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JUNE  2022
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Monday, March 18, 2024

ET TU Part Two alea

 

I have no doubt there were spies in Ravenna on 11 January, 29 BCE. There are always spies in border towns.  And traveling north out of Roman territory, the first town you reached in Cisalpine Gaul was the little fishing village of Ravenna, a quarter way down the western boot of Italy.  A man could be a dictator here.  
But just fifteen miles to the south in Ariminum, he would command no soldiers. He would be governed by the politicians 200 miles to the southwest, in the self described center of the civilized world, in Rome.  And the man the spies from Rome were watching this winter day was the governor of both CisAlpine and TransAlpine Gaul - Julius Caesar.
Caesar's stated reason for being in Ravenna was to check up on his investment in a gladiator's school (above).  That was logical - given that the tens of thousands of slaves Caesar had captured in his conquest of TransAlpine Gaul (i.e. France) and during his recent invasion of Britain. Those human beings now had be converted into cash. Laborers and house servants could quickly be sold, but Gladiators always sold at a premium. So, of course, Caesar was here to inspect the construction of his Gladiator School, and to witness a display of his gladiators in training. Then, after a light lunch, Caesar went to the baths -  another public appearance for a Roman politician.
And in the evening he sat down for a banquet, the kind of thing public officials are still expected to do.  And, according to Plutarch,  as the sun set, “...he left the company, having desired them to make merry till his return, which they would not have long to wait for."  It was enough to lull most spies to sleep. But the Romans were about to learn what the Gauls had learned before them - if you want to know what Caesar is about to do, you did not watch Caesar. You watch his troops.
Three years earlier, in December of 53 B.C., a member of the ruling First Triumvirate, the primary ally of Caesar, Crassus (above), a had been killed in Parthia. At about the same time another Caesar supporter, Tribune Publious Clodius Pulcher, had been killed in a staged brawl – something which had become common in the dying Roman Republic. 
The Tribune's angry supporters had built Plucher's funeral pyre in the Senate House, which resulted in the Senate House burning down. The Senate aristocrats used this act of vandalism as justification to elect the second member of the Triumvirate, Gnaeus Pompeius Magnus (above), as Sole Counsel, with powers to put down what was described as an insurrection. When some nervous Senators hinted that there were few soldiers in Rome to protect them, Pompey reassured the nervous Nellies, “I have only to stomp my foot to raise an army”  And while he began to arrest Caesar's supporters, on 7 January 49 B.C.E.,  the Senate voted to order Caesar to disband his own legions and return to Rome for trial. That law was vetoed by the two Tribunes who were were still loyal to Caesar, Mark Antony and Quintus Cassius Longinus. They were promptly driven out of the Rome at sword point.
Caesar (above), was just across the border, in CisAlpine Gaul.  When informed of the Senate's move against him,  he offered a compromise.  He was willing to give up  command of his army and return to Rome, if Pompey gave up his post as Sole Counsel.   Caesar also requested the Senate allow him to stand for re-election as Counsel while he was still in Gaul, with, presumably, Pompey standing for re-election as co-Counsel at the same time.  It seemed a fair compromise. If elected both men would have immunity from prosecution in the courts, and would jointly rule the city of Rome for a year. 
Pompey and the aristocrats in the Senate rejected the deal out of hand. Caesar's ten year term as Governor of both Gauls was about to run out, and as soon as he was no longer legally protected by his legions, the Senate could deal with him. So Caesar's enemies in the Senate thought they could afford to wait and watch
Caesar could not, and did not.  His 6,000 veterans of the 12th legion had been in winter barracks near present day port of Trieste, Serbia, at the head of the Adriatic. Early in January, before the Senate had even rejected his compromise, Caesar had ordered these men to sail for Ravenna. The advance elements had arrived at the little fishing village a week later. And on the afternoon of the 11 January,  5,000 infantry and 300 cavalry marched out of the “Rimi” gate, headed south.
After dusk, having slipped out on his dinner party, Caesar made his way on foot to a mill on the outskirts of the Ravinna.  Here his aides had a hired carriages, which were waiting for Caesar.  Pulled by four mules he followed a back road across the surrounding marshes.  In the dark he got lost, and his carriage got stuck in the mud. Dawn found the great Caesar on foot, asking for help from a lowly farmer. By mid morning he had joined his men, on the banks of the River Rubicon (or the red river),
the traditional northern border of Rome. 
Beyond, in the village of Rimi, was the end of the 200 year old great “Northern Road”, the Via Flaminia (above), which wound its way across the Apennines, the central mountain spine of Italy, through narrow gouges and bridging rushing torrents, to the Field of Mars, then through the Flaminia gate in the city's walls, right to the base of Capitoline Hill, the central citadel of Rome itself. Crossing this border at the head of an army had been forbidden for a Roman general for two hundred years. Crossing this border would brand Caesar and his soldiers as outlaws, subject to execution by any citizen at any time. So this called for a bit of theatre.
The veterans of the 12th legion  had followed Caesar from conquest to triumph across Gaul, had even crossed the Rhine and invaded Germania. But this was something different, this was an assault on the Senatus, Populusque, Romanus - the Senate and the People of Rome, symbolized by the S-P-Q-R atop every banner the soldiers followed, on the very coins they were paid with. Nervously the legionaries awaited the stirring speech they expected Caesar to give before asking them to commit an act of treason.
Instead, a common soldier suddenly grabbed a trumpet from one of the musicians, raced across the shallow stream blowing “the advance”.  Caesar turned to his officers, and said, “We can still retreat. But once we pass this little bridge, there is nothing left but to fight..”  Then he turned toward the bridge, and called out, “Let us go where the omens of the Gods and the crimes of our enemies summon us”   As he crossed the stream  himself, he is supposed to have said, almost to himself, "Alea iacta est”, the Latin phrase usually translated as “The die is now cast!”
He did not look over his shoulder. He knew his men were following him.
On the southern shore waited Mark Anthony and Cassius Longinus, physical evidence of the arrogance of the Senate.  Here Caesar drew the troops into a square, tore his robes in a show of humility, and led the soldiers in a personal pledge of fidelity to himself, to Caesar.  The Roman Republic was now dead. The only thing required was to bury it. According to Suetonius, his legion now “marched so fast the rest of the way that he reached Ariminum before morning and took it.”
Rome was electrified by the news.  And it quickly became clear that the Senate's arrogance had turned Caesar's march down the Via Flaminia into a triumphal parade. So great was the frustration with the Senate that city after city threw their gates open to Caesar. Forces sent to stop him, went over to his side.
Senator Favonius suggested it was high time that Pompey (above) stomped his foot. But Pompey's own legions were in Spain. The city had raised two legions and was assembling a third, but they were new recruits, and Pompey was not interested in matching them against Caesar's veterans from Gaul. Pompey did not increase his popularity when he informed the aristocratic members of the Senate that they should get out of town. Many denounced Pompey as a coward. But they still followed Pompey and their fellow aristocrats when they grabbed their wealth, and ran for Brundisium, the traditional exit port at the heel of the Italian boot. In their haste they left behind the treasury of Rome, the horde of gold and silver looted from Carthage, stolen from Egypt, taxed from Spain and Macedonia. It was the first place Caesar went, when he got to town.
They couldn't find the keys to the vaults. Caesar sent for locksmiths. A Tribune reminded Caesar he was violating the law. Caesar suggested, “If what I do displeases you, leave.” The doors were forced open, and Caesar had enough money to pay his soldiers.  But murder stepped through that door, right next to him.
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Sunday, March 17, 2024

ET TU Part One Velum surgit

 

I believe the murder was set in motion far from the scene of the crime, in modern day Turkey, in a patch of desert about ten miles north of the border with Syria. In 53 B.C.E., this spot of what was then emptiness was called Carrhae (above), and in Roman history that name is synonymous with shame. 

It was on the plain at Carrhae that 20,000 Legionaries died (above), and worse, 10,000 were captured, and even worse, it was here that the aristocrat’s aristocrat, the greedy bloodthirsty Marcus Licinius Crassus, was killed. 

Few who did not depend on Crassus for their financial security had reason to mourn his demise. But within ten years of his death, what was left of the Roman Republic would collapse, and the cause of democracy would be set back two thousand years – and all that occurred because Crassus got what he deserved. I would label all that the horrible unintended consequences of a good thing.
Marcus Licinius Crassus (above), the richest man in Rome, who also saw himself as a hero. He led the right wing at the battle of Coline Gate, which made Sulla dictator of Rome. He had defeated the slave armies of Spartacus, and lined the Appian Way with 6,000 crucified slaves. Then he had turned to running the finances of Sulla' s brutal regime. But now, at 60, he wanted to be a hero again. 
His plan to achieve this was to invade Parthia, the empire centered upon present day Iran. But age had not made Crassus more intellectually flexible or humble of spirit. When offered assistance from the King of Armenia, Crassus chose to keep all the plunder for himself.
So, in the spring of 53 B.C., at the head of seven veteran legions and 8,000 cavalry commanded by his son, Publius, Crassus crossed the Euphrates river at Zeugma, and almost immediately started making mistakes. 
He hired a guide who led him deep into a treeless desert near Carrhea (above), and then vanished. And once the legions were ankle deep in sand and desperately short of water, only then did the Parthian army appear - 10,000 cavalry armed with powerful bows.
Arrows showered upon the massed legions, wounding men and sapping moral. The Roman tactical response was to form the infantry into turtles (testudos) (above), closing ranks tightly, with the center ranks marching beneath their shields, and the soldiers on the edges presenting the enemy with a moving wall. 
But so strong were the Parthian bows that some arrows even penetrated the turtle's shell. It went on for hours. The turtles could only march in a straight line, and not very quickly under a baking desert sun. Eventually, reasoned Crassus, the Parthian bowmen would run out of arrows. But then he spotted large camel trains approaching, each dromedary carrying a fresh supply of arrows.
In desperation Publius's cavalry charged the camels, but the Parthian's proved adept at shooting while retreating - the famous Parthian shot (above), the sting in the scorpion's tail. 
Publius was killed and his cavalry scattered. The Parthians closed in again on the turtles and the arrows continued to shower down,  as did the merciless heat. Eventually Crassus was forced to retreat into the village of Carrhea.  After a night without water his officers forced Crassus to parlay with the Parthian commander. The meeting was a disaster. 
The deaf Crassus perceived an insult in some Parthian translation, and moved to remount his horse. A Parthian officer grabbed the horses' bridle. A proud Roman officer pulled his gladius to defend his commander's honor, and the Parthian generals slaughtered the Roman officers, including Marcus Licinius Crassus. After that, the Parthians fell upon the leaderless legions, and effectively wiped them out.
The legend is that after the slaughter, the Parthians poured molten gold into the severed head of the greedy Crassus. It sounds like a terrible waste of a precious metal, but then the war had been a terrible waste of seven irreplaceable Roman legions. But the two men in all the world who understood intuitively what a disaster Crassus' death really was for Rome, were his two greatest competitors.
The sardonic Sulla had nicknamed Gnaeus Pompeius, as Pompey the Great (above). But Sulla had meant it as a joke - whatever else he was, Sulla was a ruthless judge of character. Sent by Sulla to secure the Roman grain supplies in Sicily, the young Pompey had earned another nickname, 'the adolescent butcher'. 
When the citizens of one small Sicilian village argued his attack upon them was illegal, Pompey responded bluntly, “Stop quoting laws. We carry weapons!” Returning home, Pompey demanded a triumphal parade, usually reserved for military victories. After Sulla's death, the Senate dispatched Pompey to crush a rebellious general. Pompey bribed one of the rebel officers to kill the general, and then eliminated the traitor. His justification was typically blunt. “A dead man cannot bite”. And he claimed another triumph. Sent to crush pirates who were raiding Roman grain fleets, Pompey bought them off, and again, claimed a triumph - Pompey Maximus, indeed.
As the two richest and most ambitious men in Rome, Pompey and Crassus had initially cooperated to strengthen the tribuni plebis.
This was not out of some faith in the Senate, but to use the tribunes as a buffer between them. For four hundred years these 'Tribunes of the Plebs' had been a counter-balance to the aristocrats in the Senate. Elected by the whole male population, tribunes could not make laws, but they could veto any law passed by the Senate (above).  Sulla had reduced the tribunes to a ceremonial post. But Pompey and Crassus, increasingly driven apart by suspicion, paranoia and envy, used the tribunes to prevent their opponent from enacting policies they did not like. And one of the men supported by Crassus for tribune of the people had been Gaius Julius Caesar.
Sulla had taken one look at the smart, ambitious young Caesar (above), and marked him down for elimination. Julius avoided Sulla's assassins by joining the army. Once Sulla died, Julius returned to Rome, where Crassus backed his election as a Tribune and then sent him to Spain. While there Caesar had defeated two small tribes. This earned him the right to a triumph. Instead, Caesar asked Crassus for help, meaning money, to run for Tribune of the people.
Romans were so afraid of someone wanting to rule over them as a  king, that the Tribune term of office was just one year long, and there were two equal Tribunes  elected each year. Each had the power of veto over any action by the other or the Senate. This was a system designed to ensure deadlock.  As a result of the election in  60 B.C., Caesar (Crassus' man) was elected. 
But the other consul elected that year, Marcus Calpurnius Bilbus , was Pompey's man, meaning every law Crassus backed, Bibulus vetoed, and every law Pompey pushed, Caesar vetoed. And it was Caesar’s political genius that he saw the way to use this deadlock to increase his own power.
In 59 B.C., Pompey pushed for a land reform act that would give farms to veterans of his legions . Bibulus tried to veto the bill, but thugs hired by Caesar dragged Bilbulus out of the forum, threatened him and dumped a dung bucket on his head. The shaken man withdrew from public life.  Then quickly, Caesar moved to grant Pompey's veteran's equal lands. And that quickly power in Rome was changed, from a deadlocked confrontation between two men, into a more balanced government ruled by three - The First Triumvirate. As a reward for bringing peace between Crassus and Pompey, Caesar was appointed Governor of Trans-alpine Gaul, what today is France, for ten years.
Thus Caesar went to seek his future in conquering and plundering Gaul with four legions. Pompey, who left his legions in Spain,  stayed in Rome to plunder the Republic. And the financier Crassus had turned eastward, to conquer and plunder Parthia with seven legions. 
But in 53 B.C.E. Crassus (above) had gotten himself killed, and the Roman Republic, was abruptly reduced to a direct confrontation between two men. It was a contest which must result in the death of one of them, and the Republic.
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Saturday, March 16, 2024

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...Pi...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.... 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 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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