Saturday, June 19, 2010

How Can You Tell if There's an Elephant in Your Math Club?

By the pi on it's breath? 

I don't understand it. Whenever I casually remark that pi contains an infinite number of elephant jokes, I get pitying looks. Since the prospect of endless elephant jokes would surely delight anyone, I can only suppose that I am not believed. Let me explain: 


Those three dots at the end of this expansion of pi, the "ellipsis" aka "marks of elision" aka "naughty bits" (I suppose, since they are customarily left off) are what I'm talking about. That's where the elephant jokes are. In there, the "and so-on, ad infitum" of pi. 

“And so on” what

You know. Forever. Not lover's vows forever, but the real thing, the big lazy eight, infinity. Out of which, absolutely anything that can happen must happen, infinitely many times. 

Moreover, if you try to guess the next digit hiding in that ellipsis, you have exactly one chance in ten of being right. and that's not just because you're guessing. Humans are good at recognizing patterns, if any exist. Almost as good as elephants. 

Statisticians say we are right; there is no pattern. No, the elephants did not intimidate them. (OK, a little) They counted. Any digit 0-9 has an equal chance of being the next to pop out of the ellipses. It's as if there was a random digit generator in there. 

Except there isn't. It's pi. The unpredictability disappears as soon as you know that and where you are in the sequence. But you have to know where you are, or no dice—I mean, yes, dice. Die. One ten sided die. But not—I want to emphasize this—made out of ivory. 

I understand that among mathematicians it is good form to say “pi is normal,”(meaning the digits in pi are normally distributed) because if you say “pi is random” it's apt to start a food fight. On the other hand, one time I said “pi is random” and got laid.

Since pi is random and endless, we can very easily answer such questions as, “Does 0123456789 appear anywhere in pi?” The answer is yes, infinitely many times. “Oh yeah? Well, what about a hundred zeros in a row?” Same answer. And, before you ask, 314195265… is there, too, in sufficient length to have mathematicians biting their nails until some digit finally strays and there is a great sigh of relief. Infinity is like the old joke about a totalitarian country: anything that is not forbidden is mandatory. None of the above is forbidden, just highly improbable.

To go from digits to the all-important elephant jokes, we could make up a substitution cipher. But we don't need to make up our own. Let's use the one you're looking at now. We can easily expand pi in binary and, voila! Gibberish…and some of it not printable. OK, let's expand pi to the base of the computer's unicode character set. Still gibberish. But printable.

An infinite string of printable pi, and somewhere in that gibberish will be the treasure we seek: elephant jokes! Not just one or two, nor thousands nor millions, but an infinite number of elephant jokes! Elephant jokes in every language on earth, living, dead, and yet to be. Elephant jokes in Klingon. (The Federation could avert tragedies…or possibly cause one) And since we have them in a form computers can work with, we can seek them out efficiently. World—nay, universal—peace would ensue. 

Would it surprise you to learn that I have already written a program that does this? Of course, by the time an ordinary supercomputer—or even a game box—could find even one elephant joke in pi, politicians would have stopped lying, so I had to build a quantum computer. Off to the hardware store.

Writing the software was the worst part  I don't recommend quantum debugging at all. Still, one night last week, the reward for my all my hard work was nigh. The program produced its first output:

I just flew in from Nairobi, and boy are my ears tired.

This wasn't even the correct form, but the algorithm is heuristic. It learns. I pressed the punishment key and it tried again. 

Take my wife's fleas.


Knock, knock…

Punish! Punish! Punish!

How can you tell if there's a fruit bat in the bath with you? They hog the soap.

Classic, as to form, but fruit bat? Still, I pushed the reward key.

How does a fruit bat hide in the jello? Are you kidding? It's a fruit bat!

This "fruit bat" fixation might be leading it astray. Reward, punish.

What did the elephant say to the fruit bat? Nothing. Fruit bats can't talk.

Hm. Reward, reward, punish.

How does an elephant get in touch with its higher power? By ringing it up. 

Weak. But a real elephant joke. Success at last! Reward, reward, reward! I celebrated appropriately. The next day, appropriately hung over, I looked at what the program had been churning out.

How can you find an elephant in pi? Follow its tracks.

Can elephants calculate the millionth digit of pi? They don't have to. They'd just remember it.

Wow. How many digits of pi can an elephant remember? About 314,159,265.

OK. But could an elephant calculate pi? Sure. It would just use circular reasoning.

I could see a judicious application of the punishment key might improve the output, but a pattern was beginning to emerge…

Are elephants good at math? Weren't you paying attention just now?

How can you tell if there's an elephant in your math club? Ask it to recite pi. If it's still talking at the end of the meeting, its an elephant. If it says nothing, it's a fruit bat.

So, are elephants good at math? To a degree.

Then I suppose they must be educated? To a degree. Quite a few, actually. It's why they're good at circular reasoning.

How do you keep an elephant from walking in circles? Move the decimal.

How do you keep two elephants from walking in circles? Move it two places.

Can you tell if there's an elephant in your house? Yes. There will be one elephant circling your house. Unless you moved the decimal, then no.

Where do elephants go when they die? To the elision fields.

How do you know if an elephant is saintly? By the radians.

Do all of the elephant jokes in pi reference it in some way? You should ask an elephant. They're good at math, you know.

You see the pattern. It led me to an unexpected and exciting result, mcwbr's first, last and only  theorem:  

All of the elephant jokes in pi allude to pi.

Theorem, I say, because I have found a simple and elegant proof of it, which, however, is too large to fit in the margins of this blog.

Tuesday, March 9, 2010

America’s Nut Factory

Faith had just explained to her class that—even supposing fossils are real—which they aren't—whenever a new fossil is found, that would just mean that now there are two gaps in the so-called fossil record. She paused, savoring the neatness of the argument. The kids were a little young, but they were looking up at her attentively, and none of them seemed puzzled—except, of course, Clara, who raised her hand.

"Yes, Clara. What is it?"

"But, Mrs. Bottom, wouldn't the gaps get littler and littler?"

"Well, I suppose so, but there would always be gaps, wouldn't there?"

"Yes, but…" Ten year old Clara struggled. There was something wrong, but what? "When I walk to school, there are gaps between my steps, but I still get here." Dissatisfied, she bit her lip.

"But footsteps aren't fossils are they, Clara?" Faith looked around the class for support, and several of the kids dutifully snickered. More turned to stare at the heretic in their midst.

Clara knew better than to press on, but she couldn't help it. "Well, what about when we play connect the dots? If they are close together, you can see what the picture is going to be. Unless you just pretend you can't."

"I think you are the one who pretends she can." More snickering. "Besides, it doesn't matter, Clara. Satan put fossils in the ground to deceive us."

Knowing she should just shut up, Clara wailed, "But why would God let him?"

"Now, that's enough, young lady. Are you questioning the will of God? Should I speak to your parents?"

Miserable and terrified, Clara gave in. "No, ma'am." After class, when the other kids were sing-songing "Clara's going to he-ell," she resolved, not for the first time, never to ask any more questions.

Where do they come from, the people who seem ready to promote a point of view by any means, foul or fouler? Fundy school, of course. Compulsion of some kind, and deceit of every kind, are essential to the fundamentalist community. Irrational beliefs cannot be sustained otherwise.

When children are taught such nonsense as creationism, they don't just learn the nonsense. They also learn the bogus arguments offered in support of it. They learn about straw men, equivocation, appeal to authority, to the stick, to the crowd, etc, not as counterfeits to be rejected, but as sound coin of the realm of thought, accepted in all the commerce of their synapses. They become as if brain damaged, almost physiologically incapable of grasping why such argument is worthless.

Such is the fate of those to those who, unlike Clara, are not naturally bright enough to suspect something wrong with the "truths" their preacher, their parents, their Fundy School teachers insist upon. They are the lucky ones. Clara's future could be darker.

It isn't enough just to repress the normal curiosity of a child and stop asking questions. The fundamentalist community cannot brook mere acquiescence. Clara must give service of word and deed to ideas she doubts. She is terrified of hell, and wants to believe, but a sane person cannot believe something merely because she is afraid of the consequences of disbelief. Only a crazy person can do that. If the strain is too great for her, Clara may have a psychotic break—become delusional—just to convince herself she believes what she does not.

There is another possibility: If Clara is smart enough and can bear the strain long enough, she may discover that hell is a lie, that all the things the adults in her life insist she must believe—or else—are lies. By learning, precociously, to think for herself, she can escape their delusions.

This may seem a liberating step, but if Clara would also escape whipping she cannot let anyone know what her real beliefs are. She must be a conscious hypocrite. She must tell people, not what she thinks, but what they want to hear. When you do that, people don't treat you cruelly. Better, they can be talked into doing things for you. The isolation of a child in such circumstances is profound, and her contempt grows with her skills at manipulation. She is a nascent sociopath.

I hope Clara will escape both these evils, with no damage worse than years of therapy can manage. Many do. Many more, I fear, do not.

Fundy School is child abuse. Its product is damaged and dangerous adults, ready to lie for Jesus, or against global warming, or for a faith-based capitalism that would privatize everything but privacy. The only guide to "truth" they can conceive is authority. They admire what they perceive as strength—not character, but wealth, power and thuggishness—and are contemptuous of those they think weak. They are capable of atrocities in the name of Jesus or Mohamed, and incapable of perceiving the contradiction, or caring if they do. Like many abused children, they have grown up to become abusers, with an inner rage that longs for violence, providing they can feel righteous as they kill. So they wait, impatiently, for the Leader to tell them who the Jews are, this time.

Saturday, January 23, 2010

To Vibrate or not to Vibrate

Writing in Salon this week, Glenn Greenwald says we should not look to evil consequences when considering Citizen's Unived v. FEC. "...if the Constitution or other laws bar X, then X is not allowed regardless of how many good outcomes can be achieved by X." Well, that's undeniable.

I fear to disagree with Glenn Greenwald, especially once he has armed himself with the awful might of a tautology. Still, I must. I wish the Ring had never come to me.

It's true judges are bound by the law, and when the law is plain, consequences mean diddly. But when reasonable persons can disagree about the meaning or intent of a law, then consequences are invoked all the time. How else can a decision be made? Flip a coin? Cut for high card? Consult the entrails of a calf?

Chief Justice Roberts, himself, appeals to a fascinating consequence when he says denying free speech to corporations would subvert the "vibrant public discourse that is at the foundation of our democracy."

Really? I hadn't known before that democracy was meant to vibrate. Who knew the founders intended to create a sex toy? I always thought democracy was supposed to be, you know, democratic. That it was to secure human rights. That it should be a conversation among equals. But, apparently, it's supposed to give a relaxing massage.

(Roberts says far more than that, of course, but I'm picking on him. It's my blog. See Page 65 of the pdf)

Since four Justices of the Supreme Court disagree with the majority, and since many more Justices have historically disagreed with them, it appears that reasonable persons can disagree. Furthermore, since Chief Justice John Roberts makes an appeal to consequences—however dubious—he also must think the constitution is less than crystal clear about the degree to which corporations have free speech. And so does Justice Alito. And so, we may assume, do all of the majority.

Very well, then. If four Justices vehemently dissent, and even the majority apparently agree that the Constitution is not clear about the degree to which corporations enjoy free speech, then it must be safe for humble folk to assume that consequences are on the table. The majority, in fact, put them on the table.

So let us consider the consequences:

On one side of the question, democracy might cease to vibrate. On the other, why, it might cease to be. Can any doubt our Republic is now in deadly peril? Corporations enjoy privileges mortals do not enjoy. Corporations can live forever. Corporations can own other corporations. Corporations can amass unlimited wealth and power, and now, thanks to this appalling decision, they can use that wealth and power without hinderance to bend our elected representatives to their will, in spite of ours.

We have already seen a demonstration of it. From the moment Roberts™ re-opened a case that had already been decided on narrow grounds to review the broader issue of corporate free speech, the outcome was never in doubt.

Meanwhile, poll after poll demonstrated that a huge majority of Americans wanted real health care reform, with at least a public option. If our Republic was functioning as it should, the people would have gotten their will. But the will of other entities was imposed: the will of Big Insurance and Big Medicine. Apart from the power they already had—to saturate Washington with lobbyists and "campaign contributions," to create a grievously disinformed astroturf movement and send its dupes howling into town-hall meetings—fell the shadow of the power they were going to wield once the Court handed it to them, and every member of Congress felt the chill. Lobbyists would have made certain they did.

When we are governed, not by the will of the people, but by the will of corporations, then by definition we no longer live in a democracy, but in a corporatocracy, which can, in spite of the plain raison d'etre of the Constitution, destroy every happiness of the people and—oh, by the way—chuck the Constitution into a fire and laugh while it burns.

Still, against that, we must weigh that our democracy might cease to vibrate. One can see how reasonable persons might be swayed by so heavy a consequence.

Saturday, January 9, 2010

Making the War on Terror "Cost-Effective"

When it began, I was naive enough to suppose the "war on terror" would be a spook war, a war of spies—of things that go bump in the night, not boom. After all, the enemy hides among civilians. How else do you get him without harming the innocent? I thought we cared about that. Really. I did.

But wait—there's more. Of course, I thought there'd be propaganda, to polish-up the good old USA brand, but I also thought the war must have an ethical front—a "let's stop doing things that justifiably piss people off" front. Well, it would help the propaganda, wouldn't it?

Let me know when you're done giggling.

But what we did instead was make it a shooting war. What we did instead was invade other people's countries and then have to explain how it is we are not occupiers—while manifestly occupying them. What we did instead was "Shock and Awe." What we did instead was drop bombs on crowds of innocents in case some of them might be bad guys. And as for propaganda, our brilliant president advertised all of this as a "Crusade."

Surely it would have been cheaper just to pay people to join al Qaeda?

Wherein lies a hint. The fact is, from a certain perspective, spook war is just not "cost-effective." Defense contractors rake in oodles of cost-effective from a shooting war, but spies? Chump change, by comparison.

I have an app for that, a sort-of reverse follow-the-money: Deploy the money, and the strategy will follow. We must make spook-war "cost-effective." After all, the greatest country in the world should have the greatest spies and assassins—James Bond Ninjas, equipped with the best and—here's the key—most expensive gadgets.

Such as the SG17a GPS-guided, ultra light weight smart grapple: $80M each. And SG17b self-destructing rope for same: $400,000 a foot.

The Ninja Assassin Wardrobe includes the NAW-P stealth pajamas, the -T stealth tuxedo, and the -L stealth leisure suit @$20M, each. The -S laser-guided shoe tree is a bargain at only $17M.

For infiltrating the home of a terrorist who is hosting a children's birthday party (it could happen), the NAW-C clown costume, with stealth squeaky shoes and exploding hair, and the AP-1 attack pony. Total cost: $800M.

R&D should be "cost-effective," as well. Imagine the development of the SG17a smart grapple:

Because of all the other gear he or she must carry, it is naturally desired that a ninja assassin's grapple be collapsible and as light as possible. So a new carbon fiber composite is developed. Then it is discovered that it is, in fact, very difficult to throw a two ounce grapple with any accuracy or distance. After much discussion, a JATO pack is added. But the JATO pack is too heavy. A spin-off project is launched to develop a one ounce JATO pack—which turns out to need in-flight refueling.

Thinking outside the box, someone at DARPA equips a standard grapple with a pulley, that can be thrown in the usual way and then used to hoist the smart grapple into position, but this is not deemed to be cost-effective, and the researcher is let go.

We can imagine similar difficulties would be encountered by the project to develop a silent squeaky shoe.

The bottom line is, if we can get the cost of fully-trained, fully-equipped operatives up to around two billion dollars, each, I think we can get the defense industry to back a better way of fighting terrorists.

Or, more likely, we'd just create a new cost-effectiveness stream. I guess I'm still naive.