A Budget of Paradoxes Volume I Part 8

This work is directed against the plurality by an author who does not admit modern astronomy. It was occasioned by Dr. Chalmers's[175] celebrated discourses on religion in connection with astronomy. The notes contain many citations on the gravity controversy, from authors now very little read: and this is its present value. I find no mention of Maxwell, not even in Watt.[176] He communicated with mankind without the medium of a publisher; and, from Vieta till now, this method has always been favorable to loss of books.

A correspondent informs me that Alex. Maxwell, who wrote on the plurality of worlds, in 1820, was a law-bookseller and publisher (probably his own publisher) in Bell Yard. He had peculiar notions, which he was fond of discussing with his customers. He was a bit of a Swedenborgian.

INHABITED PLANETS IN FICTION.

There is a cla.s.s of hypothetical creations which do not belong to my subject, because they are _acknowledged_ to be fictions, as those of Lucian,[177] Rabelais,[178] Swift, Francis {103} G.o.dwin,[179] Voltaire, etc. All who have more positive notions as to either the composition or organization of other worlds, than the reasonable conclusion that our Architect must be quite able to construct millions of other buildings on millions of other plans, ought to rank with the writers just mentioned, in all but self-knowledge. Of every one of their systems I say, as the Irish Bishop said of Gulliver's book,--I don't believe half of it. Huyghens had been preceded by Fontenelle,[180] who attracted more attention. Huyghens is very fanciful and very positive; but he gives a true account of his method.

"But since there's no hopes of a Mercury to carry us such a journey, we shall e'en be contented with what's in our power: we shall suppose ourselves there...." And yet he says, "We have proved that they live in societies, have hands and feet...." Kircher[181] had gone to the stars before him, but would not find any life in them, either animal or vegetable.

The question of the inhabitants of a particular planet is one which has truth on one side or the other: either there are some inhabitants, or there are none. Fortunately, it is of no consequence which is true. But there are many cases where the balance is equally one of truth and falsehood, in which the choice is a matter of importance. My work selects, for the most part, sins against demonstration: but the world is full of questions of fact or opinion, in which a struggling minority will become a majority, or else will {104} be gradually annihilated: and each of the cases subdivides into results of good, and results of evil. What is to be done?

"Periculosum est credere et non credere; Hippolitus obiit quia novercae creditum est; Ca.s.sandrae quia non creditum ruit Ilium: Ergo exploranda est veritas multum prius Quam stulta prove judicet sententia."[182]

Nova Demonstratio immobilitatis terrae pet.i.ta ex virtute magnetica. By Jacobus Grandamicus. Flexiae (La Fleche), 1645, 4to.[183]

No magnetic body can move about its poles: the earth is a magnetic body, therefore, etc. The iron and its magnetism are typical of two natures in one person; so it is said, "Si exaltatus fuero a terra, omnia traham ad me ipsum."[184]

A VENETIAN BUDGET OF PARADOXES.

Le glorie degli incogniti, o vero gli huomini ill.u.s.tri dell' accademia de' signori incogniti di Venetia. Venice, 1647, 4to.

This work is somewhat like a part of my own: it is a budget of Venetian n.o.bodies who wished to be somebodies; but paradox is not the only means employed. It is of a serio-comic character, gives genuine portraits in copperplate, and grave lists of works; but satirical accounts. The astrologer Andrew Argoli[185] is there, and his son; both of whom, with some of the others, have place in modern works {105} on biography. Argoli's discovery that logarithms facilitate easy processes, but increase the labor of difficult ones, is worth recording.

Controversiae de vera circuli mensura ... inter ... C. S. Longomontanum et Jo. Pellium.[186] Amsterdam, 1647, 4to.

Longomonta.n.u.s,[187] a Danish astronomer of merit, squared the circle in 1644: he found out that the diameter 43 gives the square root of 18252 for the circ.u.mference; which gives 3.14185... for the ratio. Pell answered him, and being a kind of circulating medium, managed to engage in the controversy names known and unknown, as Roberval, Hobbes, Carcavi, Lord Charles Cavendish, Pallieur, Mersenne, Ta.s.sius, Baron Wolzogen, Descartes, Cavalieri and Golius.[188] Among them, of course, Longomonta.n.u.s was made {106} mincemeat: but he is said to have insisted on the discovery of his epitaph.[189]

{107}

THE CIRCULATING MEDIA OF MATHEMATICS.

The great circulating mediums, who wrote to everybody, heard from everybody, and sent extracts to everybody else, have been Father Mersenne, John Collins, and the late Professor Schumacher: all "late" no doubt, but only the last recent enough to be so styled. If M.C.S. should ever again stand for "Member of the Corresponding Society," it should raise an acrostic thought of the three. There is an allusion to Mersenne's occupation in Hobbes's reply to him. He wanted to give Hobbes, who was very ill at Paris, the Roman Eucharist: but Hobbes said, "I have settled all that long ago; when did you hear from Ga.s.sendi?" We are reminded of William's answer to Burnet. John Collins disseminated Newton, among others.

Schumacher ought to have been called the postmaster-general of astronomy, as Collins was called the attorney-general of mathematics.[190]

{108}

THE SYMPATHETIC POWDER.

A late discourse ... by Sir Kenelme Digby.... Rendered into English by R. White. London, 1658, 12mo.

On this work see _Notes and Queries_, 2d series, vii. 231, 299, 445, viii.

190. It contains the celebrated sympathetic powder. I am still in much doubt as to the connection of Digby with this tract.[191] Without entering on the subject here, I observe that in Birch's _History of the Royal Society_,[192] to which both Digby and White belonged, Digby, though he brought many things before the Society, never mentioned the powder, which is connected only with the names of Evelyn[193] and Sir Gilbert Talbot.[194] The sympathetic powder was that which cured by anointing the weapon with its salve instead of the wound. I have long been convinced that it was efficacious. The directions were to keep the {109} wound clean and cool, and to take care of diet, rubbing the salve on the knife or sword.[195] If we remember the dreadful notions upon drugs which prevailed, both as to quant.i.ty and quality, we shall readily see that any way of _not_ dressing the wound would have been useful. If the physicians had taken the hint, had been careful of diet etc., and had poured the little barrels of medicine down the throat of a practicable doll, _they_ would have had their magical cures as well as the surgeons.[196] Matters are much improved now; the quant.i.ty of medicine given, even by orthodox physicians, would have been called infinitesimal by their professional ancestors. Accordingly, the College of Physicians has a right to abandon its motto, which is _Ars longa, vita brevis_, meaning _Practice is long, so life is short_.

HOBBES AS A MATHEMATICIAN.

Examinatio et emendatio Mathematicae Hodiernae. By Thomas Hobbes. London, 1666, 4to.

In six dialogues: the sixth contains a quadrature of the circle.[197] But there is another edition of this work, without place or date on the t.i.tle-page, in which the quadrature is omitted. This seems to be connected with the publication {110} of another quadrature, without date, but about 1670, as may be judged from its professing to answer a tract of Wallis, printed in 1669.[198] The t.i.tle is "Quadratura circuli, cubatio sphaerae, duplicatio cubi," 4to.[199] Hobbes, who began in 1655, was very wrong in his quadrature; but, though not a Gregory St. Vincent,[200] he was not the ignoramus in geometry that he is sometimes supposed. His writings, erroneous as they are in many things, contain acute remarks on points of principle. He is wronged by being coupled with Joseph Scaliger, as the two great instances of men of letters who have come into geometry to help the mathematicians out of their difficulty. I have never seen Scaliger's quadrature,[201] except in the answers of Adria.n.u.s Roma.n.u.s,[202] Vieta and Clavius, and in the extracts of Kastner.[203] Scaliger had no right to such strong opponents: Erasmus or Bentley might just as well have tried the problem, and either would have done much better in any twenty minutes of his life.[204]

AN ESTIMATE OF SCALIGER.

Scaliger inspired some mathematicians with great respect for his geometrical knowledge. Vieta, the first man of his time, who answered him, had such regard for his opponent {111} as made him conceal Scaliger's name.

Not that he is very respectful in his manner of proceeding: the following dry quiz on his opponent's logic must have been very cutting, being true.

"In grammaticis, dare navibus Austros, et dare naves Austris, sunt aeque significantia. Sed in Geometricis, aliud est adsumpsisse circulum BCD non esse majorem triginta s.e.x segmentis BCDF, aliud circulo BCD non esse majora triginta s.e.x segmenta BCDF. Illa adsumptiuncula vera est, haec falsa."[205]

Isaac Casaubon,[206] in one of his letters to De Thou,[207] relates that, he and another paying a visit to Vieta, the conversation fell upon Scaliger, of whom the host said that he believed Scaliger was the only man who perfectly understood mathematical writers, especially the Greek ones: and that he thought more of Scaliger when wrong than of many others when right; "pluris se Scaligerum vel errantem facere quam multos [Greek: katorthountas]."[208] This must have been before Scaliger's quadrature (1594). There is an old story of some one saying, "Mallem c.u.m Scaligero errare, quam c.u.m Clavio recte sapere."[209] This I cannot help suspecting to have been a version of Vieta's speech with Clavius satirically inserted, on account of the great hostility which Vieta showed towards Clavius in the latter years of his life.

Montucla could not have read with care either Scaliger's quadrature or Clavius's refutation. He gives the first a wrong date: he a.s.sures the world that there is no question about Scaliger's quadrature being wrong, in the eyes of geometers at least: and he states that Clavius mortified him {112} extremely by showing that it made the circle less than its inscribed dodecagon, which is, of course, equivalent to a.s.serting that a straight line is not always the shortest distance between two points. Did _Clavius_ show this? No, it was Scaliger himself who showed it, boasted of it, and declared it to be a "n.o.ble paradox" that a theorem false in geometry is true in arithmetic; a thing, he says with great triumph, not noticed by Archimedes himself! He says in so many words that the periphery of the dodecagon is greater than that of the circle; and that the more sides there are to the inscribed figure, the more does it exceed the circle in which it is. And here _are_ the words, on the independent testimonies of Clavius and Kastner:

"Ambitus dodecagoni circulo inscribendi plus potest quam circuli ambitus.

Et quanto deinceps plurium laterum fuerit polygonum circulo inscribendum, tanto plus poterit ambitus polygoni quam ambitus circuli."[210]

There is much resemblance between Joseph Scaliger and William Hamilton,[211] in a certain impetuousity of character, and inapt.i.tude to think of quant.i.ty. Scaliger maintained that the arc of a circle is less than its chord in arithmetic, though greater in geometry; Hamilton arrived at two quant.i.ties which are identical, but the greater the one the less the other. But, on the whole, I liken Hamilton rather to Julius than to Joseph.

On this last hero of literature I repeat Thomas Edwards,[212] who says that a man is unlearned who, be his other knowledge what it may, does not {113} understand the subject he writes about. And now one of many instances in which literature gives to literature character in science. Anthony Teissier,[213] the learned annotator of De Thou's biographies, says of Finaeus, "Il se vanta sans raison avoir trouve la quadrature du cercle; la gloire de cette admirable decouverte etait reservee a Joseph Scalinger, comme l'a ecrit Scevole de St. Marthe."[214]

JOHN GRAUNT AS A PARADOXER.

Natural and Political Observations ... upon the Bills of Mortality. By John Graunt, citizen of London. London, 1662, 4to.[215]

This is a celebrated book, the first great work upon mortality. But the author, going _ultra crepidam_, has attributed to the motion of the moon in her orbit all the tremors which she gets from a shaky telescope.[216] But there is another paradox about this book: the above absurd opinion is attributed to that excellent mechanist, Sir William Petty, who pa.s.sed his days among the astronomers. Graunt did not write his own book! Anthony Wood[217] hints that Petty "a.s.sisted, or put into a way" his old benefactor: no doubt the two friends talked the matter over many a time.

Burnet and Pepys[218] state that Petty wrote the book. It is enough for me that {114} Graunt, whose honesty was never impeached, uses the plainest incidental professions of authorship throughout; that he was elected into the Royal Society because he was the author; that Petty refers to him as author in scores of places, and published an edition, as editor, after Graunt's death, with Graunt's name of course. The note on Graunt in the _Biographia Britannica_ may be consulted; it seems to me decisive. Mr.

C. B. Hodge, an able actuary, has done the best that can be done on the other side in the _a.s.surance Magazine_, viii. 234. If I may say what is in my mind, without imputation of disrespect, I suspect some actuaries have a bias: they would rather have Petty the greater for their Coryphaeus than Graunt the less.[219]

Pepys is an ordinary gossip: but Burnet's account has an animus which is of a worse kind. He talks of "one Graunt, a Papist, under whose name Sir William Petty[220] published his observations on the bills of mortality."

He then gives the c.o.c.k without a bull story of Graunt being a trustee of the New River Company, and shutting up the c.o.c.ks and carrying off their keys, just before the fire of London, by which a supply of water was delayed.[221] It was one of the first objections made to Burnet's work, that Graunt was _not_ a trustee at the time; and Maitland, the historian of London, ascertained from the books of the Company that he was not admitted until twenty-three days after the breaking out of the fire. Graunt's first admission {115} to the Company took place on the very day on which a committee was appointed to inquire into the cause of the fire. So much for Burnet. I incline to the view that Graunt's setting London on fire strongly corroborates his having written on the bills of mortality: every practical man takes stock before he commences a grand operation in business.

MANKIND A GULLIBLE LOT.

De Cometis: or a discourse of the natures and effects of Comets, as they are philosophically, historically, and astrologically considered.

With a brief (yet full) account of the III late Comets, or blazing stars, visible to all Europe. And what (in a natural way of judicature) they portend. Together with some observations on the nativity of the Grand Seignior. By John Gadbury, [Greek: Philomathematikos]. London, 1665, 4to.