Some poor souls, even today, assign numbers to the dif ferent letters and decide which names are lucky and which unlucky, and which boy should marry which girl and so on. It is on'e of the more laughable pseudo-sciences.

In one case, a piece of gematria had repercussions in later history. This bit of gematria is to be found in "The Revelation of St. John the Divine," the last book of the New Testament-a book which is written in a mystical fashion that defies literal understanding. The reason for the lack of clarity seems quite clear to me. The author of Revelation was denouncing the Roman government and was laying himself open to a charge of treason and to sub sequent crucifixion if he made his words too clear. Conse 153 quently, he made an effort to write in such a way as to be perfectly clear to his "in-group" audience, while remaining completely meaningless to the Roman authorities.

In the thirteenth chapter he speaks of beasts of diaboli cal powers, and in the eighteenth verse he says, "Here is wisdom. Let him that hath understandino, count the number of the beast: for it is the number of a man; and his number is Six hundred three-score and six."

Clearly, this is designed not to give the pseudo-science of gematria holy sanction, but merely to serve as a guide to the actual person meant by the obscure imagery of the chapter. Revelation, as nearly as is known, was written only a few decades after the first great persecution of Chris tians under Nero. If Nero's name ("Neron Caesar") is written in Hebrew characters the sum of the numbers rep resented by the individual letters does indeed come out to be six hundred sixty-six, "the number of the beast."

Of course, other interpretations are possible. In fact, if Revelation is taken as having significance for all time as well as for the particular time in which it was written, it may also refer to some anti-Christ of the future. For this reason, generation after generation, people have made at tempts to show that, by the appropriate ju-glings of the spelling of a name in an appropriate language, and by the appropriate assignment of numbers to letters, some par ticular personal enemy could be made to possess the num ber of the beast.

If the Christians could apply it to Nero, the Jews them selves might easily have applied it in the next century to Hadrian, if they had wished. Five centuries later it could be (and was) applied to Mohammed. At the time of the Ref ormation, Catholics calculated Martin Luther's name and found it to be the number of the beast, and Protestants re turned the compliment by making the same discovery in the case of several popes.

Later still, when religious rivalries were replaced by na tionalistic ones, Napoleon Bonaparte and William 11 were appropriately worked out. What's more, a few minutes' work with my own system of alphabet-numbers shows me that "Herr Adolif Hitler" has the number of the beast. (I need that extra "I" to make it work.)

The Roman system of number symbols had similarities to both the Greek and Babylonian systems. Like the Greeks, the Romans used letters of the alphabet. However, they did not use them in order, but use just a few letters which they repeated as often as necessary-as in the Baby lonian system. Unlike the Babylonians, the Romans did not invent a new symbol for every tenfold increase of number, but (more primitively) used new symbols for fivefold increases as well.

'Thus, to begin with, the symbol for "one" is 1, and "two," "three," and "four," can be written II, III, and IIII.

The symbol for five, then, is not 11111, but V. People have amused themselves no end trying to work out the reasons for the particular letters chosen as symbols, but there are no explanations that are universally accepted.

However, it is pleasant to think that I represents the up held fin-er and that V might symbolize the hand itself with all five fingers-one branch of the V would be the out held thumb, the other, the remaining fingers. For "six," "seven," "eight," and "nine," we would then have VI, VII, 'VIII, and VIIII.

For "ten" we would then have X, which (some peo ple think) represents both hands held wrist to wrist.

"Twenty-three" would be XXIII, "forty-eight" would be XXXXVIII, and so on. 

The symbol for "fifty" is L, for "one hundred" is C, for "five hundred" is D, and for "one thousand" is M. The C and M are easy to understand, for C is the first letter of centum (meaning "one hundred") and M is the first letter of rnille (one thousand).

For that very reason, however, those symbols are sus picious. As initials they may have come to oust the original less-meaningful symbols for those numbers. For instance, an alternative symbol for "thousand" looks something like this (1). Half of a thousand or "five hundred" is the right half of the symbol, or (1), and this may have been con verted into D. As for the L which stands for "fifty," I don't know why it is used.

Now, then, we can write nineteen sixty-four, in Roman numerals, as follows: MDCCCCLXIIII.

One advantage of writing numbers according to this sys tem is that it doesn't matter in which order the numbers are written. If I decided to write nineteen sixty-four as CDCLIIMXCICT, it would still represent nineteen sixty four if I add up the number values of each letter. However, it is not likely that anyone would ever scramble the letters in this fashion. If the letters were written in strict order of decreasing value, as I.did the first time, it would then be much simpler to add the values of the letters. And, in fact, this order of decreasing value is (except for special cases) always used.

Once the order of writing the letters in Roman numerals is made an established convention, one can make use of deviations from that set order if it will help simplify mat ters. For instance, suppose we decide that when a symbol of smaller value follows one of larger value, the two are added; while if the symbol of smaller value precedes one of larger value, the first is subtracted from the second. Thus VI is "five" plus "one" or "six,"' while IV is "five" minus "one" or "four." (One might even say that IIV is "three," but it is conventional to subtract no more than one sym bol.) In the same way LX is "sixty" while XL is "forty"; CX is "one hundred ten," while XC is "ninety"; MC is 44 one thousand one hundred," while CM is "nine hundred."

The value of this "subtractive principle" is that two sym bols can do the work of five. Why write VIIII il you can write IX; or DCCCC if you can write CM? The year nine teen sixty-four, instead of being written MDCCCCLXIIII (twelve symbols), can be written MC@XIV (seven sym bols). On the other hand, once you make the order of writing letters significant, you can no longer scramble them even if you wanted to. For instance, if MCMLXIV is scrambled to MMCLXVI it becomes "two thousand one hundred sixty-six."

The subtractive principle was used on and off in ancient times but was not regularly adopted until the Middle Ages.

One interesting theory for the delay involves the simplest use of the principle-that of IV ("four"). These are the first letters of IVPITER, the chief of the Roman gods, and the Romans may have had a delicacy about writing even the beginning of the name. Even today, on clockfaces bear ing Roman numerals, "four" is represented as 1111 and never as IV. This is not because the clockf ace does not ac cept the subtractive principle, for "nine" is represented as IX and never as VIIII.

With the symbols already,given, we can go up to the number "four thousand nine hundred ninety-nine" in Ro man numerals. This would be MMMMDCCCCLXXXX VIIII or, if the subtractive principle is used ' MMMM CMXCIX. You might suppose that "five thousand" (the next number) could be written MMMMM, but this is not quite right. Strictly speaking, the Roman system never re quires a symbol to be repeated more than four times. A new symbol is always invented to prevent that: 11111 = V; XXXXX = L; and CCCCC = D. Well, then, what is MMMMM?

No letter was decided upon for "five thousand." In an cient times there was little need in ordinary life for num bers that high. And if scholars and tax collectors had oc casion for larger numbers, their systems did not percolate down to the common man.

One method of penetrating to "five thousand" and be yond is to use a bar to represent thousands. Thus, V would represent not "five" but "five thousand." And sixty-seven thousand four hundred eighty-two would be LX-VIICD LXXXII.

But another method of writing large numbers harks back to the primitive symbol (1) for "thousand." By adding to the curved lines we can increase the number by ratios of ten. Thus "ten thousand" would be (1)), and "one hundred thousand" would be (1) Then just as "five hundred" was 1) or D, "five thousand" would be 1)) and "fifty thousand" would be I))).

Just as the Romans made special marks to indicate tbou sands, so did the Greeks. What's more, the Greeks made special marks for ten thousands and for millions (or at least some of the Greek writers did). That the Romans didn't carry this to the logical extreme is no surprise. The Romans prided themselves on being non-intellectual. That the Greeks missed it also, however, will never cease to astonish me.

Suppose that instead of making special marks for large numbers only, one were to make special marks for every type of group from the units on. If we stick to the system I introduced at the start of the chapter-that is, the one in which ' stands for units, - for tens, + for hundreds, and = for thousands-then we could get by with but one set of nine syrrbols. We could write every number with a little heading, marking off the type of groups -+-'. Then for "two thousand five hundred eighty-one" we could get by with only the letters from A to I and write it GEHA. What's more, for "five thousand five hundred fifty-five" we could write EEEE. There would be no confusion with all the E's, since the symbol above each E would indicate that one was a "five," another a "fifty," another a "five hundred," and another a "five thousand." By using additional symbols for ten thousands, hundred thousands, millions, and so on, any number, however large, could be written in this same fashion.