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Thursday, March 15, 2018

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 Subtract 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 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".  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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Wednesday, March 14, 2018

VALLEY OF DEATH Chapter Three


I can imagine the unease felt by the technicians at Power House Number One (above), three miles below the St. Francis dam. It was the generators in this building, fed by the fall of water from the reservoir  which was providing the first dependable electricity to the city of Los Angeles. The needles on their gauges indicated the water level in the reservoir had been slowly dropping for hours. 
And the night shift workers who had driven around the the reservoir and over the dam in getting to work had observed a foot drop in the road along the eastern abutment of the dam (above, right). When Ace Hopewell reported for work a few minutes later he reported hearing what he thought was a landslide somewhere in the dark near the reservoir. 
Finally, about 11:57 P.M., somebody got worried enough to pick up the phone and call the dam keeper in the smaller Power House Number Two - containing just 2 generators -  a mile and a half further below the dam. Was everything okay there? “Yes”, came the quick answer.  But the haste of the response belied its assurance. 
And fifteen seconds later, at 12:57:30, Monday, 12  March, 1928, every light in Los Angeles went out. At that instant 53 million tons of water (12 billion U.S. gallons) wrenched apart the St. Francis Dam, had released a 10 story wall of black water desperate to reach the Pacific Ocean, fifty miles away.
In August of 1924 (two months after the first bombing of the Los Angeles Aqueduct) William Mulholland began construction of a new dam at the narrowest point (above) in Francisquito (Fran-sis-kito) canyon - 50 miles north of Los Angeles.  But Mulholand consulted no geologist. in picking the site.  
Originally the unreinforced concrete gravity arch dam - held in place by its own weight -  was to be 600 across at the top and 185 feet high.  But as  bombings continued to disrupt the flow of water from the Aqueduct,  Mulholland decided to add ten feet in height, increasing the storage capacity of the future reservoir by 2,000 acre feet.  But the old man never made an attempt to widen the base. 
What  haunted Mulholland was the ease with which the angry citizens of Owens County could cut off the drinking water to the city of Los Angles. And this reservoir was the final piece in a series of dams and reservoirs which would give Los Angeles a year’s supply of water beyond the easy reach of the Dynamite Gang in the Owens Valley.
Baily Haskell was one of the construction workers and decades later he noted to a local newspaper that in their rush to finish this final addition to the aqueduct system, Muholland’s mangers were using gravel directly from the bed of Francisquito creek “They didn't use washed gravel”, he said. “I could see these great chunks of clay going right into the dam.”
A year later, as negotiations with the Watterson Brothers in the Owens Valley stalled, Mulholland increased the height of the dam by another ten feet, to 205 feet high. This increased the 3 mile long and ½ mile wide reservoir to 38,000 acre feet. But no strengthening was made to the base of the dam. On March 1, 1926 water from the Los Angeles Aqueduct began to fill the canyon above the dam.
As the great Cecilla Rasmussen, writer for the Los Angeles Times, pointed out in a February 2003 column, “From the day the St. Francis Dam opened in 1926, it leaked. The folks in the farm towns downstream used to joke that they'd see you later ‘if the dam don’t break’.” On March 7, 1928 the intakes were closed. The reservoir was now full and the water was a mere three inches from the top of the dam.
That week drivers along the east shore road above the reservoir complained that the road was sagging near the dam’s eastern abutment.  At every step in the filling of the reservoir Mulholland personally checked the dam and declared it safe -  the last time between 10:30 and 12:30 on 11 March, 1928. Again, and for the final time, Mulholland declared the dam safe.
Less than 12 hours later it collapsed.It was not a landslide that destroyed the dam. That did not occur until after the 250,000 ton concrete structure had been wrenched apart like a child’s toy by the weight of the water that had soaked into its porous concrete.
I still have a three pound chunk of the dam sitting in my living room, and what stands out to me are the large miscellaneously shaped rocks peppered throughout the concrete, and the rough and uneven feel of it in your hand.
As the dam was twisted apart a wall of black water 140 feet high burst forth and began to scour the walls of Francisquito canyon. 
The first to die was Tony Harnischfeger (above) , the watchman, who was probably inspecting the dam he was so nervous about. Tony’s body was never found. The corpse of his girlfriend, Leona Johnson (above, right), who shared his cabin a quarter mile below the dam, was found wedged between two pieces of concrete. The body of their six year old son, Coder (above, center), was found further down stream. The copse of the youngest child, in Tony's arms, was never found.
Lillian Curtis (above, right) was startled awake in her cabin near the  Power House Number Two (above) by something.  She remembered “a haze over everything”, as her “big, husky cowboy” of a husband, Lyman (above, left) , lifted Lillian and their three year old son Danny out their bedroom window.
Lyman told her to run up the hill next to the Penstock water pipes (above)  while he went back for their two daughters, Marjorie and Mazie.  Panic drove Lillian up the almost vertical slope in the dark, along with the family dog, Spot. Then...
...just moments after the initial dam collapse (now 12:02 a.m. Tuesday March 13th ) a wall of water pounded the Concret Power House to pieces, and swept the cabins and the seventy other employees and their families into oblivion.
Waist deep water pulled at her but Lillian was just able to reach the safety at the top of the ridge. Lillian and her son, and another employee, Ray Rising, were the only survivors of the seventy.
Ray had to fight to get out of his own cabin. “The water was so high we couldn't get out the front door... In the darkness I became tangled in an oak tree, fought clear and swam to the surface... I grabbed the roof of another house, jumping off when it floated to the hillside... There was no moon and it was overcast with an eerie fog - very cold.”  Where once a small village had sat, was now scraped as bare as a table top (above).  Ray lost his wife and three daughters to the flood.
Just downstream the waters engulfed the Ruiz farm (above) . Dead in an instant were wife and mother Rosaria, father Enrique and their four children, one an adult. The farmhouse and barn were wiped out as if they had never existed.
Next the tidal wave swept across the ranch and a trading post store owned by silent film star Harry Carey, before sweeping across Castaic road junction (above) where...
...a 20 foot high wave destroyed the encampment of 150 California Edison employees, killing 84 of them. The victims did not drown. They were found, mostly, caught in trees, stripped of their cloths, “battered and bruised, but didn’t show any anguish – so probably they were taken in their sleep.”
By one in the morning the reservoir was empty. “An entire lake had disappeared” in less than an hour. But the flood was just getting started. At about 1:20 a.m. the warning finally began to go out to the little farming towns ahead of the flood.
Topography squeezed the wave back to 40 feet high as it swept down the stream bed of the Santa Clarita River, plowing through orchards and farms and homes from Piru to Fillmore and through Santa Paula. It reached the ocean in Ventura just before dawn, a wave a quarter of a mile wide and “50% water, 25% mud, and 25% miscellaneous trash” according to one witness.
Along the way it had demolished at least 1,200 houses...
..and smashed 10 bridges. 
The dead, many sucked out of their beds in their sleep,  would be washing up for days as far south as San Diego and Mexico. 
The inability to build a head end reservoir had now produced dried out orchards in the Owens Valley and drowned trees in Southern California. The last known victim of the flood, although unidentified,  would be uncovered in the city of Newhall, in 1992.
How many were carried out to sea or remain buried in mud closer to home will never be known, but it seems unlikely to me that the toll of the dead could be merely the 450 officially claimed.
I would estimate it could not be much fewer than 1,000 lives, counting migratory workers and unemployed living in the fields and orchards along the river.
Mulholland began by inspecting the disaster site (above) the next morning, insisting the failure must be more work by the Owens Valley dynamiters. But the evidence and the official rush to close the matter boxed him in, until he said he “envied those who were killed.”
The corner’s jury was convened within the week, and issued its report 12 days after the disaster. 
It recommended that “…the construction and operation of a great dam should never be left to the sole judgment of one man, no matter how eminent.. .... for no one is free from error.” 
The St. Francis dam, it added, had been constructed on the site of an ancient landslide. And for seventy years that was the accepted version.
But in the late 1990’s Professor of geological engineering J. David Rogers, of Missouri University of Science & Technology reached a different conclusion. “Probably the greatest single factor", he wrote, "was the decision to heighten the dam a second time."
"Had the dam not been heightened that last 10 feet, it might have survived.” But the ultimate failure, alleged Professor Rogers, was the concrete. So rushed was the construction that it was never allowed to properly cure, and never prepared as carefully as it should have been."
 “If it had been of better quality, it (the dam) would have never fallen apart as it did. It was so filled with fractures.” The disaster’s cost was later estimated at $13 million ($156 million in 2007).
The last remaining piece of the St. Francis dam would remaining standing to this day, and residents came to call it, The Tomb Stone.
A year after the disaster William Mulholland resigned and, in the words of his grand-daughter became a “…stooped and silent” recluse.
His onetime friend, Frank Eaton, died on 12 March, 1934 at the age of 78. His grandson described his last years as bitter. “…he felt he'd been made the goat for all the troubles that came to ail the Owens Valley, and because he felt he never got the proper credit for his role in the creation of the aqueduct.”Just over a year later that other dreamer, William Mulholland, passed into the valley of death at his home, on 22 July, 1935. And the Long Valley reservoir, was finally opened in 1941, and was named after a Catholic priest who had fought for peace between the DWP and Owens Valley residents; Crowley Lake
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