Cain’s “conception, gestation, and birth all occurred within” the year 1945 (his words in quotes).The thing about numerology that makes it so attractive -- to intelligent people especially -- is that all numbers share eerie relationships with each other. The ancient Greeks were completely fascinated with the relationship of one number to another, so much so that one of the most fundamental questions in ancient Greek metaphysics is whether the most important fact is that a thing is, or that it is one. What do you mean to say that a table is one thing? It has four legs (say), and a top in addition; it has both a shape and a color; it has a massive number of molecules; why do we unify all that into a single thing?
1945 was also when Reader’s Digest published a version of Austrian free-market economist Friedrich von Hayek’s The Road to Serfdom, one of Cain’s favorite books. (A few other fans of the book: Rick Perry and Glenn Beck.)
Assuming Cain does become the 45th President of these United States, he would be inaugurated in 2013, the same year he will be celebrating his 45th wedding anniversary.
On one of the last legs of a campaign trip Cain once took, he was traveling on Flight 1045 at an altitude of 45,000 feet.
And last but by no means least, it is hard to overlook the fact that Herman Cain’s now-famous 9-9-9 tax slogan, shares a special relationship to the number 45 — just slice it down the middle, add the two numbers together, and, voilà!, you have yourself a nine. (Proof: 4+5=9)
Does that unification have any real weight, or is it just for our convenience? Before you answer, think not of a table but of a person. They also have many parts, but a single consciousness; and though they may lose (and may replace) some parts, once that single conscious nature flees at death, what remains behind is not a man at all. It doesn't make sense to say that they aren't 'really' a person while they are alive; so that unifying force has undeniable power.
Mathematical truths are the canonical example of truths that we can have a priori. It's hard to imagine why you would have occasion to ponder mathematical truths without actually experiencing 'two sheep' or 'a circle,' but in theory you can work out all the details without having to have the actual experience. Certainly it is true that you can work out the systems without direct experience of every aspect of the system -- you can prove what the size of a right triangle will be by understanding
We put so much certainty into these things that they even influence our ideas about what other universes must be like. Is it possible that there could be another universe in which the gravitational constant is different? It doesn't seem unreasonable; but it takes a lot more convincing to get someone to believe in a universe in which 2+2=5.
We have gained a great deal from this fascination with the power of numbers and their relationships, which sometimes produces an insight that proves -- perhaps most mysteriously of all -- to have widespread application in a world in which no object is really precisely geometric at all.
15 comments:
You can prove what the size of a right triangle will be by understanding the length of the hypotenuse alone...
No, you can't. 3-4-5 triangle has an area of 6. But a 4.9 - .995 - 5 triangle has an area of 2.43. Different sizes and looks, same hypotenuse.
There is a world of difference between the "magic" of mathematics as it applies to physical world, and the "magic" of numerology. (Which the author of the post you linked to recognizes at the end.) The latter oughtn't to be dignified by comparison with the former, no more than dermatology should be bracketed with palmistry.
(Number theory, on the other hand, plays around with the qualities of the integers, often just for the beauty of it, without any of the tawdry little mystic overtones that make numerology such an eye-roller.)
Before you answer, think not of a table but of a person. They also have many parts, but a single consciousness; and though they may lose (and may replace) some parts, once that single conscious nature flee at death, what remains behind is not a man at all. It doesn't make sense to say that they aren't 'really' a person while they are alive; so that unifying force has undeniable power.
You forgot the link; here, let me help.
Of course, I should have expected a Gilbert and Sullivan fan to be ready to supply me with veritable facts about the hypotenuse. I stand corrected!
I think I remember that xkcd piece. The 'arrangement' versus the 'parts,' by the way, is the form/matter distinction in the old system (called hylomorphism).
By the way, while I don't share your sense that 'mystical overtones' are necessarily tawdry, I do appreciate stripping these formal systems down for the pleasure of playing with them. I spent a good part of the day doing symbolic logic with some comrades, but I honestly prefer it without the mathematics.
The logic is the interesting part for me; but I've known enough people who find the numbers themselves to be interesting and beautiful to appreciate that there is something there, even if I've never had an ear for it (so to speak).
"Many cheerful facts," tovarish.
"Symbolic logic without the mathematics" doesn't make sense; symbolic logic is a branch of mathematics. For an amusing pair of literary illustrations, if you can find a copy of James Newman's The World of Mathematics, it contains an essay called "Symbolic Notation, Haddocks' Eyes and the Dog-Walking Ordinance" by Ernest Nagel. I think you'd enjoy it, and your local library may well have it. (That
famous book by Russell and Whitehead, which I am guessing gets a mention in your studies, was an effort to derive all of arithmetic from a few propositions in symbolic logic, just as Euclidean geometry is derived from its particular set of axioms.) That was a good way to spend an afternoon and I salute you for it.
All this is worlds above the empty game-playing of gematria and other kinds of numerology, which is no "Ground of Artes" or "Whetstone of Witte" (what a wonderful pair of names for old arithmetic texts; Newman's anthology includes an extract from their author).
"[S]ymbolic logic is a branch of mathematics."
Now, that depends on whom you ask. I have it on good authority that mathematics is a branch of philosophy. :)
All the same, although Russell is indeed a crucial figure, I've always had the feeling that it was more for the pleasure of it than any gains to be had. Not that I resent the time spent on it; but Russell's overall conjecture -- that our way of thinking could only be properly represented in an artificial language -- is exactly wrong. It's true that we don't have access to the mechanisms we use, but I think that's not because we need a better language. It's because the mechanisms belong to a higher order of consciousness in which we participate.
That was Plotinus' approach to the problem, and I think he was right. The reason consciousness arises from nature is that it was always there; the brain is a receiver, not a generator, of awareness. The answer to the xkcd question -- where is Grandpa now? -- is that he is right here. Build the right receiver, and he'll be next to you again.
We just have to figure out how to do it.
I realize I haven't given you the argument for that proposition, and also that it is a rather radical one. You'll have to bear with me, though: I haven't written it yet. :)
I've always had the feeling that it was more for the pleasure of it than any gains to be had.
May be. But if you look a little into what he did with symbolic logic, the mathematical nature of it will be very clear to you; that's why I brought him up.
Not that I resent the time spent on it; but Russell's overall conjecture -- that our way of thinking could only be properly represented in an artificial language -- is exactly wrong.
I've never heard of this conjecture, so I can't comment on it. But Russell's mathematical work stands independent of his philosophical work anyway.
Russell's work in philosophy of language is what I've always understood to be his principal contribution -- but philosophy of mathematics is not my area. However, I'm going to be visiting with a friend who does specialize in that area on Wednesday, so I'll ask him to talk me through it.
Well, Principia isn't just philosophy of mathematics, but is actual mathematics - in which he also made important contributions. Whether his philosophy was more important than his science, I can't tell you. (It certainly brought him more public notoriety.)
I'll keep a weather eye out for when you write down your radical proposition, at least if you choose to write it down here. (If that happens and I've been quiet for a while, do please drop me an email as well. It's a discussion I don't want to miss.)
P.S. - One place where I disagree with some is Russell's status as a science popularizer. I thought he was terrible - at least, I found The ABC of Relativity to be nearly unreadable, and I don't think he's a patch on George Gamow, Martin Gardner, or some of the more modern ones I know.
"Isn't just"? :) I'd have to hold that mathematics is a subset of philosophy -- so 'philosophy of mathematics' bears the same relationship to 'actual mathematics' as metaphysics bears to physics.
(I suspect even the proudest mathematician or physicist will support that assertion, too, since they'll hold that the relation is one of irrelevance! Yet the relation I mean is that the science deals with 'how does it work?' and the philosophy deals with 'what does it mean that it works that way?')
(Speaking of my friend, and the contributions of philosophy to math, I watched this friend of mine send an entire class of Math grad students into conniption fits once by proving to them that one of the fundamental principles of mathematics leads to a contradiction -- I wish I could replicate his proof, but as I said, it's not my area.)
Well, in normal language, there are differences. "Philosophy of science" is different from "science" - and you can gather data, perform useful experiments and calculations, and derive theorems without examining the underpinnings of the whole enterprise.
I see here, however, that in collaborating with Whitehead, Russell dominated the "purely philosophical" sections of the work, but collaborated with Whitehead on the actual mathematical work (i.e., the derivations) - suggesting that Russell's strength really lay in the former, no matter how you classify it.
Stamford's encyclopedia is a wonderful resource. Here is the part of Russell's work that I know best.
Thus, just as we distinguish three separate sense of “is” (the is of predication, the is of identity, and the is of existence) and exhibit these three senses using three separate logical notations (Px, x=y, and ∃x respectively)...
So that's where the prosecution went wrong. I'm afraid, even on a good day, I would've said something like, "It's the third-person singular of the verb 'to be,'" now could you please answer the question?
Side-angle doesn't let you define a triangle. You need three specs, at least one of which must be a side.
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