Recreating (and advancing) pk’s censored domains: Macroinformation.org & Knatz.com / Teaching / Society / Survival / Intelligence /
@ K. 2008 07 01
The Hindus love big numbers. Everything happens in the trillions. Christians for a couple of millenia have bandied around big concepts, many of which are just beginning to get thought out with any responsibility: concepts like infinity. God’s knowledge is perfect, his wisdom is infinite. So is his power. So is his love.
Only recently, and only among mathmaticians, and scientists (closely related), has the antonym of infinity been at all developed: a concept I term finity. With finity comes limits. The Americas may be big but late Pleistocene colonists from Asia, arriving north of Alaska, reached the southern tip of South America within a thousand years, driving most big animals to extinction as they went. European colonists hit the Atlantic coast in 1492 and the ’49ers were stealing Sutter’s gold by 1849, stripping timber and buffalo as they went, killing Sutter’s cattle when they got there. In the last centruy we omnivores burned up half the world’s oil and are swiftly beginning to learn what the cost of trying to get at the other half will be.
I doubt that there were many mathematicians, or scientists, among the ’49ers. And conservationists can’t compete against the huge budgets of the lobby-clogging despoilers. The corporations have huge advertising bugets, lawyers, and sycophants. They can keep telling the people There are no limits. Though the despoilers may see their own death coming swiftly they also see that they can get ever more rich even more swiftly. The hell with grandchildren, let’s go out with a bang, and an obscene bank account: think of all those zeros: they belong to ME!
Meantime, as I try to explain in the previous post, I see huge power in the finite.
Finitude, finite, limits, imperfect … Scribble
We have sight, we can see this, and that. But it does not follow that we can see anything? Some individuals see things others don’t. Maybe what they see is green cheese in the moon, maybe they’re Newton and what they alone see is gravity.
We have speech, we can talk. It does not follow that we perceive all messages, or understand all we do perceive.
And we certainly do not hear more than a fraction of what’s said. And we live in cultures whose nature it is in every example to avoid perceiving certain things. We dress so we don’t see the girl’s vulva, the boy’s erection, the girl’s flatness, the boy’s limpness. We know such things exist, but reserve seeing them for rare occasions. But there are other things the culture conceals that we don’t know are there, and only a Darwin or a Newton gets to see.
I believe but can’t prove, especially not in this hell-bent society, that there are many many more Darwins and Galileos and Abelards and Tuckers than Time Life tells us about.
But even ignoring ideas that are not thought and facts that are not perceived, even ignoring ideas and facts that are not repressed, how many ideas and facts that are expressed can be heard?
I read. I read a great deal. But every day more things are published than I can possibly read. Every year I read many old novels and several new ones, but if I read constantly I could not read every novel published.
or see every movie made. There: just take movies. If you see every movie released by Hollywood, how many are you missing released by Bollywood? By Japan? By Mexico?
A mere two thousand visible stars in the earth’s night sky looks like an “infinity” to many of us. How could we possibly perceive the “hundred billion” stars we are told are in our galaxy? And if our galaxy evaporated, there are hundreds of billions o other galaxies: that “science” can see! And science knows perfectly well there could vastly more that science doesn’t see.
And I assume that there is vastly more than science could not see, nor could any mystic, no matter how hard it tried and no matter how much time it had to try.
Newton talked about picking up a few pretty shells along a vast sea shore. Yes, yes. Even a caveman of indifferent intellect will notice and perhaps pick up some shells along the shore. But I love Newton’s sense of how relatively few he has picked up; and I hate the baseless assumption of pop culture that we are making significant progress and can gauge how much shore line remains to examine.
2008 06 01
I have something to say here. It’s not easy. If I thought my point was already generally understood I wouldn’t be bothering. I am not at all happy with my draft so far. But, as is my habit, I’ve already added it to Knatz.com. Taking it down for polishing would be more work than the polishing. Glance at it. If you think you know what I mean, you probably don’t. If you do, help out, damn it. Either way, check back. I may have found a way to say it so it works.
Here’s a generalization in the meantime: I suspect that the human intellect has only begun to penetrate the implications of the state of being finite. I believe we had to fumble and bumble with the concept of infinity first. Infinity is easy to be wrong about, so is finity.
Playing various forms of solitaire not just as a game but as an exercise in probability-calculation is helping me to see some small areas of the possible.
Finitude constrains probabilty, and with it, possibility.
It’s only in the last century or so that human thinking has become at all sophisticated in our concept of “infinity”: and only subsequently can we begin good thinking about the complement, the antonym, “finity.”
(If I ever believe that my own thinking on this subject approaches worthiness, I will move this module among my Thinking Tools; but I’m just exploring, an amateur exploration, and I start it in my Social Epistemology section (where some fuzziness, a shot not dead bulls eye, is more tolerable).)
I hope to find (or make) time enough to review the concept of “infinity” here, touching on Christian theology, and arriving at Georg Gamow. The concept of “finity” I review by appealing to the visitor’s sense of its near total absence: until recently. In never heard the word finite until Professor Aaron Sachs used it repeatedly in physics class. A half-century later I’ve finally produced enough fertilizer to find it sprouting.
What I say here will relate very much to ideas already covered among my Thinking Tools: ideas such as spectrum, middle, edge … especially to what I’ve said about human perception functioning best where myriad things can be grouped into small groups. A human can easily say: “There’s a goose”; “there are two geese,” “there are three geese” … We are not at all good at saying “There are nineteen geese”; There are four hundred and fourteen geese” … We take one step toward it when we can say, “There are three geese, and right by them four more, that’s seven geese.”
Georg Gamow reviews that all peoples can count to three. The concept “zero” is recent. Only civilized cultures have words for “four, five, six …” Any human can group a one, a pair, a trio; few can group eight and thirteen and seventeen … I know there are those who can; I know I can’t.
And I know that even geniuses at precisely these sorts of manipulations, Ramanujian … or Feynman — are routinely mis-estimated by their (supposed) peers. (Feynman was assumed to be doing digital calculations at unprecedented velocities when he was actually doing analogic approximations: his models were doing the calculating for him!)
Anyone can count, rapidly and reliably, to three. We can all group a trio and a quartet. Some of us can stretch to a pair of fours: thereby perceiving “eight” as a group. Maybe there are those who can see eleven, or thirteen. At age sixty-nine my mind can almost see thirteen: thirteen original “states”; thirteen cards in a suit: Ace, deuce to nine, Jack, Queen, King: thirteen. Thanks to Sudoku I’m now, recently, damn good at grouping nines: 3 x 3 … 9.
Any of us has, many times, grouped a quartet of thirteens: the full deck of playing cards: any time we’ve played poker, bridge, gin, or … solitaire. That does not mean we can group them well or at once. Card counters work at it, or something analogous.
Look how quickly, and in how many dimensions, groups can propagate: Ace, pair of Aces … four aces. Four suits. Thirteen cards, four thirteens = 52. Four people for the 52 cards, deal thirteen to each. Try dealing the same distribution of four hands of thirteen cards to many groups of four: fill the church basement with bridge tables and see how well the groups play a given set of distributions.
Johnny von Neumann, Richard Feynman … could follow far into combinations of those figures; I passed my own ability sometime back. But in jail I played a lot of solitaire, taking the occasion to think and think, the best I could, about what was at hand, among other things: and what was at hand was four suits of thirteen each. Now I can almost group fifty-two for whole fractions of a second!
In jail I also blessedly played a Lot! of chess. No, I am not changing the subject. Chess is played on a board of eight rows by eight columns. That’s sixty-four squares. The four center squares are key. The back eight squares are key. The forewardmost eight squares are key. The four corners are key. Three is key: there’s the king: that’s one. There are also major pieces, minor pieces, and pawns: another three. The one king moves one space: in any direction (in the 2-D grid). The knight adds fractions of a third dimension … since the knight can hop Over other pieces. I’m not, not in this draft, going to attempt to detail all ones, pairs, trios … in chess. Just realize: the better the player you are, the better you will be able to realize — how many patterns of potential force the player must see on the board: for himself, and for his opponent. For its first move, my knight can go there, or there. Once there, my knight can go there, there, there, or there. Meanwhile my opponent’s bishop can go there, there, there, his queen threatens there, there, there, or there, there, there …
By the time you’re a few moves into the game … Wow!
A myth about chess has it that the mathematician gave the game to the Shah. The Shah said, “Thank you, name your reward: land, jewels, gold … my daughter …” The mathematician said, “No, thank you: just put one grain of wheat on the first square (which we may call A1), then two grains of wheat on the second square (which we shall call B1) …” And few see that 1 + 263 = more wheat than the civilized world produced in a couple of millennia.
The number of possible distributions of the 52 cards of a bridge deck is 635,013,559,600! That’s almost two-thirds of a trillion!!! (Still: that’s finite; not infinite!)
Wait, I’ve already make a mistake here in scribbling this draft which I hope not to repeat in the next if I can reorder things: What I want to say foremost here does Not require super-human calculation. Let me try again from here: two steps (two!: a pair!):
If we know how many legs an insect has, we know that after we’ve counted six we don’t have to wait till hell freezes to stop counting. If we’re examining spiders, the number is eight. We should always look for seven on an insect, or nine on a spider: we might have something that is Not an insect, Not a spider; but we don’t have to keep looking till the glaciers melt. Six: that’s a full set. Eight: that’s a different full set.
If the whole deck has been dealt four ways, check, but expect there to be thirteen cards in each hand.
Now, here’s my revelation of 2007 (in this respect at least). At FDC Miami I was shown a form of Solitaire I had never seen before. I liked it. I swiftly became good at it. And I became aware of something I was thinking that helped me to become good at it.
Once you hear it you may think it’s obvious. Perhaps; but it’s implications are anything but obvious: except slowly, over time, to a few. The cards are finite.
If you’re looking for the ten of hearts to go under the Jack of hearts, know that the card has to be there: if you started with a complete deck. Every deck of bridge or solitaire cards has a ten of hearts: just one.
My beloved computer “solitaire” game of “Shanghai” uses a mahjongg assortment of tiles. The assortment always has four Season tiles, four Flower tiles, four Winds, Four Dragons. It also has double sets of Characters, Dots, Bamboo … In other words, once you learn the finite components then you will know, if you see two TwoBamboo, then you see all of them, there are no more.
In poker if you have four aces, that’s all of them. Don’t look for a fifth. (Or, do look for a fifth: if you find one, you’ve found a cheater!)
In my solitaire game, the ten of hearts, could be one of the face-down cards. We start with three groups of four of those plus another group of three, the wildcards. The total of hidden cards is thus 15. The total of cards born showing is 52 – 15 = 37. It’s more probable that the ten of hearts is one of the 37 than it is one of the 15. Twelve of the 15 you may look at at any time; the remaining 12 can only be turned over by removing all of the cards under it. If you don’t see the ten of hearts, fine, look for some other move. If you don’t find any other moves anywhere on the board, look for the ten of hearts again. Look for each of the possible move cards until you find one. The probability that there is one is much higher than the probability that there isn’t.
When you really really find none, then you’ve lost that game. But it will serve you right, give you ulcers, if the moment you give up, some kibitzer says, “Why didn’t you move the ten of hearts: it’s right there, fourth card down, column three!”
How many chances of salvation can we ignore before there are none left?
What the hell are you talking about, pk? Of course those things are true. Everybody knows those things are true. It’s obvious.
No. The implications are not obvious. A child will not know that the ten of hearts has to be there: until he sees it; even if told that it has to be there.
The virgin’s boyfriend urges her to loosen up, to open up. She does. A month later, she realizes: she’s not pregnant! Her parents, those priests, her society … were lying to her! She fucked! and she didn’t get pregnant. So she and her boyfriend fuck some more. A month goes by: she’s still not pregnant! So they fuck some more. … By the time she’s eighteen she’s pregnant with their second kid. He drops out of college to marry her. And welcome to life.
Nature gives virgins a few freebies. Even non-virgins are sterile: temporarily. It’s a trick. Nature knows that temptation will overcome resistance, become a habit … and then, sterility yields to fertility. Otherwise Adam and Eve’s kids would have been waiting till they were forty and members of the Country Club before breeding. No, nature doesn’t give a damn about your luxury; nature cares only about your breeding.
We’re tricked by numbers. We’re tricked by the finiteness of things that are too many for us to calculate easily. How many cigarettes can I smoke before I get cancer?
How much oil can we waste before we have to conserve?
How many chances of salvation can we ignore before there are none left? and we find that we are damned?
Well, maybe a lot, because there is no salvation and no damnation. But that’s not right; because I didn’t mean “salvation” literally: how about it I mean “survival”? How many good lessons from geniuses can we ignore, because they interfere with our fucking around for free, before it’s too late for good lessons from geniuses we’ve knocked into the gutter.
We were warned, but we kept fucking. Now there are five going on six, going on eight-billion of us.
Once we said that God’s powers were “infinite.” We didn’t mean much more by than that God was more powerful than you, me, or the volcano. (That’s because we hadn’t understood yet, still don’t, what a real volcano can do! (Check out super volcanos. They can sterilize a whole continent! One’s due any time now.)) Once we thought that light speed was infinite. We thought that when we still didn’t have any crisp understanding of “infinite.”
Once we learned that the velocity of light was not only finite, but specifically 186,000 miles per second, we still couldn’t tell the difference between 186,000 miles per second and “infinite.”
Meantime, someone at Jesup, a with some facility at math, taught me still another form of solitaire: Free Cell. I watched my friend play one game without understanding what he was showing me. But once at a half-way house, with access to a PC and a version of FreeCell packaged with Windows, a little fumbling resulted in my seeing what my friend had tried to show me. And my same lesson applies.
It’s not normally hard to find some move; but it’s very hard, and requires patience, to try to find a move that still leaves room for more moves, or, better yet, that creates room for more moves.
Now I’m amazed at my winning percentage at FreeCell. On a PC my percentage will be close to 100% because on the computer you can try alternate paths if you keep saving the game and restarting it: till you solve it.
But I win a lot dealing the cards out the old fashioned way, but then being cautious, trying to read ahead: as I do when playing chess.
Bobby Fischer could read ahead like nobody before him. Along comes IBM’S Big Blue which had hold enormous numbers of possibilities in memory while calculating every more, and very fast. Thanks to the computers, Karpov had a heavier set of weights to work with than Bobby ever had. Karpov has pushed his ranking way past anything even Bobby could have guessed.
But it’s still finite. Bridge, chess: the possibilities are finite.
Well, this first draft seriously needs a second. I’ve hinted at my points without making them clear. Oh, the point may be clear, but the points as logically imperative are not clear.
When I come back I’ll try analyzing some of the probabilities of FreeCell that, once seen, make it far less amazing than is at first apparent how seeming impossible hands will eventually yield to analysis. Right moves can be found where none had been apparent.
several drafts combine here, I hope I’m not scratching out anything important.
This damn app keeps “correcting” my spelling: when it doesn’t know the word I’m using / inventing. I correct it back, it “corrects” it again! These blog hosts work for the establishment, the dishonest, non-too-bright establishment. Study Erhman: the priests continually correct God.
PS I love the graphic above of Cupid embracing the reclining nymph, holding her breast. Note that the source of the pic styles itself “badcatholic”: seems to think it’s talking about God: that is, the Christian (RC) God. Uh, I don’t think so: God is a child? carries a quiver? The Roman Cupid is “infinite”? Like so many things, 99% gibberish.