Let ε < 0.

05.6.09

Murphy’s Law

Filed under: Science humor, Upper-division jokes, Urban legends — Travis @

–D. L. Klipstein

Murphy’s Law, in its simplest form, states that “If anything can go wrong, it will.” Or to state it in more exact mathematical form:

where ↵ is the mathematical symbol for “hardly ever.”

To show the all-pervasive nature of Murphy’s work, the author offers a few applications of the law to the electronic engineering industry.

Mathematics

1. Any error that can creep in, will. It will be in the direction that will do the most damage to calculations.

2. All constants are variables.

3. In a complicated calculation, one factor from the numerator will always move into the denominator, or conversely.

General engineering

4. A patent application will be preceeded by one week by a similar application made by an independent worker.

5. The more innocuous a design chage appears, the further its influence will extend.

6. All warranty and guarantee clauses become void on payment of invoice.

7. An important Instruction Manual or Operating Manual will have been discarded by the Receiving Department.

Prototyping and production

8. Any wire cut to length will be too short.

9. Tolerances will accumulate unidirectionally towards maximum difficulty of assembly.

10. Identical units tested under identical conditions will not be identical in the field.

11. If a project requires n components, there will be (n – 1) units in stock.

12. A dropped tool will land where it can do most damage; the most delicate component will be the one to drop. (Also known as the principle of selective gravity.)

13. A device selected at random from a group having 99 percent reliability will be a member of the 1 percent group.

14. A transistor protected by a fast-acting fuse will protect the fuse by blowing first.

15. A purchased component or instrument will meet its specifications long enough, and only long enough, to pass Incoming Inspection.

16. After an access cover has been secured by 16 hold-down screws, it will be discovered that the gasket has been omitted.

Condensed from “The Contribution of Edsel Murphy to the Understanding of Behaviour in Inanimate Objects,” in EEE: The Magazine of Circuit Design, August 1967.

05.5.09

Modern engineering design principles

Filed under: Science humor, Urban legends — Travis @

The US standard railroad gauge (distance between the rails) is 4 feet 8.5 inches. That’s an exceedingly odd number. Why was that gauge used? Because that’s the way they built them in England, and the US railroads were built by English expatriates.

Why did the English build them like that? Because the first rail lines were built by the same people who built the pre-railroad tramways, and that’s the gauge they used.

Why did ‘they’ use that gauge then? Because the people who built the tramways used the same jigs and tools that they used for building wagons, which used that wheel spacing.

Okay! Why did the wagons have that particular odd wheel spacing? Well, if they tried to use any other spacing the wagon wheels would break on some of the old, long distance roads in England, because that’s the spacing of the wheel ruts.

So who built those old rutted roads? The first long distance roads in Europe (and England) were built by Imperial Rome for their legions. The roads have been used ever since.

And the ruts? The initial ruts, which everyone else had to match for fear of destroying their wagon wheels and wagons, were first made by Roman war chariots. Since the chariots were made for, or by Imperial Rome, they were all alike in the matter of wheel spacing.

Thus, we have the answer to the original question. The United States standard railroad gauge of 4 feet, 8.5 inches derives from the original specification for an Imperial Roman war chariot.

Specifications and bureaucracies live forever. So the next time you are handed a specification and wonder what horse’s rear end came up with it, you may be exactly right-because the Imperial Roman war chariots were made just wide enough to accommodate the back ends of two war horses.

Now the twist to the story… There’s an interesting extension to the story about railroad gauges and horses’ behinds. When we see a Space Shuttle sitting on its launch pad, there are two big booster rockets attached to the sides of the main fuel tank. These are solid rocket boosters, or SRBs. The SRBs are made by Thiokol at their factory at Utah. The engineers who designed the SRBs might have preferred to make them a bit fatter, but the SRBs had to be shipped by train from the factory to the launch site. The railroad line from the factory had to run through a tunnel in the mountains. The SRBs had to fit through that tunnel. The tunnel is slightly wider than the railroad track, and the railroad track is about as wide as two horses behinds.

So, the major design feature of what is arguably the world’s most advanced transportation system was determined by the width of a couple of horses’ asses.

04.30.09

Poetic wisdom

Filed under: Quotes, Urban legends — Travis @

For people with small horizons, every function is constant. (Oscar Bruno)

All you need for differentiation is a strong right arm and a weak mind. (Ron Getoor)

Obvious is in the the of the beholder. (Ron Getoor)

Sometimes the Devil lurks in sets of measure zero. (Ron Getoor)

There are two kinds of results in mathematics: those that are obvious and those that are false. (Ron Getoor)

There are no deep theorems — only theorems that we have not understood very well. (Nicholas P. Goodman)

The world is everywhere dense with idiots. (L. F. S.)

It’s only the false things that are nontrivial. (Michael Sharpe)

Everything is trivial when you know the proof. (D. V. Widder)

My thanks to Jason Lee, who compiled many of these.

04.29.09

What is a mathematician?

Filed under: Quotes, Urban legends — Travis @

The good Christian should be aware of mathematicians and all those who make empty prophecies. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of Hell. (St. Augustine) 1

A man whose mind has gone astray should study mathematics. (Francis Bacon)

A person who can, within a year, solve x2 – 92y2 = 1 is a mathematician. (Brahmagupta)

A mathematician is a blind man in a dark room looking for a black cat which isn’t there. (Charles R Darwin)

A mathematician is a device for turning coffee into theorems. (P. Erdos)

Mathematicians, like cows in the dark, all look alike to me. (Abraham Flexner)

Mathematicians are like Frenchmen: whatever you say to them, they translate it into their own language, and forthwith it means something entirely different. (Johann Wolfgang von Goethe)

Medicine makes people ill, mathematics make them sad and theology makes them sinful. (Martin Luther)

He who can properly define and divide is to be considered a god. (Plato)

God geometrizes. (Pluto)

Tai Melcher suggested including this quote. Quoth she, “Maybe if they’re scared of us, they won’t laugh at us anymore. Or at least not as loudly.”

04.28.09

Famously amusing quotation

Filed under: Quotes, Urban legends — Travis @

The four branches of arithmetic — ambition, distraction, uglification and derision. (Lewis Caroll, Alice in Wonderland)

As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality. (Albert Einstein)

If you can’t explain what you are doing to a nine-year-old, then either you still don’t understand it very well, or it’s not all that worthwile in the first place. (Albert Einstein)

Only two things are infinite: the universe and human stupidity, and I’m not sure about the former. (Albert Einstein)

The two most common things in the Universe are hydrogen and stupidty. (Harlan Ellison)

I’ve heard that the government wants to put a tax on the mathematically ignorant. Funny, I thought that’s what the lottery was! (Gallagher)

Old mathematicians never die; they just lose some of their functions. (John C. George)

I turn away with fear and horror from this lamentable plague of functions which do not have derivatives. (Hermite, in a letter to Stieltjes)

Mathematics is a game played according to certain simple rules with meaningless marks on paper. (David Hilbert)

Physics is much too hard for physicists. (David Hilbert)

A Ph.D. dissertation is a paper of the professor written under aggravating circumstances. (Adolf Hurwitz)

Nature laughs at the difficulties of integration. (Pierre-Simon de Laplace)

Everything good is either illegal, immoral, or equivalent to the Axiom of Choice. (Josh Laison)

If I have seen farther than others, it is because I was standing on the shoulder of giants. (Isaac Newton)

If I have not seen as far as others, it is because giants were standing on my shoulders. (Hal Abelson)

Mathematicians stand on each other’s shoulders. (Gauss)

Computer scientists stand on each other’s feet. (Richard Hamming)

Software engineers dig each other’s graves. (unknown)

Mathematics is like checkers in being suitable for the young, not too difficult, amusing, and without peril to the state. (Plato)

Mathematics consists of proving the most obvious thing in the least obvious way. (George Polya)

As long as algebra is taught in school, there will be prayer in school. (Cokie Roberts)

Algebraic symbols are used when you do not know what you are talking about. (Philippe Shnoebelen)

Basic research is what I am doing when I don’t known what I am doing. (Werner von Braun)

In mathematics you don’t understand things. You just get used to them. (Johann von Neumann)

Five out of four people have trouble with fractions. (Steven Wright)

04.1.09

Nebraska to repeal the law of gravity

Filed under: Academic humor, Urban legends — Travis @

NEBRASKA TO REPEAL LAW OF GRAVITY

LINCOLN, NE. Today legislators in the Nebraska State Senate have begun debate on a controversial measure to forbid the teaching of gravity in all institutions accepting state funds.

Wilburt F. Harsheill, co-chair of the Religious Freedom Union of America, testified before the Senate Education Sub-Committee that “gravity is just one of many possible explanations why water flows downhill. To eliminate the possibility of Divine Intervention is an affront to the millions of church-goers in our country.”

In a long and impassioned presentation Harsheill went on to assert that “the secular humanists in charge of education policy in our nation have no explanation for the Ascension of Christ or Old Faithful and that students should be exposed to all sides equally.”

By Massimo Pigliucci.

03.2.09

The mathematical theory of big game hunting II

Filed under: Academic humor, Lion hunting, Urban legends — Travis @

Following the seminal paper by H. Petard in 1938 introducing to the mathematical theory of big game hunting, a good many others were prompted to add to this literature. The following is one of these articles.

A new method of catching a lion

– I. J. Good

In this note a definitive procedure will be provided for catching a lion in a desert (see [1]).

Let Q be the operator that encloses a word in (single) quotation marks. Its square Q2 encloses a word in double quotes. The operator clearly satisfies the law of indices, QmQn = Qm+n. Write down the word lion, without quotation marks. Apply it to the operator Q-1. Then a lion will appear on the page. It is advisable to enclose the page in a cage before applying the operator.

References

[1] H. Petard. A contribution to the mathematical theory of big game hunting, Amer. Math. Monthly 45 (1938) p446-447.

Amer. Math. Monthly 72 (1965), p. 436.

03.1.09

The mathematical theory of big game hunting I

The following is the famous, seminal paper by H. Petard*, which appeared in the American Mathematical Monthly in 1938 and introduced to the academic community at large the mathematical theory of big game hunting. As is evident from the other articles in this section, Petard’s work prompted a good many others to add to this literature. This, together the subsequent articles we shall reproduce this week, do not form a complete compendium, but they do provide the interested reader a solid introduction into this exciting branch of mathematics.

A contribution to the mathematical theory of big game hunting

– H. Petard
Princeton, New Jersey

This little known mathematical discipline has not, of recent years, received in the literature the attention which, in our opinion, it deserves. In the present paper we present some algorithms which, it is hoped, may be of interest to other workers in the field. Neglecting the more obviously trivial methods, we shall confine our attention to those which involve significant applications of ideas familiar to mathematicians and physicists.

The present time is particularly fitting for the preparation of an account of the subject, since recent advanaces both in pure mathematics and theorectical physics have made available powerful tools whose very existence was unsuspected by earlier investigators. At the same time, some of the more elegant classical methods acquire new significance in the light of modern discoveries. Like many other branches of knowledge to which mathematical techniques have been applied in recent years, the Mathematical Theory of Big Game Hunting has a singularly unifying effect on the most diverse branches of the exact sciences.

For the sake of simplicity of statement, we shall confine our attention to Lions (Felis leo) whose habitat is the Sahara Desert. The methods which we shall enumerate will easily be seen to be applicable, with obvious formal modifications, to other carnivores and to other portions of the globe. The paper is divided into three parts, which draw their material respectively from mathematics, theoretical physics, and experimental physics.

The author desires to acknowledge his indebtedness to the Trivial Club of St. John’s College, Cambridge, England; to the MIT chapter of the Society for Useless Research; to the F o P, of Princeton University; and to numerous individual contributors, known and unknown, conscious and unconscious.

1. Mathematical methods

1. The Hilbert, or axiomatic, method. We place a locked cage onto a given point in the desert. After that we introduce the following logical system:

  • Axiom I. The set of lions in the Sahara is not empty.
  • Axiom II. If there exists a lion in the Sahara, then there exists a lion in the cage.
  • Rule of procedure. If P is a theorem, and if the following is holds: “P implies Q”, then Q is a theorem.
  • Theorem 1. There exists a lion in the cage.

2. The method of inversive geometry. We place a spherical cage in the desert, enter it and lock it from inside. We then perform an inversion with respect to the cage. Then the lion is inside the cage, and we are outside.

3. The method of projective geometry. Without loss of generality, we can view the desert as a plane. We project the surface onto a line, and then project the line onto an interior point of the cage. Thereby the lion is projected onto that same point.

4. The Bolzano-Weierstrass method. Divide the desert by a line running from N-S. The lion is then either in the E portion or in the W portion; let us assume him to be in the W portion. Bisect this portion by a line running from E-W. The lion is either in the N portion or in the S portion; let us assume him to be in the N portion. We continue this process indefinitely, constructing a sufficiently strong fence about the chosen portion at each step. The diameter of the chosen portions approaches zero, so that the lion ultimately surrounded by a fence of arbitrarily small perimeter.

5. The “Mengentheoretisch” method. We observe that the desert is a separable space. It therefore contains an enumerable dense set of points, from which can be extracted a sequence having the lion as limit. We then approach the lion stealthily along this sequence, bearing with us suitable equipment.

6. The Peano method. Construct, by standard methods, a continuous curve passing through every point of the desert. It has been remarked [1]that it is possible to traverse such a curve in an arbitrarily short time. Armed with a spear, we traverse the curve in a time shorter than that in which a lion to move a distance equal to its own length.

7. A topological method. We observe that a lion has at least the connectivity of a torus. We transport the desert into four-space. Then it is possible [2] to carry out such a deformation that the lion can be returned to three-space in a knotted condition. He is then completely helpless.

8. The Cauchy, for function theoretical, method. We examine a lion-valued function f(z). Let ζ be the cage. Consider the integral

where C represents the boundary of the desert. Its value is f(ζ), i.e. there is a lion in the cage [3].

9. The Wiener-Tauberian method. We obtain a tame lion, L0, from the class L(-¥, ¥), whose Fourier transform vanishes nowhere, and release it in the desert. L0 then converges toward our cage. By Wiener’s General Tauberian Theorem [4], any other lion, L (say), will converge to the same cage. Alternatively we can approximate arbitrarily closely to L by translating L0 through the desert [5].)

10. The Eratosthenian method. Enumerate all the objects in the desert. Examine them one by one, and discard all those that are not lions. A refinement will capture only prime lions.

2. Methods from theoretical physics

11. The Dirac method. We observe that wild lions are, ipso facto, not be observable in the Sahara desert. Consequently, if there are any lions at all in the Sahara, they are tame. We leave catching a tame lion as an exercise to the reader.

12. The Schroedinger method. At any given moment there is a positive probability that there is a lion in the cage. Sit down and wait.

13. The nuclear physics method. Place a tame lion into the cage, and apply a Majorana exchange operator [6] on it and a wild lion.

As a variant, let us suppose, to fix ideas, that we require a male lion. We place a tame lioness into the cage, and apply the Heisenberg exchange operator [7] which exchanges spins.

14. A relativistic method. We distribute about the deser lion bait containing large portions of the Companion of Sirius. When enough bait has been taken, we project a beam of light across the desert. This will bend right around the lion, who will hen become so dizzy that he can be approahced with impunity.

3. Experimental physics methods

15. The thermodynamics method. We construct a semi-permeable membrane, permeable to everything except lions, and sweep it across the desert.

16. The atom-splitting method. We irradiate the desert with slow neutrons. The lion becomes radioactive, and a process of disintegration set in. When the decay has proceeded sufficiently far, he will become incapable of showing fight.

17. The magneto-optical method. We plant a large lenticular bed of catnip (Nepeta cataria), whose axis lies along the direction of the horizontal component of the earth’s magnetic field, and place a cage at one of its foci. We distribute over the desert large quantities of magnetized spinach (Spinacia oleracea), which, as is well known, has a high ferric content. The spinach is eaten by herbivorous denizens of the desert, which in turn are eaten by lions. The lions are then oriented parallel to the earth’s magnetic field, and the resulting beam of lions is focus by the catnip upon the cage.

References

[1] After Hilbert, cf. E. W. Hobson, “The Theory of Functions of a Real Variable and the Theory of Fourier’s Series” (1927), vol. 1, pp 456-457

[2] H. Seifert and W. Threlfall, “Lehrbuch der Topologie” (1934), pp 2-3

[3] According to the Picard theorem (W. F. Osgood, Lehrbuch der Funktionentheorie, vol 1 (1928), p 178) it is possible to catch every lion except for at most one.

[4] N. Wiener, “The Fourier Integral and Certain of its Applications” (1933), pp 73-74

[5] N. Wiener, ibid, p 89

[6] cf e.g. H. A. Bethe and R. F. Bacher, “Reviews of Modern Physics”, 8 (1936), pp 82-229, esp. pp 106-107

[7] ibid

This first apperared in Amer. Math. Monthly 45 (1938) p446-447. In fact, the Method 10 included here did not actually appear in the original Monthly version, but in a slightly expanded version of that appeared in Eureka.

* It is perhaps generally not known that Petard’s** full initials are H. W. O., standing for “Hoist With Own.”

** Actually, H. Petard is the pen-name for the mathematician E. S. Pondiczery***, who preferred to publish the paper pseudonymously.

*** In fact, Pondiczery himself was a fictious mathematician invented by Ralph P. Boas and Frank Smithies.****

**** This was published in The American Mathematical Monthly, 1938, with one editorial alternation: a “footnote to a footnote was ruthlessly removed.” Consider this last footnote to a footnote to a footnote of a footnote as our nod to the masters.

02.9.09

Math riots

Filed under: Academic humor, Urban legends — Travis @

Legend has it that the following column appeared in the Chicago Tribune, DuPage County edition, Tuesday June 29, 1993, page 2-1.

MATH RIOTS PROVE FUN INCALCULABLE

ERIC ZORN

News Item (June 23, 1993) — Mathematicians worldwide were excited and pleased today by the announcement that Princeton University professor Andrew Wiles had finally proved Fermat’s Last Theorem, a 365-year-old problem said to be the most famous in the field.

Yes, admittedly, there was rioting and vandalism last week during the celebration. A few bookstores had windows smashed and shelves stripped, and vacant lots glowed with burning piles of old dissertations. But overall we can feel relief that it was nothing — nothing — compared to the outbreak of exuberant thuggery that occurred in 1984 after Louis DeBranges finally proved the Bieberbach Conjecture.

“Math hooligans are the worst,” said a Chicago Police Department spokesman. “But the city learned from the Bieberbach riots. We were ready for them this time.”

When word hit Wednesday that Fermat’s Last Theorem had fallen, a massive show of force from law enforcement at universities all around the country headed off a repeat of the festive looting sprees that have become the traditional accompaniment to triumphant breakthroughs in higher mathematics.

Mounted police throughout Hyde Park kept crowds of delirious wizards at the University of Chicago from tipping over cars on the midway as they first did in 1976 when Wolfgang Haken and Kenneth Appel cracked the long-vexing Four-Color Problem. Incidents of textbook-throwing and citizens being pulled from their cars and humiliated with difficult story problems last week were described by the university’s math department chairman Bob Zimmer as “isolated.”

Zimmer said, “Most of the celebrations were orderly and peaceful. But there will always be a few — usually graduate students — who use any excuse to cause trouble and steal. These are not true fans of Andrew Wiles.”

Wiles himself pleaded for calm even as he offered up the proof that there is no solution to the equation xn + yn = zn when n is a whole number greater than two, as Pierre de Fermat first proposed in the 17th Century. “Party hard but party safe,” he said, echoing the phrase he had repeated often in interviews with scholarly journals as he came closer and closer to completing his proof.

Some authorities tried to blame the disorder on the provocative taunting of Japanese mathematician Yoichi Miyaoka. Miyaoka thought he had proved Fermat’s Last Theorem in 1988, but his claims did not bear up under the scrutiny of professional referees, leading some to suspect that the fix was in. And ever since, as Wiles chipped away steadily at the Fermat problem, Miyaoka scoffed that there would be no reason to board up windows near universities any time soon; that God wanted Miyaoka to prove it.

In a peculiar sidelight, Miyaoka recently took the trouble to secure a U.S. trademark on the equation “xn + yn = zn” as well as the now-ubiquitous expression “Take that, Fermat!” Ironically, in defeat, he stands to make a good deal of money on cap and T-shirt sales.

This was no walk-in-the-park proof for Wiles. He was dogged, in the early going, by sniping publicity that claimed he was seen puttering late one night doing set theory in a New Jersey library when he either should have been sleeping, critics said, or focusing on arithmetic algebraic geometry for the proving work ahead.

“Set theory is my hobby, it helps me relax,” was his angry explanation. The next night, he channeled his fury and came up with five critical steps in his proof. Not a record, but close.

There was talk that he thought he could do it all by himself, especially when he candidly referred to University of California mathematician Kenneth Ribet as part of his “supporting cast,” when most people in the field knew that without Ribet’s 1986 proof definitively linking the Taniyama Conjecture to Fermat’s Last Theorem, Wiles would be just another frustrated guy in a tweed jacket teaching calculus to freshmen.

His travails made the ultimate victory that much more explosive for math buffs. When the news arrived, many were already wired from caffeine consumed at daily colloquial teas, and the took to the streets en masse shouting, “Obvious! Yessss! It was obvious!”

The law cannot hope to stop such enthusiasm, only to control it. Still, one to wonder what the connection is between wanton pillaging and a mathematical proof, no matter how long-awaited and subtle.

The Victory Over Fermat rally, held on a cloudless day in front of a crowd of 30,000 (police estimate: 150,000) was pleasantly peaceful. Signs unfurled in the audience proclaimed Wiles the greatest mathematician of all time, though partisans of Euclid, Descartes, Newton, and C.F. Gauss and others argued the point vehemently.

A warmup act, The Supertheorists, delighted the crowd with a ragged song, “It Was Never Less Than Probable, My Friend,” which included such gloating, barbed verses as

I had a proof all ready
But then I did a choke-a…
Made liberal assumptions…
Damn! I’m Yoichi Miyaoka!

In the speeches from the stage, there was talk of a dynasty, specifically that next year Wiles will crack the great unproven Riemann Hypothesis (”Rie-peat! Rie-peat!” the crowd cried), and that after the Prime-Pair Problem, the Goldbach Conjecture (”Minimum Goldbach,” said one T-shirt) and so on.

They couldn’t just let him enjoy his proof. Not even for one day. Math people. Go figure ‘em.

02.2.09

Slice of pi

Filed under: Science humor, Urban legends — Travis @

This was originally posted to the newsgroup talk.origins on April Fool’s Day 1998, as well as sent to a list of New Mexican scientists and citizens interested in evolution, and printed in the April issue of the New Mexicans for Science and Reason newsletter NMSR Reports. Its talk.origins poster followed up a day later with a full confession and explanation of the prank, but it is commonly perported on the world wide web as true.

Bill seeks to change value of π

HUNTSVILLE, Ala. NASA engineers and mathematicians in this high-tech city are stunned and infuriated after the Alabama state legistature narrowly passed a law yesterday redefining π (pi), a mathematical constant used in the aerospace industry. The bill to change the value of π to exactly 3 was introduced without fanfare by Leonard Lee Lawson (R, Crossville), and rapidly gained support after a letter-writing campaign by members of the Solomon Society, a traditional values group. Governor Guy Hunt says he will sign it into law on Wednesday.

The law took the state’s engineering community by surprise. “It would have been nice if they had consulted with someone who actually uses π,” said Marshall Bergman, a manager at the Ballistic Missile Defense Organization. According to Bergman, π is a Greek letter that signifies the ratio of the circumference of a circle to its diameter. It is often used by engineers to calculate missile trajectories.

Prof. Kim Johanson, a mathematician from University of Alabama, said that π is a universal constant, and cannot arbitrarily be changed by lawmakers. Johanson explained that π is an irrational number, which means that it has an infinite number of digits after the decimal point and can never be known exactly. Nevertheless, she said, π is precisly defined by mathematics to be “3.14159, plus as many more digits as you have time to calculate”.

“I think that it is the mathematicians that are being irrational, and it is time for them to admit it,” said Lawson. “The Bible very clearly says in I Kings 7:23 that the alter font of Solomon’s Temple was ten cubits across and thirty cubits in diameter, and that it was round in compass.”

Lawson called into question the usefulness of any number that cannot be calculated exactly, and suggested that never knowing the exact answer could harm students’ self-esteem. “We need to return to some absolutes in our society,” he said, “the Bible does not say that the font was thirty-something cubits. Plain reading says thirty cubits. Period.”

Science supports Lawson, explains Russell Humbleys, a propulsion technician at the Marshall Spaceflight Center who testified in support of the bill before the legislature in Mongtomery on Monday. “π is merely an artifact of Euclidean geometry.” Humbleys is working on a theory which he says will prove that π is determined by the geometry of three-dimensional space, which is assumed by physicists to be “isotropic”, or the same in all directions.

“There are other geometries, and π is different in every one of them,” says Humbleys. Scientists have arbitrarily assumed that space is Euclidean, he says. He points out that a circle drawn on a spherical surface has a different value for the ratio of circumfence to diameter. “Anyone with a compass, flexible ruler, and globe can see for themselves,” suggests Humbleys, “it’s not exactly rocket science.”

Roger Learned, a Solomon Society member who was in Montgomery to support the bill, agrees. He said that π is nothing more than an assumption by the mathematicians and engineers who were there to argue against the bill. “These nabobs waltzed into the capital with an arrogance that was breathtaking,” Learned said. “Their prefatorial deficit resulted in a polemical stance at absolute contraposition to the legislature’s puissance.”

Some education experts believe that the legislation will affect the way math is taught to Alabama’s children. One member of the state school board, Lily Ponja, is anxious to get the new value of π into the state’s math textbooks, but thinks that the old value should be retained as an alternative. She said, “As far as I am concerned, the value of π is only a theory, and we should be open to all interpretations.” She looks forward to students having the freedom to decide for themselves what value π should have.

Robert S. Dietz, a professor at Arizona State University who has followed the controversy, wrote that this is not the first time a state legislature has attempted to redifine the value of π. A legislator in the state of Indiana unsuccessfully attempted to have that state set the value of pi to 3. According to Dietz, the lawmaker was exasperated by the calculations of a mathematician who carried π to four hundred decimal places and still could not achieve a rational number. Many experts are warning that this is just the beginning of a national battle over π between traditional values supporters and the technical elite. Solomon Society member Lawson agrees. “We just want to return π to its traditional value,” he said, “which, according to the Bible, is three.”

As a final note, while the ALabama legislature never attempted to legislate the value of pi, the state of Indiana did. In 1897, House Bill No. 246 tried to legislate, among other things, the value of pi to be 3.2 exactly. While it passed in the House, the Senate agreed to postpone it indefinitely after being “coached” by a Purdue mathematician.

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