VLEEPTRON HOLIDAY FROM THE WAR: Get your Ph.D. in JUST ONE HOUR @ SHCC! (Southeast Hoon Community College, pronounced "Shook")

image generously
provided by
Math Department
Southeast Hoon
Community College

Copyright (c) 2006 by Robert Merkin

The Zeta Beam is still broke,up on Vleeptron at the Akira Kurosawa ZB Drome, the new tube/valve arrived but it turned out to have the wrong base so they had to send it back to Yobbo and ask for the right one. I've set up jars all over Hampshire and Franklin County to collect money to pay for retro-converting the Zeta Beam to all Solid-State. Fuck tubes. They're hot, they fail, the electric bill is brutal, and you need to send money via PayPal to the Peoples Republic of China to get new ones.

Also if anybody knows this I would be very appreciative: Where did all those tube-testing machines in the drug stores go? They were everywhere for decades, and then one night they just all vanished. The new replacement tubes were in the bottom of the machines.

So here I am stuck on Earth, and the TV has invited me to join in to celebrate the 3rd Anniversary of the Iraq War.

Vleeptron would like to thank everyone who stood in front of the Courthouse in Northampton to call for a quick end to the War. And thanks to all the people who marched against the war in London, and everyone who marched from the Vietnam War Memorial across the Potomac to the Pentagon. During the Vietnam War hundreds of thousands of protesters surrounded the Pentagon and attempted to levitate it off its foundation a few inches or centimeters by a mass chant.

"Eppur si muove!"

A couple of years later, the fucking War ended. I'll see if I can dig up the chant.

The Heathkit Vacuum-Tube Time Machine (TM-200) is also not working very reliably. Last night I wanted to go to an Isadora Duncan recital, and I ended up fleeing for my life from the deadly Boston winter exploding molasses tsunami. That sucked.

So. How the fuck can I get off this rock, just for a few days?

Here, come with me, I'll get you out of this fucked-up Locus. Check out this Somewhere Else, check out this Whatchamacallit.

A Locus that hath No War, nor Violence (senseless, or the other kind), nor any Falsehood nor any Corruption whatsoever.

A Locus whose Objects last forever, whose every Truth is Forever True, or True Until The End Of Time, whichever comes first.

Gold will rust before these Objects do. The Old Man of the Mountain will tumble, Gibraltar will crumble, the Himalayas will shrink to Jack and Jill's hill, and pigs will fly before the Stuph where I'm taking you showeth a sign of change.

Did I mention there are never any wars here? No young men or women being returned to Dover, Delaware in flag-draped coffins?

We gotta get out of this Locus
if it's the last thing we ever do
We gotta get out of this Locus
Girl there's a better Locus
For me and you

(w apologies to The Animals)

{ [ ( o ) ] }

Oh bummer: Cole pulled this stunt in 1903, we missed the Centennial. Ignore the next paragraph.

The SHCC Math Department has just noticed that 2006 is the Centennial of this Thang. Betcha somebody gonna hold a Seminar somewhere. Mmmm probably in Cambridge MA USA, mmmm. Maybe NYC. I can take a train.

* * * * *

BREAKING BULLETIN:

This has all been a lie. The Vleeptron Ministry of True Things and the Dwingeloo-2 UN-PT (Ultimate Non-Personal Truth) Authority deeply apologize. This should not have happened. We take full responsibility (but accept no actual blame). We resolve to bring you More Truth in the future.

This seems not to have been what got Cole his doctorate in mathematics. He had one, but not for this.

This seems more like it. But everything else, oh yeah, pretty close to what it was like. When the TM-200 has been working, I've been therethen twice.

================

Although Lucas had shown that M67 was not a prime, it was still not known what the factors (numbers that divide evenly into it) were.

In 1903, a mathematician by the name of Frank Nelson Cole (1861 - 1926) gave a 'lecture' to the American Mathematical Society entitled 'On the Factorisation of Large Numbers'. Without saying a word, Cole proceeded to write on a blackboard the calculations for 2 to the power of 67, then carefully subtracted 1. This was M67 and it is equal to none of your beezwax. Compute it yourself.

================

We now return to your Holiday From The War. We apologize for the interruption.

================

In 1903 a Massachusetts farmer's son named Frank Nelson Cole walked up to a blackboard, picked up a piece of chalk, and started scrawling a bunch of arithmetic and numbers on the blackboard. Sitting in the audience watching him were a hundred or two hundred other guys, maybe a lady or two.

(Since its founding around 500 BC, this Kult offers full membership to women, with about 85% less bullshit than females get in other Kults.)

They probably ranged in age from 13 or 14 to 90. They'd all set an alarm to get here on time, and some had taken long train rides; they didn't want to miss this. Most of them knew each other, but a few were strangers from far away.

Dead silence in the room while Cole scrawled. It could have been a religious ceremony.

To this bunch, that's exactly what it was -- a religious ceremony their particular Kult had been waiting 262 years for.

As a piece of minor side business, it was also Cole's Ph.D. thesis, and defense, if anybody had any questions, gripes or complaints when he finished.

Don't leave yet. It doesn't get complicated or difficult right away. Maybe you think it's boring. Well, okay, it's boring at the beginning, you had all this in elementary and junior high school and probably haven't forgotten most of it.

{ [ ( o ) ] }

Across the street from Illiteracy, smiling and waving at you and offering you M&Ms, French kisses, lingerie, leisure time, and a lifetime of freedom from frustration and headaches, is Innumeracy. There's no stigma attached to being Innumerate like the stigma of being known in the community or the cell block as Illiterate.

In fact I've listened lots of times to passionate defenses of intentional Innumeracy from (otherwise) highly educated adults, why it's necessary to keep children, particularly female children, away from too much math, what to do if a child develops an unhealthy interest in mathematics.

Speak roughly to your little boy,
And beat him when he sneezes;
He only does it to annoy,
Because he knows it teases.

-- Lewis Carroll

[1 slice plain pizza: How did Caligula cure his little nephew's annoying little cough? It really works!]

You pay for Innumeracy bigtime, throughout your life, at the grocery store, at the bank, at the car dealer, but the most brutal violation the world has for Our Innumerate Friends is the broomstick that casino slot machines shove up your ass every time you yank the handle.

You can save the gas money by just throwing coins and paper currency into your toilet, and flushing. Gamble into your toilet every day for a few years and eventually -- just as often as the big payout casino slot machine does -- your toilet will spit back an enormous amount of money.

Learn some fucking elementary math and learn to play blackjack. You'll lose your money much more slowly, and they give you free drinks while you play. Order a Coke, and tip the nice woman with chips, she works hard for the money.

{ [ ( o ) ] }

If everything works the way I want it, you can see what Cole started writing on the blackboard on the left of the screen.

While Cole pours himself a glass of water while he tries to win a Ph.D., I'll tell you about this number.

{ [ ( o ) ] }

In Paris in 1644 a Minim Friar named Marin Mersenne started looking closely at numbers like this:

(2^2) - 1 = 3
(2^3) - 1 = 7
(2^4) - 1 = 15 = 3 x 5
(2^5) - 1 = 31
(2^6) - 1 = 63 = 3 x 3 x 7
(2^7) - 1 = 127
(2^8) - 1 = 255 = 5 x 51
(2^9) - 1 = 511 = 7 x 73

Without the slightest bit of anything resembling Proof, he said that if the power of 2 was

p = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257

then (2^p) - 1 would be a Prime, evenly divisible by no number except itself and one.

For every other p less than 257
(2^p) - 1 would be Composite.
It could be evenly divided by some smaller whole number.

In Europe in 1644 the most powerful, fastest digital computer was a kid named Stanislaus, who could multiply

3910228673881
x 62294488

in his head and spit every digit of the answer correct out of his mouth in about 90 seconds, without pencil and paper. His dad earned money off him at carnivals and fairs; he came on after the sword-swallower and before the human pretzel woman. The kid could also tell you the square root or the cube root of 911880072661 to the nearest whole number, although he tended to drool a little in the middle of these.

If Stan was 800 miles away and unavailable, you could use those swell logarithms and slide rules.

But not for problems in Number Theory, the Perfect Dance of the Mysterious Whole Numbers. (Yes, the Land of Ramanujan.)

If you need the exact answers about Really Big Whole Numbers from your multiplication, addition, subtraction and long division, you ask Stan to do it inside his head, or you do it yourself with lots of paper and a pen, lots of aspirin, lots of anger, lots of mistakes, lots of frustration -- ahhh, shit, most people just give up and leave the question unanswered.

Progress in Number Theory was slow and painful, and there were lots of Wild Guesses like Mersenne's floating around in the mail.

Why anyone should even want any Progress in Number Theory is quite another story.

Look -- essentially it's a Kult Thang. This Kult is bigtime into Arithmetic. They just never got over the math they teach you in elementary school, that's when most of them were first lured into this Kult.

In Crotona, in Southern Italy when it was a Greek colony, the neighbors burned down the Kult's compound twice. Another time this Kult tossed a member off a cliff to his death because he asked a simple math question and got the right answer. They murdered him for Blackboard Stuff. The rest of the Kult didn't like the answer, because The Master had said that wasn't possible.

(But after they killed the guy, they told the rest of the world that he'd proved The Master was wrong.)

You can do the Short Ones yourself with a calculator and pencil and paper. But Mersenne guessed that (2^67) - 1 was Prime, and nobody could say he was right or wrong.

It stayed a guess until Cole started writing on the blackboard in 1906.

By then they had mechanical hand-crank thingamabobies, machines for bank and business clerks that could handle numbers with about this many digits

999,999,999.99

and churn out the exact answers. Very helpful for the tiny little numbers our tiny little practical, financial and physical world (the place we call Reality) asks questions about.

My guess is Cole didn't use one. He might have used an Eberhard Faber graphite pencil with an eraser. Lots of them. And lots and lots of paper.

Ah. Cole is writing on the blackboard again.

aaaaaaaaaaaa
x bbbbbbbbbb
------------
cccccccccccccccccccc

(2^67) - 1 = aaaaaaaaaaaa x bbbbbbbbbb

Q.E.D.

By the way, a and b are both Primes. But either or both of them could be Composites and the last line on the blackboard would still be worth a Ph.D.

{ [ ( o ) ] }

My Heathkit TM-200 Time Machine is also on the fritz, but my guess is there was a lot of applause and standing up -- an authentic standing ovation. Cole had proven that Mersenne's (2^67) - 1 was Not A Prime, that Mersenne had guessed wrong. And it had only taken 262 years.

For Cole, it had probably taken six months or a year of ceaseless hand and head computations. Once you compute cccccccccccccccc and subtract one, you have to try to divide the result by every Prime low to high (you can skip 2 and 5)

2 3 5 7 11 13 17 19 23 29 ......

Right away there's trouble. No digital computers, so no Tables of Very Large Primes.

If there is a Table, and it was computed by Human Brains, by Mere Mortals, it's a certainty that it's shot full of errors, so if you use it for Something Important, you're fucked and you won't even know it until someone else proves you fucked up, and you go down unto Eternity in the History of Mathematics as a famous incompetent and publicly certified failure. There are lots of those.

This Kult plays rough with your self-image. The word "nincompoop," in scores of translations, is used a lot. There's also a famous Pons Asinorum, the Bridge of Asses, across which all bad college math students stroll to reach the Wrong Answer, and an F in the course. (You can take it over again the next year, but most don't.)

So now you have to hand-divide not by every Prime, but by every Odd Number that doesn't end in the digit 5.

If you sum all the digits of any whole number two or three digits at a time, every time they sum to 3 6 or 9, you start the sum from zero again and keep summing, so you only have to do tiny additions in your head. If the last sum you end up with is 3 6 or 9, the big number is evenly divisible by 3, so it's a Composite, Cole could skip all those. (The Rule of Threes.)

But there aren't lots more easy tricks to eliminate lots more Odd Numbers.

When could Cole stop? If Mersenne guessed right and
(2^67) - 1 was Prime, Cole would have to divide by nearly every odd number less than the square root of cccccccccccc.

(The reason is left as an Exercise for the Reader.)

{ [ ( o ) ] }

The Vleeptron
PizzaQ Honor System

Anyone want to take a whack at this one?

No Googling. No Library. No asking Mom or Dad. No phoning Klaas in Rotterdam.

HOWEVER ...

You CAN write an original COMPUTER PROGRAM to do it for you. Your own little Silicon Stanislaus.

That's what I'm in the midst of doing. Ouch. Ouch. I need to take some aspirin.

All I have to do is show My Silicon Pal what I want it to do and how to do it.

Ouch ouch.

The first problem is that my Programming Language's Floating-Point Arithmetic can't handle very large whole numbers. (Yours can't either.)

In Everyday Reality, the whole numbers it can do arithmetic with are huge -- it routinely can deal with gazillions.

But this problem needs perfect precision for numbers which far surpasseth mere gazillions.

So I have to teach My Silicon Pal addition, subtraction, multiplication and long division entirely from scratch. I have to shove 4th and 5th and 6th Grade Arithmetic into its logical little brane. Try it sometime.

Me being slow, lazy and stupid as I am, I'm probably not going to be running my KINGCOLE.EXEfor quite some time. By the time I finish this sucker, if I ever do, the War Protesters will be wearing Bermuda Shorts and T-Shirts in front of the Courthouse.

Long enough for you
to get the answer
before I do.

And if you get The Right Answer before my computer does, you get three slices of of pizza, with the toppings of your choice, and a Ph.D. degree in Number Theory and Computer Science from Southeast Hoon Community College. (SHCC is fully accredited in the Dwingeloo-2 Galaxy, but not in the Milkweg.)

If you don't try to get the answer, my Kult will laugh at you and call you a Nincompoop. Hahahaha. You are Innumerate. Maybe you're eating M&Ms and getting some French Kissing, but I feel sorry for your Innumerate ass.