A Budget of Paradoxes Volume II Part 11

t.i.t for tat is logic all the world over. By the way, what has become of the rest of the maxim: we never hear it {122} now. When I was a boy, in some parts of the country at least, it ran thus:

"t.i.t for tat; b.u.t.ter for fat: If you kill my dog, I'll kill your cat."

He is a glaring instance of the truth of the observations quoted above. I will answer for it that, at the Mersey Dock Board, he never dreams of proving that the balance at the banker's is larger than that in the book by a.s.suming that the larger sum is there, and then proving that the other supposition--the smaller balance--is upon that a.s.sumption, an absurdity. He never says to another director, How can you dare to refuse me a right to a.s.sume the larger balance, when you yourself, the other day, said,--Suppose, for argument's sake, we had 80,000l. at the banker's, though you knew the book only showed 30,000l.? This is the way in which he has supported his geometrical paradox by Euclid's example: and this is not the way he reasons at the board; I know it by the character of him as a man of business which has reached my ears from several quarters. But in geometry and rational arithmetic he is a smatterer, though expert at computation; at the board he is a trained man of business. The language of geometry is so new to him that he does not know what is meant by "two mean proportionals:" but all the phrases of commerce are rooted in his mind. He is most unerasably booked in the history of the squaring of the circle, as the speculator who took a right to a.s.sume a proposition for the destruction of other propositions, on the express ground that Euclid a.s.sumes a proposition to show that it destroys itself: which is as if the curate should demand permission to throttle the squire because St. Patrick drove the vermin to suicide to save themselves from slaughter. He is conspicuous as a speculator who, more visibly than almost any other known to history, reasoned in a circle by way of reasoning on a circle. But {123} what I have chiefly to do with is the force of instance which he has lent to my a.s.sertion that men who have not had real training in pure logic are unsafe reasoners in matter which is not familiar. It is hard to get first-rate examples of this, because there are few who find the way to the printer until practice and reflection have given security against the grossest slips. I cannot but think that his case will lead many to take what I have said into consideration, among those who are competent to think of the great mental disciplines. To this end I should desire him to continue his efforts, to amplify and develop his great principle, that of proving a proposition by a.s.suming it and taking as confirmation every consequence that does not contradict the a.s.sumption.

Since my Budget commenced, Mr. Smith has written me notes: the portion which I have preserved--I suppose several have been mislaid--makes a hundred and seven pages of note-paper, closely written. To all this I have not answered one word: but I think I cannot have read fewer than forty pages. In the last letter the writer informs me that he will not write at greater length until I have given him an answer, according to the "rules of good society." Did I not know that for every inch I wrote back he would return an ell? Surely in vain the net is spread in the eyes of anything that hath a wing. There were several good excuses for not writing to Mr. J.

Smith: I will mention five. First, I distinctly announced at the beginning of this Budget that I would not communicate with squarers of the circle.

Secondly, any answer I might choose to give might with perfect propriety be reserved for this article; had the imputation of incivility been made after the first note, I should immediately have replied to this effect: but I presumed it was quite understood. Thirdly, Mr. Smith, by his publication of E. M.'s letters against the wish of the writer, had put himself out of the pale of correspondence. Fourthly, he had also gone beyond the rules of good society in sending {124} letter after letter to a person who had shown by his silence an intention to avoid correspondence. Fifthly, these same rules of good society are contrived to be flexible or frangible in extreme cases: otherwise there would be no living under them; and good society would be bad. Father Aldrovand has laid down the necessary distinction--"I tell thee, thou foolish Fleming, the text speaketh but of promises made unto Christians, and there is in the rubric a special exemption of such as are made to Welchmen." There is also a rubric to the rules of good society; and squarers of the circle are among those whom there is special permission not to answer: they are the wild Welchmen of geometry, who are always a.s.sailing, but never taking, the Garde Douloureuse[219] of the circle. "At this commentary," proceeds the story, "the Fleming grinned so broadly as to show his whole case of broad strong white teeth." I know not whether the Welchman would have done the like, but I hope Mr. James Smith will: and I hope he has as good a case to show as Wilkin Flammock. For I wish him long life and long health, and should be very glad to see so much energy employed in a productive way. I hope he wishes me the same: if not, I will give him what all his judicious friends will think a good reason for doing so. His pamphlets and letters are all tied up together, and will form a curious lot when death or cessation of power to forage among book-shelves shall bring my little library to the hammer. And this time may not be far off: for I was X years old in A.D. X^2; not 4 in A.D. 16, nor 5 in A.D. 25, but still in one case under that law. And now I have made my own age a problem of quadrature, and Mr. J. Smith may solve it. But I protest against his method of a.s.suming a result, and making itself prove itself: he might in this way, as sure as eggs is eggs (a corruption of X is X), make me 1,864 years old, which is a great deal too much.

{125}

_April 5, 1864._--Mr. Smith continues to write me long letters, to which he hints that I am to answer. In his last, of 31 closely written sides of note-paper, he informs me, with reference to my obstinate silence, that though I think myself and am thought by others to be a mathematical Goliath, I have resolved to play the mathematical snail, and keep within my sh.e.l.l. A mathematical _snail_! This cannot be the thing so called which regulates the striking of a clock; for it would mean that I am to make Mr.

Smith sound the true time of day, which I would by no means undertake upon a clock that gains 19 seconds odd in every hour by false quadrature. But he ventures to tell me that pebbles from the sling of simple truth and common sense will ultimately crack my sh.e.l.l, and put me _hors de combat_.[220] The confusion of images is amusing: Goliath turning himself into a snail to avoid [pi] = 3-1/8, and James Smith, Esq., of the Mersey Dock Board: and put _hors de combat_--which should have been _cache_[221]--by pebbles from a sling. If Goliath had crept into a snail-sh.e.l.l, David would have cracked the Philistine with his foot. There is something like modesty in the implication that the crack-sh.e.l.l pebble has not yet taken effect; it might have been thought that the slinger would by this time have been singing--

"And thrice [and one-eighth] I routed all my foes, And thrice [and one-eighth] I slew the slain."

But he promises to give the public his nut-cracker if I do not, before the Budget is concluded, "unravel" the paradox, which is the mathematico-geometrical nut he has given me to crack. Mr. Smith is a crack man: he will crack his own nut; he will crack my sh.e.l.l; in the mean time he cracks himself up. Heaven send he do not crack himself into lateral contiguity with himself.

On June 27 I received a letter, in the handwriting of Mr. James Smith, signed Nauticus. I have ascertained {126} that one of the letters to the _Athenaeum_ signed Nauticus is in the same handwriting. I make a few extracts:

"... The important question at issue has been treated by a brace of mathematical birds with too much levity. It may be said, however, that sarcasm and ridicule sometimes succeed, where reason fails.... Such a course is not well suited to a discussion.... For this reason I shall for the future [this implies there has been a past, so that Nauticus is not before me for the first time] endeavor to confine myself to dry reasoning from incontrovertible premises.

... It appears to me that so far as his theory is concerned he comes off unscathed. You might have found "a hole in Smith's circle" (have you seen a pamphlet bearing this t.i.tle? [I never heard of it until now]), but after all it is quite possible the hole may have been left by design, for the purpose of entrapping the unwary."

[On the publication of the above, the author of the pamphlet obligingly forwarded a copy to me of _A Hole in Smith's Circle_--by a Cantab: Longman and Co., 1859, (pp. 15). "It is pity to lose any fun we can get out of the affair," says my almamaternal brother: to which I add that in such a case warning without joke is worse than none at all, as giving a false idea of the nature of the danger. The Cantab takes some absurdities on which I have not dwelt: but there are enough to afford a Cantab from every college his own separate hunting ground.]

Does this hint that his mode of proof, namely, a.s.suming the thing to be proved, was a design to entrap the unwary? if so, it bangs Banagher. Was his confounding two mean proportionals with one mean proportional found twice over a trick of the same intent? if so, it beats c.o.c.kfighting. That Nauticus is Mr. Smith appears from other internal evidence. In 1819, Mr.

J. C. Hobhouse[222] was sent to Newgate for a {127} libel on the House of Commons which was only intended for a libel on Lord Erskine.[223] The ex-Chancellor had taken Mr. Hobhouse to be thinking of him in a certain sentence; this Mr. Hobhouse denied, adding, "There is but one man in the country who is always thinking of Lord Erskine." I say that there is but one man of our day who would couple me and Mr. James Smith as a "brace of mathematical birds."

Mr. Smith's "theory" is unscathed by me. Not a doubt about it: but how does he himself come off? I should never think of refuting a theory proved by a.s.sumption of itself. I left Mr. Smith's [pi] untouched: or, if I put in my thumb and pulled out a plum, it was to give a notion of the cook, not of the dish. The "important question at issue" was not the circle: it was, wholly and solely, whether the abbreviation of _James_ might be spelled _Jimm_.[224] This is personal to the verge of scurrility: but in literary controversy the challenger names the weapons, and Mr. Smith begins with charge of ignorance, folly, and dishonesty, by conditional implication. So that the question is, not the personality of a word, but its applicability to the person designated: it is enough if, as the Latin grammar has it, _Verb.u.m personale concordat c.u.m nominativo_.[225]

I may plead precedent for taking a liberty with the orthography of _Jem_.

An instructor of youth was scandalized at the abrupt and irregular--but very effective--opening of Wordsworth's little piece:

{128}

"A simple child That lightly draws its breath, And feels its life in every limb, What should it know of death?"

So he mended the matter by instructing his pupils to read the first line thus:

"A simple child, dear brother ----."

The brother, we infer from sound, was to be James, and the blank must therefore be filled up with _Jimb_.

I will notice one point of the letter, to make a little more distinction between the two birds. Nauticus lays down--quite correctly--that the sine of an angle is less than its circular measure. He then takes 3.1416 for 180, and finds that 36' is .010472. But this is exactly what he finds for the sine of 36' in tables: he concludes that either 3.1416 or the tables must be wrong. He does not know that sines, as well as [pi], are interminable decimals, of which the tables, to save printing, only take in a finite number. He is a six-figure man: let us go thrice again to make up nine, and we have as follows:

Circular measure of 36' .010471975...

Sine of 36' .010471784...

Excess of measure over sine .000000191...

Mr. Smith invites me to say which is wrong, the quadrature, or the tables: I leave him to guess. He says his a.s.sertions "arise naturally and necessarily out of the arguments of a circle-squarer:" he might just as well lay down that all the pigs went to market because it is recorded that "_This_ pig went to market." I must say for circle-squarers that very few bring their pigs to so poor a market. I answer the above argument because it is, of all which Mr. James Smith has produced, the only one which rises to the level of a schoolboy: to meet him halfway I descend to that level.

Mr. Smith asks me to solve a problem in the _Athenaeum_: {129} and I will do it, because the question will ill.u.s.trate what is _below_ schoolboy level.

"Let x represent the circular measure of an angle of 15, and y half the sine of an angle of 30 = area of the square on the radius of a circle of diameter unity = .25. If x - y = xy, firstly, what is the arithmetical value of xy? secondly, what is the angle of which xy represents the circular measure?"

If x represent 15 and y be , xy represents 3 45', whether x - y be xy or no. But, y being , x - y is _not_ xy unless x be 1/3, that is, unless 12x or [pi] be 4, which Mr. Smith would not admit. How could a person who had just received such a lesson as I had given immediately pray for further exposure, furnis.h.i.+ng the stuff so liberally as this? Is it possible that Mr. Smith, because he signs himself Nauticus, means to deny his own very regular, legible, and peculiar hand? It is enough to make the other members of the Liverpool Dock Board cry, Mersey on the man!

Mr. Smith says that for the future he will give up what he calls sarcasm, and confine himself, "as far as possible," to what he calls dry reasoning from incontrovertible premises. If I have fairly taught him that _his_ sarcasm will not succeed, I hope he will find that his wit's end is his logic's beginning.

I now reply to a question I have been asked again and again since my last Budget appeared: Why do you take so much trouble to expose such a reasoner as Mr. Smith? I answer as a deceased friend of mine used to answer on like occasions--A man's capacity is no measure of his power to do mischief. Mr.

Smith has untiring energy, which does something; self-evident honesty of conviction, which does more; and a long purse, which does most of all. He has made at least ten publications, full of figures which few readers can criticize. A great many people are staggered to this extent, that they imagine there must be {130} the indefinite _something_ in the mysterious _all this_. They are brought to the point of suspicion that the mathematicians ought not to treat "all this" with such undisguised contempt, at least. Now I have no fear for [pi]: but I do think it possible that general opinion might in time demand that the crowd of circle-squarers, etc. should be admitted to the honors of opposition; and this would be a time-tax of five per cent., one man with another, upon those who are better employed. Mr. James Smith may be made useful, in hands which understand how to do it, towards preventing such opinion from growing. A speculator who expressly a.s.sumes what he wants to prove, and argues that all which contradicts it is absurd, _because_ it cannot stand side by side with his a.s.sumption, is a case which can be exposed to all.

And the best person to expose it is one who has lived in the past as well as the present, who takes misthinking from points of view which none but a student of history can occupy, and who has something of a turn for the business.

Whether I have any motive but public good must be referred to those who can decide whether a missionary chooses his pursuit solely to convert the heathen. I shall certainly be thought to have a little of the spirit of Col. Quagg, who delighted in strapping the Grace-walking Brethren. I must quote this myself: if I do not, some one else will, and then where am I?

The Colonel's principle is described as follows:

"I licks ye because I kin, and because I like, and because ye'se critters that licks is good for. Skins ye have on, and skins I'll have off; hard or soft, wet or dry, spring or fall. Walk in grace if ye like till pumpkins is peaches; but licked ye must be till your toe-nails drop off and your noses bleed blue ink. And--licked--they--were--accordingly."

I am reminded of this by the excessive confidence with which Mr. James Smith predicted that he would treat me as Zephaniah Stockdolloger (Sam Slick calls it _slockdollager_) treated Goliah Quagg. He has announced his {131} intention of bringing me, with a contrite heart, and clean shaved,--4159265... razored down to 25,--to a camp-meeting of circle-squarers. But there is this difference: Zephaniah only wanted to pa.s.s the Colonel's smithy in peace; Mr. James Smith sought a fight with me.

As soon as this Budget began to appear, he oiled his own strap, and attempted to treat me as the terrible Colonel would have treated the inoffensive brother.

He is at liberty to try again.

THE MOON HOAX.

The Moon-hoax; or the discovery that the moon has a vast population of human beings. By Richard Adams Locke.[226] New York, 1859, 8vo.

This is a reprint of the hoax already mentioned. I suppose R. A. Locke is the name a.s.sumed by M. Nicollet.[227] The publisher informs us that when the hoax first appeared day by day in a morning paper, the circulation increased fivefold, and the paper obtained a permanent footing. Besides this, an edition of 60,000 was sold off in less than one month.

The discovery was also published under the name of A. R. Grant.[228]

Sohncke's[229] _Bibliotheca Mathematica_ confounds this Grant with Prof. R.

Grant[230] of Glasgow, the author of the _History of Physical Astronomy_, who is accordingly made to guarantee the discoveries in the moon. I hope Adams Locke will not merge in J. C. Adams,[231] the co-discoverer of Neptune. Sohncke gives the t.i.tles of {132} three French translations of the Moon hoax at Paris, of one at Bordeaux, and of Italian translations at Parma, Palermo, and Milan.

A Correspondent, who is evidently fully master of details, which he has given at length, informs me that the Moon hoax appeared first in the _New York Sun_, of which R. A. Locke was editor. It so much resembled a story then recently published by Edgar A. Poe, in a Southern paper, "Adventures of Hans Pfaal," that some New York journals published the two side by side.

Mr. Locke, when he left the _New York Sun_, started another paper, and discovered the ma.n.u.script of Mungo Park;[232] but this did not deceive. The _Sun_, however, continued its career, and had a great success in an account of a balloon voyage from England to America, in seventy-five hours, by Mr.

Monck Mason,[233] Mr. Harrison Ainsworth,[234] and others. I have no doubt that M. Nicollet was the author of the Moon hoax,[235] written in a way which marks the practised observatory astronomer beyond all doubt, and by evidence seen in the most minute details. Nicollet had an eye to Europe. I suspect that he took Poe's story, and made it a basis for his own. Mr.

Locke, it would seem, when he attempted a fabrication for himself, did not succeed.

The Earth we inhabit, its past, present, and future. By Capt.

Drayson.[236] London, 1859, 8vo.

The earth is growing; absolutely growing larger: its diameter increases three-quarters of an inch per mile every year. The foundations of our buildings will give way in {133} time: the telegraph cables break, and no cause ever a.s.signed except s.h.i.+ps' anchors, and such things. The book is for those whose common sense is unwarped, who can judge evidence as well as the ablest philosopher. The prospect is not a bad one, for population increases so fast that a larger earth will be wanted in time, unless emigration to the Moon can be managed, a proposal of which it much surprises me that Bishop Wilkins has a monopoly.