Nothing worse will ever happen to me than the smile which individuals bestow on a man who does not _groove_. Wisdom, like religion, belongs to majorities; who can {31} wonder that it should be so thought, when it is so clearly pictured in the New Testament from one end to the other?

The counterpart of _paradox_, the isolated opinion of one or of few, is the general opinion held by all the rest; and the counterpart of false and absurd paradox is what is called the "vulgar error," the _pseudodox_. There is one great work on this last subject, the _Pseudodoxia Epidemica_ of Sir Thomas Browne, the famous author of the _Religio Medici_; it usually goes by the name of Browne "On Vulgar Errors" (1st ed. 1646; 6th, 1672). A careful a.n.a.lysis of this work would show that vulgar errors are frequently opposed by scientific errors; but good sense is always good sense, and Browne's book has a vast quant.i.ty of it.

As an example of bad philosophy brought against bad observation. The Amphisbaena serpent was supposed to have two heads, one at each end; partly from its shape, partly because it runs backwards as well as forwards. On this Sir Thomas Browne makes the following remarks:

"And were there any such species or natural kind of animal, it would be hard to make good those six positions of body which, according to the three dimensions, are ascribed unto every Animal; that is, _infra_, _supra_, _ante_, _retro_, _dextrosum_, _sinistrosum_: for if (as it is determined) that be the anterior and upper part wherein the senses are placed, and that the posterior and lower part which is opposite thereunto, there is no inferior or former part in this Animal; for the senses, being placed at both extreams, doth make both ends anterior, which is impossible; the terms being Relative, which mutually subsist, and are not without each other. And therefore this duplicity was ill contrived to place one head at both extreams, and had been more tolerable to have settled three or four at one.

And therefore also Poets have been more reasonable than Philosophers, and _Geryon_ or _Cerberus_ less monstrous than _Amphisbaena_." {32}

There may be paradox upon paradox: and there is a good instance in the eighth century in the case of Virgil, an Irishman, Bishop of Salzburg and afterwards Saint, and his quarrels with Boniface, an Englishman, Archbishop of Mentz, also afterwards Saint. All we know about the matter is, that there exists a letter of 748 from Pope Zachary, citing Virgil--then, it seems, at most a simple priest, though the Pope was not sure even of that--to Rome to answer the charge of maintaining that there is another world (_mundus_) under our earth (_terra_), with another sun and another moon. Nothing more is known: the letter contains threats in the event of the charge being true; and there history drops the matter. Since Virgil was afterwards a Bishop and a Saint, we may fairly conclude that he died in the full flower of his orthodox reputation. It has been supposed--and it seems probable--that Virgil maintained that the earth is peopled all the way round, so that under some spots there are antipodes; that his contemporaries, with very dim ideas about the roundness of the earth, and most of them with none at all, interpreted him as putting another earth under ours--turned the other way, probably, like the second piece of bread-and-b.u.t.ter in a sandwich, with a sun and moon of its own. In the eighth century this would infallibly have led to an underground Gospel, an underground Pope, and an underground Avignon for him to live in. When, in later times, the idea of inhabitants for the planets was started, it was immediately asked whether they had sinned, whether Jesus Christ died for _them_, whether their wine and their water could be lawfully used in the sacraments, etc.

On so small a basis as the above has been constructed a companion case to the persecution of Galileo. On one side the positive a.s.sertion, with indignant comment, that Virgil was deposed for antipodal heresy, on the other, serious attempts at justification, palliation, or mystification.

Some writers say that Virgil was found guilty; others that he gave satisfactory explanation, and became very good friends with {33} Boniface: for all which see Bayle. Some have maintained that the antipodist was a different person from the canonized bishop: there is a second Virgil, made to order. When your shoes pinch, and will not stretch, always throw them away and get another pair: the same with your facts. Baronius was not up to the plan of a subst.i.tute: his commentator Pagi (probably writing about 1690) argues for it in a manner which I think Baronius would not have approved. This Virgil was perhaps a slippery fellow. The Pope says he hears that Virgil pretended licence from him to claim one of some new bishoprics: this he declares is totally false. It is part of the argument that such a man as this could not have been created a Bishop and a Saint: on this point there will be opinions and opinions.[10]

Lactantius, four centuries before, had laughed at the antipodes in a manner which seems to be ridicule thrown on the idea of the earth's roundness.

Ptolemy, without reference to the antipodes, describes the extent of the inhabited part of the globe in a way which shows that he could have had no objection to men turned opposite ways. Probably, in the eighth century, the roundness of the earth was matter of thought only to astronomers. It should always be remembered, especially by those who affirm persecution of a true opinion, that but for our knowing from Lactantius that the antipodal notion had been matter of a.s.sertion and denial among theologians, we could never have had any great confidence in Virgil really having maintained the simple theory of the existence of antipodes. And even now we are not ent.i.tled to affirm it as having historical proof: the evidence {34} goes to Virgil having been charged with very absurd notions, which it seems more likely than not were the absurd constructions which ignorant contemporaries put upon sensible opinions of his.

One curious part of this discussion is that neither side has allowed Pope Zachary to produce evidence to character. He shall have been an Urban, say the astronomers; an Urban he ought to have been, say the theologians. What sort of man was Zachary? He was eminently sensible and conciliatory; he contrived to make northern barbarians hear reason in a way which puts him high among that section of the early popes who had the knack of managing uneducated swordsmen. He kept the peace in Italy to an extent which historians mention with admiration. Even Bale, that Maharajah of pope-haters, allows himself to quote in favor of Zachary, that "multa Papalem dignitatem decentia, eademque praeclara (scilicet) opera confecit."[11] And this, though so willing to find fault that, speaking of Zachary putting a little geographical description of the earth on the portico of the Lateran Church, he insinuates that it was intended to affirm that the Pope was lord of the whole. Nor can he say how long Zachary held the see, except by announcing his death in 752, "c.u.m decem annis pestilentiae sedi praefuisset."[12]

There was another quarrel between Virgil and Boniface which is an ill.u.s.tration. An ignorant priest had baptized "in nomine Patri_a_, et Fili_a_ et Spiritu_a_ Sancta." Boniface declared the rite null and void: Virgil maintained the contrary; and Zachary decided in favor of Virgil, on the ground that the absurd form was only ignorance of Latin, and not heresy. It is hard to believe that this man deposed a priest for a.s.serting the whole globe to be inhabited. To me the little information that we have seems {35} to indicate--but not with certainty--that Virgil maintained the antipodes: that his ignorant contemporaries travestied his theory into that of an underground cosmos; that the Pope cited him to Rome to explain his system, which, as reported, looked like what all would then have affirmed to be heresy; that he gave satisfactory explanations, and was dismissed with honor. It may be that the educated Greek monk, Zachary, knew his Ptolemy well enough to guess what the a.s.serted heretic would say; we have seen that he seems to have patronized geography. The _description_ of the earth, according to historians, was a _map_; this Pope may have been more ready than another to p.r.i.c.k up his ears at any rumor of geographical heresy, from hope of information. And Virgil, who may have entered the sacred presence as frightened as Jacquard, when Napoleon I sent for him and said, with a stern voice and threatening gesture, "You are the man who can tie a knot in a stretched string," may have departed as well pleased as Jacquard with the riband and pension which the interview was worth to him.

A word more about Baronius. If he had been pope, as he would have been but for the opposition of the Spaniards, and if he had lived ten years longer than he did, and if Clavius, who would have been his astronomical adviser, had lived five years longer than he did, it is probable, nay almost certain, that the great exhibition, the proceeding against Galileo, would not have furnished a joke against theology in all time to come. For Baronius was sensible and witty enough to say that in the Scriptures the Holy Spirit intended to teach how to go to Heaven, not how Heaven goes; and Clavius, in his last years, confessed that the whole system of the heavens had broken down, and must be mended.

The manner in which the Galileo case, a reality, and the Virgil case, a fiction, have been hawked against the Roman see are enough to show that the Pope and his adherents have not cared much about physical philosophy. In truth, orthodoxy has always had other fish to fry. Physics, which {36} in modern times has almost usurped the name _philosophy_, in England at least, has felt a little disposed to clothe herself with all the honors of persecution which belong to the real owner of the name. But the bishops, etc. of the Middle Ages knew that the contest between nominalism and realism, for instance, had a hundred times more bearing upon orthodoxy than anything in astronomy, etc. A wrong notion about _substance_ might play the mischief with _transubstantiation_.

The question of the earth's motion was the single point in which orthodoxy came into real contact with science. Many students of physics were suspected of magic, many of atheism: but, stupid as the mistake may have been, it was _bona fide_ the magic or the atheism, not the physics, which was a.s.sailed. In the astronomical case it was the very doctrine, as a doctrine, independently of consequences, which was the _corpus delicti_: and this because it contradicted the Bible. And so it did; for the stability of the earth is as clearly a.s.sumed from one end of the Old Testament to the other as the solidity of iron. Those who take the Bible to be _totidem verbis_ dictated by the G.o.d of Truth can refuse to believe it; and they make strange reasons. They undertake, _a priori_, to settle Divine intentions. The Holy Spirit did not _mean_ to teach natural philosophy: this they know beforehand; or else they infer it from finding that the earth does move, and the Bible says it does not. Of course, ignorance apart, every word is truth, or the writer did not mean truth. But this puts the whole book on its trial: for we never can find out what the writer meant, until we otherwise find out what is true. Those who like may, of course, declare for an inspiration over which they are to be viceroys; but common sense will either accept verbal meaning or deny verbal inspiration.

{37}

A BUDGET OF PARADOXES.

VOLUME I.

THE STORY OF BURIDAN'S a.s.s.

Questiones Morales, folio, 1489 [Paris]. By T. Buridan.

This is the t.i.tle from the Hartwell Catalogue of Law Books. I suppose it is what is elsewhere called the "Commentary on the Ethics of Aristotle,"

printed in 1489.[13] Buridan[14] (died about 1358) is the creator of the famous a.s.s which, as _Burdin's_[15] a.s.s, was current in Burgundy, perhaps is, as a vulgar proverb. Spinoza[16] says it was a jenny a.s.s, and that a man would not have been so foolish; but whether the compliment is paid to human or to masculine character does not appear--perhaps to both in one.

The story _told_ about the famous paradox is very curious. The Queen of France, Joanna or Jeanne, was in the habit of sewing her lovers up in sacks, and throwing them into the Seine; not for blabbing, but that they might not blab--certainly the safer plan. Buridan was exempted, and, in grat.i.tude, invented the sophism. What it has to do with the matter {38} has never been explained. a.s.suredly _qui facit per alium facit per se_ will convict Buridan of prating. The argument is as follows, and is seldom told in full. Buridan was for free-will--that is, will which determines conduct, let motives be ever so evenly balanced. An a.s.s is _equally_ pressed by hunger and by thirst; a bundle of hay is on one side, a pail of water on the other. Surely, you will say, he will not be a.s.s enough to die for want of food or drink; he will then make a choice--that is, will choose between alternatives of equal force. The problem became famous in the schools; some allowed the poor donkey to die of indecision; some denied the possibility of the balance, which was no answer at all.

MICHAEL SCOTT'S DEVILS.

The following question is more difficult, and involves free-will to all who answer--"Which you please." If the northern hemisphere were land, and all the southern hemisphere water, ought we to call the northern hemisphere an island, or the southern hemisphere a lake? Both the questions would be good exercises for paradoxers who must be kept employed, like Michael Scott's[17] devils. The wizard {39} knew nothing about squaring the circle, etc., so he set them to make ropes out of sea sand, which puzzled them.

Stupid devils; much of our gla.s.s is sea sand, and it makes beautiful thread. Had Michael set them to square the circle or to find a perpetual motion, he would have done his work much better. But all this is conjecture: who knows that I have not hit on the very plan he adopted?

Perhaps the whole race of paradoxers on hopeless subjects are Michael's subordinates, condemned to transmigration after transmigration, until their task is done.

The above was not a bad guess. A little after the time when the famous Pascal papers[18] were produced, I came into possession of a correspondence which, but for these papers, I should have held too incredible to be put before the world. But when one sheep leaps the ditch, another will follow: so I gave the following account in the _Athenaeum_ of October 5, 1867:

"The recorded story is that Michael Scott, being bound by contract to produce perpetual employment for a number of young demons, was worried out of his life in inventing jobs for them, until at last he set them to make ropes out of sea sand, which they never could do. We have obtained a very curious correspondence between the wizard Michael and his demon-slaves; but we do not feel at liberty to say how it came into our hands. We much regret that we did not receive it in time for the British a.s.sociation. It appears that the story, true as far as it goes, was never finished. The demons easily conquered the rope difficulty, by the simple process of making the sand into gla.s.s, and spinning the gla.s.s into thread, which they twisted.

Michael, thoroughly disconcerted, hit upon the plan of setting some to {40} square the circle, others to find the perpetual motion, etc. He commanded each of them to transmigrate from one human body into another, until their tasks were done. This explains the whole succession of cyclometers, and all the heroes of the Budget. Some of this correspondence is very recent; it is much blotted, and we are not quite sure of its meaning: it is full of figurative allusions to driving something illegible down a steep into the sea. It looks like a humble pet.i.tion to be allowed some diversion in the intervals of transmigration; and the answer is--

Rumpat et serpens iter inst.i.tutum,[19]

--a line of Horace, which the demons interpret as a direction to come athwart the proceedings of the Inst.i.tute by a sly trick. Until we saw this, we were suspicious of M. Libri,[20] the unvarying blunders of the correspondence look like knowledge. To be always out of the road requires a map: genuine ignorance occasionally lapses into truth. We thought it possible M. Libri might have played the trick to show how easily the French are deceived; but with our present information, our minds are at rest on the subject. We see M. Chasles does not like to avow the real source of information: he will not confess himself a spiritualist."

PHILO OF GADARA.

Philo of Gadara[21] is a.s.serted by Montucla,[22] on the {41} authority of Eutocius,[23] the commentator on Archimedes, to have squared the circle within the _ten-thousandth_ part of a unit, that is, to _four_ places of decimals. A modern cla.s.sical dictionary represents it as done by Philo to _ten thousand_ places of decimals. Lacroix comments on Montucla to the effect that _myriad_ (in Greek _ten thousand_) is here used as we use it, vaguely, for an immense number. On looking into Eutocius, I find that not one definite word is said about the extent to which Philo carried the matter. I give a translation of the pa.s.sage:

"We ought to know that Apollonius Pergaeus, in his Ocytocium [this work is lost], demonstrated the same by other numbers, and came nearer, which seems more accurate, but has nothing to do with Archimedes; for, as before said, he aimed only at going near enough for the wants of life. Neither is Porus of Nicaea fair when he takes Archimedes to task for not giving a line accurately equal to the circ.u.mference. He says in his Cerii that his teacher, Philo of Gadara, had given a more accurate approximation ([Greek: eis akribesterous arithmous agagein]) than that of Archimedes, or than 7 to 22. But all these [the rest as well as Philo] miss the intention. They multiply and divide by _tens of thousands_, which no one can easily do, unless he be versed in the logistics [fractional computation] of Magnus [now unknown]."

Montucla, or his source, ought not to have made this mistake. He had been at the Greek to correct Philo _Gadeta.n.u.s_, as he had often been called, and he had brought away {42} and quoted [Greek: apo Gadaron]. Had he read two sentences further, he would have found the mistake.

We here detect a person quite unnoticed hitherto by the moderns, Magnus the arithmetician. The phrase is ironical; it is as if we should say, "To do this a man must be deep in c.o.c.ker."[24] Accordingly, Magnus, Baveme,[25]

and c.o.c.ker, are three personifications of arithmetic; and there may be more.

ON SQUARING THE CIRCLE.

Aristotle, treating of the category of relation, denies that the quadrature has been found, but appears to a.s.sume that it can be done. Boethius,[26] in his comment on the pa.s.sage, says that it has been done since Aristotle, but that the demonstration is too long for him to give. Those who have no notion of the quadrature question may look at the _English Cyclopaedia_, art. "Quadrature of the Circle."

Tetragonismus. Id est circuli quadratura per Campanum, Archimedem Syracusanum, atque Boetium mathematicae perspicacissimos adinventa.--At the end, Impressum Venetiis per Ioan. Bapti. Sessa. Anno ab incarnatione Domini, 1503. Die 28 Augusti.

{43}

This book has never been noticed in the history of the subject, and I cannot find any mention of it. The quadrature of Campa.n.u.s[27] takes the ratio of Archimedes,[28] 7 to 22 to be absolutely correct; the account given of Archimedes is not a translation of his book; and that of Boetius has more than is in Boet_h_ius. This book must stand, with the next, as the earliest in print on the subject, until further showing: Murhard[29] and Kastner[30] have nothing so early. It is edited by Lucas Gauricus,[31] who has given a short preface. Luca Gaurico, Bishop of Civita Ducale, an astrologer of astrologers, published this work at about thirty years of age, and lived to eighty-two. His works are collected in folios, but I do not know whether they contain this production. The poor fellow could never tell his own fortune, because his father neglected to note the hour and minute of his birth. But if there had been anything in astrology, he could have worked back, as Adams[32] and Leverrier[33] did when they caught {44} Neptune: at sixty he could have examined every minute of his day of birth, by the events of his life, and so would have found the right minute. He could then have gone on, by rules of prophecy. Gauricus was the mathematical teacher of Joseph Scaliger,[34] who did him no credit, as we shall see.

BOVILLUS ON THE QUADRATURE PROBLEM.

In hoc opere contenta Epitome.... Liber de quadratura Circuli....

Paris, 1503, folio.

The quadrator is Charles Bovillus,[35] who adopted the views of Cardinal Cusa,[36] presently mentioned. Montucla is hard on his compatriot, who, he says, was only saved from the laughter of geometers by his obscurity.

Persons must guard against most historians of mathematics in one point: they frequently attribute to _his own_ age the obscurity which a writer has in _their own_ time. This tract was printed by Henry Stephens,[37] at the instigation of Faber Stapulensis,[38] {45} and is recorded by Dechales,[39]

etc. It was also introduced into the _Margarita Philosophica_ of 1815,[40]

in the same appendix with the new perspective from Viator. This is not extreme obscurity, by any means. The quadrature deserved it; but that is another point.

It is stated by Montucla that Bovillus makes [pi] = [root]10. But Montucla cites a work of 1507, _Introductorium Geometric.u.m_, which I have never seen.[41] He finds in it an account which Bovillus gives of the quadrature of the peasant laborer, and describes it as agreeing with his own. But the description makes [pi] = 3-1/8, which it thus appears Bovillus could not distinguish from [root]10. It seems also that this 3-1/8, about which we shall see so much in the sequel, takes its rise in the thoughtful head of a poor laborer. It does him great honor, being so near the truth, and he having no means of instruction. In our day, when an ignorant person chooses to bring his fancy forward in opposition to demonstration which he will not study, he is deservedly laughed at.