A Budget of Paradoxes Volume I Part 23

The Celtic Druids. By G.o.dfrey Higgins,[603] Esq. of Skellow Grange, near Doncaster. London, 1827, 4to.

Anacalypsis, or an attempt to draw aside the veil of the Saitic Isis: or an inquiry into the origin of languages, nations, and religions. By G.o.dfrey Higgins, &c..., London, 1836, 2 vols. 4to.

The first work had an additional preface and a new index in 1829. Possibly, in future time, will be found bound up with copies of the second work two sheets which Mr. Higgins circulated among his friends in 1831: the first a "Recapitulation," the second "Book vi. ch. 1."

The system of these works is that--

"The Buddhists of Upper India (of whom the Phenician Canaanite, Melchizedek, was a priest), who built the Pyramids, Stonehenge, Carnac, &c.

will be shown to have founded all the ancient mythologies of the world, which, however varied and corrupted in recent times, were originally one, and that one founded on principles sublime, beautiful, and true."

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These works contain an immense quant.i.ty of learning, very honestly put together. I presume the enormous number of facts, and the goodness of the index, to be the reasons why the _Anacalypsis_ found a permanent place in the _old_ reading-room of the British Museum, even before the change which greatly increased the number of books left free to the reader in that room.

Mr. Higgins, whom I knew well in the last six years of his life, and respected as a good, learned, and (in his own way) _pious_ man, was thoroughly and completely the man of a system. He had that sort of mental connection with his theory that made his statements of his authorities trustworthy: for, besides perfect integrity, he had no bias towards alteration of facts: he saw his system in the way the fact was presented to him by his authority, be that what it might.

He was very sure of a fact which he got from any of his authorities: nothing could shake him. Imagine a conversation between him and an Indian officer who had paid long attention to Hindoo antiquities and their remains: a third person was present, _ego qui scribo_. _G. H._ "You know that in the temples of I-forget-who the Ceres is always sculptured precisely as in Greece." _Col._ ----, "I really do not remember it, and I have seen most of these temples." _G. H._ "It is so, I a.s.sure you, especially at I-forget-where." _Col._ ----, "Well, I am sure! I was encamped for six weeks at the gate of that very temple, and, except a little shooting, had nothing to do but to examine its details, which I did, day after day, and I found nothing of the kind." It was of no use at all.

G.o.dfrey Higgins began life by exposing and conquering, at the expense of two years of his studies, some shocking abuses which existed in the York Lunatic Asylum. This was a proceeding which called much attention to the treatment of the insane, and produced much good effect. He was very resolute and energetic. The magistracy of his {276} time had such scruples about using the severity of law to people of such station as well-to-do farmers, &c.: they would allow a great deal of resistance, and endeavor to mollify the rebels into obedience. A young farmer flatly refused to pay under an order of affiliation made upon him by G.o.dfrey Higgins. He was duly warned; and persisted: he shortly found himself in gaol. He went there sure to conquer the Justice, and the first thing he did was to demand to see his lawyer. He was told, to his horror, that as soon as he had been cropped and prison-dressed, he might see as many lawyers as he pleased, to be looked at, laughed at, and advised that there was but one way out of the sc.r.a.pe.

Higgins was, in his speculations, a regular counterpart of Bailly; but the celebrated Mayor of Paris had not his nerve. It was impossible to say, if their characters had been changed, whether the unfortunate crisis in which Bailly was not equal to the occasion would have led to very different results if Higgins had been in his place: but a.s.suredly const.i.tutional liberty would have had one chance more. There are two works of his by which he was known, apart from his paradoxes. First, _An apology for the life and character of the celebrated prophet of Arabia, called Mohamed, or the Ill.u.s.trious_. London, 8vo. 1829. The reader will look at this writing of our English Buddhist with suspicious eye, but he will not be able to avoid confessing that the Arabian prophet has some reparation to demand at the hands of Christians. Next, _Horae Sabaticae; or an attempt to correct certain superst.i.tions and vulgar errors respecting the Sabbath_. Second edition, with a large appendix. London, 12mo. 1833. This book was very heterodox at the time, but it has furnished material for some of the clergy of our day.

I never could quite make out whether G.o.dfrey Higgins took that system which he traced to the Buddhists to have a Divine origin, or to be the result of good men's meditations. Himself a strong theist, and believer in a future {277} state, one would suppose that he would refer a _universal_ religion, spread in different forms over the whole earth from one source, directly to the universal Parent. And this I suspect he did, whether he knew it or not.

The external evidence is balanced. In his preface he says:

"I cannot help smiling when I consider that the priests have objected to admit my former book, _The Celtic Druids_, into libraries, because it was antichristian; and it has been attacked by Deists, because it was superfluously religious. The learned Deist, the Rev. R. Taylor [already mentioned], has designated me as the _religious_ Mr. Higgins."

The time will come when some profound historian of literature will make himself much clearer on the point than I am.

ON POPE'S DIPPING NEEDLE.

The triumphal Chariot of Friction: or a familiar elucidation of the origin of magnetic attraction, &c. &c. By William Pope.[604] London, 1829, 4to.

Part of this work is on a dipping-needle of the author's construction. It must have been under the impression that a book of naval magnetism was proposed, that a great many officers, the Royal Naval Club, etc. lent their names to the subscription list. How must they have been surprised to find, right opposite to the list of subscribers, the plate presenting "the three emphatic letters, J. A. O." And how much more when they saw it set forth that if a square be inscribed in a circle, a circle within that, then a square again, &c., it is impossible to have more than fourteen circles, let the first circle be as large as you please. From this the seven attributes of G.o.d are unfolded; and further, that all matter was _moral_, until Lucifer _churned_ it into _physical_ "as far as the third circle in Deity": this Lucifer, called Leviathan in Job, being thus the moving cause of {278} chaos. I shall say no more, except that the friction of the air is the cause of magnetism.

Remarks on the Architecture, Sculpture, and Zodiac of Palmyra; with a Key to the Inscriptions. By B. Prescot.[605] London, 1830, 8vo.

Mr. Prescot gives the signs of the zodiac a Hebrew origin.

THE JACOTOT METHOD.

Epitome de mathematiques. Par F. Jacotot,[606] Avocat. 3ieme edition, Paris, 1830, 8vo. (pp. 18).

Methode Jacotot. Choix de propositions mathematiques. Par P. Y.

Sepres.[607] 2nde edition. Paris, 1830, 8vo. (pp. 82).

Of Jacotot's method, which had some vogue in Paris, the principle was _Tout est dans tout_,[608] and the process _Apprendre quelque chose, et a y rapporter tout le reste_.[609] The first tract has a proposition in conic sections and its preliminaries: the second has twenty exercises, of which the first is finding the greatest common measure of two numbers, and the last is the motion of a point on a surface, acted on by given forces. This is topped up with the problem of sound in a tube, and a slice of Laplace's theory of the tides. All to be studied until known by heart, and all the rest will come, or at least join on easily when it comes. There is much truth in the a.s.sertion that new knowledge {279} hooks on easily to a little of the old, thoroughly mastered. The day is coming when it will be found out that crammed erudition, got up for examinations, does not cast out any hooks for more.

Lettre a MM. les Membres de l'Academie Royale des Sciences, contenant un developpement de la refutation du systeme de la gravitation universelle, qui leur a ete presentee le 30 aout, 1830. Par Felix Pa.s.sot.[610] Paris, 1830, 8vo.

Works of this sort are less common in France than in England. In France there is only the Academy of Sciences to go to: in England there is a reading public out of the Royal Society, &c.

A DISCOURSE ON PROBABILITY.

About 1830 was published, in the _Library of Useful Knowledge_, the tract on _Probability_, the joint work of the late Sir John Lubbock[611] and Mr.

Drinkwater (Bethune).[612] It is one of the best elementary openings of the subject. A binder put my name on the outside (the work was anonymous) and the consequence was that nothing could drive out of people's heads that it was written by me. I do not know how many denials I have made, from a pa.s.sage in one of my own works to a letter in the _Times_: and I am not sure that I have succeeded in establishing the truth, even now. I accordingly note the fact once more. But as a book has no right here unless it contain a paradox--or thing counter to general opinion or practice--I will produce two small ones. Sir John Lubbock, with whom lay the executive arrangement, had a strong objection to the last word in "Theory of Probabilities," he maintained that the singular _probability_, should be used; and I hold him quite right.

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The second case was this: My friend Sir J. L., with a large cl.u.s.ter of intellectual qualities, and another of social qualities, had one point of character which I will not call bad and cannot call good; he never used a slang expression. To such a length did he carry his dislike, that he could not bear _head_ and _tail_, even in a work on games of chance: so he used _obverse_ and _reverse_. I stared when I first saw this: but, to my delight, I found that the force of circ.u.mstances beat him at last. He was obliged to take an example from the race-course, and the name of one of the horses was _Bessy Bedlam_! And he did not put her down as _Elizabeth Bethlehem_, but forced himself to follow the jockeys.

[Almanach Romain sur la Loterie Royale de France, ou les Etrennes necessaires aux Actionnaires et Receveurs de la dite Loterie. Par M.

Menut de St.-Mesmin. Paris, 1830. 12mo.

This book contains all the drawings of the French lottery (two or three, each month) from 1758 to 1830. It is intended for those who thought they could predict the future drawings from the past: and various sets of _sympathetic_ numbers are given to help them. The principle is, that anything which has not happened for a long time must be soon to come. At _rouge et noir_, for example, when the red has won five times running, sagacious gamblers stake on the black, for they think the turn which must come at last is nearer than it was. So it is: but observation would have shown that if a large number of those cases had been registered which show a run of five for the red, the next game would just as often have made the run into six as have turned in favor of the black. But the gambling reasoner is incorrigible: if he would but take to squaring the circle, what a load of misery would be saved. A writer of 1823, who appeared to be thoroughly acquainted with the gambling of Paris and London, says that the gamesters by {281} profession are haunted by a secret foreboding of their future destruction, and seem as if they said to the banker at the table, as the gladiators said to the emperor, _Morituri te salutant_.[613]

In the French lottery, five numbers out of ninety were drawn at a time. Any person, in any part of the country, might stake any sum upon any event he pleased, as that 27 should be drawn; that 42 and 81 should be drawn; that 42 and 81 should be drawn, and 42 first; and so on up to a _quine determine_, if he chose, which is betting on five given numbers in a given order. Thus, in July, 1821, one of the drawings was

8 46 16 64 13.

A gambler had actually predicted the five numbers (but not their order), and won 131,350 francs on a trifling stake. M. Menut seems to insinuate that the hint what numbers to choose was given at his own office. Another won 20,852 francs on the quaterne, 8, 16, 46, 64, in this very drawing.

These gains, of course, were widely advertised: of the mult.i.tudes who lost nothing was said. The enormous number of those who played is proved to all who have studied chances arithmetically by the numbers of simple quaternes which were gained: in 1822, fourteen; in 1823, six; in 1824, sixteen; in 1825, nine, &c.

The paradoxes of what is called chance, or hazard, might themselves make a small volume. All the world understands that there is a long run, a general average; but great part of the world is surprised that this general average should be computed and predicted. There are many remarkable cases of verification; and one of them relates to the quadrature of the circle. I give some account of this and another. Throw a penny time after time until _head_ arrives, which it will do before long: let this be called a _set_.

Accordingly, H is the smallest set, TH the next smallest, then TTH, &c. For abbreviation, let a set in which seven _tails_ {282} occur before _head_ turns up be T^{7}H. In an immense number of trials of sets, about half will be H; about a quarter TH; about an eighth, T^{2}H. Buffon[614] tried 2,048 sets; and several have followed him. It will tend to ill.u.s.trate the principle if I give all the results; namely, that many trials will with moral certainty show an approach--and the greater the greater the number of trials--to that average which sober reasoning predicts. In the first column is the most likely number of the theory: the next column gives Buffon's result; the three next are results obtained from trial by correspondents of mine. In each case the number of trials is 2,048.

H 1,024 1,061 1,048 1,017 1,039 TH 512 494 507 547 480 T^{2}H 256 232 248 235 267 T^{3}H 128 137 99 118 126 T^{4}H 64 56 71 72 67 T^{5}H 32 29 38 32 33 T^{6}H 16 25 17 10 19 T^{7}H 8 8 9 9 10 T^{8}H 4 6 5 3 3 T^{9}H 2 3 2 4 T^{10}H 1 1 1 T^{11}H 0 1 T^{12}H 0 0 T^{13}H 1 1 0 T^{14}H 0 0 T^{15}H 1 1 &c. 0 0 ----- ----- ----- ----- ----- 2,048 2,048 2,048 2,048 2,048

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In very many trials, then, we may depend upon something like the predicted average. Conversely, from many trials we may form a guess at what the average will be. Thus, in Buffon's experiment the 2,048 first throws of the sets gave _head_ in 1,061 cases: we have a right to infer that in the long run something like 1,061 out of 2,048 is the proportion of heads, even before we know the reasons for the equality of chance, which tell us that 1,024 out of 2,048 is the real truth. I now come to the way in which such considerations have led to a mode in which mere pitch-and-toss has given a more accurate approach to the quadrature of the circle than has been reached by some of my paradoxers. What would my friend[615] in No. 14 have said to this? The method is as follows: Suppose a planked floor of the usual kind, with thin visible seams between the planks. Let there be a thin straight rod, or wire, not so long as the breadth of the plank. This rod, being tossed up at hazard, will either fall quite clear of the seams, or will lay across one seam. Now Buffon, and after him Laplace, proved the following: That in the long run the fraction of the whole number of trials in which a seam is intersected will be the fraction which twice the length of the rod is of the circ.u.mference of the circle having the breadth of a plank for its diameter. In 1855 Mr. _Ambrose_ Smith, of Aberdeen, made 3,204 trials with a rod three-fifths of the distance between the planks: there were 1,213 clear intersections, and 11 contacts on which it was difficult to decide. Divide these contacts equally, and we have 1,218 to 3,204 for the ratio of 6 to 5[pi], presuming that the greatness of the number of trials gives something near to the final average, or result in the long run: this gives [pi] = 3.1553. If all the 11 contacts had been treated as intersections, the result would have been {284} [pi] = 3.1412, exceedingly near. A pupil of mine made 600 trials with a rod of the length between the seams, and got [pi] = 3.137.

This method will hardly be believed until it has been repeated so often that "there never could have been any doubt about it."

The first experiment strongly ill.u.s.trates a truth of the theory, well confirmed by practice: whatever can happen will happen if we make trials enough. Who would undertake to throw tail eight times running?

Nevertheless, in the 8,192 sets tail 8 times running occurred 17 times; 9 times running, 9 times; 10 times running, twice; 11 times and 13 times, each once; and 15 times twice.]