Chapter 4 - Natural Mathematics

Mathematics give us the "exact sciences." "Solid" as Prof. Drummond tells us the laws of nature are, in mathematics at least they are so, beyond the possibility of intelligent question. No one, that I am aware, has ever accused them of poetic license, although poetry on her side does not refuse their alliance. And as we build our foundations of what we can find most solid, it need be no wonder that in proportion as we go down to the foundations of the earth, so do we find mathematics more and more revealing themselves in proportional numbers and in geometric forms. Chemistry has become in our day penetrated with arithmetic; and chemistry deals with those elementary principles, the combination of which gives us the material world. "Chemistry," says Herschel, is, in a most pre-eminent degree, the science of quantity; and to enumerate the discoveries which have arisen for it from the mere determination of weights and measures would be nearly to give a synopsis of this branch of knowledge."

What is this but as if you were to go into some ancient structure, as the pyramids, and find upon the stones the builder's hieroglyph? We have been only learning to find deeper truth than we were at all aware of in the prophet's challenge, "Who hath measured the waters in the hollow of His hand, and meted out heaven with a span, and comprehended the dust of the earth in a measure, and weighed the mountains in scales, and the hills in a balance?" (Is. xl. 12.) What science of the day in which that question was asked knew any thing about such measurement? How many centuries has it taken to bring man's tardy feet to where the prophet stood? But we are able now to see that we may take this as true in the most absolute way, that every bit of the earth's dust is weighed and measured.

"The law of simple numerical ratios," says Dr. Cooke, "Is the fundamental law of crystallography, and gives to the science a mathematical basis. Similar numerical relations appear when we study the formation of chemical compounds. I have already defined a chemical element as a substance which has never as yet been decomposed, and all the matter with which man is now acquainted is composed of one or more of at most seventy elementary substances. When two of these elements unite together to form a compound body, the proportions in which they combine are not decided by chance. You cannot unite these elementary substances in any proportion you The proportion in each case is determined by an unvarying law, and the amounts required of either substance are weighed out by nature in her delicate scales with a nicety which no art can attain. Thus, for Instance, 23 ounces of sodium will unite with exactly 35.5 ounces of chlorine; and if you use precisely these proportions of the two elements, the whole of each will disappear, and become merged in the compound which is our common table salt. But if, in attempting to make salt, we bring together clumsily 23.5 ounces of sodium and 35.5 ounces of chlorine, Nature will simply put the extra half-ounce of sodium on one side, and the rest will unite. This law which governs all chemical combinations is known as 'the law of definite proportions.'

"Tables will be found in works on chemistry, which give, opposite to the name of each elementary substance, a numerical value, usually called its atomic weight, and in all cases where the elements are capable of combining with each other, they either unite in the exact proportions indicated by these numbers, or else in some simple multiple of these proportions."

Thus these elements are themselves manufactured articles, and are stamped indelibly with the Manufacturer's name. For nothing addresses itself more to mind as from mind than just such relations as are discovered here. As another has said, "The most careful structure of brown stone is not so precise in number, relation, and dimensions of its blocks as are molecules, the first terms in matter, in their atomic formation." It should be as easy, then to refer the natural product to the workmanship of eternal mind, the recent structure to man's hand and mind. And who would have a doubt as to the latter?

Having got so far, moreover, ought we not to be able to go further? Ought not these numbers individually to have a voice for us, and in their relation to one another also? If all things are full of reason, is it too much to expect that these proportions have a reason too? Oh, for some interpreter here, some master mind, lowly and reverent enough to follow out this clue, and tell us whither it leads! But we must not expect these elements to speak yet clearly. Pythagoras has given place to Darwin; and final cause to formal cause; and we must wait for the wheel to come round again.

As to relations as indicated by the numbers we have just a hint: -
"Attempts have been made in the same science," say M'Cosh & Dickie, in their work on "Typical Forms," "to form bodies into groups or congeners. M. Dumas, in particular, has detected a number of triads, or series of three bodies, which have analogous properties, and showing a singular numerical profession in their equivalent weights; the equivalents of two of these added together, and divided by two, giving approximately the equivalent of the third, thus: -

Chlorine 35 } Potassium 40 }
Bromine }80 Sodium }24
Iodine 125 } Lithium 7 }
Calcium 20 } Sulphur 16 }
Strontium }44 Selenium }40
Barium 69 } Tellurium 64 }

" 'Regarding,' says Faraday, 'chlorine, bromine, and iodine as one triad, it will be seen that between the first and the last there is recognizable a well-marked progression of qualities. Thus chlorine is a gas, under ordinary temperatures and pressures; bromine, a fluid; and iodine, a solid; in this manner displaying a progression in the difference of cohesive force. Again, chlorine is yellow; bromine, red; iodine, black, or in vapor, a reddish violet.' "

This glimmer of light seems to have well-nigh gone out. The atomic weight of some of these has been since doubled, and of others more or less changed. At the best, it carries us but a little way upon the road we seek. None the less sure is it that there is a numerical impress upon all nature.
"Indeed," says Sir John Herschel again, "it is a character of all the higher laws of nature to assume the form of a precise quantitative statement."

And Humboldt declares, -
"It may be said that the only remaining and widely diffused hieroglyphic characters still In our writing - numbers - appear to us again as powers of the cosmos, although in a wider sense than that applied to them by the Italian School."

Much more might be said here, but it needs not to try more to establish what no science of the day will attempt to dispute. It is the meaning of admitted facts that we are seeking; and this is just what is so hard to reach. Save in their testimony to an Author of nature, they are yet dumb and unspiritual: how shall we spiritualize them? Is it not possible - yea, rather, may we not expect, that God has given us somewhere some clue to their interpretation, by which we may follow on to find ourselves more in the presence of the King? Nature seems to us as yet dumb, and God, if we own Him there, yet distant; where shall we find, then, the interpreter we seek, if not in Revelation?