Humble pi

In honor of Pi Day, we at komplexify want to clear  up a widespread $pi$ myth.   Namely, the following “news article,”  which turns up in my email inbox at least once a year every year, is completely false.

Pretty damn funny, but utterly, utterly false.

Bill seeks to change value of $pi$

HUNTSVILLE, Ala. NASA engineers and mathematicians in this high-tech city are stunned and infuriated after the Alabama state legislature narrowly passed a law yesterday redefining $pi$, a mathematical constant used in the aerospace industry. The bill to change the value of $pi$ 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 $pi$,” said Marshall Bergman, a manager at the Ballistic Missile Defense Organization. According to Bergman, $pi$ 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 $pi$ is a universal constant, and cannot arbitrarily be changed by lawmakers. Johanson explained that $pi$ 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, $pi$ 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 Montgomery on Monday. “$pi$ is merely an artifact of Euclidean geometry.” Humbleys is working on a theory which he says will prove that pi 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 $pi$ 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 pi 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 $pi$ 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 $pi$ 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 $pi$ 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 redefine the value of $pi$. 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 $pi$ 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 $pi$ between traditional values supporters and the technical elite. Solomon Society member Lawson agrees. “We just want to return $pi$ to its traditional value,” he said, “which, according to the Bible, is three.”

In fact, this was an April Fool’s Day piece of humor posted to the newsgroup talk.origins on April 1, 1998.   It was also sent to 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.   The authors confessed that it was a gag the following day, but by then, due to the unforseen power of Teh IntraWeb, it spread to inboxes everywhere and acquired an air of authenticity (mostly because the first line of the article, which mentions an April holiday by the Associmated Press, conveniently disappeared).   A full debunking is over at Snopes.

That being said, there are two aspects of this prank that are true, which is interesting in and of itself, and make for fine discussion on this most transcendental of holidays.

The first aspect is  the reference to 1 Kings 7:23 is, in fact, true.   It reads:

And he [Hiram on behalf of King Solomon] made a molten sea, ten cubits from the one brim to the other: it was circular in compass, and its height was five cubits: and a line of thirty cubits did compass it round about.

This verse is famous for its implicit approximation of $pi$, namely, $pi = 3$, and infamous for the nutjob defenders and decriers it inspires.   Atheists and non-Christians love to point out that God can’t even get $pi$ correct, which kinda disproves His whole infallibility thing.   (“‘Oh dear,’ says God, ‘I hadn’t thought of that,’ and vanishes in a puff of logic.”)

Bible-thumpers, on the other hand, give elaborate physical constructs for the “molten sea” and magically convenient units for “cubits” and “handwidths” that give extraordinarily accurate approximations of $pi$, the justification for their choices based solely on axiom of the Infallibility of God.   Interested readers might take a look at Russell Grigg’s nicely justified argument that the 10 cubits described in the Bible do not correspond to the diameter of the circle, thereby allowing God to save face.

The second, and more surprising, aspect is the reference to Indiana attempting to legislate the value of $pi$.   The article claims that the Indiana legislature once considered legislation to set the value of $pi$ to be 3.   That is completely false — no body of legislators has ever been dumb enough to try that.   That’s just stupid.

No, Indiana tried to legislate that $pi$ was 3.2.   Apples and oranges, buddy.

Here’s the story.   In 1897, the House passed Engrossed House Bill No. 246, a piece of legislation authored by amateur mathematician and bona fide crank William Goodwin that, among other things, legislates that the diameter of a circle is to the circumference as five-fourths is to four.    Said differently,  House Bill 246  establishes 3.2 as the exact value of $pi$.   (Section 2 of the Bill goes on in great detail about this, asserting that  a square inscribed in a circle of diameter 10 implies the following relationships among the circumference of the circle and perimeter of the square:

Astute eyes will note that, in addition to giving $pi$ a value of 32/10, this figure also implies that \$lates sqrt{2}\$ is equal to both 10/7 and 7/5 at the same time.   Neat!)

Apparently, Goodwin was convinced he’d discovered that the Archimedian formula for the area of a circle — you know, the “$pi , r^2$” one — was incorrect.   In fact, Goodwin claimed (without proof) that the area of a circle was the same as the area of a square with the same perimeter, and then copyrighted his formula along with a corresponding “solution” the the Greek “quadrature of the circle” construction.     His idea was to offer these new and improved facts for free to schools in Indiana, but to charge a royalty for their use outside the state.   He was apparently pretty persuasive too, because he convinced  the  House of Representatives to  pass it by a vote of 67-0 on February 5, 1897.

The bill appeared to be fast-tracked for approval by the Senate as well, but luckily for the future reputation of Indiana, a mathematics  professor from Purdue named Clarence Waldo (who was  lobbying the state for University funding at the time) caught wind of the bill and  hurriedly “coached” a number of state Senators on the bill.   That is, he gave them a  “basic geometry for dummies” refresher course.   Apparently it took, since the Senate voted on February 12 to “postpone indefinitely” the so-called Indiana Pi Bill, thereby preserving the March 14 status of Pi Day for perpetuity.   Or until the next whackjob squares the circle.

Anyways, here is Engrossed House Bill No. 246, in its entirety.

Engrossed House Bill No. 246

A Bill for an act introducing a new mathematical truth and offered as a contribution to education to be used only by the State of Indiana free of cost by paying any royalties whatever on the same, provided it is accepted and adopted by the official action of the Legislature of 1897.

Section 1

Be it enacted by the General Assembly of the State of Indiana: It has been found that a circular area is to the square on a line equal to the quadrant of the circumference, as the area of an equilateral rectangle is to the square on one side. The diameter employed as the linear unit according to the present rule in computing the circle’s area is entirely wrong, as it represents the circle’s area one and one-fifth times the area of a square whose perimeter is equal to the circumference of the circle. This is because one fifth of the diameter fails to be represented four times in the circle’s circumference. For example: if we multiply the perimeter of a square by one-fourth of any line one-fifth greater than one side, we can in like manner make the square’s area to appear one-fifth greater than the fact, as is done by taking the diameter for the linear unit instead of the quadrant of the circle’s circumference.

Section 2

It is impossible to compute the area of a circle on the diameter as the linear unit without trespassing upon the area outside of the circle to the extent of including one-fifth more area than is contained within the circle’s circumference, because the square on the diameter produces the side of a square which equals nine when the arc of ninety degrees equals eight. By taking the quadrant of the circle’s circumference for the linear unit, we fulfill the requirements of both quadrature and rectification of the circle’s circumference. Furthermore, it has revealed the ratio of the chord and arc of ninety degrees, which is as seven to eight, and also the ratio of the diagonal and one side of a square which is as ten to seven, disclosing the fourth important fact, that the ratio of the diameter and circumference is as five-fourths to four; and because of these facts and the further fact that the rule in present use fails to work both ways mathematically, it should be discarded as wholly wanting and misleading in its practical applications.

Section 3

In further proof of the value of the author’s proposed contribution to education and offered as a gift to the State of Indiana, is the fact of his solutions of the trisection of the angle, duplication of the cube and quadrature of the circle having been already accepted as contributions to science by the American Mathematical Monthly, the leading exponent of mathematical thought in this country. And be it remembered that these noted problems had been long since given up by scientific bodies as insolvable mysteries and above man’s ability to comprehend.

As a final postscript to this story, after the Senate debate, a Representative offered to introduce Professor Waldo to the bill’s author Mr. Goodwin.   Waldo declined, remarking “I am already acquainted with as many crazy people as I care to know.”   Snap!

Happy Pi Day, everybody!

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