A Budget of Paradoxes Volume II Part 18

Every person who knows anything of the progress of physics understands what is meant; but not the reviewers I speak of. Many of them consider A. B. as _adopting_ the spirit-hypothesis. The whole book was written, as both the authors point out, to suggest inquiry to those who are curious; C. D.

firmly believing, A. B. as above. Neither C. D. nor A. B. make any other pretence. Both dwell upon the absence of authentications and the suppression of names as utterly preventive of anything like proof. And A. B. says that his reader "will give him credit, if not himself a goose, for seeing that the tender of an anonymous cheque would be of equal effect, whether drawn on the Bank of England or on Aldgate Pump." By this test a number of the reviewers are found to be geese: for they take the authors as offering proof, and insist, against the authors, on the very point on which the authors had themselves insisted beforehand.

Leaving aside imperceptions of this kind, I proceed to notice a clerical and medical review. I have lived much in the middle ages, especially since the invention of printing; and from thence I have brought away a high respect for and grateful recollection of--the priest in everything but theology, and the physician in everything but medicine. The professional harness was unfavorable to all progress, except on a beaten road; the professional blinkers prevented all but the beaten road from being seen: the professional reins were pulled at the slightest attempt to quicken pace, even on the permitted path; and the {199} professional whip was heavily laid on at the slightest attempt to diverge. But when the intelligent man of either cla.s.s turned his attention out of his ordinary work, he had, in most cases, the freshness and vigor of a boy at play, and like the boy, he felt his freedom all the more from the contrast of school-restraint.

In the case of medicine, and physics generally, the learned were, in some essential points, more rational than many of their present impugners. They pa.s.s for having put _a priori_ obstacles in the way of progress: they might rather be reproved for too much belief in progress obtained by _a priori_ means. They would have shouted with laughter at a dunce who--in a review I read, but without making a note--declared that he would not believe his senses except when what they showed him was capable of explanation upon some known principle. I have seen such stuff as this attributed to the schoolmen; but only by those who knew nothing about them. The following, which I wrote some years ago, will give a notion of a distinction worth remembering. It is addressed to the authorities of the College of Physicians.

"The ignominy of the word _empiric_ dates from the ages in which scholastic philosophy deduced physical consequences _a priori_;--the ages in which, because a lion is strong, rubbing with lion's fat would have been held an infallible tonic. In those happy days, if a physician had given decoction of a certain bark, only because in numberless instances that decoction had been found to strengthen the patient, he would have been a miserable empiric. Not that the colleges would have pa.s.sed over his returns because they were empirical: they knew better. They were as skilful in finding causes for facts, as facts for causes. The president and the elects of that day would have walked out into the forest with a rope, and would have pulled heartily at the tree which yielded the bark: nor would they ever have left it until they had pulled out a legitimate {200} reason. If the tree had resisted all their efforts, they would have said, 'Ah! no wonder now; the bark of a strong tree makes a strong man.' But if they had managed to serve the tree as you would like to serve h.o.m.oeopathy, then it would have been 'We might have guessed it; all the _virtus roborativa_ has settled in the bark.' They admitted, as we know from Moliere, the _virtus dormitiva_[343] of opium, for no other reason than that opium _facit dormire_.[344] Had the medicine not been previously _known_, they would, strange as it may seem to modern pharmacopoeists, have accorded a _virtus dormitiva_ to the new _facit dormire_. On this point they have been misapprehended. They were p.r.o.ne to infer _facit_ from a _virtus_ imagined _a priori_; and they were ready in supplying _facit_ in favor of an orthodox _virtus_. They might have gone so far, for example, under pre-notional impressions, as the alliterative allopath, who, when maintenance of truth was busy opposing the progress of science called _vaccination_, declared that some of its patients coughed like cows, and bellowed like bulls; but they never refused to find _virtus_ when _facit_ came upon them, no matter whence. They would rather have accepted Tenterden steeple than have rejected the Goodwin Sands. They would have laughed their modern imitators to scorn: but as they are not here, we do it for them.

"The man of our day--the _a priori_ philosopher--tries the question whether opium can cause sleep by finding out in the recesses of his own noddle whether the drug can have a dormitive power: Well! but did not the schoolman do the same? He did; but mark the distinction. The schoolman had recourse to first principles, when there was no opium to try it by: our man settles the point in the same way _with a lump of opium before him_. The schoolman shifted his principles with his facts: the man of our drawing-rooms will fight facts with his principles, just as an old {201} physician would have done in actual practice, with the rod of his _Church_ at his back.

"The story about Galileo--which seems to have been either a joke made against him, or by him--ill.u.s.trates this. _Nature abhors a vacuum_ was the explanation of the water rising in a pump: but they found that the water would not rise more than 32 feet. They asked for explanation: what does the satirist make the schoolmen say? That the stoppage is _not_ a fact, because nature abhors a vacuum? No! but that the principle should be that nature abhors a vacuum as far as 32 feet. And this is what would have been done.

"There are still among us both priests and physicians who would have belonged, had they lived three or four centuries ago, to the glorious band of whom I have spoken, the majority of the intelligent, working well for mankind out of the professional pursuit. But we have a great many who have helped to abase their cla.s.ses. Go where we may, we find specimens of the lower orders of the ministry of religion and the ministry of health showing themselves smaller than the small of other pursuits. And how is this?

First, because each profession is entered upon a mere working smack of its knowledge, without any depth of education, general or professional. Not that this is the whole explanation, nor in itself objectionable: the great ma.s.s of the world must be tended, soul and body, by those who are neither Hookers[345] nor Harveys[346]: let such persons not venture _ultra crepidam_, and they are useful and respectable. But, secondly, there is a vast upheaving of thought from the depths of commonplace learning. I am a clergyman! Sir! I am a medical man! Sir! and forthwith the nature of things is picked to pieces, and there is a race, with the last the winner, between Philosophy mounted on Folly's donkey, and Folly mounted on Philosophy's donkey. How fortunate {202} it is for Law that her battles are fought by politicians in the Houses of Parliament. Not that it is better done: but then _politics_ bears the blame."

I now come to the medical review. After a quant.i.ty of remark which has been already disposed of, the writer shows Greek learning, a field in which the old physician would have had a little knowledge. A. B., for the joke's sake, had left untranslated, as being too deep, a remarkably easy sentence of Aristotle, to the effect that what has happened was possible, for if impossible it would not have happened. The reviewer, in "simple astonishment,"--it was simple--at the pretended incapacity--I was told by A. B. that the joke was intended to draw out a reviewer--translates:--He says that this sentence is A. B.'s summing up of the evidence of Spiritualism. Now, being a sort of _alter ego_[347] of A. B., I do declare that he is not such a fool as to rest the evidence of Spiritualism--the _spirit explanation_--upon the occurrence of certain facts proving the possibility of those very facts. In truth, A. B. refuses to receive spiritualism, while he receives the facts: this is the gist of his whole preface, which simply admits spiritualism among the qualified candidates, and does not know what others there may be.

The reviewer speaks of Aristotle as "that clear thinker and concise writer." I strongly suspect that his knowledge of Aristotle was limited to the single sentence which he had translated or got translated. Aristotle is concise in _phrase_, not in book, and is powerful and profound in thought: but no one who knows that his writing, all we have of him, is the very opposite of clear, will pretend to decide that he thought clearly. As his writing, so probably was his thought; and his books are, if not anything but clear, at least anything good but clear. n.o.body thinks them clear except a person who always clears difficulties: which I have no doubt was the reviewer's habit; that is, if he ever took the field {203} at all. The gentleman who read Euclid, all except the As and Bs and the pictures of scratches and scrawls, is the type of a numerous cla.s.s.

The reviewer finds that the word _amosgepotically_, used by A. B., is utterly mysterious and incomprehensible. He hopes his translation of the bit of Greek will shield him from imputation of ignorance: and thinks the word may be referred to the "obscure dialect" out of which sprung _aneroid_, _kalos geusis sauce_, and _Anaxyridian trousers_. To lump the first two phrases with the third smacks of ignorance in a Greek critic; for [Greek: anaxuridia], _breeches_, would have turned up in the lexicon; and _kalos geusis_, though absurd, is not obscure. And [Greek: amosgepos], _somehow or other_, is as easily found as [Greek: anaxuridia]. The word _aneroid_, I admit, has puzzled better scholars than the critic: but never one who knows the unscholarlike way in which words ending in [Greek: eides]

have been rendered. The _aneroid barometer_ does _not_ use a column of air in the same way as the old instrument. Now [Greek: aeroeides]--properly _like_ the atmosphere--is by scientific non-scholarship rendered having to do with the atmosphere; and [Greek: anaeroeides]--say _anaeroid_--denies having to do with the atmosphere; a nice thing to say of an instrument which is to measure the weight of the atmosphere. One more absurdity, and we have _aneroid_, and there you are. The critic ends with a declaration that nothing in the book shakes his faith in a _Quarterly_ reviewer who said that suspension of opinion, until further evidence arrives, is justifiable: a strange summing up for an article which insists upon utter rejection being unavoidable.[348] The expressed aim of both A. B. and C. D.

was to excite inquiry, and get further evidence: until this is done, neither asks for a verdict.

Oh where! and oh where! is old Medicine's learning gone! There _was_ some in the days of yore, when Popery {204} was on! And it's oh! for some Greek, just to find a word upon! The reviewer who, lexicon in hand, can neither make out _anaxyridical_, _amosgepotical_, _kalos geusis_, nor distinguish them from _aneroid_, cannot be trusted when he says he has translated a sentence of Aristotle. He may have done it; but, as he says of spiritualism, we must suspend our opinion until further evidence shall arrive.

We now come to the theological review. I have before alluded to the faults of logic which are Protestant necessities: but I never said that Protestant argument had _nothing but_ paralogism. The writer before me attains this completeness: from beginning to end he is of that confusion and perversion which, as applied to interpretation of the New Testament, is so common as to pa.s.s unnoticed by sermon-hearers; but which, when applied out of church, is exposed with laughter in all subjects except theology. I shall take one instance, putting some words in italics.

_A. B._ _Theological Critic._

My state of mind, which refers ... he proceeds to argue that the whole _either_ to unseen he himself is outside its intelligence, _or something sacred pale because he refers which man has never had any all these strange phenomena to conception of_, proves me to _unseen spiritual be out of the pale of the intelligence_.

Royal Society.

The possibility of a _yet unimagined_ cause is insisted on in several places. On this ground it is argued by A. B. that spiritualists are "incautious" for giving in at once to the spirit doctrine. But, it is said, they may be justified by the philosophers, who make the flint _axes_, as they call them, to be the works of men, because no one can see _what else they can be_. This kind of adoption, _condemned_ as a conclusion, is _approved_ as a provisional theory, suggestive of direction of inquiry: experience having shown that {205} inquiry directed by a _wrong_ theory has led to more good than inquiry without any theory at all. All this A. B. has fully set forth, in several pages. On it the reviewer remarks that "with infinite satisfaction he tries to justify his view of the case by urging that there is no other way of accounting for it; after the fashion of the philosophers of our own day, who conclude that certain flints found in the drift are the work of men, because the geologist does not see what else they can be." After this twist of meaning, the reviewer proceeds to say, and A. B. would certainly join him, "There is no need to combat any such mode of reasoning as this, because it would apply with equal force and justice to any theory whatever, however fantastic, profane, or silly." And so, having shown how the reviewer has hung himself, I leave him funipendulous.

One instance more, and I have done. A reviewer, not theological, speaking of the common argument that things which are derided are not _therefore_ to be rejected, writes as follows:--"It might as well be said that they who laughed at Jenner[349] and vaccination were, in a certain but very unsatisfactory way, witnesses to the possible excellence of the system of St. John Long."[350] Of course it _might_: and of course it _is_ said by all people of common sense. In introducing the word "possible," the reviewer has. .h.i.t the point: I suspect that this word was introduced during revision, to put the sentence into fighting order; hurry preventing it being seen that the sentence was thus made to fight on the wrong side.

Jenner, who was laughed at, was right; therefore, it is not impossible--that is, it is _possible_--that a derided system may be right.

Mark the three gradations: _in medio tutissimus ibis_.[351]

{206}

_Reviewer._--If a system be derided, it is no ground of suspense that derided systems have turned out true: if it were, you would suspend your opinion about St. John Long on account of Jenner.--_Ans._ You ought to do so, as to _possibility_; and _before examination_; not with the notion that J. proves St. J. _probable_; only _possible_.

_Common Sense._--The past emergence of truths out of derided systems proves that there is a practical certainty of like occurrence to come. But, inasmuch as a hundred speculative fooleries are started for one truth, the mind is permitted to approach the examination of any one given novelty with a bias against it of a hundred to one: and this permission is given because so it will be, leave or no leave. Every one has licence not to jump over the moon.

_Paradoxer._--Great men have been derided, and I am derided: which proves that my system ought to be adopted. This is a summary of all the degrees in which paradoxers contend for the former derision of truths now established, giving their systems _probability_. I annex a paragraph which D [e &c.]

inserted in the _Athenaeum_ of October 23, 1847.

"_Discoverers and Discoveries._

"Aristotle once sent his servant to the cellar to fetch wine:--and the fellow brought him back small beer. The Stagirite (who knew the difference) called him a blockhead. 'Sir,' said the man, 'all I can say is, that I found it in the cellar.' The philosopher muttered to himself that an affirmative conclusion could not be proved in the second figure,--and Mrs.

Aristotle, who was by, was not less effective in her remark, that small beer was not wine because it was in the same cellar. Both were right enough: and our philosophers might take a lesson from either--for they insinuate an affirmative conclusion in the second figure. Great discoverers have been little valued by established {207} schools,--and they are little valued. The results of true science are strange at first,--and so are their's. Many great men have opposed existing notions,--and so do they. All great men were obscure at first,--and they are obscure. Thinking men doubt,--and they doubt. Their small beer, I grant, has come out of the same cellar as the wine; but this is not enough. If they had let it stand awhile in the old wine-casks, it might have imbibed a little of the flavor."

There are better reviews than I have noticed; which, though entirely dissenting, are una.s.sailable on their own principles. What I have given represents five-sixths of the whole. But it must be confessed that the fraction of fairness and moderation and suspended opinion which the doctrine of _Spirit Manifestations_ has met with--even in the lower reviews--is strikingly large compared to what would have been the case fifty years ago. It is to be hoped that our popular and periodical literatures are giving us one thinker created for twenty geese double-feathered: if this hope be realized, we shall do! Seeing all that I see, I am not prepared to go the length of a friend of mine who, after reading a good specimen of the lower reviewing, exclaimed--Oh! if all the fools in the world could be rolled up into one fool, what a reviewer he would make!

Calendrier Universel et Perpetuel; par le Commandeur P. J. Arson.[352]

Publie par ses Enfans (Oeuvre posthume). Nice, 1863, 4to.

I shall not give any account of this curious calendar, with all its changes and symbols. But there is one proposal, which, could we alter the general notions of time--a thing of very dubious possibility--would be convenient.

The week is made to wax and wane, culminating on the Sunday, {208} which comes in the middle. Thursday, Friday, Sat.u.r.day, are ascending or waxing days; Monday, Tuesday, Wednesday, are descending or waning days. Our six days, lumped together after the great distinguishing day, Sunday, are too many to be distinctly thought of together: a division of three preceding and three following the day of most note would be much more easily used.

But all this comes too late. It may be, nevertheless, that some individuals may be able to adjust their affairs with advantage by referring Thursday, Friday, Sat.u.r.day, to the following Sunday, and Monday, Tuesday, Wednesday, to the preceding Sunday. But M. Arson's proposal to alter the names of the days is no more necessary than it is practicable.

CYCLOMETRY.

I am not to enter anything I do not possess. The reader therefore will not learn from me the feats of many a man-at-arms in these subjects. He must be content, unless he will bestir himself for himself, not to know how Mr.

Patrick Cody trisects the angle at Mullinavat, or Professor Recalcati squares the circle at Milan. But this last is to be done by subscription, at five francs a head: a banker is named who guarantees rest.i.tution if the solution be not perfectly rigorous; the banker himself, I suppose, is the judge. I have heard of a man of business who settled the circle in this way: if it can be reduced to a debtor and creditor account, it can certainly be done; if not, it is not worth doing. Montucla will give the accounts of the lawsuits which wagers on the problem have produced in France.

Neither will I enter at length upon the success of the new squarer who advertises (Nov. 1863) in a country paper that, having read that the circular ratio was undetermined, "I thought it very strange that so many great scholars in all ages should have failed in finding the true ratio, and have been determined to try myself.... I am about to secure the {209} benefit of the discovery, so until then the public cannot know my new and true ratio." I have been informed that this trial makes the diameter to the circ.u.mference as 64 to 201, giving [pi] = 3.140625 exactly. The result was obtained by the discoverer in three weeks after he first heard of the existence of the difficulty. This quadrator has since published a little slip, and entered it at Stationers' Hall. He says he has done it by actual measurement; and I hear from a private source that he uses a disk of 12 inches diameter, which he rolls upon a straight rail. Mr. James Smith did the same at one time; as did also his partisan at Bordeaux. We have, then, both 3.125 and 3.140625, by actual measurement. The second result is more than the first by about one part in 200. The second rolling is a very creditable one; it is about as much below the mark as Archimedes was above it. Its performer is a joiner, who evidently knows well what he is about when he measures; he is not wrong by 1 in 3,000.

The reader will smile at the quiet self-sufficiency with which "I have been determined to try myself" follows the information that "so many great scholars in all ages" have failed. It is an admirable spirit, when accompanied by common sense and uncommon self-knowledge. When I was an undergraduate there was a little attendant in the library who gave me the following,--"As to cleaning this library, Sir, if I have spoken to the Master once about it, I have spoken fifty times: but it is of no use; he will not employ _littery_ men; and so I am obliged to look after it myself."

I do not think I have mentioned the bright form of quadrature in which a square is made equal to a circle by making each side equal to a quarter of the circ.u.mference. The last squarer of this kind whom I have seen figures in the last number of the _Athenaeum_ for 1855: he says the thing is no longer a _problem_, but an _axiom_. He does not know that the area of the circle is greater than that of any other figure of the same circuit. This any one might see without {210} mathematics. How is it possible that the figure of greatest area should have any one length in its circuit unlike in form to any other part of the same length?

The feeling which tempts persons to this problem is that which, in romance, made it impossible for a knight to pa.s.s a castle which belonged to a giant or an enchanter. I once gave a lecture on the subject: a gentleman who was introduced to it by what I said remarked, loud enough to be heard by all around, "Only prove to me that it is impossible, and I will set about it this very evening."

This rinderpest of geometry cannot be cured, when once it has seated itself in the system: all that can be done is to apply what the learned call prophylactics to those who are yet sound. When once the virus gets into the brain, the victim goes round the flame like a moth; first one way and then the other, beginning where he ended, and ending where he begun: thus verifying the old line

"In girum imus nocte, ecce! et consumimur igni."[353]

Every mathematician knows that scores of methods, differing altogether from each other in process, all end in this mysterious 3.14159..., which insists on calling itself the circ.u.mference to a unit of diameter. A reader who is competent to follow processes of arithmetic may be easily satisfied that such methods do actually exist. I will give a sketch, carried out to a few figures, of three: the first two I never met with in my reading; the third is the old method of Vieta.[354] [I find that both the first and second methods are contained in a theorem of Euler.]

What Mr. James Smith says of these methods is worth noting. He says I have given three "_fancy_ proofs" of the value of [pi]: he evidently takes me to be offering demonstration. He proceeds thus:--

"His first proof is traceable to the diameter of a circle {211} of radius 1. His second, to the side of any inscribed equilateral triangle to a circle of radius 1. His third, to a radius of a circle of diameter 1. Now, it may be frankly admitted that we can arrive at the same result by many other modes of arithmetical calculation, all of which may be shown to have some sort of relation to a circle; but, after all, these results are mere exhibitions of the properties of numbers, and have no more to do with the ratio of diameter to circ.u.mference in a circle than the price of sugar with the mean height of spring tides. (_Corr._ Oct. 21, 1865)."

I quote this because it is one of the few cases--other than absolute a.s.sumption of the conclusion--in which Mr. Smith's conclusions would be true if his premise were true. Had I given what follows as _proof_, it would have been properly remarked, that I had only exhibited properties of numbers. But I took care to tell my reader that I was only going to show him _methods_ which end in 3.14159.... The proofs that these methods establish the value of [pi] are for those who will read and can understand.

200000000 31415 3799 66666667 2817 26666667 1363 11428571 661 5079365 321 2308802 156 1065601 76 497281 37 234014 18 110849 9 52785 5 25245 2 12118 1 5834 -------- -------- ------- 314153799 31415 9265

{212}

1. Take any diameter, double it, take 1-3d of that double, 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on. The sum of all is the circ.u.mference of that diameter. The preceding is the process when the diameter is a hundred millions: the errors arising from rejection of fractions being lessened by proceeding on a thousand millions, and striking off one figure. Here 200 etc. is double of the diameter; 666 etc. is 1-3rd of 200 etc.; 266 etc. is 2-5ths of 666 etc.; 114 etc. is 3-7ths of 266 etc.; 507 etc. is 4-9ths of 114 etc.; and so on.

2. To the square root of 3 add its half. Take _half_ the third part of this; half 2-5ths of the last; half 3-7ths of the last; and so on. The sum is the circ.u.mference to a unit of diameter.