Monthly Archives: May 2009

A gematria revelation

Back in the summer of 2006 I read a series of online articles about the mathematical properties of the first verse in the Bible. Using standard Hebrew gematria, Genesis 1:1 adds up to 2,701 — a number with some interesting properties, being not only the 73rd triangular number, but also the product of the fourth hex number (37) and the fourth star number (73). Not many numbers are the product of the nth hex and nth star — 2,701 is only the fourth such number, and the next two are 7,381 and 16,471. Aside from its gematria properties, Genesis 1:1 consists of 28 letters, which is also a triangular number.

Since at that time I’d been playing around with English-language gematria, it occurred to me to see if I could find an English passage that could duplicate some of the mathematical properties of Genesis 1:1. Ideally I wanted a text which is to English what the Bible is to Hebrew, so I tried the first verse of the Book of Mormon — looked it up online, calculated its value using S:E:G: (A=1, B-2,… Z=26), and found the result mathematically boring. Moved on to other pastimes.

A few months later I was at a friend’s house reading a Whitley Strieber novel when suddenly a passage from the Book of Mormon popped into my head: “…and all things are become slippery, and we cannot hold them.” Immediately, and inexplicably, an idea about that passage popped into my head and, not having a Book of Mormon or a computer handy, I jotted it down on my bookmark to check later. I wrote: “all things are become slippery — complete quote — same properties as Gen 1:1.”

Later, at home, I searched for that passage on lds.organd found the complete quotation of which it was a part, from the sermon of Samuel the Lamanite, in the 13th chapter of Helaman. It was rather long:

O that we had remembered the Lord our God in the day that he gave us our riches, and then they would not have become slippery that we should lose them; for behold, our riches are gone from us. Behold, we lay a tool here and on the morrow it is gone; and behold, our swords are taken from us in the day we have sought them for battle. Yea, we have hid up our treasures and they have slipped away from us, because of the curse of the land. O that we had repented in the day that the word of the Lord came unto us; for behold the land is cursed, and all things are become slippery, and we cannot hold them. Behold, we are surrounded by demons, yea, we are encircled about by the angels of him who hath sought to destroy our souls. Behold, our iniquities are great. O Lord, canst thou not turn away thine anger from us?

It took me a few minutes, but I added it all up using S:E:G: and got 7,381 — a triangular number. It’s the product of 61 and 121, which are, respectively the fifth hex number and the fifth star number. (You can see this on a Chinese checkers board, which has 121 holes, 61 of which are in the central hexagon.) To complete the parallel with Genesis, I counted up the letters in the passage and found that there are 630 — which, as you can see below, is also a triangular number.

What to make of it? It’s not all that surprising that buried somewhere in the middle of the Book of Mormon is a passage with similar mathematical properties to Genesis 1:1 — but it is surprising, inexplicable really, that that particular passage, together with the knowledge that it had said properties, would pop into my head out of nowhere more than five years after I’d last read the Book of Mormon. It seems almost miraculous.

I say almost because, after all, I had read the Book of Mormon before, so all the data needed to produce this numerological discovery was already stored away in my head somewhere. Consciously, I couldn’t even remember the content of the complete passage, nor did I consciously know what number it added up to — but could it be that my subconscious had been quietly working for months, plugging through the Book of Mormon by memory and testing every passage to see if it fit what I had been looking for? I guess that would be my pet theory, since viewing it as a literal revelation (from whom? why?) makes even less sense.

About a year ago, this whole thing was brought back into my mind because of a dream I had. I saw the prophet Jeremiah staring at a large matrix of numbers — I had the impression that it was a magic square of order 11 (anachronistically written out in Arabic numerals, my BS detector reminds me, lest I be tempted to think I’d had a vision of the “real” Jeremiah). He explained to me that the entire Book of Lamentations had been revealed to him through contemplating those numbers. In fact, he said, he could have written a much longer book using this method, since there were infinitely many levels on which the numbers could be interpreted. The next morning, out of curiosity, I tried writing out an order-11 magic square just to see if it suggested anything to me about the sacking of Jerusalem. It didn’t, of course, but I did notice something else: the sum of all the numbers in an order-11 magic square is 7,381, and that number seemed awfully familiar.

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Meaningful freedom

In his Philosophical Dictionary, Voltaire dismisses the idea of “the liberty of indifference… the liberty of spitting on the right or on the left, of sleeping on my right side or on my left, of taking a walk of four turns or five.” If you have no preference for any one option over the others, then any choice you make will be random and arbitrary, and such “freedom” is meaningless. On the other hand, if you have an overwhelming and obvious preference for one option — when, say, the choice is between cooperating with the police and being shot — that doesn’t feel like meaningful freedom, either. You’re not really free in such a situation; you have to do what the police say. Here it’s not that your choice is random but that it’s predetermined, a foregone conclusion, a no-brainer.

Christians will often make a similar point, focusing on how various degrees of certainty can affect our preferences or lack thereof. Two roads may in fact lead to very different places, one of them vastly preferable to the other — but if I have no idea which one leads where, my choice to take the one or the other will be random. If, on the other hand I’m 100% sure that the one road leads to paradise and the other to hell, I likewise have no real choice to make. This, the Christian will say, is where faith comes in. By giving us just the right degree of certainty — evidence but not proof, faith but not sight — God preserves our free will.

This doesn’t really work, though. It’s the same old philosophical trap of insisting that our actions be neither predetermined nor random, neither caused nor uncaused — when logically they must be the one or the other, or a combination of the two. Throwing just the right amount of randomness into a deterministic system won’t magically create meaningful freedom, and neither will a moderate degree of uncertainty. This way of thinking about freedom is a dead end. We need something better.

So here’s my approach.

First of all, meaningful freedom should be thought of as something psychological, not metaphysical. It refers not to some arcane interplay of chance and necessity, but to the kind of choice people find it psychologically satisfying to make.

Second, I think it’s useful to take the word “meaningful” quite literally. A choice is meaningful if it means something in the same way that a sentence means something — that is, if it communicates information about something other than itself — specifically, if it tells us something about the person who makes it. A random choice, made in complete ignorance or indifference, tells us nothing; it’s just noise. A no-brainer choice tells us virtually nothing, because virtually any person would have done the same thing in the situation. A meaningful choice is a choice which a different sort of person would have made differently.

Of course there are degrees of meaningfulness. The choice to order chicken rather than seafood in a restaurant is meaningful, but just barely. Really meaningful choices convey information about the things we humans care about — virtue or vice, strength or weakness, high or low social status. The most meaningful choices are those that separate the sheep from the goats, those that we can feel proud or ashamed of having made. Think about the expressions we use. “Thanks. Not everyone would have done that.” “Oh, it was nothing. Anyone would have done the same.” If anyone would have done the same, then it was nothing — meaningless.

That’s why “perfect justice” scenarios such as karma or heaven-and-hell would be dehumanizing if they could be proven with absolute certainty to be true. In such a world, the person who wants to do the right thing because it is right and the hedonist who just wants to pursue his own self-interest (the sort of person who might have been a sociopath if he didn’t live in a perfect-justice world) would consistently make exactly the same choices. Those choices would therefore be meaningless, signifying nothing about the person who makes them.

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The seven walruses

I was thinking in a idle moment about the parodic possibilities of an apocalyptic scenario involving, say, seven sea lions, when it hit me — or walruses. A walrus is a kind of seal. So naturally I put on Magical Mystery Tour to check if, by any chance, “I Am the Walrus” happens to repeat that word seven times.

I doesn’t — only four. But four is still good. The word walrus, after all, comes from “whale-horse,” and the four apocalyptic horses and horsemen are probably the best-known part of the seven seals prophecy. And, though it doesn’t have seven walruses, the song is still divided into seven parts, four of them punctuated with “I am the walrus,” and the other three with “I’m crying.”

And I saw in the right hand of him that sat on the throne a book written within and on the backside, sealed with seven seals. And I saw a strong angel proclaiming with a loud voice, Who is worthy to open the book, and to loose the seals thereof? And no man in heaven, nor in earth, neither under the earth, was able to open the book, neither to look thereon. And I wept much, because no man was found worthy to open and to read the book, neither to look thereon. (Revelation 5:1-4)

I’m crying.

So, how well do the seven seals from the Book of Revelation match up with the seven sections of “I Am the Walrus”? Here’s what I’ve come up with:

  1. a conqueror with a bow — “see how they run like pigs from a gun” (the modern equivalent of a bow)
  2. a red horse bringing war — “stupid bloody Tuesday
  3. a pair of balances (symbol of justice and the law) — “pretty little policemen in a row”
  4. Death on a pale horse — “yellow matter custard, dripping from a dead dog’s eye”
  5. buried martyrs waiting for the Lord to avenge them — “sitting in an English garden” (cemetery) “waiting for the Son”
  6. sun and moon darkened (because of dust in the atmosphere?) — “choking smokers”; all tears wiped away — “the joker laughs at you… see how they smile”
  7. the slaughtered wicked devoured by birds — “Edgar Allan Poe” (of “Raven” fame)

Sometime I’ll also have to take a look at the Lewis Carroll connections (the walrus is from “The Walrus and the Carpenter,” the eggman is Humpty Dumpty), but not right now.

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Fun with 666

Outside of Jewish circles, interest in gematria tends to focus on a single number — 666, gematria’s unholy grail. One can only tinker around with gematria for so long before succumbing to the temptation to play “pin the tail on the antichrist” — it’s just too much fun. Here I’ll be using my own pet system, S:E:G: (Simple English Gematria, in which A=1 and Z=26), to explore this most deliciously evil of numbers.

The idea of the number of the beast comes from Revelation 13:18 in the Bible: “Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six.” S:E:G: points us to that very verse.

  • Revelation of Jesus to John, thirteenth chapter, eighteenth verse = 666
  • Bible, Revelation of St. John the Divine, chapter thirteen, verse eighteen = 666
  • Wisdom: Let him that hath understanding count the number of the beast. = 666

Aside from its biblical significance, 666 has some interesting mathematical properties. It is the 36th triangular number — that is, the sum of all the integers from 1 to 36.

  • the thirty-sixth triangular number, declared the number of the beast = 666
  • a numeral thrice repeated, the triangular expansion of thirty-six = 666

Unlike, say, Greek isopsephy or Hebrew gematria, which are based on powers of ten and can represent thee- and four-digit numbers with just a few letters, S:E:G: can requires a fairly long string to yield a number as large as 666. So when it comes to pegging an actual person as “the beast,” an unadorned name is not enough; some kind of title or description must be added. Here are a few examples:

  • the ridiculous Scientologist actor Thomas Cruise Mapother IV = 666
  • George Walker Bush, the Texan President of the United States of America = 666
  • Jann Wenner, who publishes Rolling Stone and other such magazines = 666
  • Hu Jintao, Paramount Leader of the Communist [expletive] occupying China = 666
  • Joseph Smith, Jr., of the Church of Jesus Christ of Latter-day Saints = 666
  • folk music icon Robert Allen Zimmerman, commonly known as Bob Dylan = 666
  • Professor Clinton Richard Dawkins, famous ethologist and atheist = 666
  • William James (also abbreviated Wm Jas) Tychonievich, the second of that name = 666

If you think the people listed above are not really antichrists but have been unfairly accused, don’t blame me; blame the English language. Maybe the alphabet itself is evil!

  • a bee cee dee e ef gee haitch i jay kay el em en o pee cue ar ess tee u vee double-u ex wy zee = 666.

Or perhaps the real blame lies with the book that gave us the whole idea of 666 and the antichrist: the New Testament.

  • the Gospels, the Acts of the Apostles, the Epistles, and the Apocalypse = 666

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No freedom to fight for

I’m only going to talk about the first line of this untitled poem by Lord Byron, but it’s short enough that there’s no good reason not to quote the whole thing.

When a man hath no freedom to fight for at home,
Let him combat for that of his neighbours;
Let him think of the glories of Greece and of Rome,
And get knock’d on the head for his labours.
To do good to mankind is the chivalrous plan,
And is always as nobly requited;
Then battle for freedom wherever you can,
And, if not shot or hang’d, you’ll get knighted.

There’s much to like in this little ditty — it’s clever and quotable — but for me it’s that first line that’s the real stroke of genius, and an excellent example of what poetry is all about: namely, using language in such a way that its surface characteristics (rhyme and rhythm most obviously, but also syntactic and lexical quirks) harmonize with, reinforce, and even add to the meaning it conveys.

“When a man hath no freedom to…” sounds like it’s talking about a man whose freedom is limited — another way of saying “When a man is not free to…” — and you expect it to be followed by a verb phrase indicating what he is not free to do. When the next words are “fight for,” another possible interpretation become salient (it would be the only interpretation if the clause ended there), but the first is still possible. (You might say, for example, that a man who has been barred from military service, “hath no freedom to fight for his country.”) It’s not until “fight for” is followed by “at home,” rather than by the noun object that the first interpretation requires, that the reader is forced to reanalyze the syntax, realizing that “freedom to fight for” is actually a phrase of the same type as “work to do” or “new worlds to conquer.”

Byron’s got the right idea, but in my opinion he doesn’t lead the reader far enough down the garden path before forcing the syntactic reframe. If I were Byron, I would have put a line break between “fight” and “for,” and then followed “for” with something which the reader could misinterpret as being its object. Here’s how I might have written the first stanza:

It is said when a man has no freedom to fight
For his country and people and home and birthright
Will all lose their appeal. Then crusading he goes
To win other men’s freedom from other men’s foes.

The garden path, whether my version or Byron’s, isn’t there just for the hell of it, but is central to the meaning of the poem. After getting the mistaken idea that we’re talking about a man who lacks freedom, the reader realizes, with at least a little bit of subconscious surprise, that, no, the man in question actually has no freedom to fight for — which means that he does have freedom, as much freedom as he could possibly want, that he is in no danger of losing it, and that he is therefore not free to fight for… wait, how’s that again? The lack of freedom we encountered on the garden path comes back to get us.

Because people — some people, anyway — don’t just want freedom, they want the experience of fighting for freedom. Maybe Greece needed Byron, but it’s much more obvious that Byron needed Greece; and if we ever have a world where all people everywhere are granted freedom and liberty, the Byrons of the world will be going crazy, itching for a fight, and feeling — however paradoxical it may seem — unfree.

The dynamic Byron described is very clearly at work in the modern West — not only in the obvious case of the American neocons fighting for Iraqi democracy, but in that of pampered classes in any number of countries agitating on behalf of their local oppressed (or not-so-oppressed) minorities. Trying to write something of my own in the spirit of Byron’s first line, I came up with the following:

How the masses grew restless and got out of hand
In their anger at having no rights to demand!

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What’s up with the firmament?

The creation story in Genesis 1 is divided into eight creative acts — light, the firmament, dry land, plants, heavenly bodies, fish and fowl, land animals, and man — and similar language is used to describe each act, a formula beginning with “And God said, Let…” and ending with “…and God saw that it was good.”

But there’s one exception to the formula. Have you ever noticed it? I’ve been reading the Bible for 20-some years now, and I never noticed it until just now — which is weird, given the way a break in a pattern usually tends to jump right out at you. Maybe it’s because it occurs so early in the sequence, before the formula has been firmly established by repetition. Take a look at the second day:

And God said, Let there be a firmament in the midst of the waters, and let it divide the waters from the waters. And God made the firmament, and divided the waters which were under the firmament from the waters which were above the firmament: and it was so. And God called the firmament Heaven. And the evening and the morning were the second day. (Gen. 1:6-8)

Do you see it now? That’s right, it seems that the firmament is the only thing God creates that isn’t good. Everything else is proclaimed good as soon as it is created; this is the only exception. The firmament is proclaimed good only at the very end of the story, after the creation of man, when “God saw every thing that he had made, and, behold, it was very good” (Gen. 1:31). So it’s not that the firmament is bad; it just doesn’t become good until after man has been created. How’s that for a riddle? What to make of it?

One possibility is that it doesn’t mean anything at all, that somewhere along the line someone just carelessly left out part of the formula and the error has been perpetuated by scribes and copyists ever since. That’s possible, but far too boring to bother thinking about.

An only slightly less boring explanation would be that the firmament is just an expanse of empty space, and therefore God doesn’t see it and it can’t be good or bad or anything else because it simply isn’t anything. I don’t buy that. The firmament isn’t nothing, it’s air, and the ancients thought it was a solid object (hence the word “firmament”), a literal vault of heaven. Besides, verse 7 says very clearly that God made the firmament, and verse 31 says just as clearly that God saw everything he had made was good. I think we simply have to take the implications of that last verse seriously — that, though the firmament was created on the second day and had birds flying around in it on the fifth, it couldn’t serve its true function and become truly good until after human beings had been created. Why?

My first interpretation was that, humans having such nearly unlimited potential, God saw how good it was that he had created all that empty space for them in which to grow and do their thing.

That’s the feel-good humanist interpretation, but I think there’s another one that better fits the overall context of Genesis: that the main purpose of the firmament is to keep us the hell out of heaven by establishing a very, very wide gulf between the angels above and the overweening mortals below. Later, both the Flood and the confusion of tongues would be provoked by those who tried to cross that gulf — whether angels coming down and intermarrying with mortals, or mortals building a tower to ascend to heaven. The firmament, in its role as an impassable chasm, is good, and God won’t stand for it’s being breached.

This is the theme of Byron’s unfinished verse drama “Heaven and Earth,” which presents the Flood as punishment in kind. Angels and mortals having shown their contempt for the firmament by crossing it to intermarry, the Lord in effect says, “Fine, have it your way. Let’s not keep heaven and earth separate” — at which point the waters above and the waters below (which, you will recall, the firmament was created to divide) come together and the world is flooded.

So that’s my interpretation, and I’d be very interested to hear others. It’s a fascinating riddle and, despite it’s being conspicuously located right there in the first chapter of the Bible, I’ve never seen the question addressed by anyone.

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More rhyme subversion

Here’s my latest attempt at poetic rhyme subversion.

I worry so for dear old Bill,
So long abed, so very ill,
For if old Bill does not get well,
Then he will die and go too soon
To tell the tale he came to tell
And sing out his appointed tune.

Does it work? Although it does rely on the old comic cliché of “Hey, betcha thought I was gonna cuss!”, I think it still manages to be a poem rather than a mere gag.

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