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Friday, March 13, 2015

A PLATE OF HUMBLE PI

I suspect the problem begins with the oft quoted but not well understood phrase, “pie are squared.” In the first place, it’s not. It is a fact that you cannot square a circle, and yet it is done everyday, out of sight for those of use who are math-impaired. This is so because  pi is the relationship between the length of the line forming a circle, divided by the distance across that same circle. And this relationship somehow always works out to be 3.141592653589793238…etcetera, etcetera, ad infinitas, add nfelicitous, and never ever repeating. This makes Pi an irrational number, which is confusing again because I find all numbers irrational, even on Pi day (3/15).
To find the area of a living room you simply ask a realtor, and then add  10%. But to find the area of a circle you must  measure the radius of a circle and then square it -  or to put it another way, the radius of the circle times the radius of the circle times the radius of the circle - three times.  In the shorthand of math-speak that becomes, A(rea)= pi Radius squared. This is true math-media.      
What this mystery formula really means is that you can never turn a circle into a square of the exact same size: close, but never exactly. 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..
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 remained for years.
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. Besides, every time I make a mistake, I learn something new. Things my mistakes have taught me so far include, never turn down a chance to use the bathroom, never loan money to attractive women, never invest in Nigerian lottery tickets, never give out my social security number over the net, and never question the value of pi. But, why pi?
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 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 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".  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 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.  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 plain old 3 or dull old 4, there would be no sex. Sex is made possible by being 3.14159265358979.... etceteraetcetera.. And it cannot be and will not be controlled. And certainly not owned.
A physician and a crackpot amateur mathematician from Solitude, Indiana named Dr. Edwin J. Goodwin thought that he had “solved” pi to the last digit - and none of this irrational numerical horse feathers for him!  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, “…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 in 1897. 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, run a radio station, 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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Sunday, March 08, 2015

EASTER SUNDAY Part Three

I find it perfectly logical that so much began in Florence. Wool from Europe and dyes from Asian ports met in Tuscany, which was far enough from Rome that religious strictures against profits could be stretched, and in a region so poor the nobility, the only people with any money, were willing to experiment with capitalism. A cultural and economic “rinascità”, or renaissance was set off. And riding the first wave in 1378 was Salvestro de'Medici, a black sheep of his clan.
Salvestro led the popolo minuto, the little people, the unskilled Ciompi textile workers in demanding the right to form their own guilds. Their rulers, the popolo grasso, the fat ones, initially gave in, but a month later, when the workers followed one of their own, Michele di Lando, in storming the Palazzo Vecchio, the textile makers closed their shops, and Salvestro remained silent. Within days hunger forced the unpaid workers to surrender. But the Medici family had established their reputation as defenders of the common man. And thanks to Salvestro they built a great fortune by using that populist image selectively
And on the heartless application of violence. One hundred years later, on 26 April 1478, as soon as Lorenzo Medici escaped from the cathedral, he dispatched forces to retrieve his brother's mutilated body, left to bleed out on the cathedral floor. From a second story window of his home Lorenzo then appeared to a crowd of supporters, showing he was still alive, if wounded. His survival inspired the Medici forces to strike back without pity.
Archbishop Francesco Salviati was already in custody in the Palazzo Vecchio. He was quickly joined by his brother, Jacopo Salviati, and his cousin, Bartolomeo Salviati. Both men had been in the cathedral during the murders of Guiliano Medici and Frecesco Nori. In addition, armed men were dispatched to the Pazzi home, where Francesco Pazzi, still bleeding, was arrested. They were all questioned at an rump trial by the eight members of the City Council. The results were, it might be said, per-ordained.
Within the hour Francisco Pazzi was stripped naked. A noose was thrown around his neck. Then he was pushed from the second story window of the Palzzo Vecchio. The drop was not intended to be far enough to break his neck. It was intended that he should slowly strangled for the amusement of the jeering mob gathered in the square. And while he still writhed at the end of the rope, Archbishop Salviati, also naked, was shoved out the window, to writhe in desperate agony until, as an observer noted, his eyes bugged out. Once both men were finally dead, the ropes were cut and the bodies dropped into the square, where the mob beat and dismembered the corpses. One enraged man, said a witness, even bit into the dead Francesco's chest.
Next out the window was the two Salviati cousins, to dance to the crowd's delight, who then vented their blood lust upon the dead bodies. Then the priests, Setefano da Bagnone and Antonio Maffei de Volterra, the pair who had attacked Lorenzo, had their noses and ears cut off, before being castrated. Then, they were thrown from the window, to dance for the mob. Now, eager to prove their loyalty to the Medici family and with their blood lust released, the mob tracked down as many Pazzi and Pergia supporters as they could find, breaking into private homes and public buildings, even churches, to kill them. At least eighty were butchered that Easter Sunday on the streets or in their homes, with many thrown from the Vecchio's clock tower. Guilt in the murder or the plot was no longer required. The Pazzi name was enough.
Jacopo Pazzi was trying to reach Pisa, but only managed to get as far as the tiny mountain village of Castagno, about seven miles west of Florence, before he was captured, beaten and returned to the city. He then flew out the Palazzo Vecchio window, like his nephew and sons. After he was buried in the family crypt, a drunken mob disentered his corpse, and dragged it through the streets. It was then reburied outside the city walls, but dug up again, this time by children, who used the head to pound on the Pazzi family front door. When no one answered, the rotted corpse was dragged to the river Arno and tossed into the water. It was last seen, decomposing in the shallows.
Those Pazzi males not killed outright were arrested. and confined in the new prison fortress in Volterra, twenty miles southwest of Florence. It was so secure, it is still being used as high security prison today.Guglielmo Pazzi, Francesco’s brother, was spared execution only because he was married to a Medici daughter. He was banished from Florence for life, along with all Pazzi females, old men and children. All Pazzi gold and silver in Europe were ordered seized, their homes, businesses and estates plundered and confiscated. No Pazzi was ever again allowed to hold public office in Florence. The family crest of two dolphins was removed wherever found, as were all images of Pazzi faces in paintings . So complete and absolute was the Medici revenge, that the name Pazzi became, in English, to define anyone who could be implicated in a crime - a patsy.
Then there was the case of Giovanni Batista da Montesecco, a cousin to the Duke of Urbano. He had originally been chosen to kill Lorenzo, but bowed out after realizing the murders were to occur in the cathedral during Easter services. But neither had he warned the Medici of the plot. Arrested after being implicated by the unfortunate Setefano and Antonio, Giovanni revealed how deeply Pope Sixtus' had been involved. In return for his testimony, he was merely beheaded. The man who had officiated at the Easter Mass and Sixtus' nephew, Cardinal Raphael Riario, was held incommunicado for a month before Lorenzo decided he was only naive, and allowed him to return to Rome.
Bernardo Bandini, who had helped Francesco Pazzi murder Guiliani Medici, managed to get as far away as Constantinople. But the Medici bank reached that far, and 18 months after the attack Bernardo was kidnapped and hustled aboard a fast ship back to Italy and Florence. Immediately after his arrival, on 29 December, 1479, Bandini also flew out the Palazzo Vecchio window, still dressed in his Muslim disguise Leonardo Di Vinci sketched him hanging there.
After the Easter Sunday massacre, all of Italy had to pick sides, and most either joined the Pope or chose not to support the Medici. The King of Naples, Ferdinand I, sent an army to lay siege to Florence. And while the King of France offered an army to Lorenzo, the surviving Medici son knew the cost of such support would be disastrous for the rest of Italy. And so in December of 1479 Lorenzo changed the rules of the game. He sneaked out of Florence, and took ship for Naples. He was instantly imprisoned by Ferdinand, but the monarch was convinced by Lorenzo's own wounds that the Pope had precipitated this crises. Also, Naples was clearly on the French wish list of Italian properties to grab, if an invasion was possible. Ferdinand forced Sixtus to reconcile with the Medici, and the war quickly came to an end. From that day forward, Lorenzo would be known as Lorenzo the Magnificent.
Sixtus (above left) would sit on Peter's throne for another six years, and be best remembered for this Easter Sunday attack, for the Sistine Chapel he had built, for two decrees approving of black slavery in the new world, and for appointing Tomás Torquemada (above right) as the Grand Inquisitor of the infamous Holy Office of the Inquisition. This worldly Pope died in 1484 a bitter and disappointed man.
Lorenzo Medici (above) ruled Florence for another fifteen years, gradually more openly as a dictator. .He tracked down the new born son his brother had fathered with Fioretta Gorini, and had the boy brought into the family home and raised and educated as a full Medici. When he died in 1492, Lorenzo de Medici would mostly be remembered for his wise rule, and the great public art works he commissioned, including the magnificent tomb containing his own and his brother' Guiliano's bones in the Church of San Lorenzo in Florence, a tomb designed and carved by Michelangelo.
But the ultimate Medici revenge of Sixtus came when Lorenzo's son, Giovanni de Medici, became Pope Leo X in 1513, and was succeeded by Giuliano's son, Giulio de Medici, as Pope Clement VII in 1523 It is said, if you can't beat 'em, join 'em. And the Medici of Florence did both.
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