A Budget of Paradoxes Volume II Part 28

"Prof. De Morgan, who, from his position in the scientific world, might fairly afford to look favourably on less practised efforts than his own, seems to delight in ridiculing the discoverer. Science is, of course, a very respectable person when he comes out and makes himself useful in the world [it must have been a lady; each s.e.x gives science to the other]: but when, like a monk of the Middle Ages, he shuts himself up [it must have been a lady; they always snub the bachelors] in his cloistered cell, repeating his mumpsimus from day to day, and despising the labourers on the outside, we begin to think of Galileo,[624] Jenner,[625] Harvey,[626] and other glorious trios, who have been contemned ..."

The writer then called upon Mr. James Smith[627] to come {337} forward. The irony was not seen; and that day fortnight appeared the first of more than thirty letters from his pen. Mr. Smith was followed by Mr. Reddie,[628]

Zadkiel,[629] and others, on their several subjects. To some of the letters I have referred; to others I shall come. The _Correspondent_ was to become a first-cla.s.s scientific journal; the time had arrived at which truth had an organ: and I received formal notice that I could not stifle it by silence, nor convert it into falsehood by ridicule. When my reader sees my extracts, he will readily believe my declaration that I should have been the last to stifle a publication which was every week what James Mill[630]

would call a dose of capital for my Budget. A few anti-paradoxers brought in common sense: but to the ma.s.s of the readers of the journal it all seemed to be the difference between Tweedledum and Tweedledee. Some said that the influx of scientific paradoxes killed the journal: but my belief is that they made it last longer than it otherwise would have done. Twenty years ago I recommended the paradoxers to combine and publish their views in a common journal: with a catholic editor, who had no pet theory, but a stern determination not to exclude anything merely for absurdity. I suspect it would answer very well. A strong t.i.tle, or motto, would be wanted: not so coa.r.s.e as was roared out in a Cambridge mob when I was an undergraduate--"No King! No Church! No House of Lords! No nothing, blast me!"--but something on that _principle_.

At the end of 1867 I addressed the following letter to the _Athenaeum_:

PSEUDOMATH, PHILOMATH, AND GRAPHOMATH.

_December 31, 1867_

Many thanks for the present of Mr. James Smith's letters {338} of Sept. 28 and of Oct. 10 and 12. He asks where you will be if you read and digest his letters: you probably will be somewhere first. He afterwards asks what the WE of the _Athenaeum_ will be if, finding it impossible to controvert, it should refuse to print. I answer for you, that We-We of the _Athenaeum_, not being Wa-Wa the wild goose, so conspicuous in "Hiawatha," will leave what controverts itself to print itself, if it please.

_Philomath_ is a good old word, easier to write and speak than _mathematician_. It wants the words between which I have placed it. They are not well formed: _pseudomathete_ and _graphomathete_ would be better: but they will do. I give an instance of each.

The _pseudomath_ is a person who handles mathematics as the monkey handled the razor. The creature tried to shave himself as he had seen his master do; but, not having any notion of the angle at which the razor was to be held, he cut his own throat. He never tried a second time, poor animal! but the pseudomath keeps on at his work, proclaims himself clean-shaved, and all the rest of the world hairy. So great is the difference between moral and physical phenomena! Mr. James Smith is, beyond doubt, the great pseudomath of our time. His 3-1/8 is the least of a wonderful chain of discoveries. His books, like Whitbread's barrels, will one day reach from Simpkin & Marshall's to Kew, placed upright, or to Windsor laid length-ways. The Queen will run away on their near approach, as Bishop Hatto did from the rats: but Mr. James Smith will follow her were it to John o' Groats.

The _philomath_, for my present purpose, must be exhibited as giving a lesson to presumption. The following anecdote is found in Thiebault's[631]

_Souvenirs de vingt ans de sejours a Berlin_, published in 1804. The book itself got a high character for truth. In 1807 Marshal Mollendorff[632]

{339} answered an inquiry of the Duc de Ba.s.sano,[633] by saying that it was the most veracious of books, written by the most honest of men. Thiebault does not claim personal knowledge of the anecdote, but he vouches for its being received as true all over the north of Europe.[634]

Diderot[635] paid a visit to Russia at the invitation of Catherine the Second. At that time he was an atheist, or at least talked atheism: it would be easy to prove him either one thing or the other from his writings.

His lively sallies on this subject much amused the Empress, and all the younger part of her Court. But some of the older courtiers suggested that it was hardly prudent to allow such unreserved exhibitions. The Empress thought so too, but did not like to muzzle her guest by an express prohibition: so a plot was contrived. The scorner was informed that an eminent mathematician had an algebraical proof of the existence of G.o.d, which he would communicate before the whole Court, if agreeable. Diderot gladly consented. The mathematician, who is not named, was Euler.[636] He came to Diderot with the gravest air, and in a tone of perfect conviction said, "_Monsieur!_

(a + b^n)/n = x

_donc Dieu existe; repondez!_"[637] Diderot, to whom algebra was Hebrew, though this is expressed in a very roundabout way by Thiebault--and whom we may suppose to have expected some verbal argument of alleged algebraical closeness, was disconcerted; while peals of laughter sounded on all sides.

Next day he asked permission to return to France, which was granted. An algebraist would have {340} turned the tables completely, by saying, "Monsieur! vous savez bien que votre raisonnement demande le developpement de x suivant les puissances entieres de n".[638] Goldsmith could not have seen the anecdote, or he might have been supposed to have drawn from it a hint as to the way in which the Squire demolished poor Moses.

The _graphomath_ is a person who, having no mathematics, attempts to describe a mathematician. Novelists perform in this way: even Walter Scott now and then burns his fingers. His dreaming calculator, Davy Ramsay, swears "by the bones of the immortal Napier." Scott thought that the the philomaths wors.h.i.+ped relics: so they do, in one sense. Look into Hutton's[639] Dictionary for _Napier's Bones_, and you shall learn all about the little knick-knacks by which he did multiplication and division.

But never a bone of his own did he contribute; he preferred elephants'

tusks. The author of _Headlong Hall_[640] makes a grand error, which is quite high science: he says that Laplace proved the precession of the equinoxes to be a periodical inequality. He should have said the variation of the obliquity. But the finest instance is the following: Mr.

Warren,[641] in his well-wrought tale of the martyr-philosopher, was incautious enough to invent the symbols by which his _savant_ satisfied himself Laplace[642] was right on a doubtful point. And this is what he put together--

[sqrt]-3a^2, [rectangle]y^2 / z^2 + 9 - n = 9, n log e.

Now, to Diderot and the ma.s.s of mankind this might be Laplace all over: and, in a forged note of Pascal, would {341} prove him quite up to gravitation. But I know of nothing like it, except in the lately received story of the American orator, who was called on for some Latin, and perorated thus: "Committing the destiny of the country to your hands, Gentlemen, I may without fear declare, in the language of the n.o.ble Roman poet,

E pluribus unum, Multum in parvo, Ultima Thule, Sine qua non."[643]

But the American got nearer to Horace than the martyr-philosopher to Laplace. For all the words are in Horace, except _Thule_, which might have been there. But [rectangle] is not a symbol wanted by Laplace; nor can we see how it could have been; in fact, it is not recognized in algebra. As to the junctions, etc., Laplace and Horace are about equally well imitated.

Further thanks for Mr. Smith's letters to you of Oct. 15, 18, 19, 28, and Nov. 4, 15. The last of these letters has two curious discoveries. First, Mr. Smith declares that he has _seen_ the editor of the _Athenaeum_: in several previous letters he mentions a name. If he knew a little of journalism he would be aware that editors are a peculiar race, obtained by natural selection. They are never seen, even by their officials; only heard down a pipe. Secondly, "an ellipse or oval" is composed of four arcs of circles. Mr. Smith has got hold of the construction I was taught, when a boy, for a pretty four-arc oval. But my teachers knew better than to call it an ellipse: Mr. Smith does not; but he produces from it such confirmation of 3-1/8 as would convince any _honest_ editor.

Surely the cyclometer is a Darwinite development of a spider, who is always at circles, and always begins again when his web is brushed away. He informs you that he {342} has been privileged to discover truths unknown to the scientific world. This we know; but he proceeds to show that he is equally fortunate in art. He goes on to say that he will make use of you to bring those truths to light, "just as an artist makes use of a dummy for the purpose of arranging his drapery." The painter's lay-figure is for flowing robes; the hairdresser's dummy is for curly locks. Mr. James Smith should read Sam Weller's pathetic story of the "four wax dummies." As to _his_ use of a dummy, it is quite correct. When I was at University College, I walked one day into a room in which my Latin colleague was examining. One of the questions was, "Give the lives and fates of Sp.

Maelius,[644] and Sp. Ca.s.sius."[645] Umph! said I, surely all know that Spurius Maelius was whipped for adulterating flour, and that Spurius Ca.s.sius was hanged for pa.s.sing bad money. Now, a robe arranged on a dummy would look just like the toga of Ca.s.sius on the gallows. Accordingly, Mr. Smith is right in the drapery-hanger which he has chosen: he has been detected in the attempt to pa.s.s bad circles. He complains bitterly that his geometry, instead of being read and understood by you, is handed over to me to be treated after my scurrilous fas.h.i.+on. It is clear enough that he would rather be handled in this way than not handled at all, or why does he go on writing? He must know by this time that it is a part of the inst.i.tution that his "untruthful and absurd trash" shall be distilled into mine at the rate of about 3-1/8 pages of the first to one column of the second. Your readers will never know how much they gain by the process, until Mr. James Smith publishes it all in a big book, or until they get hold of what he has already published. I have six pounds avoirdupois of pamphlets and letters; and there is more than half a pound of letters {343} written to you in the last two months. Your compositor must feel aggrieved by the rejection of these clearly written doc.u.ments, without erasures, and on one side only.

Your correspondent has all the makings of a good contributor, except the knowledge of his subject and the sense to get it. He is, in fact, only a mask: of whom the fox

"O quanta species, inquit, cerebrum non habet."[646]

I do not despair of Mr. Smith on any question which does not involve that unfortunate two-stick wicket at which he persists in bowling. He has published many papers; he has forwarded them to mathematicians: and he cannot get answers; perhaps not even readers. Does he think that he would get more notice if you were to print him in your journal? Who would study his columns? Not the mathematician, we know; and he knows. Would others?

His b.a.l.l.s are aimed too wide to be blocked by any one who is near the wicket. He has long ceased to be worth the answer which a new invader may get. Rowan Hamilton,[647] years ago, completely knocked him over; and he has never attempted to point out any error in the short and easy method by which that powerful investigator condescended to show that, be right who may, he must be wrong. There are some persons who feel inclined to think that Mr. Smith should be argued with: let those persons understand that he has been argued with, refuted, and has never attempted to stick a pen into the refutation. He stated that it was a remarkable paradox, easily explicable; and that is all. After this evasion, Mr. James Smith is below the necessity of being told that he is unworthy of answer. His friends complain that I do nothing but _chaff_ him. Absurd! I winnow him; and if nothing but chaff results, whose fault is that? I am usefully employed: for he is the type of a cla.s.s which ought to be known, and which I have done much to make known.

{344}

Nothing came of this until July 1869, when I received a reprint of the above letter, with a comment, described as Appendix D of a work in course of publication on the geometry of the circle. The _Athenaeum_ journal received the same: but the Editor, in his private capacity, received the whole work, being _The Geometry of the Circle and Mathematics as applied to Geometry by Mathematicians, shown to be a mockery, delusion, and a snare_, Liverpool, 8vo, 1869. Mr. J. S. here appears in deep fight with Professor Whitworth,[648] and Mr. Wilson,[649] the author of the alleged amendment of Euclid. How these accomplished mathematicians could be inveigled into continued discussion is inexplicable. Mr. Whitworth began by complaining of Mr. Smith's attacks upon mathematicians, continued to correspond after he was convinced that J. S. proved an arc and its chord to be equal, and only retreated when J. S. charged him with believing in 3-1/8, and refusing acknowledgment. Mr. Wilson was introduced to J. S. by a volunteer defense of his geometry from the a.s.saults of the _Athenaeum_. This the editor would not publish; so J. S. sent a copy to Mr. Wilson himself. Some correspondence ensued, but Mr. Wilson soon found out his man, and withdrew.

There is a little derision of the _Athenaeum_ and a merited punishment for "that unscrupulous critic and contemptible mathematical twaddler, De Morgan."

MR. REDDIE'S ASTRONOMY.

At p. 183 I mentioned Mr. Reddie,[650] the author of _Vis Inertiae Victa_ and of _Victoria toto coelo_,[651] which last is not {345} an address to the whole heaven, either from a Roman G.o.ddess or a British Queen, whatever a scholar may suppose. Between these Mr. Reddie has published _The Mechanics of the Heavens_, 8vo, 1862: this I never saw until he sent it to me, with an invitation to notice it, he very well knowing that it would catch. His speculations do battle with common notions of mathematics and of mechanics, which, to use a feminine idiom, he blasphemes so you can't think! and I suspect that if you do not blaspheme them too, _you_ can't think. He appeals to the "truly scientific," and would be glad to have readers who have read what he controverts, i.e., Newton's _Principia_: I wish he may get them; I mean I hope he may obtain them. To none but these would an account of his speculations be intelligible: I accordingly disposed of him in a very short paragraph of description. Now many paradoxers desire notice, even though it be disparaging. I have letters from more than one--besides what have been sent to the Editor of the _Athenaeum_--complaining that they are not laughed at; although they deserve it, they tell me, as much as some whom I have inserted. Mr. Reddie informs me that I have not said a single word against his books, though I have given nearly a column to sixteen-string arithmetic, and as much to animalcule universes. What need to say anything to readers of Newton against a book from which I quoted that revolution by gravitation is _demonstrably_ impossible? It would be as useless as evidence against a man who has pleaded guilty. Mr. Reddie derisively thanks me for "small mercies"; he wrote me private letters; he published them, and more, in the _Correspondent_. He gave me, _pro viribus suis_,[652] such a dressing you can't think, both for my Budget non-notice, and for reviews which he a.s.sumed me to have written. He outlawed himself by declaring (_Correspondent_, Nov. 11, 1856) that I--in a review--had made a quotation which was "garbled, evidently on purpose {346} to make it appear that" he "was advocating solely a geocentric hypothesis, which is not true." In fact, he did his best to get larger "mercy." And he shall have it; and at a length which shall content him, unless his mecometer be an insatiable apparatus. But I fear that in other respects I shall no more satisfy him than the Irish drummer satisfied the poor culprit when, after several times changing the direction of the stroke at earnest entreaty, he was at last provoked to call out, "Bad cess to ye, ye spalpeen! strike where one will, there's no _plasing_ ye!"

Mr. Reddie attaches much force to Berkeley's[653] old arguments against the doctrine of fluxions, and advances objections to Newton's second section, which he takes to be new. To me they appear "such as have been often made,"

to copy a description given in a review: though I have no doubt Mr. Reddie got them out of himself. But the whole matter comes to this: Mr. Reddie challenged answer, especially from the British a.s.sociation, and got none.

He presumes that this is because he is right, and cannot be answered: the a.s.sociation is willing to risk itself upon the counter-notion that he is wrong, and need not be answered; because so wrong that none who could understand an answer would be likely to want one.

Mr. Reddie demands my attention to a point which had already particularly struck me, as giving the means of showing to _all_ readers the kind of confusion into which paradoxers are apt to fall, in spite of the clearest instruction. It is a very honest blunder, and requires notice: it may otherwise mislead some, who may suppose that no one able to read could be mistaken about so simple a matter, {347} let him be ever so wrong about Newton. According to his own mis-statement, in less than five months he made the Astronomer Royal abandon the theory of the solar motion in s.p.a.ce.

The announcement is made in August, 1865, as follows: the italics are not mine:

"The third (_Victoria ..._), although only published in September, 1863, has already had its triumph. _It is the book that forced the Astronomer Royal of England, after publicly teaching the contrary for years, to come to the conclusion, "strange as it may appear," that "the whole question of solar motion in s.p.a.ce is at the present time in doubt and abeyance."_ This admission is made in the Annual Report of the Council of the Royal Astronomical Society, published in the Society's _Monthly Notices_ for February, 1864."

It is added that solar motion is "full of self-contradiction, which "the astronomers" simply overlooked, but which they dare not now deny after being once pointed out."

The following is another of his accounts of the matter, given in the _Correspondent_, No. 18, 1865:

"... You ought, when you came to put me in the 'Budget,' to have been aware of the Report of the Council of the Royal Astronomical Society, where it appears that Professor Airy,[654] with a better appreciation of my demonstrations, had admitted--'strange,' say the Council, 'as it may appear,'--that 'the whole question of solar motion in s.p.a.ce [and here Mr. Reddie omits some words] is now in _doubt and abeyance_.' You were culpable as a public teacher of no little pretensions, if you were 'unaware' of this. If aware of it, you ought not to have suppressed such an important testimony to my really having been 'very successful'

in drawing the teeth of the pegtops, though you thought them so firmly fixed. And if you still suppress {348} it, in your Appendix, or when you reprint your 'Budget,' you will then be guilty of a _suppressio veri_, also of further injury to me, who have never injured you...."

Mr. Reddie must have been very well satisfied in his own mind before he ventured such a challenge, with an answer from me looming in the distance.

The following is the pa.s.sage of the Report of the Council, etc., from which he quotes:

"And yet, strange to say, notwithstanding the near coincidence of all the results of the before-mentioned independent methods of investigation, the inevitable logical inference deduced by Mr. Airy is, that the whole question of solar motion in s.p.a.ce, _so far at least as accounting for the proper motion of the stars is concerned_, [I have put in italics the words omitted by Mr. Reddie] appears to remain at this moment in doubt and abeyance."

Mr. Reddie has forked me, as he thinks, on a dilemma: if unaware, culpable ignorance; if aware, suppressive intention. But the thing is a _trilemma_, and the third horn, on which I elect to be placed, is surmounted by a doubly-stuffed seat. First, Mr. Airy has not changed his opinion about the _fact_ of solar motion in s.p.a.ce, but only suspends it as to the sufficiency of present means to give the amount and direction of the motion. Secondly, all that is alluded to in the Astronomical Report was said and printed before the Victoria proclamation appeared. So that the author, instead of drawing the tooth of the Astronomer Royal's pegtop, has burnt his own doll's nose.

William Herschel,[655] and after him about six other astronomers, had aimed at determining, by the proper motions of the stars, the point of the heavens towards which the solar system is moving: their results were tolerably accordant. Mr. Airy, in 1859, proposed an improved method, and, applying it to stars of large proper motion, produced {349} much the same result as Herschel. Mr. E. Dunkin,[656] one of Mr. Airy's staff at Greenwich, applied Mr. Airy's method to a very large number of stars, and produced, again, nearly the same result as before. This paper was read to the Astronomical Society in _March_, 1863, was printed in abstract in the _Notice_ of that month, was printed in full in the volume then current, and was referred to in the Annual Report of the Council in _February_, 1864, under the name of "the Astronomer Royal's elaborate investigation, as exhibited by Mr. Dunkin." Both Mr. Airy and Mr. Dunkin express grave doubts as to the sufficiency of the data: and, regarding the coincidence of all the results as highly curious, feel it necessary to wait for calculations made on better data. The report of the Council states these doubts. Mr.

Reddie, who only published in _September_, 1863, happened to see the Report of February, 1864, a.s.sumes that the doubts were then first expressed, and declares that his book of September had the triumph of forcing the Astronomer Royal to abandon the _fact_ of motion of the solar system by the February following. Had Mr. Reddie, when he saw that the Council were avowedly describing a memoir presented some time before, taken the precaution to find out _when_ that memoir was presented, he would perhaps have seen that doubts of the results obtained, expressed by one astronomer in March, 1863, and by another in 1859, could not have been due to his publication of September, 1863. And any one else would have learnt that neither astronomer doubts the _solar motion_, though both doubt the sufficiency of present means to determine its _amount_ and _direction_.

This is implied in the omitted words, which Mr. Reddie--whose omission would have been dishonest if he had seen their meaning--no doubt took for pleonasm, superfluity, overmuchness. The rashness which pushed him headlong {350} into the quillet that _his_ thunderbolt had stopped the chariot of the Sun and knocked the Greenwich Phaeton off the box, is the same which betrayed him into yet grander error--which deserves the full word, _quidlibet_--about the _Principia_ of Newton. There has been no change of opinion at all. When a person undertakes a long investigation, his opinion is that, at a certain date, there is _prima facie_ ground for thinking a sound result may be obtained. Should it happen that the investigation ends in doubt upon the sufficiency of the grounds, the investigator is not put in the wrong. He knew beforehand that there was an alternative: and he takes the horn of the alternative indicated by his calculations. The two sides of this case present an instructive contrast. Eight astronomers produce nearly the same result, and yet the last two doubt the sufficiency of their means: compare them with the what's-his-name who rushes in where thing-em-bobs fear to tread.

I was not aware, until I had written what precedes, that Mr. Airy had given a sufficient answer on the point. Mr. Reddie says (_Correspondent_, Jan.

20, 1866):

"I claim to have forced Professor Airy to give up the notion of 'solar motion in s.p.a.ce' altogether, for he admits it to be 'at present in doubt and abeyance.' I first made that claim in a letter addressed to the Astronomer Royal himself in June, 1864, and in replying, very courteously, to other portions of my letter, he did not gainsay that part of it."

Mr. Reddie is not ready at reading satire, or he never would have so missed the meaning of the courteous reply on one point, and the total silence upon another. Mr. Airy must be one of those peculiar persons who, when they do not think an a.s.sertion worth notice, let it alone, without noticing it by a notification of non-notice. He would never commit the bull of "Sir! I will not say a word on that subject." He would put it thus, "Sir! I will only say ten words on that subject,"--and, having thus said them, would {351} proceed to something else. He a.s.sumed, as a matter of form, that Mr. Reddie would draw the proper inference from his silence: and this because he did not care whether or no the a.s.sumption was correct.