Wednesday, December 24, 2008

The Math of America.

May I share some mathematical models of America with you? They won't be elaborate or complex -- more like intellectual doodling, but I hope they will be fun/serious. For what it's worth, I do have a Doctorate in math, but I’d like to limit things to a couple of mathematical snapshots of America.

(1.) This is the concept of reductio ad absurdum which is intimately related to something called "proof by contradiction". Not all mathematicians like this proof, since its "indirect", but sometimes that's all you've got.

It works, briefly, like this. Let's say you're convinced that A, B, and C are true propositions, but you just can't seem to prove D in the same way you proved A, B, and C (i.e., "directly"). So sometimes you fall back on proof by contradiction which works like this (be warned, it's a weird way to prove things).

You say, well what if we assumed D was "false" and then rigorously derived what that would imply. And IF D was false (remember, you want to prove that it is true), and IF this implied that A, B, or C was false (which you "know" are true), then (voila!), you've just proved that D is true. Sounds a little like a slight of hand, doesn't it, but believe it or not, this kind of reasoning was the origin of non Euclidian geometry (another story).

OK, now to politics.

I'm leaving out some steps here (which students always appropriately resent), but the above is all of a piece with something called the "contrapositive". You will see the similarity as we proceed and also see that this analysis relates perfectly to the fascist right wing (dem & pug equally) "model" of human existence.

But first to the logic. The contrapositve of A implies B, is Not B implies Not A. Indeed these two conditional statements are logically equivalent. Here's how it works: If you're in Albuquerque, then you're in New Mexico (a conditional statement which is clearly true). Now for the contrapositive: If you're Not in New Mexico, then you're Not in Albuquerque.

These can (and frequently do) take the form of syllogisms (at least 2 premises and a conclusion) and some of these syllogisms go all the way back to Aristotle, who even though he was totally wrong about practically everything in the physical world (note Galileo Galilei -- who was punished terribly for sticking a pin into Aristotle's TOTAL misunderstanding of motion, etc.), he had it all together when it came to logic. Indeed, Euclid based his Elements on Aristotle's insightful logic.

Well, I hope you're still with me (and even enjoying things a little?), so we can now talk about dem/pug fascism (dem/pug, because after the 2006 Congress of dem Republican, we now know that right wing dems = right wing pugs).

Here's the conditional statement. IF the Bush/fascist/Republican/neocon agenda was truly in touch with the social reality of human existence, than our economy would be great, our children wouldn't be massacred in money cow oil wars for the elites, Mother Nature wouldn't be gang banged by Texas energy corporations, our retirements would be solid, out heath plans would be solid, and American science wouldn't be under funded into an intellectual embarrassment (for the first time in American history!), and Wall Street would be a raging bull.

Formally put, IF A, then B.

But, remember Not B implies Not A, and since the United States of America is now wall to wall "Not B", the logical/mathematical implication is clearly Not A, i.e., the Bush/fascist/Republican/neocon take on human existence is FALSE.

Said more poetically, give a fool (why does president pinhead come to mind?) enough rope and he will hang himself.

Jesus put it even more succinctly: "Ye shall judge them by their fruits". And the left over fruits of these last eight years are rotten with failure.

Hey, we gave A a chance (eight years of a chance!), but the thumb of deductive logic is pointing straight down.

(2.) Shall we try another one? I'm not sure how I'm going to bring this one off, but it has to do with one of the most powerful and subtle concepts in the whole of mathematics, and this concept (or truth, since it’s more than a mere concept) is that of the Limit of calculus (or more generally, analysis).

Now even Newton was fuzzy about the limit (not about much else!), and this led to a very rare event in Western History. The event is that a contemporary of Newton, an exceedingly bright philosopher/theologian named Bishop Berkeley, correctly rapped Newton's knuckles about what Newton called "infinitesimals" (sorry, but that's a very long story), so let's try to be "intuitive" about the limit, even though that's often a mathematically slippery way to avoid really taking care of business.

Here's an example. Imagine the following function: y = f(x) = 1/x, and then ask yourself what does 1/x "get infinitely close to" as x "approaches infinity”.

There are all kinds of fancy notation for this, but I'm deliberately avoiding it since I don't want to reinforce what I believe to be the most common misunderstanding of mathematics. And for a change, this is easy to put into words.

*drum roll*

The most common misunderstanding of mathematics is confusing the "reality" of mathematics (a big and much argued topic) with the "symbology" of mathematics. And I confess when I was learning this subject, I too fell prey "quasi consciously" to that belief. After all, the notation was so impressive and "different" that it seemed like what I saw on the page WAS mathematics.

However, in due course I outgrew that belief (as do nearly all mathematicians -- I assume), and realized a better way to understand the symbology was to see it much the same way you look at musical notion. After all, no one thinks that notation "is" music, because they understand musical notion is basically "directions" for you to follow, and if you follow the directions well, "something happens" which we call music.

Actually, almost EXACTLY the same thing is true for mathematical notation. The notation is telling you something to do "in your head" and if you carry out those instructions properly, you will hear (can we be poetic again!) "mathematical music". In short, the notation is not the "real thing"; rather they are instructions to follow so you have the opportunity to experience the real thing. It's very intellectually liberating to get this straight, so you stop (in the words of my former high school debate coach) putting the emPHAsis on the wrong syLLAble.

Well, I keep going off on tangents, don't I? I guess my only excuse is that this is fun for me and I increasing suspect I really don't WANT to get back to politics and all that b.s.

However, the limit thing is so beautiful and powerful; I'm determined to make a connection between it and the world we wake up to in the morning.

Here's an "intuitive" definition of the limit. It's giving you an exact description of a place you'll never reach, and even though that should be qualified, let's run with it anyway. For example the limit of 1/x as x goes to infinity, is zero (we never said what it was before). Think of it like a plane in a science fiction movie that "approaches" the runway, and indeed gets unimaginably (literally) "close" to the runway, but never makes contact.

You see, that is what is happening to 1/x as x keeps getting larger and larger. 1/x will NEVER "equal" 0 (in fact, 1/x = 0 is a contradiction because it has no solution), but the LIMIT of 1/x as x gets huge is zero. When x equals a billion, you can take it to the bank that 1/x is very, VERY close to zero -- even though it is not and never can be zero.

Finally, the limit concept is the soul of calculus and since calculus was the supreme mathematical tool of science for a couple of centuries, it is clearly a very "deep" concept. Sometimes I tell my students the limit is not the Cheshire Cat; it's more like the "smile" of the Cheshire Cat. For those of you who know calculus, you also know that differentiation and integration are simply two different applications of the limit.

Hence, all roads in calculus lead to the limit -- which, notice involves infinity ("infinitely close") which is the real reason it is such a profound intuition.

OK, time to relate the "limit" to human, social existence.

Arguably, politics is not only more part of the problem than the solution, it IS the problem, since it promises much, but always delivers next to nothing. Said more exactly, "politics" is the social/political game created by the elites to seduce and control the human race, and thus it all comes down to two choices:

(a.) We can "play" this game (and ALWAYS lose, since all the game rules were created by the elites). For example, for many (most?) of the people who elected Barrack Obama, it looks very much like the cards were stacked (again!) and we're getting, not the campaign rhetoric Obama, but an elite bought and paid for Obama. However, he gets his hundred days, and then we will know everything.

(b.) The other option is to "transcend" the game. But what does this mean? Well, it almost certainly means a kind a consciousness quantum jump into a different social dimension. Notice, "politics" isn’t even mentioned in this dimension, since the political game (in the words of a very wise Zen Master) is like trying to wash off blood with blood. And if and when a critical mass of Americans (or more generally, human Earthlings) get this straight, the game will no longer have any meaning. In short, it will be like realizing that if you're trapped in a table card game which is hopeless, all you have to do is kick over the card table.

You see, that's the second option. Kick over the card table of the elite game. Which means what? It means that the "will of the people" overwhelms the "will of the elites" (and their army of dem/pug puppets). And “overwhelm” here means DOING WHATEVER WE HAVE TO DO to take back our county, planet, and lives from the gaggle of national/international vampire elites (aka, the “Have’s”).

Another Zen saying: If you don’t get it from yourself, where will you go for it?” Hence, screw politics. Critical mass has been reached. It’s time to revolt (God willing, non-violently, but . . .).

The "limit" in all this, to use it very loosely, is what the elites everlastingly dangle in front of the working class (or the middle and lower classes, i.e., 98% of the human race). It's the pseudo payoff of playing the political game. But that payoff, however much we sacrifice and work to play the game (just as we did for Barrack Obama) is something we "never quite reach". It seems like we're getting closer (we elected Obama), but like touching the runway for the plane, it never, NEVER happens.

So for us, it's not the smile of the Cheshire Cat -- it's the fascist sneer of the elites and their dem/pug puppets who well know their political game can never, never be won.

That's why they invented it.

And that’s why we should immediately stop playing it. And do what? Well, that’s what God and/or evolution gave us the internet to work out.

I’m outta here after this one, but one of the most brilliant philosopher’s of the 20th Century, Ludwig Wittgenstein, pointed out that many problems which can’t be “solved”, can be “dissolved”. This exactly relates to what we’re talking about now, since even though the political problem is “insoluble”, (a lose/lose game for the middle and lower classes), it is “dissolvable”. And we dissolve it by simply ceasing to play the lose/lose game of “politics”.

Our birthright intelligence, conscience, and creativity are more than enough to transcend politics, so what are we waiting for? Playing the political game is a form of suicide. Transcending the political game is a form of liberation.