The pyramidal tombs of Egyptian kings were an evolution in stone or brick from the tumulus of earth which in prehistoric ages was heaped over the body of the war chief. They are objects of rare dignity and interest, not only from their immense size, but from sundry peculiarities in their construction. In their orientation great care was taken, though usually with imperfect success. Their sides face the four cardinal points, and the descending entry-way forms a kind of telescope, from the bottom of which an observer, sixty centuries ago, could look out at what was then the polestar. These and other features of the pyramids are no doubt connected with Egyptian religion, and may very likely have subserved astrological purposes. But what say the pyramid cranks, or "pyramidalists," as they have been called?
According to them, the builders of the Great Pyramid were supernaturally instructed, probably by Melchizedek, King of Salem. Thus they were enabled to place it in latitude 30° N.; to make its four sides face the cardinal points; to adopt the sacred cubit, or one twenty millionth part of the earth's polar axis, as their unit of length; "and to make the side of the square base equal to just so many of these sacred cubits as there are days and parts of a day in a year. They were further by supernatural help enabled to square the circle, and symbolized their victory over this problem by making the pyramid's height bear to the perimeter of the base the ratio which the radius of a circle bears to the circumference."[48] In like manner, by immediate divine revelation, the builders of the pyramid were instructed as to the exact shape and density of the earth, the sun's distance, the precession of the equinoxes, etc., so that their figures on all these subjects were more accurate than any that modern science has obtained, and these figures they built into the pyramid. They also built into it the divinely revealed and everlasting standards of "length, area, capacity, weight, density, heat, time, and money," and finally they wrought into its structure the precise date at which the millennium is to begin. All this valuable information, handed down directly from heaven, was thus securely bottled up in the Great Pyramid for six thousand years or so, awaiting the auspicious day when Mr. Piazzi Smyth should come and draw the cork. Why so much knowledge should have been bestowed upon the architects of King Cheops, only to be concealed from posterity, is a pertinent question; and one may also ask, why was it worth while to bring a Piazzi Smyth into the world to reveal it, since plodding human reason had after all by slow degrees discovered every bit of it, except the date of the millennium? Why, moreover, did the revelation thus elaborately buried in or about b. c. 4000 come just abreast of the scientific knowledge of a. d. 1864, and there stop short? Is it credible that old Melchizedek knew nothing about the telephone, or the Roentgen ray, or the cholera bacillus? Our pyramidalists should be more enterprising, and elicit from their venerable fetish some useful hints as to wireless telegraphy, or the ventilation of Pullman cars, or the purification of Pennsylvania politics. Perhaps the last-named problem might vie in difficulty with squaring the circle!
The lucubrations of Piazzi Smyth, like those of Miss Delia Bacon, called into existence a considerable quantity of eccentric literature. For example, there is Skinner's "Key to the Hebrew-Egyptian Mystery in the Source of Measures originating the British Inch and the Ancient Cubit," published in Cincinnati in 1875, a tall octavo of 324 pages, bristling with diagrams and decimals, Hebrew words and logarithms. The book begins by getting the circle neatly squared, and then goes on to aver that sundry crosses, including the Christian cross, are an emblematic display of the origin of measures. The "mound-builders" come in for a share of the author's attention; for the mounds are "alike Typhonic emblems with the pyramid of Egypt and with Hebrew symbols." A Typhonic emblem relates to Typhon, the "lord of sepulture," whose Egyptian representative was the crocodile, as his Hebrew representative was the hog; "exemplified in the Christian books by the devil leaving the man and passing into the herd of swine, which thereupon rushed into the sea, another emblem of Typhon." Yet another such emblem is a mound in Ohio which simulates the contour of an alligator. A certain Aztec pyramid, described by Humboldt, has 318 niches, apparently in allusion to the days of the old Mexican civil calendar. Mr. Skinner sees in this numeral the value of Pi, and furthermore informs us that 318 is the Gnostic symbol for Christ, as well as the number of Abraham's trained servants. Frequent use of it is made in the Great Pyramid; for example, multiplied by six it gives the height of the king's chamber, and multiplied by two it gives half the base side of that apartment. Our author then puts the pyramid into a sphere, and after this feat it is an easy transition to Noah's flood, the zodiac, and modern ritualism. Of similar purport, though more concise than this octavo, is Dr. Watson Quinby's "Solomon's Seal, a Key to the Pyramid," published at Wilmington, Delaware, in 1880. From this little book we learn that "in the early days of the world some one measured the earth, and found its diameter, in round numbers, to be 41,569,000 feet, or 498,828,000 inches;" also that "Vishnu means Fish-Nuh, Noah-the-Fish, in allusion to his sojourn in the ark." Moreover, the Institutes of Manu were written by Noah, since Maha-Nuh = Great-Noah! With equal felicity, Rev. Edward Dingle (in his "The Balance of Physics, the Square of the Circle, and the Earth's True Solar and Lunar Distances," London, 1885, pp. 246) declares that "my success, let it be held what it may, was secured by cleaving to the Mosaic initiation of the Sabbatic number for my radius." At the end of his book Mr. Dingle exclaims: "To the Lord be all thanksgiving, who has kept my intellect and the directing of its thoughts sound, while seeking to deliver his word from the exulting shouts of his enemies and the seducers of mankind!"
From these grotesque rigmaroles it is not a long step to the lucubrations of the writers in whose bonnets the bee of prophecy has buzzed until they have come to fancy themselves skilled interpreters. There is apt to be the same droll mixing of arithmetic with history that we find among the pyramid cranks, and to the performance of such antics the book of Daniel and the Apocalypse present irresistible temptations. In my library days, I never used to pick up a commentary on either of those books without looking for some of the stigmata or witch-marks of crankery. Many a feeble intellect has been toppled over by that shining image, with head of gold and feet of iron and clay, which Nebuchadnezzar beheld in a dream. For example, let us take a few sentences from "Emmanuel: An Original and Exhaustive Commentary on Creation and Providence Alike. By an Octogenarian Layman," London, 1883, pp. 420: "Upwards of thirty years ago, a fancy for chronological research, fostered by boundless leisure and a competent facility in mental calculation, riveted my attention on the metallic image, in the vague hope of symmetrizing the four sections of the collective emblem with the successive dominations of the individual empires. Failing in so shadowy an aspiration, I seemed to be more than compensated by detecting an identity of duration, equally pregnant and positive, between the gold and the silver and the brass and the iron taken together on the one hand, and the mountain that was to crush them all to powder on the other,—the former aggregate being assumed to stretch from Nebuchadnezzar's succession in 606 b. c. to the dethronement of Augustulus in 476 a. d., and the latter again from the epoch just specified to Elizabeth's purgation of the Sanctuary in 1558." Having thus taken two equal periods of 1082 years, our Octogenarian proceeds to break them up (Heaven knows why!) each into four periods of 68, 204, 269, and 541 years. Then we are treated to the following equations:—
68 = 2 × 34
204 = 6 × 34
269 = 5 × 34 + 3 × 33
541 = 13 × 34 + 3 × 33
Hence, "with such a fulcrum as the Lamb slain before the foundation of the world, and such a lever as the span of the Victim's sublunary humiliation, was I too rash in aiming at a result infinitely grander than Archimedes's speculative displacement of the earth?"
That eminent mathematician, Dr. Nathaniel Bowditch, used to say that sometimes, when Laplace passed from one equation to the next with an "evidently," he would find a week's study necessary to cross the abyss which the transcendent mind of the master traversed in a single leap. I fancy that more than a week would be needed to fathom the Octogenarian's "hence," and it would by no means be worth while to go through so much and get so little. After a few pages of the Octogenarian, we are prepared to hear that in 1750 one Henry Sullamar squared the circle by the number of the Beast with seven heads and ten horns; and that in 1753 a certain French officer, M. de Causans, "cut a circular piece of turf, squared it, and deduced original sin and the Trinity."[49]
The reader is doubtless by this time weary of so much tomfoolery; but as it is needful, for the due comprehension of crankery and its crotchets, that he should by and by have still more of it, I will give him a moment's relief while I tell of a little game with which De Morgan and Whewell once amused themselves. The task was to make a sentence which should contain all the letters of the alphabet, and each only once. "No one," says De Morgan, "has done it with v and j treated as consonants; but you and I can do it" (u and i: oh, monstrous pun!). Dr. Whewell got only separate words, and failed to make a sentence: phiz, styx, wrong, buck, flame, quid. Very pretty, but De Morgan beat him out of sight with this weird sentiment; I, quartz pyx, who fling muck beds! Well, what in the world can that mean? "I long thought that no human being could say it under any circumstances. At last I happened to be reading a religious writer—as he thought himself—who threw aspersions on his opponents thick and threefold. Heyday! came into my head, this fellow flings muck beds: he must be a quartz pyx. And then I remembered that a pyx is a sacred vessel, and quartz is a hard stone, as hard as the heart of a religious foe-curser. So that the line is the motto of the ferocious sectarian, who turns his religious vessels into mud-holders for the benefit of those who will not see what he sees."[50]
I cite this drollery to show the world-wide difference between the playful nonsense of the wise man and the strenuous nonsense of the monomaniac; in this little cabbala alphabetica, moreover, a great deal of the cabalistic lore which cumbers library shelves is neatly satirized.