Life of Emanuel Swedenborg by William White - HTML preview

FOOTNOTES

[1] The following account of Charles XII., written by Emanuel Swedenborg, was printed in the “Gentleman’s Magazine,” for September, 1754. It is a portion of a letter which Swedenborg wrote to M. Nordberg, while the latter was engaged in writing his “Life of Charles XII.,” in which work the letter appeared at full length. It is too long to be quoted here; the following extracts contain the pith of it. It may be proper to observe, that it was written by the author prior to his being called to the sacred office which occupied the last twenty-nine years of his life. This accounts for his speaking of the celebrated Swedish hero with so much greater respect than he is known to have afterwards entertained for his memory.

“Having been frequently admitted to the honor of hearing his late most excellent Majesty, Charles XII. discourse on mathematical subjects, I presume an account of a new arithmetic invented by him, may merit the attention of my readers.

“His Majesty observed then, that the denary arithmetic, universally received and practiced, was most probably derived from the original method of counting on the fingers; that illiterate people of old, when they had run through the fingers of both hands, repeated new periods over and over again, and every time spread open both hands; which being done ten times, they distinguished each step by proper marks, as by joining two, three, or four fingers. Afterwards, when this method of numeration on the fingers came to be expressed by proper characters, it soon became firmly and universally established, and so the denary calculus has been retained to this day. But surely, were a solid geometrician, thoroughly versed in the abstract nature and fundamentals of numbers, to set his mind upon introducing a still more useful calculus into the world, instead of ten, he would select such a perfect square, or cube number, as by continual bisection, or halving, would at length terminate in unity, and be better adapted to the subdivisions of measures, weights, coins, etc.

“Thus intent on a new arithmetic, the hero pitched upon the number eight, as most fit for the purpose, since it could not only be halved continually down to unity, without a fraction, but contained within it the square of 2, and was itself the cube thereof, and was also applicable to the received denomination of several sorts of weights and coins, rising to 16 and 32, the double and quadruple of 8. Upon these first considerations, he was pleased to command me to draw up an essay on an octonary calculus, which I completed in a few days, with its application to the received divisions, coins, measures, and weights, a disquisition on cubes and squares, and a new and easy way of extracting roots, all illustrated with examples.

“His Majesty having cast his eye twice or thrice over it, and observing, perhaps from some hints in the essay, that the denary calculus had several advantages not always attended to, he did not at that time seem absolutely to approve of the octonary: or, it is likely he might conceive, that though it seemed easy in theory, yet it might prove difficult to introduce it to practice. Be this as it may, he insisted on fixing upon some other that was both a cube and a square number, referrible to 8, and divisible down to unity by bisection. This could be no other than 64, the cube of 4, and square of 8, divisible down to unity without a fraction.

“I immediately presumed to object that such a number would be too prolix, as it rises through a series of entirely distinct and different numbers, up to 64, and then again to its duplicate 4,096, and on to its triplicate 262,144, before the fourth step commences; so that the difficulty of such a calculus would be incredible, not only in addition and subtraction, but to a still higher degree in multiplication and division; for the memory must necessarily retain in the multiplication table, 3,969 distinct products of the 63 numbers of the first step multiplied into one another; whereas only 49 are necessary in the octonary, and but 81 are required in the denary arithmetic; which last is difficult to be remembered and applied in practice, by some capacities. But the stronger my objections were, the more resolute was his royal mind upon attempting such a calculus.

Obstructions made him eagerly aspire

All to surmount, and nobly soar the higher.

He insisted that the alleged difficulties might be overbalanced by very many advantages.

“A few days after this I was called before his Majesty, who, resuming the subject, demanded if I had made a trial. I still urging my former objections, he reached me a paper written with his own hand, in new characters and terms of denomination, the perusal of which, he was pleased, at my entreaty, to grant me; wherein, to my great surprise, I found not only new characters and numbers, (the one almost naturally expressive of the other) in a continued series to 64, so ranged as easily to be remembered, but also new denominations, so contrived by pairs, as to be easily extended to myriads by a continued variation of the character and denomination. And further casting my eye on several new methods of his for addition and multiplication by this calculus, either artificially contrived, or else inherent in the characters of the numbers themselves, I was struck with the profoundest admiration of the force of his Majesty’s genius, and with such strange amazement, as obliged me to esteem this eminent personage, not my rival, but by far my superior in my own art. And having the original still in my custody, at a proper time I may publish it, as it highly deserves; whereby it will appear with what discerning skill he was endowed, or how deeply he penetrated into the obscurest recesses of the arithmetical science.

“Besides, his eminent talents in calculation further appear by his frequently working and solving the most difficult numerical problems, barely by thought and memory; in which operations others are obliged to take great pains and tedious labor.

“Having duly weighed the vast advantages arising from mathematical and arithmetical knowledge in most occasions of human life, he frequently used it as an adage, that he who is ignorant of numbers is scarce half a man.

“While he was at Bender, he composed a complete volume of military exercises, highly esteemed by those who are best skilled in the art of war.”

[2] The bookseller referred to was Mr. Bohn, of Henrietta street, Covent Garden.

[3] It is not to be supposed that this time was wasted in sleep. In his meditations and spiritual intercourse, he, no doubt, loved the seclusion of his quiet chamber.

[4] This is quite a mistake. His work he had in contemplation for some years. It is probable the revisal, alterations, and additions in the MS and in the proofs, led Paulus into this misconception.