or dead, is neither intended nor should be inferred. Faustus Mortal is delivering a lecture on his newly proposed device for use in desert areas: Someone once asked me what was the liquid dripping from the exhaust pipe of an automobile after it has been running. I replied "Water," for after all the combustion of gasoline, a hydrocarbon, produces Carbon Dioxide and water as the principle components of combustion. In fact this is generally true for any combustion such as burning wood, coal, or plastics. Ninety-seven percent of the combustion product are Carbon Dioxide and Water in the form of steam. This generally goes up in smoke. Now smoke may also contain other substances, like Carbon Monoxide, Sulfur, Iron, Lead, and Mercury, to name a few. But the preponderance of smoke is water vapor and Carbon Dioxide. Even alcohol, Ethyl Alcohol, CH3CH2OH burns into Carbon Dioxide and water. Now consider the wild fires burning this summer. They are burning plants whose principal components are Carbon, Hydrogen, and Oxygen, albeit in the form of grass or bush. They could be harvested and converted into energy and water. This water is formed from Hydrogen "locked into" the dry plant. I recall some time in the past, the exact year eludes me now, when loggers pressed to harvest timber from the forests in the Pacific Northwest. The government, coddling the tree-huggers, refused them permission. Millions if not billions of dollars in timber was "saved." However, there came huge forest fires, totally obliterating and destroying the forests. The tree-huggers became ash-huggers and much needed export was lost for a generation. Wise move on the part of the government. Need I say more? This fact stands for itself. Now I propose a machine unlike any made before. Removing strips of dry vegetation from drought-parched prairie will inhibit raging wild fires. But what of the material removed? Does it not have the potential of creating energy and making water as a by product? Faustus opens a presentation showing a shaft with a piston-like disk. He continues: Here we have a hole one meter in diameter. Notice the piston resting near the bottom. This piston has embedded magnets and the walls of the hole have woven bundles of wire. Whenever the piston rises or falls, electricity is produced. This electricity is stored briefly in a capacitor then "bled" into batteries. Faustus opens a second slide showing a side shaft and a coil-like exhaust port. He points to the coil-like exit port and explains: The smoke travels through these coils and cools. Water vapor condenses and precipitates. This water is life-giving to man, beast, and crops. The smoke is generated from finely ground vegetation fed down an input port. A grinder pulverizes the organic material and blows the combustible dust along with air, which is about 20% Oxygen, into the chamber below the piston. It is ignited by an electrical spark and the conversion of Carbohydrates into Carbon Dioxide and Water raises the piston, generating a massive pulse of electricity as the magnetic lines of flux cut through the wires. This is easily understood from Electricity of Magnetism (E&M), a college course taken by many and passed by few. So, we remove excess dry and combustible vegetation, feed it into a pulverizer, ignite the "dust" and drive up the piston, creating electricity. Then let gravity return the piston, forcing the smoke through a coiled exhaust port, vis-a-vis a moonshiner still, to capture the water from steam. And the surplus electricity can be fed back into the grid. You are asking how this will be assembled and serviced. Simply open the input port and wench the piston out. This leaves a one-meter diameter access portal to the valves, pulverizer, capacitor, and batteries. At any rate, this is an idea to generate power and water from dangerously dry and useless brown foliage. Water can thus be created and the underground coil-like tubing collects the water. Some purification and filtering may be needed, but most probably the impurities can be settled out by sedimentation. 13 September 2011