[305] M. Voltaire; M. Cheneviere; Theol. Essays, Vol. I. p. 456.

[306] Humboldt's Cosmos, Vol. I. p. 139; Herschel's Outlines, 380; Kendall's Uranography, 205.

[307] Somerville's Connection of the Physical Sciences, 171, 337, 315; Architecture of the Heavens, 286.

[308] Genesis, chap. xv. 5.

[309] Cosmos I. 140.

[310] Ehrenberg computes that there are forty-one millions of the sh.e.l.ls of animalculae in a cubic inch of Bilier Slate.

[311] Annual of Scientific Discovery, 1860, p. 341.

[312] Psalm cxlvii. 4.

[313] d.i.c.k's Sidereal Heavens, 59; Herschel's Outlines.

[314] Architecture of the Heavens, 62.

[315] Architecture of the Heavens, 64. These unresolved milky streaks and patches have since been discovered to be true nebulae, or phosphoric clouds, in some way connected with their adjacent stars.

[316] Architecture of the Heavens, 144.

[317] Job, chap. x.x.xviii. 31. Psalm cxlvii. 4.

[318] Genesis, chap. xxii. 16.

[319] Galatians, chap. iii. 14, 29. Gen. xxii. 16, 17.

[320] Architecture of the Heavens, 217.

[321] Architecture of the Heavens, 77, 130.

CHAPTER XIII.

SCIENCE, OR FAITH?

"Faith is destined to be left behind in the onward march of the human intellect. It belongs to an infantile stage of intellectual development, when experience, dependent on testimony, becomes the slave of credulity.

Children and childish nations are p.r.o.ne to superst.i.tion. Religion belongs properly to such. Hence the endless controversies of religious sects. But as man advances into the knowledge of the physical sciences, and becomes familiarized with mathematical demonstration and scientific experiment, he demands substantial proofs for all kinds of knowledge, and rejects that which is merely matter of faith. The certainties of science succeed the controversies of creeds. Science thus becomes the grave of religion, as religion is vulgarly understood. But science gives a new and better religion to the world. Instead of filling men's minds with the vague terrors of an unknown futurity, it directs us to the best modes of improving this life."--"This life being the first in certainty, give it the first place in importance; and by giving human duties in reference to men the _precedence_, secure that all interpretations of spiritual duty shall be in harmony with human progress."--"Nature refers us to science for help, and to humanity for sympathy; love to the lovely is our only homage, study our only praise, quiet submission to the inevitable our duty; and truth is our only worship."--"Our _knowledge_ is confined to this life; and _testimony_, and _conjecture_, and _probability_, are all that can be set forth in regard to another."--"Preach nature and science, morality and art; _nature, the only subject of knowledge_; morality, the harmony of action; art, the culture of the individual and society."[322]

Or, if you will insist upon preaching religion, support it "with such proofs as accompany physical science. This I have always loved; for I never find it deceives me. I rest upon it with entire conviction. There is no mistake, and can be no dispute in mathematics. And if a revelation comes from G.o.d, why have we not such evidence for it as mathematical demonstration?"

Such is the language now used by a large cla.s.s of half-educated people, who, deriving their philosophy from Comte, and their religion from the _Westminster Review_, invite us to spend our Sabbaths in the study of nature in the fields and museums, turn our churches into laboratories, exchange our Bibles for encyclopedias, give ourselves no more trouble about religion, but try hard to learn as much science, make as much money, and enjoy as much pleasure in this life as we can; because we _know_ that we live now, and can only _believe_ that we shall live hereafter. I do not propose to take any notice here of the proposal of Secularism--for that is the new name of this unG.o.dliness--to deliver men from their l.u.s.ts by scientific lectures, and keep them moral by overturning religion. That experiment has been tried already. But it is worth while to inquire, Is science really so positive, and religion so uncertain, as these persons allege? Is a knowledge of the physical sciences so all-sufficient for our present happiness, so attainable by all mankind, and so certain and infallible, that we should barter our immortality for it? And, on the other hand, are the great facts of religious experience, and the foundations of our religious faith, so dim, and vague, and utterly uncertain, that we may safely consign them to oblivion, or that we can so get rid of them if we would?

The object of this chapter is to refute both parts of the Secularist's statement; to show some of the uncertainties, errors, contradictions, and blunders of the scientific men on whose testimony they receive their science; and to exhibit a few of the facts of religious experience which give a sufficient warrant for the Christian's faith.

Scientific observations are made by fallible men exposed to every description of error, prejudice and mistake; men who can not possibly divest themselves of their preconceived opinions in observing facts, and framing theories.

Lord Bacon long ago observed that "the eye of the human intellect is not dry, but receives a suffusion from the will and the affections, so that it may be almost said to engender any science it pleases. For what a man wishes to be true, that he prefers believing." "If the human intellect hath once taken a liking to any doctrine, either because received and credited, or because otherwise pleasing, it draws everything else into harmony with that doctrine, and to its support; and albeit there may be found a more powerful array of contradictory instances, these, however, it does not observe, or it contemns, or by distinction extenuates, and rejects."[323]

A prejudiced observer sees the facts distorted and exaggerated. "Thus it is that men will not see in the phenomena what alone is to be seen; in their observations they interpolate and expunge; and this mutilated and adulterated product they call a fact. And why? Because the real phenomena, if admitted, would spoil the pleasant music of their thoughts, and convert its fact.i.tious harmony into a discord. In consequence of this many a system professing to be reared exclusively on observation and fact, rests, in reality, mainly upon hypothesis and fiction. A pretended experience is indeed the screen behind which every illusive doctrine regularly retires. 'There are more false facts,' says Cullen, 'current in the world than false theories.' Fact, observation, induction, have always been the watchwords of those who have dealt most extensively in fancy."[324] We propose, therefore, to show that, _I. The students of the physical sciences have no such certain knowledge of their facts and theories as Secularists pretend._

1. Mathematical science relating merely to abstract truth is supposed to possess powers of demonstration, and capability of scientific certainty superior to all other kinds of knowledge, but the moment we begin to apply it to any existing facts we enter the domain of liability to errors as numerous as our fallible observations of these facts; and when we attempt to apply mathematical demonstration to the infinite, and to enter the domain of faith, in which as immortals we are chiefly concerned, it baffles, deceives, and insults our reason. Take the following ill.u.s.trations:

Let an infinite whole be divided into halves; the parts must be either finite or infinite. But they can not be finite, else an infinite whole would consist of a finite number of parts; neither can they be infinite, being each less than the infinite whole.

Again: it is mathematically demonstrable, that any piece of matter is infinitely divisible. A line therefore of half an inch long is infinitely divisible, or divisible into an infinite number of parts.

Thus we have an infinite half inch. Further, for a moving body to pa.s.s a given point requires some time; and to pa.s.s an infinite number of points must require an infinite number of portions of time, or an eternity; therefore, as half an inch contains an infinite number of points, it will require eternity to pa.s.s half an inch.

Again: it is mathematically demonstrable, that a straight line, the asymptote of a hyperbola, may _eternally approach_ the curve of the hyperbola and _never meet_ it. But no axiom can be plainer than that if two lines continually approach each other they must at length meet. Here is a demonstration contradicting an axiom; and no man has ever yet shown the possibilities of reconciling them, nor yet of denying either side of the contradiction.

Again: it is a fundamental axiom, contained in the definition of a circle, that it must have a center; but the non-existence of this center is mathematically demonstrable, as follows: Let the diameter of the circle be bisected into two equal parts; the center must be in one, or the other, of these parts, or between them. It can not be in one of these parts, for they are equal; and, therefore, if it is in the one, it must also be in the other, and thus the circle would have two centers, which is absurd. Neither can it be between them, for they are in contact. Therefore the center must be a point, dest.i.tute of extension, something which does not occupy or exist in s.p.a.ce. But as all existences exist in s.p.a.ce, and this supposed center does not, it can not be an existence; therefore it is a non-existence.

In like manner it has been mathematically demonstrated,[325] that motion, or any change in the rate of progress in a moving body, is impossible; because in pa.s.sing from any one degree of rapidity to another, all the intermediate degrees must be pa.s.sed through. As when a train of cars moving four miles an hour strikes a train at rest, the resulting instantaneous motion is two miles an hour; and the first train must therefore be moving at the rate of four, and at the rate of two miles an hour at the same time, which is impossible. And so the ancients demonstrated the impossibility of motion.

Thus the non-existence of the most undeniable truths, and the impossibilities of the most common facts are mathematically demonstrable; and the proper refutation of such reasoning is, not the scientific, but the common sensible; as when Plato refuted the demonstration of the impossibility of motion, by getting up and walking across the floor. In the hyperbola we have the mathematical demonstration of the error of an axiom. In the infinite inch we behold an absurdity mathematically demonstrated. So that it appears we can give mathematical demonstration in support of untruth, impossibilities and absurdities; and our reason can not discover the error of the reasoning!

Alas, for poor humanity, if an endless destiny depended upon such scientific certainty! Yet mathematical reasoning about abstract truth is universally conceded to be less liable to error than any other form of scientific a.n.a.lysis. This line, then, is too short to fathom the ocean of destiny; too weak to bear inferences from even the facts of common life.

Attempts have indeed been made to apply mathematics to the facts of life in what is called the doctrine of chances. By this kind of calculation it can be shown, that the chances were a thousand millions to one that you and I should never have been born. Yet here we are.

But when we begin to apply mathematics to the affairs of every-day life, we immediately multiply our chances of error by the number and complexity of these facts. The proper field of mathematics is that of magnitude and numbers. But very few subjects are capable of a mathematical demonstration. _No fact_ whatever which depends on the will of G.o.d or man can be so proved. For mathematical demonstration is founded on necessary and eternal relations, and admits of no contingencies in its premises. The mathematician may demonstrate the size and properties of a triangle, but he can not demonstrate the continuance of any actual triangle for one hour, or one minute, after his demonstration. And if he could, how many of my most important affairs can I submit to the multiplication table, or lay off in squares and triangles? It deals with purely ideal figures, which never did or could exist. There is not a mathematical line--length without breadth--in the universe. When we come to the application of mathematics, we are met at once by the fact that there are no mathematical figures in nature. It is true we speak of the orbits of the planets as elliptical or circular, but it is only in a general way, as we speak of a circular saw, the outline of its teeth being regularity itself compared with the perturbations of the planets. We speak of the earth as a spheroid, but it is a spheroid pitted with hollows as deep as the ocean, and crusted with irregular protuberances as vast as the Himalaya and the Andes, in every conceivable irregularity of form. Its seas, coasts, and rivers follow no straight lines nor geometrical curves. There is not an acre of absolutely level ground on the face of the earth; and even its waters will pile themselves up in waves, or dash into breakers, rather than remain perfectly level for a single hour. Its minuter formations present the same regular irregularity of form. Even the crystals, which approach the nearest of any natural productions to mathematical figures, break with compound irregular fractures at their bases of attachment. The surface of the pearl is proportionally rougher than the surface of the earth, and the dew-drop is not more spherical than a pear. As nature then gives no mathematical figures, mathematical measurements of such figures can be only approximately applied to natural objects.

The utter absence of any regularity, or a.s.similation to the spheroidal figure, either in meridia.n.a.l, equatorial, or parallel lines, mountain ranges, sea beaches, or courses of rivers, is fatal to mathematical accuracy in the more extended geographical measurements. It is only by taking the mean of a great many measurements that an approximate accuracy can be obtained. Where this is not possible, as in the case of the measurements of high mountains, the truth remains undetermined by hundreds of feet; or, as in the case of the earth's spheroidal axis, Bessel's measurement differs from Newton's, by fully eleven miles.[326]

The smaller measures are proportionately as inaccurate. No field, hill, or lake, has an absolute mathematical figure; but its outline is composed of an infinite mult.i.tude of irregular curves too minute for man's vision to discover, and too numerous for his intellect to estimate. No natural figure was ever measured with absolute accuracy.

All the resources of mathematical science were employed by the constructors of the French Metric System; but the progress of science in seventy years has shown that _every element_ of their calculations was erroneous. They tried to measure a quadrant of the earth's circ.u.mference, supposing the meridian to be circular; but Schubert has shown that that is far from being the case; and that no two meridians are alike; and Sir John Herschel, and the best geologists, show cause to believe that the form of the globe is constantly changing; so that the ancient Egyptians acted wisely in selecting the axis of the earth's rotation, which is invariable, and not the changing surface of the earth, as their standard of measure.

The Astronomer Royal, Piazzi Smyth, thus enumerates the errors of practice, which they added to those of their erroneous theory: "Their trigonometrical survey for their meter length has been found erroneous, so that their meter is no longer sensibly a meter; and their standard temperature of 0 centigrade is upset one way for the length of their scale, and another way for the density of the water employed; and their mode of computing the temperature correction is proved erroneous; and their favorite natural reference of a quadrant of the earth is not found a scientific feature capable of serving the purpose they have been employing it for; and even their own sons show some dislike to adopt it fully, and adhere to as much of the ancient system as they can."[327]

But coming down to more practical and every-day calculations, in which money is invested, how very erroneous are the calculations of our best engineers, and how fatal their results. Nineteen serious errors were discovered in an edition of _Taylor's Logarithms_, printed in 1796; some of which might have led to the most dangerous results in calculating a ship's place, and were current for thirty-six years. In 1832 the _Nautical Almanac_ published a correction which was itself erroneous by one second, and a new correction was necessary the next year. But in making this correction a _new error was committed of ten degrees_.[328]

Who knows how many ships were run ash.o.r.e by that error?

Nor can our American mathematicians boast of superior infallibility to the French or British. In computing the experiments which were made at Lowell (for a new turbine wheel), it was found that when the gate was fully open, the quant.i.ty of water discharged through the guides was _seventy per cent. of the theoretical discharge_. (An error of thirty per cent.) The effect of the wheel during these experiments was eighty-one and a half per cent. of the power expended; but when the gate was half open the effect was sixty-seven per cent. of the power, while the discharge through the guides eleven per cent. more than the theoretical discharge. But when the opening of the gate was still further reduced to one-fourth of the full opening, the effect was also reduced to forty-five per cent. of the power, while the discharging velocity was raised to _forty-nine per cent. more than that given by the theory_.[329] An unscientific man would hardly call that good guessing; but it was the best result of labored and expensive scientific calculation. No wonder the _London Mechanics' Magazine_ says: "More can be learned in this way (testing engines in the workshop) in half an hour, than can be derived from the theoretical instructions, however good, in a year." So much for the infallibility of a mathematical demonstration. In regard even to the very limited circle of our relations which can be measured by the foot rule, and the small number of our anxieties which may be resolved by an equation, if by mathematical accuracy be meant anything more than tolerable correctness, or by mathematical demonstration a very high degree of probability, mathematical certainty is all a fable.

2. _Astronomy._

The omniscience and prescience of the human intellect have been largely glorified by some Infidel lecturers, upon the strength of the accuracy with which it is possible to calculate and predict eclipses, and to the disparagement of Bible predictions. And this glorification has been amazingly swollen by Le Verrier's prediction in 1846 of the discovery of the planet Neptune. But the prediction of some unknown motion would form a more correct basis for a comparison of the prophecies of science with those of Scripture; such, for instance, as Immanuel Kant's prediction of the period of Saturn's rotation at six hours twenty-three minutes fifty-three seconds; "which mathematical calculation of an unknown motion of a heavenly body," he says, "_is the only prediction of that kind in pure Natural Philosophy_, and awaits confirmation at a future period." It is a pity that this unique scientific prediction should not have had better luck, for the encouragement of other guessers; but after waiting long and vainly, for the expected confirmation, it was finally falsified by Herschel's discovery of spots on the surface of the planet, and observation of the true time, ten hours sixteen minutes forty-four seconds.[330] This, however, was not his only astronomical prediction. He predicted that immense bodies in a transition state between planets and comets, and of very eccentric orbits, would be found beyond the orbit of Saturn, and intersecting it, but no such bodies have been discovered. Ura.n.u.s and Neptune have no cometary character whatever, their orbits are less eccentric than others and do not intersect, nor approach within millions of miles of Saturn's...o...b..t. The verification of Le Verrier's prediction affords even a more satisfactory proof of the necessarily conjectural character of astronomical computations of unknown quant.i.ties and distances. The planet Neptune has not one-half the ma.s.s which he had calculated; his...o...b..t, which was calculated as very elliptical, is nearly circular; and the error of the calculation of his distance is three hundred millions of miles![331]

"Let us then be candid," says Loomis, "and claim no more for astronomy than is reasonably due. When in 1846 Le Verrier announced the existence of a planet hitherto unseen, and when he a.s.signed it its exact position in the heavens, and declared that it shone like a star of the eighth magnitude, and with a perceptible disc, _not an astronomer of France, and scarce an astronomer in Europe, had sufficient faith in the prediction to prompt him to point his telescope to the heavens_. But when it was announced that the planet had been seen at Berlin, that it was found within one degree of the computed place, that it was indeed a star of the eighth magnitude, and had a sensible disc--then the enthusiasm not only of the public generally, but of astronomers also, was even more wonderful than their former apathy. The sagacity of Le Verrier was felt to be almost superhuman. Language could scarce be found strong enough to express the general admiration. The praise then lavished upon Le Verrier was somewhat extravagant. _The singularly close agreement between the observed and computed places of the planet was accidental._ So exact a coincidence could not reasonably have been antic.i.p.ated. If the planet had been found even ten degrees from what Le Verrier a.s.signed as its probable place, _this discrepancy would have surprised no astronomer_. The discovery would still have been one of the most remarkable events in the history of astronomy, and Le Verrier would have merited the t.i.tle of First Astronomer of the age."[332]

Nevertheless, astronomy from the comparative simplicity of the bodies and forces with which it has to deal, and the approximate regularity of the paths of the heavenly bodies, may be regarded as the science in which the greatest possible certainty is attainable. It opens at once the widest field to the imagination, and the n.o.blest range to the reason; it has attracted the most exalted intellects to its pursuit, and has rewarded their toils with the grandest discoveries. These discoveries have been grossly abused by inferior minds, ascribing to the discoverers of the laws of the universe the glory due to their Creator; and boasting of the power of the human mind, as if it were capable of exploring the infinite in s.p.a.ce, and of calculating the movements of the stars through eternity. Persons who could not calculate an eclipse to save their souls, have risked them upon the notion that, because astronomers can do so with considerable accuracy, farmers ought to reject the Bible, unless its predictions can be calculated by algebra.

It may do such persons good, or at least prevent them from doing others harm, to take a cursory view of the errors of astronomers; errors necessary as well as accidental.

Sir John Herschel, than whom none has a better right to speak on this subject, and whose devotion to that n.o.ble science precludes all supposition of prejudice against it, devotes a chapter to _The Errors of Astronomy_,[333] which he cla.s.sifies and enumerates: