Now, there can be but two suppositions possible as to this uniform combination by which the number five is five times repeated in the human organism. The cause, whatever that may be, which produces these invariable equations must be endowed with intelligence or not. There is no other conceivable alternative; for the abscissio infiniti effected by the word not, in logical division, always exhausts the whole category of things, both real and imaginary. Every object must be rational or not—rational in thought and in fact.
Therefore all these millionary equations of fives must have been produced by a cause, or causes, possessed of reason, or by a power destitute of that attribute. If we assume the first alternative there will be no chances for calculation, the efficient itself being amply adequate to develop the mathematical harmony.
But take up the other and only remaining supposition, that the causal agent producing the human organism is mere blind force of some unknown and unimaginable nature; what are the chances against such a hypothesis? We might say, in all logical strictness, that as we have no scientific knowledge of any such unintelligent cause capable of effecting the given phenomena of order, while we are acquainted with an efficient fully competent for the purpose, the chances against the naked assumption of blind force must be stated as infinity to zero. The chances against the equation of five fingers on each hand would be twenty-five. Add the five toes on each foot, and the chances will be six hundred and twenty-five. Then incorporate into the calculation the five senses, and the chances are three thousand one hundred and twenty-five. Let me procure a larger sheet, as the measureless sea of infinite and nameless numbers is flowing fast upon me. Next reckon the chances in the case of two persons, and they swell to the vast sum of nine millions, seven hundred and sixty-five thousand, six hundred and twenty-five; while the chances for four men will be the square of that number, and so on for ever. But the enormous sums soon overpower all the magnificent processes of our algebra, and no logarithmic abbreviations can aid us to grasp what stretches away into the unexplored fields of immensity. The attempt to apply the calculation even to the inhabitants now living on the globe would be as idle as the endeavor to enumerate the sunbeams shed during a solar year. The arithmetic of the archangel would perhaps be insufficient for the mighty computation.
In reference also to a single individual the subject might be pushed indefinitely farther—to the bones of the arms, head, feet, and the convolutions of the brain; for everywhere, and all through the physical framework, there runs a wonderful duality, where the series of constant equations counterbalance each other.
It must be borne in mind that I have shown in my major premise the necessity of rationality in the cause which effects mathematical order in the sequences of any natural phenomena. Hence such a cause is demonstrated for the whole of humanity. But, apart from the rigid logic of the argument, the question presents itself to popular apprehension: Could a cause without the intellect to perceive, the faculty to calculate and arrange, numerical relations, produce this infinity of mathematical harmonies?
If it be answered that the efficient is some unknown power or secret quality involved in the facts themselves or concealed beneath them, the problem still remains unsolved and rebounds upon us with accumulated force: Is that supposed secret power or occult quality self-conscious? Hath it the attribute of mathematical reason competent to the calculation and production of all these beautiful and boundless equations?
INSTANCE II.—CHEMISTRY.
Let us take our next comparisons from chemistry, that youngest sister of all the sciences, the splendid child of the galvanic battery, whose birth was brilliant as that of lightning.
Go analyze a cup of water. You find it composed of two parts of hydrogen to one of oxygen by volume, and eight parts of oxygen to one of hydrogen by weight. Nor do these numerical ratios ever vary. Freeze it into ice hard as the crystal of the jewelled mountains; dissipate it into vapor of such exquisite tenuity that a million acres of floating mist would scarcely form a single dewdrop; bring it from the salt solitudes of the ocean, or from the central curve of a rainbow, and submit it to the test of analysis; and still the pale chemist, as he watches the evolutions of the perpetual wonder from the depths of his laboratory, calls out: “Two to one, and one to eight, now and for ever!”
Let no one hope to estimate the chances against the hypothesis of the production of these mathematical relations by an unintelligent agent, unless he can first reckon the drops of a thunder-storm or measure the capacity of the sea.