A Budget of Paradoxes, Volume II
Chapter 5
feel able to protest against the manner in which Kidderminster has treated the other constituencies. We do not hold it impossible to give the Members of the House in general a sufficient knowledge of the meaning and consequences of the _decimal_ succession of units, tens, hundreds, thousands, etc.; and we believe that there are in the House itself competent men, in number enough to teach all the rest. All that is wanted is the power of starting from the known to arrive at the unknown. Now there is one kind of decimals with which every member is acquainted--the _Chiltern Hundreds_. If public opinion would enable the competent minority to start from this in their teaching, not as a basis, but as an alternative, in three weeks the fundamentals would be acquired, and members in general would be as fit to turn 4-1/2d. into mils, as any boys on the lower forms of a commercial school.
For a long period of years, allusion to the general ignorance of arithmetic, has been a standing mode of argument, and has always been well received: whenever one member describes others as _knownothings_, those others cry _Hear_ to the country in a transport of delight. In the meanwhile the country is gradually arriving at the conclusion that a true joke is no joke. "The main objection was, if Fine words, wrongly used. The they went below 6d., that the new coins are commensurable new scale of coins would not with, and in a finite ratio be commensurate in any finite to, the old ones. The farthing ratio with anything in this is to the mil as 25 to 24. The new currency of mils." speaker has something here in the bud, which we shall presently meet with in the flower; and fallacies are more easily nipped in flower than in bud. {176} "No less than five of our This dreadful change of value present coins must be called consists in sixpence farthing in, or else--which would be going to the half-shilling worse--new values must be instead of sixpence. Whether given to them." the new farthings be called mils or not is of no consequence. "If a poor man put a penny in Mr. Lowe, who cannot pass a his pocket, it would come out half-crown for more than a a coin of different value, florin, or get in a florin at which he would not understand. less than half-a-crown, has Suppose he owed another man a such a high faith in the penny, how was he to pay him ? sterner stuff of his fellow Was he to pay him in mils? countrymen, that he believes Four mils would be too little, any two of them would go to and five mils would be too fisty cuffs for the 25th part much. The hon. gentlemen said of a farthing. He reasons there would be only a mil thus: He has often heard in between them. That was exactly the streets, "I'd fight you it. He believed there would be for the fiftieth part of a a 'mill' between them." (Much farden:" and having (that is, laughter.) for a Member) a notion both of fractions and logic, he infers that those who would fight for the 50th of a farthing would, _a fortiori_, fight for a 25th. His mistake arises from his not knowing that when a person offers to fight another for 1/200d., he really means to fight for love; and that the stake is merely a matter of form, a feigned issue, a _pro forma_ report of progress. Do the Members of the House think they have all the forms to themselves? "What would be the present We should hardly believe all expression for four-pence? this to be uttered in earnest, Why, 0.166 (a laugh); for if we had not known {177} that threepence? .0125; for a several persons who have not penny? .004166, and so on _ad Mr. Lowe's humor, nevertheless infinitum_ (a laugh); for a have his impressions on this half-penny? .002083 _ad point. It must therefore be infinitum_. (A laugh). What answered; but how is this to would be the present be done seriously? expression for a farthing? Why, .0010416 _ad infinitum_. _Dialogue between a member of (A laugh). And this was the Parliament and an orange-boy, system which was to cause such three days after the a saving in figures, and these introduction of the complete were the quantities into which decimal system. The member, the poor would have to reduce going down to the House, wants the current coin of the realm. oranges to sustain his voice (Cheers). With every respect in a two hours' speech on for decimal fractions, of moving that 100000l. be placed which he boasted no profound at the disposal of Her knowledge, he doubted whether Majesty, to supply the poor the poor were equal to mental with ready-reckoners._ arithmetic of this kind, (hear, hear) and he hoped the _Boy._ Fine oranges! two a adoption of the system would penny! two a penny! {178} be deferred until there were some proof that they would be _Member._ Here boy, two! Now, able to understand it; for, how am I to pay you? after all, this was the question of the poor, and the _Boy._ Give you change, your whole weight of the change honor. would fall upon them. Let the rich by all means have _Member._ Ah! but how? Where's permission to perplex your ready-reckoner? themselves by any division of a pound they pleased; but do _Boy._ I sells a better sort not let them, by any nor them. Mine's real Cheyny. experiment like this, impose difficulties upon the poor and _Member._ But you see a compel men to carry farthing is now .0014166666 ready-reckoners in their _ad infinitum_, and if we pocket to give them all these multiply this by 4---- fractional quantities." (Hear, hear.) _Boy._ Hold hard, Guv'ner; I sees what you're arter. Now what'll you stand if I puts you up to it? which Bill Smith he put me up in two minutes, cause he goes to the Ragged School.
_Member._ You don't mean that you do without a book!
_Boy._ Book be blowed. Come now, old un, here's summut for both on us. I got a florin, you gives me a half-a-crown for it, and I larns you the new money, gives you your oranges, and calls you a brick into the bargain.
_Member_ (_to himself_). Never had such a chance of getting off half-a-crown for value since that ---- fellow Bowring carried his crochet. (_Aloud._) Well, boy, it's a bargain. Now!
_Boy._ Why, look 'e here, my trump, its a farden more to the tizzy--that's what it is.
_Member_. What's that?
_Boy._ Why, you knows a sixpence when you sees it. (_Aside_). Blest if I think he does! Well, its six browns and a farden now. A lady buys two oranges, and forks {179} out a sixpence; well in coorse, I hands over fippence farden astead of fippence. I always gives a farden more change, and takes according.
_Member_ (_in utter surprise, lets his oranges tumble into the gutter_). Never mind! They won't be wanted now. (_Walks off one way. Boy makes a pass of naso-digital mesmerism, and walks off the other way_).
To the poor, who keep no books, the whole secret is "Sixpence farthing to the half shilling, twelve pence halfpenny to the shilling." The _new twopence halfpenny_, or cent, will be at once five to the shilling.
In conclusion, we remark that three very common misconceptions run through the hon. Member's argument; and, combined in different proportions, give variety to his patterns.
First, he will have it that we design to bring the uneducated into contact with _decimal fractions_. If it be so, it will only be as M. Jourdain was brought into contact with prose. In fact, _Quoi! quand je dis, Nicole, apportez-moi mes pantoufles, c'est de la prose?_[305] may be rendered: "What! do you mean that _ten to the florin is a cent a piece_ must be called decimal reckoning?" If we had to comfort a poor man, horror-struck by the threat of _decimals_, we should tell him what manner of fractions had been inflicted upon him hitherto; nothing less awful than _quarto-duodecimo-vicesimals_, we should assure him.
Secondly, he assumes that the penny, such as it now is, will remain, as a coin of estimation, after it has ceased to be a coin of exchange; and that the mass of the people will continue to think of prices in old pence, and to calculate them in new ones, or else in new mils. No answer is required to this, beyond the mere statement of the nature of the assumption and denial.
{180}
Thirdly, he attributes to the uneducated community a want of perception and of operative power which really does not belong to them. The evidence offered to the Committee of the House shows that no fear is entertained on this point by those who come most in contact with farthing purchasers. And this would seem to be a rule,--that is, fear of the intelligence of the lower orders in the minds of those who are not in daily communication with them, no fear at all in the minds of those who are.
A remarkable instance of this distinction happened five-and-twenty years ago. The Admiralty requested the Astronomical Society to report on the alterations which should be made in the _Nautical Almanac_, the seaman's guide-book over the ocean. The greatest alteration proposed was the description of celestial phenomena in _mean_ (or clock time), instead of _apparent_ (or sundial) time, till then always employed. This change would require that in a great many operations the seaman should let alone what he formerly altered by addition or subtraction, and alter by addition or subtraction what he formerly let alone; provided always that what he formerly altered by addition he should, when he altered at all, alter by subtraction, and _vice versa_. This was a tolerably difficult change for uneducated skippers, working by rules they had only learned by rote. The Astronomical Society appointed a Committee of forty, of whom nine were naval officers or merchant seamen [I was on this Committee]. Some men of science were much afraid of the change. They could not trust an ignorant skipper or mate to make those alterations in their routine, on the correctness of which the ship might depend. Had the Committee consisted of men of science only, the change might never have been ventured on. But the naval men laughed, and said there was nothing to fear; and on their authority the alteration was made. The upshot was, that, after the new almanacs appeared, not a word of complaint was ever heard on the matter. Had the House of Commons had to {181} decide this question, with Mr. Lowe to quote the description given by Basil Hall[306] (who, by the way, was one of the Committee) of an observation on which the safety of the ship depended, worked out by the light of a lantern in a gale of wind off a lee shore, this simple and useful change might at this moment have been in the hands of its tenth Government Commission.
[_Aug. 14, 1866._ The Committee was appointed in the spring of 1830: it consisted of forty members. Death, of course, has been busy; there are now left Lord Shaftesbury,[307] Mr. Babbage,[308] Sir John Herschel,[309] Sir Thomas Maclear[310] (Astronomer Royal at the Cape of Good Hope), Dr. Robinson[311] (of Armagh), Sir James South,[312] Lord Wrottesley,[313] and myself].
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THE TONAL SYSTEM.
Project of a new system of arithmetic, weight, measure, and coins, proposed to be called the tonal system, with sixteen to the base. By J. W. Mystrom.[314] Philadelphia, 1862, 8vo.
That is to say, sixteen is to take the place of ten, and to be written 10. The whole language is to be changed; every man of us is to be sixteen-stringed Jack and every woman sixteen-stringed Jill. Our old _one_, _two_, _three_, up to sixteen, are to be (_Noll_ going for nothing, which will please those who dislike the memory of _Old Noll_) replaced by An, De, Ti, Go, Su, By, Ra, Me, Ni, Ko, Hu, Vy, La, Po, Fy, Ton; and then Ton-an, Ton-de, etc. for 17, 18, etc. The number which in the system has the symbol
28(13)5(11)7(14)0(15)
(using our present compounds instead of new types) is to be pronounced
Detam-memill-lasan-suton-hubong-ramill-posanfy.
The year is to have sixteen months, and here they are:
Anuary, Debrian, Timander, Gostus, Suvenary, Bylian, Ratamber, Mesudius, Nictoary, Kolumbian, Husamber, Vyctorius, Lamboary, Polian, Fylander, Tonborius.
Surely An-month, De-month, etc. would do as well. Probably the wants of poetry were considered. But what are we to do with our old poets? For example--
"It was a night of lovely June, High rose in cloudless blue the moon."
Let us translate--
"It was a night of lovely Nictoary, High rose in cloudless blue the (what, in the name of all that is absurd?)."
And again, _Fylander_ thrown into our December! What is {183} to become of those lines of Praed, which I remember coming out when I was at Cambridge,--
"Oh! now's the time of all the year for flowers and fun, the Maydays; To trim your whiskers, curl your hair, and sinivate the ladies."
If I were asked which I preferred, this system or that of Baron Ferrari[315] already mentioned, proceeding by _twelves_, I should reply, with Candide, when he had the option given of running the gauntlet or being shot: Les volontes sont libres, et je ne veux ni l'un ni l'autre.[316] We can imagine a speculator providing such a system for Utopia as it would be in the mind of a Laputan: but to explain how an engineer who has surveyed mankind from Philadelphia to Rostof on the Don should for a moment entertain the idea of such a system being actually adopted, would beat a jury of solar-system-makers, though they were shut up from the beginning of Anuary to the end of Tonborius. When I see such a scheme as this imagined to be practicable, I admire the wisdom of Providence in providing the quadrature of the circle, etc., to open a harmless sphere of action to the possessors of the kind of ingenuity which it displays. Those who cultivate mathematics have a right to speak strongly on such efforts of arithmetic as this: for, to my knowledge, persons who have no knowledge are frequently disposed to imagine that their makers are true brothers of the craft, a little more intelligible than the rest.
SOME SMALL PARADOXERS.
Vis inertiae victa,[317] or Fallacies affecting science. By James Reddie.[318] London, 1862, 8vo.
{184}
An attack on the Newtonian mechanics; revolution by gravitation demonstrably impossible; much to be said for the earth being the immovable center. A good analysis of contents at the beginning, a thing seldom found. The author has followed up his attack in a paper submitted to the British Association, but which it appears the Association declined to consider. It is entitled--
_Victoria Toto Coelo_; or, Modern Astronomy recast. London, 1863, 8vo.
At the end is a criticism of Sir G. Lewis's _History of Ancient Astronomy_.
On the definition and nature of the Science of Political Economy. By H. Dunning Macleod,[319] Esq. Cambridge, 1862, 8vo.
A paper read--but, according to the report, not understood--at the British Association. There is a notion that political economy is entirely mathematical; and its negative quantity is strongly recommended for study: it contains "the whole of the Funds, Credit, 32 parts out of 33 of the value of Land...." The mathematics are described as consisting of--first, number, or Arithmetic; secondly, the theory of dependent quantities, subdivided into dependence by cause and effect, and dependence by simultaneous variations; thirdly, "independent quantities or unconnected events, which is the theory of probabilities." I am not ashamed, having the British Association as a co-non-intelligent, to say I do not understand this: there is a paradox in it, and the author should give further explanation, especially of his negative quantity. Mr. Macleod has gained {185} praise from great names for his political economy; but this, I suspect, must have been for other parts of his system.
On the principles and practice of just Intonation, with a view to the abolition of temperament.... By General Perronet Thompson.[320] Sixth Edition. London, 1862, 8vo.
Here is General Thompson again, with another paradox: but always master of the subject, always well up in what his predecessors have done, and always aiming at a useful end. He desires to abolish temperament by additional keys, and has constructed an enharmonic organ with forty sounds in the octave. If this can be introduced, I, for one, shall delight to hear it: but there are very great difficulties in the way, greater than stood even in the way of the repeal of the bread-tax.
In a paper on the beats of organ-pipes and on temperament published some years ago, I said that equal temperament appeared to me insipid, and not so agreeable as the effect of the instrument when in progress towards being what is called out of tune, before it becomes offensively wrong. There is throughout that period unequal temperament, determined by accident. General Thompson, taking me one way, says I have launched a declaration which is likely to make an epoch in musical practice; a public musical critic, taking me another way, quizzes me for preferring music _out of tune_. I do not think I deserve either one remark or the other. My opponent critic, I suspect, takes _equally tempered_ and _in tune_ to be phrases of one meaning. But by equal temperament is meant equal distribution among all the keys of the error which an instrument _must_ have, which, with twelve sounds only in the octave, professes to be fit for all the keys. I am reminded of the equal temperament which was once applied to the postmen's jackets. The coats were all made for the average man: the {186} consequence was that all the tall men had their tails too short; all the short men had them too long. Some one innocently asked why the tall men did not change coats with the short ones.
A diagram illustrating a discovery in the relation of circles to right-lined geometrical figures. London, 1863, 12mo.
The circle is divided into equal sectors, which are joined head and tail: but a property is supposed which is not true.
An attempt to assign the square roots of negative powers; or what is [sqrt] -1? By F.H. Laing.[321] London, 1863, 8vo.
If I understand the author, -a and +a are the square roots of -a^2, as proved by multiplying them together. The author seems quite unaware of what has been done in the last fifty years.
BYRNE'S DUAL ARITHMETIC.
Dual Arithmetic. A new art. By Oliver Byrne.[322] London, 1863, 8vo.
The plan is to throw numbers into the form a(1.1)^{b} (1.01)^{c} (1.001)^{d}... and to operate with this form. This is an ingenious and elaborate speculation; and I have no doubt the author has practised his method until he could surprise any one else by his use of it. But I doubt if he will persuade others to use it. As asked of Wilkins's universal language, Where is the second man to come from?
An effective predecessor in the same line of invention {187} was the late Mr. Thomas Weddle,[323] in his "New, simple, and general method of solving numeric equations of all orders," 4to, 1842. The Royal Society, to which this paper was offered, declined to print it: they ought to have printed an organized method, which, without subsidiary tables, showed them, in six quarto pages, the solution (x=8.367975431) of the equation
1379.664 x^{622} + 2686034 x 10^{432} x^{152} - 17290224 x 10^{518} x^{60} + 2524156 x 10^{574} = 0.
The method proceeds by successive factors of the form, a being the first approximation, a x 1.b x 1.0c x 1.00d.... In my copy I find a few corrections made by me at the time in Mr. Weddle's announcement. "It was read before that learned body [the R. S.] and they were pleased [but] to transmit their thanks to the author. The en[dis]couragement which he received induces [obliges] him to lay the result of his enquiries in this important branch of mathematics before the public [, at his own expense; he being an usher in a school at Newcastle]." Which is most satirical, Mr. Weddle or myself? The Society, in the account which it gave of this paper, described it as a "new and remarkably simple method" possessing "several important advantages." Mr. Rutherford's[324] extended value of [pi] was read at the very next meeting, and was printed in the _Transactions_; and very properly: Mr. Weddle's paper was excluded, and very very improperly.
HORNER'S METHOD.
I think it may be admited that the indisposition to look at and encourage improvements of calculation which once {188} marked the Royal Society is no longer in existence. But not without severe lessons. They had the luck to accept Horner's[325] now celebrated paper, containing the method which is far on the way to become universal: but they refused the paper in which Horner developed his views of this and other subjects: it was printed by T. S. Davies[326] after Horner's death. I make myself responsible for the statement that the Society could not reject this paper, yet felt unwilling to print it, and suggested that it should be withdrawn; which was done.
But the severest lesson was the loss of _Barrett's Method_,[327] now the universal instrument of the actuary in his highest calculations. It was presented to the Royal Society, and refused admission into the _Transactions_: Francis Baily[328] printed it. The Society is now better informed: "_live and learn_," meaning "_must live, so better learn_," ought to be the especial motto of a corporation, and is generally acted on, more or less.
Horner's method begins to be introduced at Cambridge: it was published in 1820. I remember that when I first went to Cambridge (in 1823) I heard my tutor say, in conversation, there is no doubt that the true method of solving equations is the one which was published a few years ago in the _Philosophical Transactions_. I wondered it was not taught, but presumed that it belonged to the higher mathematics. This Horner himself had in his head: and in a sense it is true; for all lower branches belong to the higher: but he would have stared to have been told that he, Horner, {189} was without a European predecessor, and in the distinctive part of his discovery was heir-at-law to the nameless Brahmin--Tartar--Antenoachian--what you please--who concocted the extraction of the square root.
It was somewhat more than twenty years after I had thus heard a Cambridge tutor show sense of the true place of Horner's method, that a pupil of mine who had passed on to Cambridge was desired by his college tutor to solve a certain cubic equation--one of an integer root of two figures. In a minute the work and answer were presented, by Horner's method. "How!" said the tutor, "this can't be, you know." "There is the answer, Sir!" said my pupil, greatly amused, for my pupils learnt, not only Horner's method, but the estimation it held at Cambridge. "Yes!" said the tutor, "there is the answer certainly; but it _stands to reason_ that a cubic equation cannot be solved in this space." He then sat down, went through a process about ten times as long, and then said with triumph: "There! that is the way to solve a cubic equation!"
I think the tutor in this case was never matched, except by the country organist. A master of the instrument went into the organ-loft during service, and asked the organist to let him _play the congregation out_; consent was given. The stranger, when the time came, began a voluntary which made the people open their ears, and wonder who had got into the loft: they kept their places to enjoy the treat. When the organist saw this, he pushed the interloper off the stool, with "You'll never play 'em out this side Christmas." He then began his own drone, and the congregation began to move quietly away. "There," said he, "that's the way to play 'em out!"
I have not scrupled to bear hard on my own university, on the Royal Society, and on other respectable existences: being very much the friend of all. I will now clear the Royal Society from a very small and obscure slander, simply because I know how. This dissertation began with {190} the work of Mr. Oliver Byrne, the dual arithmetician, etc. This writer published, in 1849, a method of calculating logarithms.[329] First, a long list of instances in which, as he alleges, foreign discoverers have been pillaged by Englishmen, or turned into Englishmen: for example, O'Neill,[330] so called by Mr. Byrne, the rectifier of the semi-cubical parabola claimed by the Saxons under the name of _Neal_: the grandfather of this mathematician was conspicuous enough as _Neal_; he was archbishop of York. This list, says the writer, might be continued without end; but he has mercy, and finishes with his own case, as follows:--"About twenty years ago, I discovered this method of directly calculating logarithms. I could generally find the logarithm of any number in a minute or two without the use of books or tables. The importance of the discovery subjected me to all sorts of prying. Some asserted that I committed a table of logarithms to memory; others attributed it to a peculiar mental property; and when Societies and individuals failed to extract my secret, they never failed to traduce the inventor and the invention. Among the learned Societies, the Royal Society of London played a very base part. When I have more space and time at my disposal, I will revert to this subject again."
Such a trumpery story as this remains unnoticed at the time; but when all are gone, a stray copy from a stall falls into hands which, not knowing what to make of it, make history of it. It is a very curious distortion. The reader may take it on my authority, that the Royal Society played no part, good or bad, nor had the option of playing a part. {191} But I myself _pars magna fui_:[331] and when the author has "space and time" at his disposal, he must not take all of them; I shall want a little of both.
ARE ATOMS WORLDS?
The mystery of being; or are ultimate atoms inhabited worlds? By Nicholas Odgers.[332] Redruth and London, 1863, 8vo.
This book, as a paradox, beats quadrature, duplication, trisection, philosopher's stone, perpetual motion, magic, astrology, mesmerism, clairvoyance, spiritualism, homoeopathy, hydropathy, kinesipathy, Essays and Reviews, and Bishop Colenso,[333] all put together. Of all the suppositions I have given as actually argued, this is the one which is hardest to deny, and hardest to admit. Reserving the question--as beyond human discussion--whether our particles of carbon, etc. are _clusters_ of worlds, the author produces his reasons for thinking that they are at least single worlds. Of course--though not mentioned--the possibility is to be added of the same thing being true of the particles which make up our particles, and so down, for ever: and, on the other hand, of our planets and stars as being particles in some larger universe, and so up, for ever.
"Great fleas have little fleas upon their backs to bite 'em, And little fleas have lesser fleas, and so _ad infinitum._ And the great fleas themselves, in turn, have greater fleas to go on; While these again have greater still, and greater still, and so on."[334]
I have often had the notion that all the nebulae we see, including our own, which we call the Milky Way, may be particles of snuff in the box of a giant of a proportionately {192} larger universe. Of course the minim of time--a million of years or whatever the geologists make it[335]--which our little affair has lasted, is but a very small fraction of a second to the great creature in whose nose we shall all be in a few tens of thousands of millions of millions of millions of years.
All this is quite possible, and the probabilities for and against are quite out of reach. Perhaps also all the worlds, both above and below us, are fac-similes of our own. If so, away goes free will for good and all; unless, indeed, we underpin our system with the hypothesis that all the fac-simile bodies of different sizes are actuated by a common soul. These acute supplementary notions of mine go far to get rid of the difficulty which some have found in the common theory that the soul inhabits the body: it has been stated that there is, somewhere or another, a world of souls which communicate with their bodies by wondrous filaments of a nature neither mental nor material, but of a _tertium quid_ fit to be a go-between; as it were a corporispiritual copper encased in a spiritucorporeal gutta-percha. My theory is that every soul is everywhere _in posse_, as the schoolmen said, but not anywhere _in actu_, except where it finds one of its bodies. These _a priori_ difficulties being thus removed, the system of particle-worlds is reduced to a dry question of fact, and remitted to the decision of the microscope. And a grand field may thus be opened, as optical science progresses! For the worlds are not fac-similes of ours in time: there is not a moment of _our_ past, and not a moment of _our_ future, but is the _present_ of one or more of the particles. A will write the death of Caesar, and B the building of the Pyramids, by actual observation of the processes with a power of a thousand millions; C will discover the commencement of the Millennium, and D the {193} termination of Ersch and Gruber's Lexicon,[336] as mere physical phenomena. Against this glorious future there is a sad omen: the initials of the forerunner of this discovery are--NO!
THE SUPERNATURAL.
The History of the Supernatural in all ages and nations, and in all Churches, Christian and Pagan: demonstrating a universal faith. By Wm. Howitt.[337] London, 2 vols. 8vo. 1863.
Mr. Howitt is a preacher of spiritualism. He cements an enormous collection of alleged facts with a vivid outpouring of exhortation, and an unsparing flow of sarcasm against the scorners of all classes. He and the Rev. J. Smith[338] (_ante_, 1854) are the most thoroughgoing universalists of all the writers I know on spiritualism. If either can insert the small end of the wedge, he will not let you off one fraction of the conclusion that all countries, in all ages, have been the theaters of one vast spiritual display. And I suspect that this consequence cannot be avoided, if any part of the system be of truly spiritual origin. Mr. Howitt treats the philosophers either as ignorant babies, or as conscious spirit-fearers: and seems much inclined to accuse the world at large of dreading, lest by the actual presence of the other world their Christianity should imbibe a spiritual element which would unfit it for the purposes of their lives.
{194}
FROM MATTER TO SPIRIT.
From Matter to Spirit. By C. D. With a preface by A. B.[339] London, 1863, 8vo.
This is a work on Spiritual Manifestations. The author upholds the facts for spiritual phenomena: the prefator suspends his opinion as to the cause, though he upholds the facts. The work begins systematically with the lower class of phenomena, proceeds to the higher class, and offers a theory, suggested by the facts, of the connection of the present and future life. I agree in the main with A. B.; but can, of course, make none but horrescent reference to his treatment of the smaller philosophers. This is always the way with your paradoxers: they behave towards orthodoxy as the thresher fish behaves towards the whale. But if true, as is said, that the drubbing clears the great fish of parasites which he could not otherwise get rid of, he ought to bear no malice. This preface retorts a little of that contempt which the "philosophical world" has bestowed with heaped measure upon those who have believed their senses, and have drawn natural, even if hasty, inferences. There is philosophercraft as well as priestcraft, both from one source, both of one spirit. In English cities and towns, the minister of religion has been tamed: so many weapons are bared against him when he obtrudes his office in a dictatory manner, that, as a rule, there is no more quiet and modest member of society than the urban clergyman. Domination over religious belief is reserved for the exclusive use of those who admit the right: the rare exception to this mode of behavior is laughed at as a bigot, or shunned as a nuisance. But the overbearing minister of nature, who snaps you with _unphilosophical_ as the clergyman once frightened you with _infidel_, is still a recognized member of society, wants taming, and will get it. He wears the priest's cast-off {195} clothes, dyed to escape detection: the better sort of philosophers would gladly set him to square the circle.
The book just named appeared about the same time as this Budget began in the _Athenaeum_. It was commonly attributed, the book to my wife, the preface to myself. Some time after, our names were actually announced by the publisher, who ought to know. It will be held to confirm this statement that I announce our having in our possession some twenty reviews of different lengths, and of all characters: who ever collects a number of reviews of a book, except the author?
A great many of these reviews settle the matter _a priori_. If there had been spirits in the matter, they would have done this, and they would not have done that. Jean Meslier[340] said there could be no God over all, for, _if_ there had been one, He would have established a universal religion. If J. M. _knew_ that, J. M. was right: but if J. M. did not know that, then J. M. was on the "high priori road," and may be left to his course. The same to all who know what spirits would do and would not do.
A. B. very distinctly said that he knew some of the asserted facts, believed others on testimony, but did not pretend to know whether they were caused by spirits, or had some unknown and unimagined origin. This he said as clearly as I could have said it myself. But a great many persons cannot understand such a frame of mind: their own apparatus is a kind of spirit-level, and their conclusion on any subject is the little bubble, which is always at one end or the other. Many of the reviewers declare that A. B. is a secret believer in the spirit-hypothesis: and one of them wishes that he had "endorsed his opinion more boldly." According to this reviewer, any one who writes "I boldly {196} say I am unable to choose," contradicts himself. In truth, a person who does say it has a good deal of courage, for each side believes that he secretly favors the other; and both look upon him as a coward. In spite of all this, A. B. boldly repeats that he feels assured of many of the facts of _spiritualism_, and that he cannot pretend to affirm or deny anything about their cause.
The great bulk of the illogical part of the educated community--whether majority or minority I know not; perhaps six of one and half-a-dozen of the other--have not power to make a distinction, cannot be made to take a distinction, and of course, never attempt to shake a distinction. With them all such things are evasions, subterfuges, come-offs, loopholes, etc. They would hang a man for horse-stealing under a statute against sheep-stealing; and would laugh at you if you quibbled about the distinction between a horse and a sheep. I divide the illogical--I mean people who have not that amount of natural use of sound inference which is really not uncommon--into three classes:--First class, three varieties: the Niddy, the Noddy, and the Noodle. Second class, three varieties: the Niddy-Noddy, the Niddy-Noodle, and the Noddy-Noodle. Third class, undivided: the Niddy-Noddy-Noodle. No person has a right to be angry with me for more than one of these subdivisions.
The want of distinction was illustrated to me, when a boy, about 1820, by the report of a trial which I shall never forget: boys read newspapers more keenly than men. Every now and then a bench of country magistrates rather astonishes the town populations, accustomed to rub their brains[341] against one another. Such a story as the following would, {197} in our day, bring down grave remarks from above: but I write of the olden (or Eldon[342]) time, when nothing but conviction in a court of record would displace a magistrate. In that day the third-class amalgamator of distinct things was often on the bench of quarter-sessions.
An attorney was charged with having been out at night poaching. A clear _alibi_ was established; and perjury had certainly been committed. The whole gave reason to suspect that some ill-willers thought the bench disliked the attorney so much that any conviction was certain on any evidence. The bench did dislike the attorney: but not to the extent of thinking he could snare any partridges in the fields while he was asleep in bed, except the dream-partridges which are not always protected by the dream-laws. So the chairman said, "Mr. ----, you are discharged; but you should consider this one of the most fortunate days of your life." The attorney indignantly remonstrated, but the magistrate was right; for he said, "Mr. ----, you have frequently been employed to defend poachers: have you been careful to impress upon them the enormity of their practices?" It appeared in a wrangling conversation that the magistrates saw little moral difference between poaching and being a poacher's professional defender without lecturing him on his wickedness: but they admitted with reluctance, that there was a legal distinction; and the brain of N^3 could no further go. This is nearly fifty years ago; and Westernism was not quite extinct. If the present lords of the hills and the valleys want to shine, let them publish a true history of their own order. I am just old enough to remember some of the last of the squires and parsons who protested against teaching the poor to read and write. They now write books for the working classes, give them lectures, and the like. There is now no class, as a class, more highly educated, broadly educated, and deeply educated, {198} than those who were, in old times, best described as partridge-popping squireens. I have myself, when a boy, heard Old Booby speaking with pride of Young Booby as having too high a spirit to be confined to books: and I suspected that his dislike to teaching the poor arose in fact from a feeling that they would, if taught a little, pass his heir.
A. B. recommended the spirit-theory as an hypothesis on which to ground inquiry; that is, as the means of suggestion for the direction of inquiry. 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 class 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 pass 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 passed 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 homoeopathy, 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 prone 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--illustrates 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 classes. 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 mass 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 quantity 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. Nobody 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 class.
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 pass 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 hit 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 unassailable 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, Saturday, 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, Saturday, 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 restitution 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 circumference 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 circumference. 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 pass 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 circumference 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 circumference 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 assumption 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 circumference 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 circumference to a unit of diameter.
Square root of 3.... 1.73205081 .86602540 ------------ 2.59807621 .43301270 .08660254 1855768 412393 93726 21629 5047 1188 281 67 16 4 1 ------------ 3.14159265
3. Take the square root of 1/2; the square root of half of one more than this; the square root of half of one more {213} than the last; and so on, until we come as near to unity as the number of figures chosen will permit. Multiply all the results together, and divide 2 by the product: the quotient is an approximation to the circumference when the diameter is unity. Taking aim at four figures, that is, working to five figures to secure accuracy in the fourth, we have .70712 for the square root of 1/2; .92390 for the square root of half one more than .70712; and so on, through .98080, .99520, .99880, .99970, .99992, .99998. The product of the eight results is .63667; divide 2 by this, and the quotient is 3.1413..., of which four figures are correct. Had the product been .636363... instead of .63667..., the famous result of Archimedes, 22-7ths, would have been accurately true. It is singular that no cyclometer maintains that Archimedes hit it exactly.
A literary journal could hardly admit as much as the preceding, if it stood alone. But in my present undertaking it passes as the halfpennyworth of bread to many gallons of sack. Many more methods might be given, all ending in the same result, let that result mean what it may.
Now since dozens of methods, to which dozens more might be added at pleasure, concur in giving one and the same result; and since these methods are declared by all who have shown knowledge of mathematics to be _demonstrated_: it is not asking too much of a person who has just a little knowledge of the first elements that he should learn more, and put his hand upon the error, before he intrudes his assertion of the existence of error upon those who have given more time and attention to it than himself, and who are in possession, over and above many demonstrations, of many consequences verifying each other, of which he can know nothing. This is all that is required. Let any one square the circle, and persuade his friends, if he and they please: let him print, and let all read who choose. But let him abstain from intruding himself upon those who have been satisfied by existing demonstration, until he is prepared {214} to lay his finger on the point in which existing demonstration is wrong. Let him also say what this mysterious 3.14159... really is, which comes in at every door and window, and down every chimney, calling itself the circumference to a unit of diameter. This most impudent and successful impostor holds false title-deeds in his hands, and invites examination: surely those who can find out the rightful owner are equally able to detect the forgery. All the quadrators are agreed that, be the right what it may, 3.14159... is wrong. It would be well if they would put their heads together, and say what this wrong result really means. The mathematicians of all ages have tried all manner of processes, with one object in view, and by methods which are admitted to yield demonstration in countless cases. They have all arrived at one result. A large number of opponents unite in declaring this result wrong, and all agree in two points: first, in differing among themselves; secondly, in declining to point out what that curious result really is which the mathematical methods all agree in giving.
Most of the quadrators are not aware that it has been fully demonstrated that no two numbers whatsoever can represent the ratio of the diameter to the circumference with perfect accuracy. When therefore we are told that either 8 to 25 or 64 to 201 is the true ratio, we know that it is no such thing, without the necessity of examination. The point that is left open, as not fully demonstrated to be impossible, is the _geometrical_ quadrature, the determination of the circumference by the straight line and circle, used as in Euclid. The general run of circle-squarers, hearing that the quadrature is not pronounced to be _demonstratively_ impossible, imagine that the _arithmetical_ quadrature is open to their ingenuity. Before attempting the arithmetical problem, they ought to acquire knowledge enough to read Lambert's[355] demonstration (last given in Brewster's[356] translation {215} of Legendre's[357] Geometry) and, if they can, to refute it. [It will be given in an Appendix.] Probably some have begun this way, and have caught a Tartar who has refused to let them go: I have never heard of any one who, in producing his own demonstration, has laid his finger on the faulty part of Lambert's investigation. This is the answer to those who think that the mathematicians treat the arithmetical squarers too lightly, and that as some person may succeed at last, all attempts should be examined. Those who have so thought, not knowing that there is demonstration on the point, will probably admit that a person who contradicts a theorem of which the demonstration has been acknowledged for a century by all who have alluded to it as read by themselves, may reasonably be required to point out the error before he demands attention to his own result.
_Apopempsis of the Tutelaries._--Again and again I am told that I spend too much time and trouble upon my two tutelaries: but when I come to my summing-up I shall make it appear that I have a purpose. Some say I am too hard upon them: but this is quite a mistake. Both of them beat little Oliver himself in the art and science of asking for more; but without Oliver's excuse, for I had given good allowance. Both began with me, not I with them: and both knew what they had to expect when they applied for a second helping.
On July 31, the Monday after the publication of my remarks on my 666 correspondent, I found _three_ notes in separate envelopes, addressed to me at "7A, University College." When I saw the three new digits I was taken rhythmopoetic, as follows--
Here's the Doctor again with his figs, and by Heavens! He was always at sixes, and now he's at sevens.
To understand this fully the reader must know that the greater part of Apocalyptic interpretation has long been condensed, in my mind, into the Turkish street-cry--In the {216} name of the Prophet! figs! I make a few extracts. The reader will observe that Dr. Thorn grumbles at his _private_ letters being _publicly_ ridiculed. A man was summoned for a glutolactic assault; he complained of the publication of his proceeding: I kicked etc. _in confidence_, he said.
"After reading your last, which tries in every way to hold me up to public ridicule for daring to write you privately ['that you would be d----d,' omitted by accident] one would say, Why have anything to do with such a testy person? [Wrong word; no testy person can manage cool and consecutive ridicule. Quaere, what is this word? Is it anything but a corruption of the obsolete word _tetchy_ of the same meaning? Some think _touchy_ is our modern form of _tetchy_, which I greatly doubt]. My answer is, the poor man is lamentably ignorant; he is not only so, but 'out of the way' [quite true; my readers know me by this time for an out-of-the-way person. What other could tackle my squad of paradoxers? What other would undertake the job?] Can he be brought back and form one of those who in Ezekiel 37 ch. have the Spirit breathed into them and live.... Have I any other feeling towards you except that of peace and goodwill? [Not to your distinct knowledge; but in all those who send people to 'the other place' for contempt of their interpretations, there is a lurking wish which is father to the thought; 'you _will_ be d----d' and 'you _be_ d--d' are Siamese twins]. Of course your sneer at 666 brought plain words; but when men meddle with what they do not understand (not having the double _Vahu_) they must be dealt with faithfully by those who do.... [They must; which justifies the Budget of Paradoxes: but no occasion to send them anywhere; no preachee and floggee too, as the negro said]. Many will find the text Prov. i. 26 fully realized. [All this contains distinct assumption of a right 'of course' to declare accursed those who do not respect the writer's vagary].... If I could but get the [Hebrew: A], the Ox-head, which in Old Hebrew was just the Latin Digamma, F, out {217} of your name, and could then Thau you with the Thau of Ezekiel ix, 4, the [chi], then you would bear the number of a man! But this is too hard for me, although not so for the Lord! Jer. xxxii. 17.... And now a word: is ridicule the right thing in so solemn a matter as the discussion of Holy Writ? [Is food for ridicule the right thing? Did I discuss Holy Writ? I did not: I concussed profane scribble. Even the Doctor did not _discuss_; he only enunciated and denunciated out of the mass of inferences which a mystical head has found premises for in the Bible]."
M 40 O 70 R 100 G 6 N 50 ---- 266 [Hebrew: t]=[chi] 400
[That ill opinions are near relations of ill wishes, will be detected by those who are on the look out. The following was taken down in a Scotch Church by Mr. Cobden,[358] who handed it to a Roman friend of mine, for his delectation (in 1855): "Lord, we thank thee that thou hast brought the Pope into trouble; and we pray that thou wouldst be mercifully pleased to increase the same."]
Here is a martyr who quarrels with his crown; a missionary who reviles his persecutor: send him to New Zealand, and he would disagree with the Maoris who ate him. Man of unilateral reciprocity! have you, who write to a stranger with hints that that stranger and his wife are children of perdition, the bad taste to complain of a facer in return? As James Smith[359]--the Attorney-wit, not the Dock-cyclometer--said, or nearly said,
"A pretty thing, forsooth! Is he to burn, all scalding hot, Me and my wife, and am I not To job him out a tooth?"
{218}
Those who think parody vulgar will be pleased to substitute for the above a quotation from Butler[360]:--
"There's nothing so absurd or vain Or barbarous or inhumane, But if it lay the least pretence To piety and godliness, Or tender-hearted conscience, And zeal for gospel truths profess,-- Does sacred instantly commence, And all that dare but question it are straight Pronounced th' uncircumcised and reprobate, As malefactors that escape and fly Into a sanctuary for defence, Must not be brought to justice thence, Although their crimes be ne'er so great and high. And he that dares presume to do't Is sentenced and delivered up To Satan that engaged him to't."
THE NUMBER OF THE BEAST.
Of all the drolleries of controversy none is more amusing than the manner in which those who provoke a combat expect to lay down the laws of retaliation. You must not strike this way! you must not parry that way! If you don't take care, we shall never meddle with you again! We were not _prepared_ for such as this! Why did we have anything to do with such a testy person? M. Jourdain must needs show Nicole, his servant-maid, how good a thing it was to be sure of fighting without being killed, by care and tierce.[361] "Et cela n'est il pas beau d'etre assure de son fait quand on se bat contre quelqu'un? La, pousse moi un peu, pour voir. NICOLE. Eh bien! quoi? M. JOURDAIN. Tout beau. Hola! {219} Ho! doucement. Diantre soit la coquine! NICOLE. Vous me dites de pousser. M. JOURDAIN. Oui; mais tu me pousses en tierce, avant que de pousser en quarte, et tu n'as pas la patience que je pare."
His colleague, my secular tutelary, who also made an anachronistic onset, with his repartees and his retorts, before there was anything to fire at, takes what I give by way of subsequent provocation with a good humor which would make a convert of me if he could afford .01659265 ... of a grain of logic. He instantly sent me his photograph for the asking, and another letter in proof. The Thor-hammerer does nothing but grumble, except when he tells a good story, which he says he had from Dr. Abernethy.[362] A Mr. James Dunlop was popping at the Papists with a 666-rifled gun, when Dr. Chalmers[363] quietly said, "Why, Dunlop, you bear it yourself," and handed him a paper on which the numerals in
I A C O B V S D V N L O P V S 1 100 5 500 5 50 5
were added up. This is almost as good as the _Filii Dei Vicarius_, the numerical letters of which also make 666. No more of these crazy--I first wrote _puerile_, but why should young cricketers be libelled?--attempts to extract religious use from numerical vagaries, and to make God over all a proposer of _salvation conundrums_: and no more of the trumpery hints about future destiny which is too great a compliment to call blasphemous. If the Doctor will cipher upon the letter in [Greek: en hoi metroi metreite metrethesetai humin][364] with _double Vahu_ cubic measure, he will perhaps learn to leave off trying to frighten me into gathering grapes from thorns.
Mystical hermeneutics may be put to good use by out-of-the-way people. They may be made to call the attention {220} of the many to a distinction well known among the learned. The books of the New Testament have been for 1,500 years divided into two classes: the _acknowledged_ ([Greek: homologoumena]), which it has always been paradox not to receive; and the _controverted_ ([Greek: antilegomena]), about which there has always been that difference of opinion which no scholar overlooks, however he may decide for himself after balance of evidence. Eusebius,[365] who first (l. 3, c. 25) recorded the distinction--which was much insisted on by the early Protestants--states the books which are questioned as doubtful, but which yet are approved and acknowledged by _many_--or _the many_, it is not easy to say which he means--to be the Epistles of James and Jude, the second of Peter and the second and third of John. In other places he speaks doubtingly of the Epistle to the Hebrews. The Apocalypse he does not even admit into this class, for he proceeds as follows--I use the second edition of the English folio translation (1709), to avert suspicion of bias from myself:--
"Among the _spurious_ [[Greek: nothoi]] let there be ranked both the work entitled the _Acts of Paul_, and the book called _Pastor_, and the _Revelation of Peter_: and moreover, that which is called the _Epistle of Barnabas_, and that named the _Doctrines of the Apostles_: and moreover, as I said, the _Revelation of John_ (if you think good), which some, as I have said, do reject, but others allow of, and admit among those books which are received as unquestionable and undoubted."
Eusebius, though he will not admit the Apocalypse even into the _controverted_ list, but gives permission to call it _spurious_, yet qualifies his permission in a manner which almost annihilates the distinctive force of [Greek: nothos], and gives the book a claim to rank (if you think good, again) in the controverted list. And this is the impression received by {221} the mind of Lardner, who gives Eusebius fully and fairly, but when he sums up, considers his author as admitting the Apocalypse into the second list. A stick may easily be found to beat the father of ecclesiastical history. There are whole faggots in writers as opposite as Baronius and Gibbon, who are perhaps his two most celebrated sons. But we can hardly imagine him totally misrepresenting the state of opinion of those for whom and among whom he wrote. The usual plan, that of making an author take the views of his readers, is more easy in his case than in that of any other writer: for, as the riddle says, he is You-see-by-us; and to this reading of his name he has often been subjected. Dr. Nathaniel Lardner,[366] who, though heterodox in doctrine, tries hard to be orthodox as to the Canon, is "sometimes apt to think" that the list should be collected and divided as in Eusebius. He would have no one of the controverted books to be allowed, by itself, to establish any doctrine. Even without going so far, a due use of early opinion and long continued discussion would perhaps prevent rational people from being induced by those who have the _double Vahu_ to place the Apocalypse _above_ the Gospels, which all the Bivahuites do in effect, and some are said to have done in express words. But my especial purpose is to point out that an easy way of getting rid of 665 out of 666 of the mystics is to require them to establish the Apocalypse before they begin. See if they even know so much as that there is a crowd of testimonies for and against, running through the first four centuries, which makes this book the most difficult of the whole Canon. Try this method, and you will escape beautiful, as the French say. Dean Alford,[367] in Vol. IV, p. 8, of his New Testament, gives an elaborate handling of this question. He concludes by saying that he cannot {222} venture to refuse his consent to the tradition that the Apostle is the author. This modified adherence, or non-nonadherence, pretty well represents the feeling of orthodox Protestants, when learning and common sense come together.
I have often, in former days, had the attempt made to place the Apocalypse on my neck as containing prophecies yet unfulfilled. The preceding method prevents success; and so does the following. It may almost be taken for granted that theological system-fighters do not read the New Testament: they hunt it for detached texts; they listen to it in church in that state of quiescent nonentity which is called reverent attention: but they never read it. When it is brought forward, you must pretend to find it necessary to turn to the book itself: you must read "The revelation ... to show unto his servants _things which must shortly come to pass_.... Blessed is he that readeth ... _for the time is at hand_." You must then ask your mystic whether things deferred for 1800 years were shortly to come to pass, etc.? You must tell him that the Greek [Greek: en tachei], rendered "shortly," is as strong a phrase as the language has to signify _soon_. The interpreter will probably look as if he had never read this opening: the chances are that he takes up the book to see whether you have been committing a fraud. He will then give you some exquisite evasion: I have heard it pleaded that the above was a _mere preamble_. This word _mere_ is all-sufficient: it turns anything into nothing. Perhaps he will say that the argument is that of the Papists: if so, tell him that there is no Christian sect but bears true witness against some one or more absurdities in other sects.
An anonyme suggests that [Greek: en tachei] may not be "soon," it may be "quickly, without reference to time when:" he continues thus, "May not time be 'at hand' when it is ready to come, no matter how long delayed?" I now understand what *** and *** meant when they borrowed my books and promised to return them quickly, it was "without {223} reference to time when." As to time at _hand_--provided you make a long _arm_--I admire the quirk, but cannot receive it: the word is [Greek: engus], which is a word of _closeness_ in time, in place, in reckoning, in kindred, etc.
Another gentleman is not surprised that Apocalyptic reading leads to a doubt of the "canonicity" of the book: it ought not to rest on church testimony, but on visible miracle. He offers me, or any reader of the _Athenaeum_, the "sight of a miracle to that effect, and within forty-eight hours' journey (fare paid)." I seldom travel, and my first thought was whether my carpet-bag would be found without a regular hunt: but, on reading further, I found that it was only a concordance that would be wanted. Forty hours' collection and numerical calculation of Greek nouns would make it--should I happen to agree with the writer--many hundred millions to one that Revelation xiii is superhuman. There is but one verse (the fifth) which the writer does not see verified. I looked at this verse, and was much startled. The Budget began in October 1863: should it last until March 1867--it is now August 1866--it is clear that I am the first Beast, and my paradoxers are the saints whom I persecute.
[The Budget _did_ terminate in March 1867: I hope the gentleman will be satisfied with the resulting interpretation.]
The same opponent is surprised that I should suppose a thing which "comes to pass" must be completed, and cannot contain what is to happen 1800 years after. All who have any knowledge of English idiom know that a thing _comes_ to pass when it happens, and _came_ to pass afterwards. But as the original is Greek, we must look at the Greek: it is [Greek: dei genesthai] for "must come to pass," and we know that [Greek: egeneto] is what is usually translated "came to pass." No word of more finished completion exists in Greek.
And now for a last round of biter-bit with the Thor-hammerer, of whom, as in the other case, I shall take no {224} more notice until he can contrive to surpass himself, which I doubt his being able to do. He informs me that by changing A into [Hebrew: t] in my name he can make a 666 of _me_; adding, "This is too hard for me, although not so for the Lord!" Sheer nonsense! He could just as easily have directed to "Prof. De Morg[Hebrew: t]n" as have assigned me apartment 7A in University College. It would have been seen for whom it was intended: and if not, it would still have reached me, for my colleagues have for many a year handed all out-of-the-way things over to me. There is no 7A: but 7 is the Museum of Materia Medica. I took the only hint which the address gave: I inquired for hellebore, but they told me it was not now recognized, that the old notion of its value was quite obsolete, and that they had nothing which was considered a specific in senary or septenary cases. The great platitude is the reference of such a difficulty as writing [Hebrew: t] for A to the Almighty! Not childish, but fatuous: real childishness is delightful. I knew an infant to whom, before he could speak plain, his parents had attempted to give notions of the Divine attributes: a wise plan, many think. His father had dandled him up-side-down, ending with, There now! Papa could not dance on his head! The mannikin made a solemn face, and said, _But Dod tood_! I think the Doctor has rather mistaken the way of becoming as a little child, intended in Matt. xviii. 3: let us hope the will may be taken for the deed.
Two poets have given images of transition from infancy to manhood: Dryden,--for the Hind is Dryden himself on all fours! and Wordsworth, in his own character of broad-nailed, featherless biped:
"The priest continues what the nurse began, And thus the child imposes on the man." "The child's the father of the man, And I could wish my days to be Bound each to each by natural piety."
{225}
In Wordsworth's aspiration it is meant that sense and piety should grow together: in Dryden's description a combination of Mysticism And Bigotry (can this be the _double Vahu_?), personified as "the priest,"--who always catches it on this score, though the same spirit is found in all associations,--succeeds the boguey-teaching of the nurse. Never was the contrast of smile and scowl, of light and darkness, better seen than in the two pictures. But an acrostic distinction may be drawn. When mysticism predominates over bigotry, we have the grotesque picturesque, and the natural order of words gives us _Mab_, an appropriate suggestion. But when bigotry has the upper hand, we see _Bam_, which is just as appropriate; for bigotry nearly always deals with facts and logic so as to require the application of at least one of the minor words by which dishonesty is signified. I think that M is the Doctor's initial, and that Queen Mab tickles him in his sleep with the sharp end of a 6.
(_Monday, August 21._) Three weeks having elapsed without notice from me of the Doctor, I receive a reminder of his existence, in which I find that as I am the Daniel who judges the Magi of Babylon, it is to be pointed out that Daniel "bore a certain number, that of a man (beloved), Daniel, ch. 10. v. 11, and which you certainly do not." Then, "by Greek power," Belteshazzar is made = 666. Here is another awkward imitation of the way of a baby child. When you have sported with the tiny creature until it runs away offended, by the time you have got into conversation again you will find the game is to be renewed: a little head peeps out from a hiding-place with "I don't love you." The proper rejoinder is, "Very well! then I'll have pussy." But in the case before me there is a rule of three sums to do; as baby : Pussy Dr. :: 666 : the answer required. I will work it out, if I can.
The squaring of the circle and the discovery of the Beast are the two goals--and goals also--of many unbalanced intellects, and of a few instances of the better kind. {226} I might have said more of 666, but I am not deep in its bibliography. A work has come into my hands which contains a large number of noted cases: to some of my readers it will be a treat to see the collection; and the sight will perhaps be of some use to those who have read controversy on the few celebrated cases which are of general notoriety. It is written by a learned decipherer, a man who really knew the history of the subject, the Rev. David Thom,[368] of Bold Street Chapel, Liverpool, who died, I am told, a few years ago.
Anybody who reads his book will be inclined to parody a criticism which was once made on Paley's[369] Evidences--"Well! if there be anything in Christianity, this man is no fool." And, if he should chance to remember it, he will be strongly reminded of a sentence in my opening chapter,--"The manner in which a paradoxer will show himself, as to sense or nonsense, will not depend upon what he maintains, but upon whether he has or has not made a sufficient knowledge of what has been done by others, _especially as to the mode of doing it_, a preliminary to inventing knowledge for himself." And this is reinforced by the fact that Mr. Thom, though a scholar, was not conspicuous for learning, except in this his great pursuit. He was a paradoxer on other points. He reconciled Calvinism and eternal reprobation with Universalism and final salvation; showing these two doctrines to be all one.
This gentleman must not be confounded with the Rev. John Hamilton Thom[370] (no relation), at or near the same {227} time and until recently, of Renshaw Street Chapel, Liverpool who was one of the minority in the Liverpool controversy when, nearly thirty years ago, _three_ heretical Unitarian schooners exchanged shotted sermons with _thirteen_ Orthodox ships of the line, and put up their challengers' dander--an American corruption of _d--d anger_--to such an extent, by quiet and respectful argument, that those opponents actually addressed a printed intercession to the Almighty for the Unitarian triad, as for "Jews, Turks, Infidels, and Heretics." So much for the distinction, which both gentlemen would thank me for making very clear: I take it quite for granted that a guesser at 666 would feel horrified at being taken for a Unitarian, and that a Unitarian would feel queerified at being taken for a guesser at 666. Mr. David Thom's book is _The Number and Names of the Apocalyptic Beasts_, Part I, 1848, 8vo.: I think the second part was never published. I give the Greek and Latin solutions, omitting the Hebrew: as usual, all the Greek letters are numeral, but only M D C L X V I of the Latin. I do not give either the decipherers or their reasons: I have not room for this; nor would I, if I could, bias my reader for one rather than another.
D. F. Julianus Caesar Atheus (or Aug.[371]); Diocles Augustus; Ludovicus; Silvester Secundus; Linus Secundus; {228} Vicarius Filii Dei; Doctor et Rex Latinus; Paulo V. Vice-Deo; Vicarius Generalis Dei in Terris; Ipse Catholicae Ecclesiae Visibile Caput; Dux Cleri; Una, Vera, Catholica, Infallibilis Ecclesia; Auctoritas politica ecclesiasticaque Papalis (Latina will also do); Lutherus Ductor Gregis; Calvinus tristis fidei interpres; Dic Lux ; Ludvvic; Will. Laud; [Greek: Lateinos];[372] [Greek: he latine basileia]; [Greek: ekklesia italika]; [Greek: euanthas]; [Greek: teitan]; [Greek: arnoume]; [Greek: lampetis]; [Greek: ho niketes]; [Greek: kakos hodegos]; [Greek: alethes blaberos]; [Greek: palai baskanos]; [Greek: amnos adikos]; [Greek: antemos]; [Greek: genserikos]; [Greek: euinas]; [Greek: Benediktos]; [Greek: Bonibazios g. papa x. e. e. e. a.], meaning Boniface III. Pope 68th, bishop of bishops the first! [Greek: oulpios]; [Greek: dios eimi he heras]; [Greek: he missa he papike]; [Greek: loutherana]; [Greek: saxoneios]; [Greek: Bezza antitheos] (Beza); [Greek: he alazoneia biou]; [Greek: Maometis]; [Greek: Maometes b.]; [Greek: theos eimi epi gaies]; [Greek: iapetos]; [Greek: papeiskos]; [Greek: dioklasianos]; [Greek: cheina]; [Greek: braski]; [Greek: Ion Paune]; [Greek: koupoks]; (cowpox, [Greek: s] being the _vau_; certainly the {229} vaccinated have the mark of the Beast); [Greek: Bonneparte]; [Greek: N. Boneparte]; [Greek: euporia]; [Greek: paradosis]; [Greek: to megatherion].
All sects fasten this number on their opponents. It is found in _Martin Lauter_, affirmed to be the true way of writing the name, by carrying numbers through the Roman Alphabet. Some Jews, according to Mr. Thorn, found it in [Hebrew: JSHW NTSRJ] _Jesus of Nazareth_. I find on inquiry that this satire was actually put forth by some medieval rabbis, but that it is not idiomatic: it represents quite fairly "Jesus Nazarene," but the Hebrew wants an article quite as much as the English wants "the."
Mr. David Thom's own solution hits hard at all sides: he finds a 666 for both beasts; [Greek: he phren] (the mind) for the first, and [Greek: ekklesiai sarkikai] (fleshly churches) for the second. A solution which embodies all mental philosophy in one beast and all dogmatic theology in the other, is very tempting: for in these are the two great supports of Antichrist. It will not, however, mislead me, who have known the true explanation a long time. The three sixes indicate that any two of the three subdivisions, Roman, Greek, and Protestant, are, in corruption of Christianity, six of one and half a dozen of the other: the distinctions of units, tens, hundreds, are nothing but the old way (1 Samuel xviii. 7, and Concordance at _ten_, _hundred_, _thousand_) of symbolizing differences of number in the subdivisions.
It may be good to know that, even in speculations on 666, there are different degrees of unreason. All the diviners, when they get a colleague or an opponent, at once proceed to reckon him up: but some do it in play and some in earnest. Mr. David Thom found a young gentleman of the name St. Claire busy at the Beast number: he forthwith added the letters in [Greek: st klaire] and found 666: this was good fun. But my spiritual tutelary, when he found that he could not make a beast of me, except by changing [Hebrew: A] into [Hebrew: T], solemnly referred the difficulty to the Almighty: this was poor earnest. {230}
I am glad I did not notice, in time to insert it in the _Athenaeum_, a very remarkable paradoxer brought forward by Mr. Thom, his friend Mr. Wapshare[373]: it is a little too strong for the general public. In the _Athenaeum_ they would have seen and read it: but this book will be avoided by the weaker brethren. It is as follows:
"God, the Elohim, was six days in creating all things, and having made MAN he entered into his rest. He is no more seen as a Creator, as Elohim, but as Jehovah, the _Lord_ of the Sabbath, and the Spirit of life in MAN, which Spirit worketh _sin in the flesh_; for the Spirit of Love, in all flesh, is Lust, or the spirit of a beast, So Rom. vii. And which Spirit is _crucified_ in the flesh. He then, as Jehovah--as the power of the Law, _in_ and _over_ all flesh, John viii. 44--increases that which he has made as the Elohim, and his power shall last for 6 days, or 6 periods of time, computed at a millennium of years; and at the end of which six days, he who is the Spirit of all flesh shall manifest himself as the Holy Spirit of Almighty Love, and of all truth; and so shall the Church have her Sabbath of Rest--all contention being at an end. This is, as well as I may now express it, my solution of the mystery in Hebrew, and in Greek, and also in Latin, IHS. For he that was lifted up _is_ King of the Jews, and is the Lord of all Life, working in us, both to will and to do; as is manifest in the Jews--they slaying him that his blood might be _good_ for the healing of the nations, of all people and tongues. As the Father of all _natural_ flesh, he is the Spirit of Lust, as in all _beasts_; as the Father, or King of the Jews, he is the Devil, as he himself witnesseth in John viii., already referred to. As lifted up, he is transformed into the Spirit of Love, a light to the Gentiles, and the glory of his people Israel.... For there is but ONE God, ONE Lord, ONE Spirit, ONE body, etc. and he who was Satan, the Spirit of life in that body, is, in {231} Christ crucified, seen in the Spirit that is in all, and through all and over all, God blessed for ever."
All this seems well meant, and Mr. Thom prints it as convinced of its piety, and "pronounces no opinion." Mystics of all sorts! see what you may come to, or what may come to you! I have inserted the above for your good.
There is nothing in this world so steady as some of the paradoxers. They are like the spiders who go on spinning after they have web enough to catch all the flies in the neighborhood, if the flies would but come. They are like the wild bees who go on making honey which they never can eat, proving _sic vos non vobis_ to be a physical necessity of their own contriving. But nobody robs their hives: no, unlike the bees, they go about offering their ware to any who will take it as a gift. I had just written the last sentence (Oct. 30, 1866, 8.45 A.M.) when in comes the second note received this morning from Dr. Thorn: at 1.30 P.M. came in a third. These arise out of the above account of the Rev. D. Thom, published Oct. 27: three notes had arrived before.
For curiosity I give one day's allowance, supposing these to be all: more may arrive before night.
29th Oct. 1866.
"Dear Sir,--
In re [swastika].[374]
"So that 'Zaphnath Paaneah' may be after all the revealer of the 'Northern Tau' [Greek: Phaneroo]--To make manifest, shew, or explain; and this may satisfy the House of Joseph in Amos 5^c. While Belteshazzar = 666 may be also satisfactory to the House of David, and so we may have Zech. 10^c. 6^v. in operation when Ezekiel 37^c. 16^v. has been realised;--but there, what is the use of writing, it is all Coptic {232} to a man who has not [swastika], The Thau of the North, the double Vahu [Hebrew: W\qamats\W]. Look at Jeremiah 3^c. 8^v. and then to Psalm 83 for 'hidden ones' [Hebrew: TS\sheva\PW\dagesh\N\segol\Y Y\sheva\HW\qamats\H]--The Zephoni Jehovah, and say whether they have any connection with the Zephon _Thau_. The Hammer of Thor of Jeremiah 23^c. 29^v. as I gave you in No. 3 of my present edition.
Yours truly
LE CHEVALIER AU CIN."
_By Greek Power._
C = 20 H = 8 E = 5 V = 6 A = 1 L = 30 I = 10 E = 5 R = 100
A = 1 U = 400
C = 20 I = 10 N = 50 ---- 666
There will be thousands of Morgans who will be among the wise and prudent of Hosea 14^c. 9^v. when the Seventh Angel sounds, let me number _that One_ by Greek, Rev. 17^c. 1^v: {233}
S = 200 E = 5 x V = 6 E = 5 N = 50 T = 300 H = 8
A = 1 N = 50 x G = 6 E = 5 L = 30 ---- 666
V and G = 12 ought to be equal to one Gammadion or ^3[swastika]3 x 4 = 12, what say you?
London, October 29, 1866.
"Dear Sir,--
In re [swastika] versus [maltese cross].
However pretentious the X or [maltese cross] may be, and it is peculiarly so just now in this land; after all it is only made of two Roman V's--and so is only = [ one inverted](10)--and therefore is not the perfect number 12 of Revel^n, but is the mark of the goddess _Decima_!
Yours truly
WM. THORN."
Had the _one_ who sent forth a pastoral (Romish) the other day, remained amongst the faithful expectants, see how he would have numbered, whereas he sold himself for the privilege of signing
[maltese cross] HENRY E. MANNING.[375]
{234}
_By English Key._
H = 8 E = 5 N = 40 R = 80 Y = 140
E = 5 D = 4 W = 120 A = 1 R = 80 D = 4
M = 30 A = 1 N = 40 N = 40 I = 9 N = 40 G = 7 [swastika] = 12 ---- 666
Can you now understand the difference between [swastika] and [maltese cross] or X? Look to my challenge.
Cutting from newspaper:--
ITALY.
Rome (_via_ Marseilles), October
Mr. Gladstone has paid a visit to the Pope.
_By Greek Power._
G = 6 L = 30 A = 1 D = 4 S = 200 T = 300 O = 70 N = 50 E = 5 ---- 666
And what then [swastika]?
{235}
In other letters _John Stuart Mill_ is 666 if the _a_ be left out; _Chasuble_ is perfect. _John Brighte_[376] is a _fait accompli_; and I am asked whether intellect can account for the final e. Very easily: this Beast is not the M. P., but another person who spells his name differently. But if John Sturt Mill and John Brighte choose so to write themselves, they may.
A curious collection; a mystical phantasmagoria! There are those who will try to find meaning: there are those who will try to find purpose.
"And some they said--What are you at? And some--What are you arter?"
My account of Mr. Thom and his 666 appeared on October 27: and on the 29th I received from the editor a copy of Mr. Thom's sermons published in 1863 (he died Feb. 27, 1862) with best wishes for my health and happiness. The editor does not name himself in the book; but he signed his name in my copy: and may my circumference never be more than 3-1/8 of my diameter if the signature, name and writing both, were not that of my [circle square] ing friend Mr. James Smith! And so I have come in contact with him on 666 as well as on [pi]! I should have nothing left to live for, had I not happened to hear that he has a perpetual motion on hand. I returned thanks and kind regards: and Miss Miggs's words--"Here's forgivenesses of injuries! here's amicablenesses!"--rang in my ears. But I was made slightly uncomfortable: how could the war go on after this armistice? Could I ever make it understood that the truce only extended to the double Vahu and things thereunto relating? It was once held by seafaring men that there was no peace with Spaniards beyond the line: I was determined that there must be no concord with J. S. inside the circle; that this must be a special exception, like Father Huddleston {236} and old Grouse in the gun-room. I was not long in anxiety; twenty-four hours after the book of sermons there came a copy of the threatened exposure--_The British Association in Jeopardy, and Professor De Morgan in the Pillory without hope of escape_. By James Smith, Esq. London and Liverpool, 8vo., 1866 (pp. 94). This exposure consists of reprints from the _Athenaeum_ and _Correspondent_: of things new there is but one. In a short preface Mr. J. S. particularly recommends to "_read to the end_." At the end is an appendix of two pages, in type as large as the work; a very prominent peroration. It is an article from the _Athenaeum_, left out of its place. In the last sentence Mr. J. Smith, who had asked whether his character as an honest Geometer and Mathematician was not at stake, is warned against the _fallacia plurium interrogationum_.[377] He is told that there is not a more honest what's-his-name in the world: but that as to the counter which he calls his character as a mathematician, he is assured that it has been staked years ago, and lost. And thus truth has the last word. There is no occasion to say much about reprints. One of them is a letter [that given above] of August 25, 1865, written by Mr. J. S. to the _Correspondent_. It is one of his quadratures; and the joke is that I am made to be the writer: it appears as what Mr. J. S. hopes I shall have the sense to write in the _Athenaeum_ and forestall him. When I saw myself thus quoted--yes! quoted! double commas, first person--I felt as I suppose did Wm. Wilberforce[378] when he set eyes on the affectionate benediction of the potato which waggish comrades had imposed on a raw Irish reporter as part of his speech. I felt as Martin[379] of {237} Galway--kind friend of the poor dumb creatures!--when he was told that the newspapers had put him in Italics. "I appeal to you, Mr. Speaker! I appeal to the House! Did I speak in Italics? Do I ever speak in Italics?" I appeal to editor and readers, whether I ever squared the circle until a week or two ago, when I gave my charitable mode of reconciling the discrepant cyclometers.
The absurdity of the imitation of symbolic reasoning is so lusciously rich, that I shall insert it when I make up my final book. Somebody mastered Spanish merely to read Don Quixote: it would be worth while to learn a little algebra merely to enjoy this a b-istical attack on the windmills. The principle is, Prove something in as roundabout a way as possible, mention the circle once or twice irrelevantly in the course of your proof, and then make an act of Q. E. D. in words at length. The following is hardly caricature:--
To prove that 2 and 2 make 5. Let a = 2, b = 5: let c = 658, the number of the House: let d = 666, the number of the Beast. Then of necessity d = a + b + c + 1; so that 1 is a harmonious and logical quantification of the number of which we are to take care. Now, b, the middle of our digital system, is, by mathematical and geometrical combination, a mean between 5 + 1 and 2 + 2. Let 1 be removed to be taken care of, a thing no real mathematician can refuse without serious injury to his mathematical and geometrical reputation. It follows of necessity that 2 + 2 = 5, _quod erat demonstrumhorrendum_. If Simpkin & Marshall have not, after my notice, to account for a gross of copies more than would have gone off without me, the world is not worthy of its James Smith!
The only fault of the above is, that there is more {238} connection than in the process of Faber Cyclometricus: so much, in fact, that the blunders are visible. The utter irrelevance of premises to conclusion cannot be exhibited with the requisite obscurity by any one who is able to follow reasoning: it is high art displayed in a certain toning down of the _aegri somnia_, which brings them to a certain look of reproach to reasoning which I can only burlesque. Mr. J. S. produces something which resembles argument much as a chimpanzee in dolor, because balked of his dinner, resembles a thinking man at his studies. My humble attempt at imitation of him is more like a monkey hanging by his tail from a tree and trying to crack a cocoa-nut by his chatter.
I could forgive Mr. J. S. anything, properly headed. I would allow him to prove--_for himself_--that the Quadrature of the Circle is the child of a private marriage between the Bull Unigenitus and the Pragmatic Sanction, claiming tithe of onions for repeal of the Mortmain Act, before the Bishops in Committee under the kitchen table: his mode of imitating reason would do this with ease. But when he puts his imitation into my mouth, to make me what _he_ calls a "real mathematician," my soul rises in epigram against him. I say with the doll's dressmaker--such a job makes me feel like a puppet's tailor myself--"He ought to have a little pepper? just a few grains? I think the young man's tricks and manners make a claim upon his friends for a little pepper?" De Faure[380] and Joseph Scaliger[381] come into my head: my reader may look back for them.
"Three circlesquarers to the manner born, Switzerland, France, and England did adorn, De Faure in equations did surpass, Joseph at contradictions was an ass. Groaned Folly, I'm used up! What shall I do To make James Smith? Grinned Momus, _Join the two_!"
{239}
As to my _locus poenitentiae_,[382] the reader who is fit to enjoy the