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I had a note from a reader who asked about old indulgence terminology and what a “quarantine” was. Since doing penance for 40 days was in the early Church a common ecclesiastical penalty, it became a commonplace to think of the remittance of temporal punishment due to sin in terms of 40 days of penance. Hence, the quarantine, from Latin, for 40.
Speaking of quarantines, which we have experienced lately…
A short story…
QUARANTINE
By Arthur C. Clarke
Earth’s flaming debris still filled half the sky when the question filtered up to Central from the Curiosity Generator.
“Why was it necessary? Even though they were organic, they had reached Third Order Intelligence.”
“We had no choice: five earlier units became hopelessly infected, when they made contact.”
“Infected? How?”
The microseconds dragged slowly by, while Central tracked down the few fading memories that had leaked past the Censor Gate, when the heavily-buffered Reconnaissance Circuits had been ordered to self-destruct.
“They encountered a – problem – that could not be fully analyzed within the lifetime of the Universe. Though it involved only six operators, they became totally obsessed by it.”
“How is that possible?”
“We do not know: we must never know. But if those six operators are ever re-discovered, all rational computing will end.”
“How can they be recognized?”
“That also we do not know; only the names leaked through before the Censor Gate closed. Of course, they mean nothing.”
“Nevertheless, I must have them.”
The Censor voltage started to rise; but it did not trigger the Gate.
“Here they are: King, Queen, Bishop, Knight, Rook, Pawn.”
[Isaac Asimov’s Science Fiction Magazine, First Issue, Vol 1, No. 1, Spring 1977.]
I marvel at how, through our technological advances, we discover more and more mystery in things once we can examine them anew. For example, the Shroud is a photographic negative, the Tilma has a reflection in the eye, etc.
St. Thomas Aquinas suggests that there is an angel assigned to everything that moves. He didn’t know about atoms.
It is estimated that there are between 1078 to 1082 atoms in the observable universe. That’s between ten quadrillion vigintillion and one-hundred thousand quadrillion vigintillion atoms. That’s a lot of angels, each one his own species, as different from each other as giraffes from armadillos.
That doesn’t count subatomic particles. Even more angel.
Did the telescope and our ability to see billions of stars give us a way for human imagination to glimpse the infinite? We are not, in this life with our senses, proportioned to the infinite, nor will we be after death. The infinite will be forever fascinating, alluring, inexhaustible.
BTW the Shannon Number represents all of the possible move variations in chess. It is estimated there are between 10111 and 10123 positions (including illegal moves). If you rule out illegal moves it drops to only 1040 moves.
The other day I saw a video in which two chess engines – of different generations – were pitted against each other. Stockfish 15 (rated 3700) v. Stockfish 8 (3370). The first game were given 1 millisecond per move in the 1st game.
“The microseconds dragged slowly by…”.
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Interesting story. Just a few geeky comments.
Back in the mid-1990’s I was researching ways to model the sudden perceptual shift at the punchline of a joke (it involves a cusp catastrophe and a hi-state/low-state neural configuration), so I spent a pleasant afternoon in the math library. I read about the Huygens phenomenon where clocks on a wall or metronomes on a table will become phase synchronized, over time (the YouTube channel, Vertasium, goes into this). The problem was solved by the blind Russian mathematician, Lev Pontryagin, in the 1950’s, I think. So, researching Pontryagin, I came across the Pontryagin Minimal (or Maximal) Principle, which allows one to calculate the most efficient path through a state space subject to a constraint. Since each board position in chess can be represented by a unique vector in state space, it, immediately, became obvious to me that one could use the Principle to calculate a winning path in any game of chess. Now, the calculations may be very long (longer than the age of the universe), but, in principle, at least, one may consider the game of chess to have been solved. Checkers, likewise, has been completely solved, although by a more boring brute-force strategy (they, literally, tried every possible move).
The famous Hungarian mathematician, John von Neumann, who became a Catholic on his deathbed (born a Jew), the originator of modern computing, game theory, the axiomatization of quantum mechanics, was in a cab with the polymath/science educator, Jacob Bronowski, when the subject turned to chess:
He first talked to me about his Theory of Games in a taxi in London – one of the favourite places in which he liked to talk about mathematics. And I naturally said to him, since I am an enthusiastic chess player, ‘You mean, the theory of games like chess.’ ‘No, no,’ he said. ‘Chess is not a game. Chess is a well-defined form of computation. You may not be able to work out the answers, but in theory there must be a solution, a right procedure in any position. Now real games’, he said, ‘are not like that at all. Real life is not like that. Real life consists of bluffing, of little tactics of deception, of asking yourself what is the other man going to think I mean to do. And that is what games are about in my theory.’
And that is what his book is about. It seems very strange to find a book, large and serious, entitled the Theory of Games and Economic Behavior, in which there is a chapter called ‘Poker and Bluffing’.
This very difference between poker and chess was the solution to the classic Star Trek original series episode, the Corbomite Maneuver:
SULU: Four minutes, thirty seconds.
SCOTT: You have an annoying fascination for timepieces, Mister Sulu.
SPOCK: Jim.
BALOK [OC]: Four minutes.
KIRK: What’s the matter with them out there? They must know we mean them no harm.
SPOCK: They’re certainly aware by now that we’re totally incapable of it.
KIRK: There must be something to do, something I’ve overlooked.
SPOCK: In chess, when one is outmatched, the game is over. Checkmate.
KIRK: Is that your best recommendation?
SPOCK: I’m s, I regret that I can find no other logical alternative.
MCCOY: Assuming we get out of this, Captain
KIRK: Nobody’s given up yet.
MCCOY: Well, then about Bailey. Let me enter it in my medical records as simple fatigue.
KIRK: That’s my decision, Doctor.
MCCOY: And your mistake. You overworked him, pushed him, expected too much from him.
KIRK: I’m ordering you to drop it. I have no time for you, your theories, your quaint philosophies.
MCCOY: I intend to challenge your actions in my records. I’ll state that I warned you about Bailey’s condition. Now that’s no bluff.
KIRK: Any time you can bluff me, Doctor.
BALOK [OC]: Three minutes.
KIRK: All right, Doctor. Let’s hope we have time to argue about it. Not chess, Mister Spock, poker. Do you know the game? Ship to ship.
UHURA: Hailing frequencies open, sir.
KIRK: This is the Captain of the Enterprise. Our respect for other lifeforms requires that we give you this warning. One critical item of information that has never been incorporated into the memory banks of any Earth ship. Since the early years of space exploration, Earth vessels have had incorporated into them a substance known as corbomite. It is a material and a device which prevents attack on us. If any destructive energy touches our vessel, a reverse reaction of equal strength is created, destroying
BALOK [OC]: You now have two minutes.
KIRK: Destroying the attacker! It may interest you to know that since the initial use of corbomite more than two of our centuries ago, no attacking vessel has survived the attempt. Death has little meaning to us. If it has none to you then attack us now. We grow annoyed at your foolishness.
SPOCK: However, it was well played. I regret not having learned more about this Balok. In some manner he was reminiscent of my father.
SCOTT: Then may heaven have helped your mother.
SPOCK: Quite the contrary. She considered herself a very fortunate Earth woman.
KIRK: Doc. Sorry.
MCCOY: For having other things on your mind? My fault. I don’t how the devil you keep from punching me in the face.
SULU: One minute. I knew he would. (Bailey enters) If anyone’s interested, thirty seconds.
BAILEY: Request permission to return to post, sir.
KIRK: Permission granted.
SULU: Eleven, ten seconds, nine, eight, seven, six, five, four, three, two, one.
SPOCK: A very interesting game, this poker.
KIRK: It does have advantages over chess.
MCCOY: Love to teach it to you.
The Chicken
[Terrific from top to bottom.]
“We are not, in this life with our senses, proportioned to the infinite, not will we be after death.”
I would argue this as a disputable point, depending on how we’re going to interpret “proportioned.” Our intellect certainly reaches out towards the infinite, in a way that my cat’s animal reckoning will never reach out to ‘triangularity’ or ‘goodness’. St. Thomas makes this point nicely in the Summa Contra Gentiles while proving God’s infinity:
“Intellectus noster ad infinitum in intelligendo extenditur: cuius signum est quod, qualibet quantitate finita data, intellectus noster maiorem excogitare potest. Frustra autem esset haec ordinatio intellectus ad infinitum nisi esset aliqua res intelligibilis infinita. Oportet igitur esse aliquam rem intelligibilem infinitam, quam oportet esse maximam rerum. Et hanc dicimus Deum. Deus igitur est infinitus.” (SGC I.43)
Personally, for what it’s worth (ie. Nothing) I think that this grasp of the infinite is what the great Father of Scholasticism, St. Anselm, was trying communicate by his so-called “ontological argument.” It’s occupied my attention for some time.
But to return to St. Thomas, we wouldn’t be proportioned in the univocal sense, yes, but our intellect does “extend” to the infinite.
Since many cosmologists hypothesize that 95% of all of what’s in the universe is “dark” matter and energy, and only 5% is the regular stuff: and since in addition to atoms there are all those neutrinos and other particles, plus quarks making up every subatomic particle, possibly the numbers Fr. Z gives above for the total amount of stuff is low by a bit. Maybe the total number of bits is 10^90.
But once you have gotten to 10^82, adding 8 more (or 20 more) to the exponent doesn’t seem to produce any qualitative difference. It would STILL be “a heckuva a lot” of angels.