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Updated: May 18, 2025
The activity of mind awakened by music over waters is very different from that awakened by the binomial theorem. Some things interest the intellect, others the emotions; and it is only things of prime importance that interest them both in equal measure.
For these a rule may have to be provided, which, although it may not be inconsistent with the scientific theorem, differs from it in form. The Devil is not an invention of priests for priestly purposes, nor is he merely a hypothesis to account for facts, but he has been forced upon us in order that we may be able to deal with them.
According to Christianity, in making it, He set it free. God had written, not so much a poem, but rather a play; a play he had planned as perfect, but which had necessarily been left to human actors and stage-managers, who had since made a great mess of it. I will discuss the truth of this theorem later.
The occasion was memorable in other ways a long conversation between Maury and a defunct crab, which he was dragging around on the end of a string, as to whether the crab was fully conversant with the applications of the binomial theorem, and the aforementioned race in two hansom cabs with the sedate and impressive shadows of Fifth Avenue for audience, ending in a labyrinthine escape into the darkness of Central Park.
The fact is not improbable: but a mathematician like Newton, who seemed to arrive per saltum at principles and conclusions that ordinary mathematicians only reached by a succession of steps, certainly could not have performed the comparison in question without being led by it to the a priori ground of the law; since any one who understands sufficiently the nature of multiplication to venture upon multiplying several lines of symbols at one operation, can not but perceive that in raising a binomial to a power, the co-efficients must depend on the laws of permutation and combination: and as soon as this is recognized, the theorem is demonstrated.
No man whatever believes, or can believe, exactly what his grandfather believed: he enlarges somewhat, by fresh discovery, his view of the Universe, and consequently his Theorem of the Universe, which is an infinite Universe, and can never be embraced wholly or finally by any view or Theorem, in any conceivable enlargement: he enlarges somewhat, I say; finds somewhat that was credible to his grandfather incredible to him, false to him, inconsistent with some new thing he has discovered or observed.
Life became a divine gift for every moment and sensation of which, were it even the sight of a single leaf hanging on the twig of a tree, his soul should praise and thank the Giver. The world for all its solid substance and complexity no longer existed for his soul save as a theorem of divine power and love and universality.
As to myself, I am undetermined which of these opinions is the most probable, and therefore I leave the matter to your determination and decision." Having thus concluded he descended from the desk, and delivered the tunic, the robe, and the cap, to the third, who mounting into the desk began as follows: "How little qualified is a youth like myself for the investigation of so sublime a theorem!
In demonstrating an algebraical theorem, or in resolving an equation, we travel from the datum to the quæsitum by pure ratiocination; in which the only premises introduced, besides the original hypotheses, are the fundamental axioms already mentioned—that things equal to the same thing are equal to one another, and that the sums of equal things are equal.
It is a question, not of miracle, but of evolution, of growth. Newton had to master the multiplication table, then the four rules of arithmetic, then the rudiments of algebra, before he came to the binomial theorem. At each point, there was attention, concentration, insight; until these were attained, no progress to the next point was possible. So with Darwin.
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