HUMBLE PI

 

I suspect the problem begins with the oft quoted but shockingly misunderstood phrase, “pi are squared.”  It is a fact that you cannot perfectly square a circle. Which is comforting for those of us who are math-impaired. Seems obvious. Seems logical. But prove it.

You can, but you have to use math. And in proving it you stumble across something very odd. There is a constant mathematical relationship between the length of the line forming a circle, divided by the distance across that same circle. And this relationship, no matter how large or small the circle,  always works out to be 3.141592653589793238…etcetera, etcetera, ad infinitas, add infelicitous, and never ever repeating. This makes Pi an irrational number, which is confusing again because I find all numbers irrational, even on Pi day.

To express the problem in another way,  A(rea) of a circle equals the radius of the circle squared. But you see...     

...you can never turn a circle into a square of the exact same size. Close, but never exactly the same size.  And it doesn’t matter if it is a great big circle or an itty-bitty one. Pi is always 3.141 etcetera, etcetera, etcetera, but never ending and never reaching zero no matter how many places beyond the decimal point you go.  It's been tried. And is still being tried.

If you are a math freak this is obvious, while the rest of us have to be satisfied with accepting that Pi is an irrational number and live with it. But I ask you, what is the value of knowing pi? 

I had a fourth grade teacher who was so obsessed with having her students memorize the value of Pi to twenty decimal places that she had us memorize the following poem: “Sir, I send a rhyme excelling, In sacred truth and rigid spelling, Numerical sprites elucidate, For me the lexicon’s full weight”. Each of the 20 words of that poem has the number of letters required to read out the first twenty digits of pi, in order.  I had to memorized that poem again in my thirties because as a ten year old I couldn’t spell the word Nantucket, and as a sixty year old I rely upon a spell checker to detail any word long enough to rhyme with  “elucidate”. So this poem was as much a mystery to me then as the number Pi remains.

But I am older now and I have grown so used to making mistakes in public that I hardly notice the embarrassment anymore. So I openly admit that I still find pi a puzzle. What's so special about pi? And why Pi, anyway?

Legend has it that the great Greek mathematician Archimedes of Syracuse was struggling over the solution to pi when a Roman soldier blundered into his garden. The old man supposedly snapped, “Don’t touch my circles!”, whereupon the chastised legionary pulled his Gladius and separated Archimedes’ head from his face. I suppose that if Archimedes had been sitting in his bathtub, as he allegedly was when he discovered that displaced water could be used to measure density (Eureka!), something else might have been separated. But, suffice it to say that before computers, finding pi was a great big pain in the Archimedes. He managed to figure out that pi was somewhere between 3 10/71 and 3 1/7. He might have done better if he had invented the decimal point, first. But...

About the year 480 CE the Chinese mathematician Zu Chongzhi figured out that pi was a little more than 3.1415926 and a little less than 3.1415927. After that the decimal point zealots took over. The German mathematician and fencing instructor Ludolf van Ceulen worked out pi to 35 decimal places. And in 1873 the amateur geek, William Shanks, worked it out to 707 decimal places. But William made one tiny little mistake in the 528th number and that threw everything else off. But it was such a good try that nobody noticed his screw up until 1944. Today computers have figured pi out to one trillion digits to the right of the decimal point and still no repeatable pattern has been detected, and still it never quite reaches zero.  It is still a little bit less than 3.15 and a little bit more than 3.14. All that has changed is the definition of “a little bit”. It keeps getting smaller and smaller -  but it will never be zero.

But what does that mean? What does Pi mean, beyond its face value? Well, it turns you can find it in the  curve of the double helix of a DNA molecule, the chemical code of all living plants, animals and bacteria, and the behavior of light coming from distant galaxies, or out of our sun.  Einstein himself realized that if you want to describe why and how a river "meanders"  to the sea, you need to use Pi , because the actual length of a stream, with twists and bends,  is usually between 1.3 and 1.4 times the straight line distance - called the "meander ratio".  It's always pi! All the geologists have to do is plug in the variables for soil type, and angle of slope and latitude and drawing rivers on a map becomes predictable. Pi is why why so many rivers look the same when seen from space or on a big map. Pi is what all rivers have in common with DNA. And airplane wings. And sewer pipes. And eye balls, human and otherwise. 

Pi reveals the underlying structure of the universe, the lines of force - magnetic,  gravity, chemical or electrical.  Even atomic. Pi is like a master key, that with a little jiggling, can be made to open just about any door. The mere fact that such a key exists, tells you that everything we can see, hear and feel is connected to everything else, even the stuff we can't see. Pi tells you the chaos inside an exploding super nova is governed by the same laws that control the budding of a flower. It is the mathematical proof that there is a logic to the entire universe, and that logic is 3.141592653589793238...etcetera, etcetera.        

Thus pi is the “admirable number” according to the devilish little Polish poetess Wislawa Szmborska. While being infinitely long it includes “…my phone number, your shirt size, the year nineteen hundred and seventy-three, sixth floor number of inhabitants, sixty-five cents, hip measurement, two fingers, a charade and a code, in which we find how blithe the trostle sings!” (…and no, I have no idea what or who the hell a trostle is or what makes it blithe or unblithe. Do you?)

Daniel Rockmore, in the pages of "The Chronicle of High Education" for 12 March 1999, wrote that Pi was "Foreign, unpredictable, otherworldly, yet as common as a circle...it's easy to find, but hard to know. Among mathematicians there still rages a fierce, unsettled debate about whether pi is a "normal" number--that is, whether each of the digits 0 through 9 each occur on average one-tenth of the time in the never-ending decimal expansion of pi...making...Pis...a veritable poster number for the fashion world's ambiguous and androgynous advertising campaigns."  And you thought mathematics had no sex appeal  Why, if Pi was a plain old 3 or a dull old 4, there would be no sex. Sex is made possible by being 3.14159265358979.... etcetera, etcetera.. And it cannot be and will not be controlled. And certainly not owned.

A physician and a crackpot amateur mathematician from Solitude, Indiana named Doctor Edwin J. Goodwin,  thought that he had “solved” pi to the last digit - and none of this irrational numerical horse feathers for him!  And having achieved that which no other human had ever done, he decided to make Pi his own personal private property by copyrighting it. But in order to profit from his discovery (you know how wealthy the Pythagoras estate is) Dr. Goodwin needed a legal endorsement. And rather than subject his brainchild to the vagaries of the copyright peer review, the good doctor instead offered his theory as an accomplished fact to the local politicians. 

The proposal, Indiana House Bill 246, sponsored by Representative T.J. Record of Posey, Indiana, was  “…an act introducing a new mathematical truth and offered…to be used only by the State of Indiana free of cost…provided it is accepted and adopted by the official action of the Legislature…”. This insanity actually made it through the Committee on Canals and Swamps (Perfect place for it!) in record time, and was passed by the full Indiana house on 5 February, 1897, by a vote of 67 to 0.  Who says politicians don't spend time on important issues?

Unfortunately, in the Indiana Senate some wiseacre showed the bill to a visiting Purdue party- pooper, Professor of Mathematics C.A. Waldo. And now we at last know where Waldo was, at least was in 1897.  He was on the banks of the Wabash. The lawmaker asked if the professor would like the honor of meeting the amazing Dr. Goodwin, and Professor Waldo replied that he already knew all the lunatics he cared to know, thank you very much. And with that comment Dr. Goodwin’s brief bubble of fame was burst. On 12 February, 1897 any further vote on the bill to copywrite the perfect definitive solution to Pi was postponed indefinitely.  Hoosier lunatics have since moved on to more productive fields.

It was not a victory for logic so much as an avoidance of a victory for ignorance, which is pretty much the same thing that happened in Tennessee about 30 years later when they tried to make evolution illegal. Don't tell the whales. They'll have to go back to being dogs. 

Still pi remains one of the most popular mathematical equations, if mostly poorly appreciated by those of us who aren’t trying to generate a random number or navigate a jet plane across the North Pole, or predict the next stock market bubble, or launch a satellite, or run a radio station, or process an X-ray or a Cat-scan, drive a submarine, drill for oil, purify gold or etcetera, etcetera, ad infinitas, add infelicity.

Just trust me, and always trust pi. It lifts your spirit, gives you a sense of security and keeps your circles on the square. To share it just try singing..."Pi, Pi, Me oh my, Nothing tastes sweet, wet, salty and dry, all at once, ...oh my, I love pi!

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