A Budget of Paradoxes Volume II Part 6

The author is the late Mr. Peter Legh,[148] of Norbury Booths Hall, Knutsford, who published for eight or ten {69} years the _Ombrological Almanac_, a work of a.s.serted discovery in meteorology. The theory of comets is that the joint attraction of the new moon and several planets in the direction of the sun, draws off the gases from the earth, and forms these cometic meteors. But how these meteors come to describe orbits round the sun, and to become capable of having their returns predicted, is not explained.

A NEW PHASE OF MORMONISM.

The Mormon, New York, Sat.u.r.day, Oct. 27, 1855.

A newspaper headed by a grand picture of starred and striped banners, beehive, and eagle surmounting it. A scroll on each side: on the left, "Mormon creed. Mind your own business. Brigham Young;"[149] on the right, "Given by inspiration of G.o.d. Joseph Smith."[150] A leading article on the discoveries of Prof. Orson Pratt[151] says, "Mormonism has long taken the lead in religion: it will soon be in the van both in science and politics."

At the beginning of the paper is Professor Pratt's "Law of Planetary Rotation." The cube roots of the densities of the planets are as the square roots of their periods of rotation. The squares of the cube roots of the ma.s.ses divided by the squares of the diameters are as the periods of rotation. Arithmetical verification attempted, and the whole very modestly stated {70} and commented on. Dated G. S. L. City, Utah Ter., Aug. 1, 1855.

If the creed, as above, be correctly given, no wonder the Mormonites are in such bad odor.

MATHEMATICAL ILl.u.s.tRATIONS OF DOCTRINE.

The two estates; or both worlds mathematically considered. London, 1855, small (pp. 16).

The author has published mathematical works with his name. The present tract is intended to ill.u.s.trate mathematically a point which may be guessed from the t.i.tle. But the symbols do very little in the way of ill.u.s.tration: thus, x being the _present value_ of the future estate (eternal happiness), and a of all that this world can give, the author impresses it on the mathematician that, x being infinitely greater than a, x + a = x, so that a need not be considered. This will not act much more powerfully on a mathematician by virtue of the symbols than if those same symbols had been dispensed with: even though, as the author adds, "It was this method of neglecting infinitely small quant.i.ties that Sir Isaac Newton was indebted to for his greatest discoveries."

There has been a moderate quant.i.ty of well-meant attempt to enforce, sometimes motive, sometimes doctrine, by arguments drawn from mathematics, the proponents being persons unskilled in that science for the most part.

The ground is very dangerous: for the ill.u.s.tration often turns the other way with greater power, in a manner which requires only a little more knowledge to see. I have, in my life, heard from the pulpit or read, at least a dozen times, that all sin is infinitely great, proved as follows.

The greater the being, the greater the sin of any offence against him: therefore the offence committed against an infinite being is infinitely great. Now the mathematician, of which the proposers of this argument are not aware, is perfectly familiar with quant.i.ties which increase together, and never cease increasing, but so that one of them remains finite when {71} the other becomes infinite. In fact, the argument is a perfect _non sequitur_.[152] Those who propose it have in their minds, though in a cloudy and indefinite form, the idea of the increase of guilt being _proportionate_ to the increase of greatness in the being offended. But this it would never do to state: for by such statement not only would the argument lose all that it has of the picturesque, but the a.s.serted premise would have no strong air of exact truth. How could any one undertake to appeal to conscience to declare that an offence against a being 4-7/10 times as great as another is exactly, no more and no less, 4-7/10 times as great an offence against the other?

The infinite character of the offence against an infinite being is laid down in Dryden's _Religio Laici_,[153] and is, no doubt, an old argument:

"For, granting we have sinned, and that th' offence Of man is made against Omnipotence, Some price that bears proportion must be paid, And infinite with infinite be weighed.

See then the Deist lost; remorse for vice Not paid; or, paid, inadequate in price."

Dryden, in the words "bears proportion" is in verse more accurate than most of the recent repeaters in prose. And this is not the only case of the kind in his argumentative poetry.

My old friend, the late Dr. Olinthus Gregory,[154] who was a sound and learned mathematician, adopted this dangerous kind of ill.u.s.tration in his _Letters on the Christian Religion_. {72} He argued, by parallel, from what he supposed to be the necessarily mysterious nature of the _impossible_ quant.i.ty of algebra to the necessarily mysterious nature of certain doctrines of his system of Christianity. But all the difficulty and mystery of the impossible quant.i.ty is now cleared away by the advance of algebraical thought: and yet Dr. Gregory's book continues to be sold, and no doubt the ill.u.s.tration is still accepted as appropriate.

The mode of argument used by the author of the tract above named has a striking defect. He talks of reducing this world and the next to "present value," as an actuary does with successive lives or next presentations.

Does value make interest? and if not, why? And if it do, then the present value of an eternity is _not_ infinitely great. Who is ignorant that a perpetual annuity at five per cent is worth only twenty years' purchase?

This point ought to be discussed by a person who treats heaven as a deferred perpetual annuity. I do not ask him to do so, and would rather he did not; but if he _will_ do it, he must either deal with the question of discount, or be asked the reason why.

When a very young man, I was frequently exhorted to one or another view of religion by pastors and others who thought that a mathematical argument would be irresistible. And I heard the following more than once, and have since seen it in print, I forget where. Since eternal happiness belonged to the particular views in question, a benefit infinitely great, then, even if the probability of their arguments were small, or even infinitely small, yet the product of the chance and benefit, according to the usual rule, might give a result which no one ought in prudence to pa.s.s over. They did not see that this applied to all systems as well as their own. I take this argument to be the most perverse of all the perversions I have heard or read on the subject: there is some high authority for it, whom I forget.

The moral of all this is, that such things as the preceding should be kept out of the way of those who are not {73} mathematicians, because they do not understand the argument; and of those who are, because they do.

[The high authority referred to above is Pascal, an early cultivator of mathematical probability, and obviously too much enamoured of his new pursuit. But he conceives himself bound to wager on one side or the other.

To the argument (_Pensees_, ch. 7)[155] that "le juste est de ne point parier," he answers, "Oui: mais il faut parier: vous etes embarque; et ne parier point que Dieu est, c'est parier qu'il n'est pas."[156] Leaving Pascal's argument to make its way with a person who, _being a sceptic_, is yet positive that the issue is salvation or perdition, if a G.o.d there be,--for the case as put by Pascal requires this,--I shall merely observe that a person who elects to believe in G.o.d, as the best chance of gain, is not one who, according to Pascal's creed, or any other worth naming, will really secure that gain. I wonder whether Pascal's curious imagination ever presented to him in sleep his convert, in the future state, shaken out of a red-hot dice-box upon a red-hot hazard-table, as perhaps he might have been, if Dante had been the later of the two. The original idea is due to the elder Arn.o.bius,[157] who, as cited by Bayle,[158] speaks thus:

"Sed et ipse [Christus] quae pollicetur, non probat. Ita est. Nulla enim, ut dixi, futurorum potest existere comprobatio. c.u.m ergo haec sit conditio futurorum, ut teneri et comprehendi nullius possint antic.i.p.ationis attactu; nonne {74} purior ratio est, ex duobus incertis, et in ambigua expectatione pendentibus, id potius credere, quod aliquas spes ferat, quam omnino quod nullas? In illo enim periculi nihil est, si quod dicitur imminere, ca.s.sum fiat et vacuum: in hoc d.a.m.num est maximum, id est salutis amissio, si c.u.m tempus advenerit aperiatur non fuisse mendacium."[159]

Really Arn.o.bius seems to have got as much out of the notion, in the third century, as if he had been fourteen centuries later, with the arithmetic of chances to help him.]

NOVUM ORGANUM MORALIUM.

The Sentinel, vol. ix. no. 27. London, Sat.u.r.day, May 26, 1855.

This is the first London number of an Irish paper, Protestant in politics.

It opens with "Suggestions on the subject of a _Novum Organum Moralium_,"

which is the application of algebra and the differential calculus to morals, socials, and politics. There is also a leading article on the subject, and some applications in notes to other articles. A separate publication was afterwards made, with the addition of a long Preface; the author being a clergyman who I presume must have been the editor of the _Sentinel_.

Suggestions as to the employment of a _Novum Organum Moralium_. Or, thoughts on the nature of the Differential Calculus, and on the application of its principles to metaphysics, with a view to the attainment of demonstration and certainty in moral, {75} political and ecclesiastical affairs. By Tresham Dames Gregg,[160] Chaplain of St.

Mary's, within the church of St. Nicholas intra muros, Dublin. London, 1859, 8vo. (pp. xl + 32).

I have a personal interest in this system, as will appear from the following extract from the newspaper:

"We were subsequently referred to De Morgan's _Formal Logic_ and Boole's _Laws of Thought_[161] both very elaborate works, and greatly in the direction taken by ourselves. That the writers amazingly surpa.s.s us in learning we most willingly admit, but we venture to p.r.o.nounce of both their learned treatises, that they deal with the subject in a mode that is scholastic to an excess.... That their works have been for a considerable s.p.a.ce of time before the world and effected nothing, would argue that they have overlooked the vital nature of the theme.... On the whole, the writings of De Morgan and Boole go to the full justification of our principle without in any wise so trenching upon our ground as to render us open to reproach in claiming our Calculus as a great discovery.... But we renounce any paltry jealousy as to a matter so vast. If De Morgan and Boole have had a priority in the case, to them we cheerfully shall resign the glory and honor. If such be the truth, they have neither done justice to the discovery, nor to themselves [quite true]. They have, under the circ.u.mstances, acted like 'the foolish man, who roasteth not that which he taketh {76} in hunting.... It will be sufficient for us, however, to be the Columbus of these great Americi, and popularize what they found, _if_ they found it. We, as from the mountain top, will then become _their_ trumpeters, and cry glory to De Morgan and glory to Boole, under Him who is the source of all glory, the only good and wise, to Whom be glory for ever!

_If_ they be our predecessors in this matter, they have, under Him, taken moral questions out of the category of probabilities, and rendered them perfectly certain. In that case, let their books be read by those who may doubt the principles this day laid before the world as a great discovery, by our newspaper. Our cry shall be [Greek: eurekasi]![162] Let us hope that they will join us, and henceforth keep their light [_sic_] from under their bushel."

For myself, and for my old friend Mr. Boole, who I am sure would join me, I disclaim both priority, simultaneity, and posteriority, and request that nothing may be trumpeted from the mountain top except our abjuration of all community of thought or operation with this _Novum Organum_.

To such community we can make no more claim than Americus could make to being the forerunner of Columbus who popularized his discoveries. We do not wish for any [Greek: eurekasi] and not even for [Greek: heurekasi]. For self and Boole, I point out what would have convinced either of us that this house is divided against itself.

[Alpha] being an apostolic element, [delta] the doctrinal element, and [Chi] the body of the faithful, the church is [Alpha] [delta] [Chi], we are told. Also, that if [Alpha] become negative, or the Apostolicity become Diabolicity [my words]; or if [delta] become negative, and doctrine become heresy; or if [Chi] become negative, that is, if the faithful become unfaithful; the church becomes negative, "the very opposite to what it ought to be." For self and Boole, I admit this. But--which is not noticed--if [Alpha] and [delta] should _both_ become negative, diabolical origin {77} and heretical doctrine, then the church, [Alpha] [delta] [Chi], is still positive, what it ought to be, unless [Chi] be also negative, or the people unfaithful to it, in which case it is a bad church. Now, self and Boole--though I admit I have not asked my partner--are of opinion that a diabolical church with false doctrine does harm when the people are faithful, and can do good only when the people are unfaithful. We may be wrong, but this is what we _do_ think. Accordingly, we have caught nothing, and can therefore roast nothing of our own: I content myself with roasting a joint of Mr. Gregg's larder.

These mathematical vagaries have uses which will justify a large amount of quotation: and in a score of years this may perhaps be the only attainable record. I therefore proceed.

After observing that by this calculus juries (heaven help them! say I) can calculate damages "almost to a nicety," and further that it is made abundantly evident that c e x is "the general expression for an individual," it is noted that the number of the Beast is not given in the Revelation in words at length, but as [Greek: chxw'].[163] On this the following remark is made:

"Can it be possible that we have in this case a specimen given to us of the arithmetic of heaven, and an expression revealed, which indicates by its function of addibility, the name of the church in question, and of each member of it; and by its function of multiplicability the doctrine, the mission, and the members of the great Synagogue of Apostacy? We merely propound these questions;--we do not pretend to solve them."

After a translation in blank verse--a very pretty one--of the 18th Psalm, the author proceeds as follows, to render it into differential calculus:

{78}

"And the whole tells us just this, that David did what he could. He augmented those elements of his const.i.tution which were (_exceptis excipiendis_)[164] subject to himself, and the Almighty then augmented his personal qualities, and his vocational _status_. Otherwise, to throw the matter into the expression of our notation, the variable e was augmented, and c x rose proportionally. The law of the variation, according to our theory, would be thus expressed. The resultant was David the king c e x [c = r?] (who had been David the shepherd boy), and from the conditions of the theorem we have

du/de = ce(dx/de) + ex(dc/de)x + cx

which, in the terms of ordinary language, just means, the increase of David's educational excellence or qualities--his piety, his prayerfulness, his humility, obedience, etc.--was so great, that when multiplied by his original talent and position, it produced a product so great as to be equal in its amount to royalty, honor, wealth, and power, etc.: in short, to all the attributes of majesty."[165]

The "solution of the family problem" is of high interest. It is to determine the effect on the family in general from a change [of conduct] in one of them. The person chosen is one of the maid-servants.

"Let c e x be the father; c_1e_1x_1 the mother, etc. The family then consists of the maid's master, her mistress, her young master, her young mistress, and fellow servant. Now the master's calling (or c) is to exercise his share of control over this servant, and mind the rest of his business: call this remainder a, and let his calling generally, or all his affairs, be to his maid-servant as m : y, i.e., y = (mz/c); ... {79} and this expression will represent his relation to the servant. Consequently,

c e x = (a + mz/c)e x; otherwise (a + mz/c)e x

is the expression for the father when viewed as the girl's master."

I have no objection to repeat so far; but I will not give the formula for the maid's relation to her young master; for I am not quite sure that all young masters are to be trusted with it. Suffice it that the son will be affected directly as his influence over her, and inversely as his vocational power: if then he should have some influence and no vocational power, the effect on him would be infinite. This is dismal to think of.

Further, the formula brings out that if one servant improve, the other must deteriorate, and _vice versa_. This is not the experience of most families: and the author remarks as follows: