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By Alfred de Grazia

Part Three: Working of the Mind



[1] Professor Irving Michelson wrote a little piece of "hard science" (his term) called "Scientifically Speaking..." and subtitled "19- year Lunar Calendar Cycle: Accurate Adjustment to 365 1/ 4- Day Civil Calendar" [2] . A Greek named Meton of about 432 B. C. is credited with having discovered the 19-years repetitive coincidence of lunar month and tropical solar year. Michelson said that Meton's "discovery of the 19-year cycle presupposes precise knowledge of the length of the lunar month as well as of the solar (tropical) year of 365.2421988 days, to the second-decimal accuracy at least." He then claimed that such evolved knowledge would have taken observation of so long a period of regular celestial motions that no catastrophe could have occurred, as the Velikovsky circle believed, in the seventh or eighth centuries. The present writer addressed an ironical reply to these ideas in a related journal.

A comment on Irving Michelson's column
"Scientifically Speaking..."

With all due respect to Professor Michelson, I cannot understand the rationale behind Pensée's having allowed him (or anyone else for that matter) to pretend to be "Scientifically Speaking..." It is a usurpation of authority, and an implication that other contributors to Pensée have written unscientifically. "Science" is exhibited in a work itself or in a judgment rendered afterwards upon it; it is also a propaganda term when employed in Professor Michelson's usage. The phrase "hard science" adds insult to injury.

But rather than continue along this vein, I should like to turn to the substance of Professor Michelson's arguments. They are misleading and moreover incorrect. They are also irrelevant to Dr. Velikovsky's theories, which they strain to affect.

Michelson says that "hard science" comes into being when the moon's revolution is measured to the accuracy of an eight-digit number. But eight digits can be attached to an IQ score, an automobile license, the average height of Americans, the temperature of a frying pan, a tonal harmony in music, a rhythmic sequence of Indian dance, and so on. And if we proceeded to an accuracy of ten digits, or twelve, we might find the moon revolving a bit irregularly, which a genial mechanism such as Professor Michelson might trace back to an old disaster.

The important questions are what the number means and what purpose it serves. In the present case, we are held to believe that this eight-digit number will be shown to (a) have been used or discovered by a Greek named Meton about 432 B. C., or (b) have been known to the ancients at a time when catastrophes are alleged to have involved the moon in changed behaviors. Neither of these is demonstrated, and indeed, Michelson indicates later on that both implications are unnecessary to his story of Meton. Michelson further presumes that 250 years are not long enough for a changed lunar month to be noticed or calculated, but offers no argument on the point.

What Michelson does ultimately argue is that by 432 B. C. (255 years after the presumed Mars disaster), a four-digit lunar cycle calculation would have been sufficiently accurate to permit the design of a 19-year calendar involving an intercalation of moon and sun, granted of course, the sun's 365.25 figure was known (as he takes for granted and I would not oppose) and provided that anyone cared about the mater.

This is a useful line of inquiry, no matter how deviously pursued. It can help us understand what was going on in those days.

What was going on? I hope that I may be forgiven for presenting some fictional excerpts from the recently recovered journal of Kakrates, research assistant to the astronomer Meton, the Hero of the Golden Letters of 432 B. C. (Incidentally, I doubt that any Olympic games of that year were held in Athens, as Michelson says, unless some athlete hurled a discuss awfully far.)


Tablet ? .
My friend Mikelson and I were drinking a bit heavily last night and I bet him that I could produce a good all-purpose calendar without the resources of a holy temple at my disposal. From a window of my house, I can see a skinny tree on the eastern horizon that I can use for orientation.

Tablet ? .
I have observed the sunrise every day. I noted that after 365.25 days (or was it 365.24 or 365.26?) [3] the rim of the sun peeks up at the edge of the tree again from the left or north side. I was cheered because I caught the cycle so closely (I didn't touch a drop of wine the night before). Hence I continued.

Tablet ? .
I watched for another cycle, and then another. It does appear to be 365.25 alright. Meanwhile, I have learned that various watchtowers and astologers in Thebes, Syracuse, Memphis, etc. re getting the same effect. Some of them take this game seriously. If 365.25 is not observed perfectly, it can certainly be inferred from statistical averaging. I haven't told Meton what I'm doing yet, but when I told him of my concept of averaging, he smiled and patted me on the shoulder. He is busy with city planning. I could bring his associate, Euktemon, into the picture, but why complicate matters?

Tablet ? .
I have also been observing the moon-days from the opposite windows of my house, as it sets in the bay. The new moon turned out to repeat its appearance 12 times plus a tenth less than 11 sun-days in the time it took the sun to touch back upon the tree. I subtracted the 10.9 days from 365.25, and got 354.35. To get an average month, I divided this by 12 and got 29.53 days. Suppose I distribute the 11 days among the months, giving half-days to seven and one and a half days to 5 months. I'd have a workable calendar! I shall do something later with that little lost time, maybe spread it over the years. Some of my politician friends have become excited by the game and chipped in funds to hire a diligent research assistant to help with the sightings. The watchtower and astrological societies from here and there confirm that their instruments give the same readings. (I am glad that I entertained several of these chaps at Selena's taverna during the last Olympics.) Anyhow, it averages out. One phenomenal Chaldean with sophisticated equipment (I hear he foretold the death of the king's mother-in-law) reported that he got 29.5306 with averaging. Wow! Six digits! But who needs it. It's just pedantic overkill.

Tablet ? .
(I wish I could afford papyrus.) Now I added up three solar years of moon-cycles and discovered that 37 cycles came within a little over four days of matching perfectly. Carrying out the arithmetical calculations further, I got rid of practically all of the four-day fraction in 19 years. Much more refined observations would be needed to improve this cycle. As it stands, even though I have not based it upon observations for a full cycle, I can see that it will give enough accuracy for centuries. The days will not perceptibly march ahead of each other over a person's lifetime, or even over the lifetime of a kingdom.

Tablet ? .
I mentioned that I can match the sun and moon cycles almost exactly on a 19-years base to the politicians in Selena's taverna, and they are going to make a political issue of the Calendar. Others said, though, that the idea is politically impractical; a 19-years "year" that means nothing will bring only ridicule. I said, however, that maybe I could please the priests and cultists by getting the artist Petty to draw illustrations for each month using the Roman vestal virgins as models. This must have been what Mikelson meant when he mumbled something about "pretty-girl calendars," no doubt a Socratic slip of the tongue [4] . It won't work, they said; these soft-heads want a year for the sun, a year for the moon, a year for the seasons, a year to begin with the bacchanalia, or the saturnalia, solstices, or what-not. And, of course, the archons like to have the years named after their period in office.

Tablet ? .
I must find a way to appease the priests and cultists. They don't like the idea of automatic calendars (the damned humanists). Maybe I'll intercalate days by the magic number of seven. I'll figure out a common denominator and then decide what to do with the extra time. Just as the festival and political calendars do nowadays, I'll take care of the half-day problem by alternating 29-day and 30-day months. Then, to take care of the surplus of days, I'll put in an extra thirteenth month of 29 days (the cultists will like that 13-business); placing it in the years 3,6,8,11,14,17, and 19 will give us the magic number 7, the number of moving celestial bodies (I'll call them "eternal" since everyone likes the word.) It also sets well with the 7-stringed lyre. Mikelson has left town and I can't collect on the bet.

Papyrus ? .
I'm in trouble. The priests won't buy my 19-years calendar. All this talk of late about "an emerging power elite of secular science and politics" doesn't stand up when the fortune-tellers start demonstrating on the street. They are pressuring Meton to stop my moonlighting. He pointed out to them that an issue of academic freedom was involved. Privately, he gave me to understand that the results of my work have to be published, of course, in his name. He also insisted that I begin the year on the summer solstice and that I count months by full moons. Moreover, we must wait for a full 19-years cycle to prove my contentions. Mere prediction is not enough. Fortunately, some far-sighted statesman has given Meton a research grant sufficient to set up an observation post with a panel of three assistants (with myself in charge), and a few other amenities, including a site-visit to Jerusalem. I put a brass stake by the tree and bought a donkey, but now visit the research station mostly to pay the assistants and check out the tree (fortunately, it scarcely grows at all and one of the assistants keeps the dogs away).

... Here occurs a long time gap in the journal...

Papyrus ? .
I wonder why other Greeks haven't climbed aboard the wagon? Everyone still acts as if they didn't need an automatic and standard calendar and now we're moving into the 19th year. The other day I actually saw a priest of one kind or another taste the soil to see whether spring had begun - with a crowd around him. At least they don't sacrifice humans anymore to get the crops going. Are scholars afraid to tackle the problem? Haven't the times been ripe for invention? The priests are always yapping against "taking the human element out" of calendars. (their human element!).

I suppose that I should have confessed in the beginning that the Chaldeans and Egyptians knew all of this. But it was pure patriotism that motivated me to suppress the information. The Greeks must pretend to invent everything. Especially the Athenians. They would have killed the project if they had thought foreigners had beaten us to the results. Anyhow, this is all a problem for psychologists and political scientists - the soft science guys.

Papyrus ? .
Finally! After 20 years. Everyone professes to be amazed. Our party is in power. The Athenians are ablaze with patriotism. They praise Meton all over town. They are certifying my formula in golden letters on a prime wall location! In Meton's name, of course. That will impress the watchtowers and astrological societies - their President in Gold Letters! He has authorized me to give them all free tickets to the Olympic Games. But not to that Barbarian who had the gall to write him, "Meton, stop reinventing the wheel. The Chinese have used your cycle for 100 years, and even the seven intercalations." Not to mention that anonymity from Egypt who sent him a tablet with just the obscenity "A" inscribed on it.

Tablet ? .
The gold letters are staying up, but the opposition is too strong. Meton's calendar will not be adopted after all. They claim that they will check things by the formula from time to time. Why do they do this? For as long as anyone can recollect, the skies have been perfectly regular and before that, well, forever. Yet these unscientific idiots pretend that they have to take their measure every day and every month to be sure things are the same - as if the skies would fall if these nitpickers turned to more important problems - like better housing, exclusion of aliens, etc.

... end of Kakrates' journal...

Since I was dubious of Kakrates' work, I asked a living historian of science about the matter. This was Professor Livio Stecchini, who is an historian of science and has done much work with ancient calendars and measurements. Professor Stecchini believes (as, in fact, do I) that Meton knew all the while that the solar year was 365.25 and the lunar month about 29.5 days, for Stecchini shows, in the following paper, how readily Meton might have concocted the Metonic cycle, getting the .03 by chance, and then how Callippus and Hipparchus improved upon it.

Meton was probably offering a simple formula from his stock of astronomical knowledge to some people who were interested in routinizing and mechanizing the calendar. It was ordinary applied scientific research and consultation. To demonstrate his formula (or, better, to replicate the foreign experience for Greek eyes) one would need only "poorboy" techniques. The Athenians, agree Meritt, Pritchett, and Neugebauer, did not follow the Metonic cycle, and Meritt says that the Athenians did not tie their months to lunar observations but followed a rule of convenience with alternate 29 and 30 day months and an occasional check upon the Moon and Meton to prevent the calendar from wandering too far astray. Moreover, the four-digit stability of the moon's revolution, which had been in effect for a couple of centuries, could have been proven out in a few years, and had nothing to do with when the last destabilizing encounter involving the moon had taken place. Finally, I leave it to others to make fact out of my fable in the Meton case, that is, to show how politics determines practical sciences in calendar-making as in other areas.

Notes (Chapter 17: Making Moonshine with Hard Science)

1. Adapted from Kronos (Fall 1975) 52-6. L. C. Stecchini elaborates on the matter in the same issue, p. 57. See, as supporting sources: Encyclopedia Britannica (1973) edition), "Calendar," Vol. III; Benjamin D. Meritt, The Athenian Calendar in the Fifth Century (Cambridge: Harvard Univ Press, 1928); Benjamin D. Meritt, The Athenian Year (Berkeley: Univ of California Press, 1961); William K. Pritchett and Otto Neugebauer, The Calendars of Athens (Cambridge: Harvard Univ. Press. 1947).

2. Pensée (Winter 1974-5), 50-2.

3. Editor's note: for convenience, the fractional numbers that Kakrates used have been converted to the modern decimal system wherever they occur in the journal.

4. Editor's note: the mistake was not Mikelson's. A tablet has come to light disclosing that the slip was made by another taverna habitué, a scribe and a copyist.


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