A Benjamin Franklin Reader (22 page)

As an Assembly clerk in Philadelphia, Franklin used to amuse himself with a mathematical curiosity: the creation of what he called magic squares. He sent a description of them to his friend in London, Peter Collinson.

T
O
P
ETER
C
OLLINSON
,
C
. 1752

Sir,

According to your request, I now send you the Arithmetical Curiosity, of which this is the history.

Being one day in the country, at the house of our common friend, the late learned Mr. Logan, he showed me a folio French book, filled with magic squares, wrote, if I forget not, by one M. Frenicle, in which he said the author had discovered great ingenuity and dexterity in the management of numbers; and, though several other foreigners had distinguished themselves in the same way, he did not recollect that any one Englishman had done any thing of the kind remarkable.

I said, it was, perhaps, a mark of the good sense of our English mathematicians, that they would not spend their time in things that were merely
difficiles nugae,
incapable of any useful application. He answered, that many of the arithmetical or mathematical questions, publicly proposed and answered in England, were equally trifling and useless. Perhaps the considering and answering such questions, I replied, may not be altogether useless, if it produces by practice an habitual readiness and exactness in mathematical disquisitions, which readiness may, on many occasions, be of real use. In the same way, says he, may the making of these squares be of use. I then confessed to him, that in my younger days, having once some leisure, (which I still think I might have employed more usefully) I had amused myself in making these kind of magic squares, and, at length, had acquired such a knack at it, that I could fill the cells of any magic square, of reasonable size, with a series of numbers as fast as I could write them, disposed in such a manner, as that the sums of every row, horizontal, perpendicular, or diagonal, should be equal; but not being satisfied with these, which I looked on as common and easy things, I had imposed on myself more difficult tasks, and succeeded in making other magic squares, with a variety of properties, and much more curious. He then showed me several in the same book, of an uncommon and more curious kind; but as I thought none of them equal to some I remembered to have made, he desired me to let him see them; and accordingly, the next time I visited him, I carried him a square of 8, which I found among my old papers, and which I will now give you, with an account of its properties.

The properties are,

1. That every strait row (horizontal or vertical) of 8 numbers added together, makes 260, and half each row half 260.

2. That the bent row of 8 numbers, ascending and descending diagonally, viz, from 16 ascending to 10, and from 23 descending to 17; and every one of its parallel bent rows of 8 numbers, make 260. Also the bent row from 52, descending to 54, and from 43 ascending to 45; and every one of its parallel bent rows of 8 numbers, make 260. Also the bent row from 45 to 43 descending to the left, and from 23 to 17 descending to right, and every one of its parallel bent rows of 8 numbers make 260. Also the bent row from 52 to 54 descending to the right, and from 10 to 16 descending to the left, and every one of its parallel bent rows of 8 numbers make 260. Also the parallel bent rows next to the above-mentioned, which are shortened to 3 numbers ascending, and 3 descending, &c. as from 53 to 4 ascending, and from 29 to 44 descending, make, with the 2 corner numbers, 260. Also the 2 numbers 14, 61 ascending, and 36, 19 descending, with the lower 4 numbers situated like them, viz. 50, 1, descending, and 32, 47, ascending, make 260. And, lastly, the 4 corner numbers, with the 4 middle numbers, make 260.

So this magical square seems perfect in its kind. But these are not all its properties; there are 5 other curious ones, which, at some other time, I will explain to you.

Mr. Logan then showed me an old arithmetical book, in quarto, wrote, I think, by one Stifelius, which contained a square of 16, that he said he should imagine must have been a work of great labor; but if I forget not, it had only the common properties of making the same sum, viz. 2056, in every row, horizontal, vertical, and diagonal. Not willing to be out-done by Mr. Stifelius, even in the size of my square, I went home, and made, that evening, the following magical square of 16, which, besides having all the Properties of the foregoing square of 8, i.e. it would make the 2056 in all the same rows and diagonals, had this added, that a four square hole being cut in a piece of paper of such a size as to take in and show through it, just 16 of the little squares, when laid on the greater square, the sum of the 16 numbers so appearing through the hole, wherever it was placed on the greater square, should likewise make 2056. This I sent to our friend the next morning, who, after some days, sent it back in a letter, with these words: I return to thee thy astonishing or most stupendous piece of the magical square, in which but the compliment is too extravagant, and therefore, for his sake, as well as my own, I ought not to repeat it. Nor is it necessary; for I make no question but you will readily allow this square of 16 to be the most magically magical of any magic square ever made by any magician.

I did not, however, end with squares, but composed also a magic circle, consisting of 8 concentric circles, and 8 radial rows, filled with a series of numbers, from 12 to 75, inclusive, so disposed as that the numbers of each circle, or each radial row, being added to the central number 12, they made exactly 360, the number of degrees in a circle; and this circle had, moreover, all the properties of the square of 8. If you desire it, I will send it; but at present, I believe, you have enough on this subject. I am, &c.

B.F.

He also discoursed with Collinson on political philosophy. One such letter shows the emergence of Franklin’s middle-class populist conservatism. Although he was a generous and charitable man, always concocting civic improvement schemes, he worried that welfare laws and government handouts might have an unintended effect of promoting laziness and dependency. He also praised the natural ways of the Indians and made fun of white colonists who tried to educate them to their own ways.

T
O
P
ETER
C
OLLINSON
, M
AY
9, 1753

Sir,

I received your favor of the 29th. August last and thank you for the kind and judicious remarks you have made on my little piece. Whatever further occurs to you on the same subject, you will much oblige me in communicating it.

I have often observed with wonder, that temper of the poor English Manufacturers and day laborers which you mention, and acknowledge it to be pretty general. When any of them happen to come here, where labor is much better paid than in England, their industry seems to diminish in equal proportion. But it is not so with the German laborers; They retain the habitual industry and frugality they bring with them, and now receiving higher wages an accumulation arises that makes them all rich.

When I consider, that the English are the offspring of Germans, that the climate they live in is much of the same temperature; when I can see nothing in nature that should create this Difference, I am apt to suspect it must arise from institution, and I have sometimes doubted, whether the laws peculiar to England which compel the rich to maintain the poor, have not given the latter a dependence that very much lessens the care of providing against the wants of old age.

I have heard it remarked that the poor in Protestant countries on the continent of Europe, are generally more industrious than those of Popish countries, may not the more numerous foundations in the latter for the relief of the poor have some effect towards rendering them less provident. To relieve the misfortunes of our fellow creatures is concurring with the Deity, ’tis Godlike, but if we provide encouragements for laziness, and supports for folly, may it not be found fighting against the order of God and Nature, which perhaps has appointed want and misery as the proper punishments for, and cautions against as well as necessary consequences of idleness and extravagancy.

Whenever we attempt to mend the scheme of Providence and to interfere in the government of the world, we had need be very circumspect lest we do more harm than good. In New England they once thought Blackbirds useless and mischievous to their corn, they made laws to destroy them, the consequence was, the Blackbirds were diminished but a kind of worms which devoured their grass, and which the Blackbirds had been used to feed on increased prodigiously; then finding their loss in grass much greater than their saving in corn they wished again for their Blackbirds.

We had here some years since a Transylvanian Tartar, who had traveled much in the East, and came hither merely to see the West, intending to go home thro the Spanish West Indies, China &c. He asked me one day what I thought might be the reason that so many and such numerous nations, as the Tartars in Europe and Asia, the Indians in America, and the Negroes in Africa, continued a wandering careless life, and refused to live in cities, and to cultivate the arts they saw practiced by the civilized part of mankind. While I was considering what answer to make him; I’ll tell you, says he in his broken English, God make man for Paradise, he make him for to live lazy; man make God angry, God turn him out of Paradise, and bid him work; man no love work; he want to go to Paradise again, he want to live lazy; so all mankind love lazy. However this may be it seems certain, that the hope of becoming at some time of life free from the necessity of care and labor, together with fear of penury, are the mainsprings of most people’s industry.

To those indeed who have been educated in elegant plenty, even the provision made for the poor may appear misery, but to those who have scarce ever been better provided for, such provision may seem quite good and sufficient, these latter have then nothing to fear worse than their present conditions, and scarce hope for any thing better than a Parish maintenance; so that there is only the difficulty of getting that maintenance allowed while they are able to work, or a little shame they suppose attending it, that can induce them to work at all, and what they do will only be from hand to mouth.

The proneness of human nature to a life of ease, of freedom from care and labor appears strongly in the little success that has hitherto attended every attempt to civilize our American Indians, in their present way of living, almost all their wants are supplied by the spontaneous productions of Nature, with the addition of very little labor, if hunting and fishing may indeed be called labor when game is so plenty, they visit us frequently, and see the advantages that Arts, Sciences, and compact society procure us, they are not deficient in natural understanding and yet they have never shown any Inclination to change their manner of life for ours, or to learn any of our Arts; When an Indian Child has been brought up among us, taught our language and habituated to our Customs, yet if he goes to see his relations and make one Indian Ramble with them, there is no persuading him ever to return, and that this is not natural to them merely as Indians, but as men, is plain from this, that when white persons of either sex have been taken prisoners young by the Indians, and lived a while among them, though ransomed by their friends, and treated with all imaginable tenderness to prevail with them to stay among the English, yet in a short time they become disgusted with our manner of life, and the care and pains that are necessary to support it, and take the first good opportunity of escaping again into the woods, from whence there is no reclaiming them. One instance I remember to have heard, where the person was brought home to possess a good estate; but finding some care necessary to keep it together, he relinquished it to a younger brother, reserving to himself nothing but a gun and a match-coat, with which he took his way again to the wilderness.

Though they have few but natural wants and those easily supplied. But with us are infinite artificial wants, no less craving than those of Nature, and much more difficult to satisfy; so that I am apt to imagine that close societies subsisting by labor and arts, arose first not from choice, but from necessity: When numbers being driven by war from their hunting grounds and prevented by seas or by other nations were crowded together into some narrow territories, which without labor would not afford them food. However as matters stand with us, care and industry seem absolutely necessary to our well being; they should therefore have every encouragement we can invent, and not one motive to diligence be subtracted, and the support of the poor should not be by maintaining them in idleness, but by employing them in some kind of labor suited to their abilities of body &c. as I am informed of late begins to be the practice in many parts of England, where work houses are erected for that purpose. If these were general I should think the poor would be more careful and work voluntarily and lay up something for themselves against a rainy day, rather than run the risk of being obliged to work at the pleasure of others for a bare subsistence and that too under confinement.

The little value Indians set on what we prize so highly under the name of learning appears from a pleasant passage that happened some years since at a Treaty between one of our Colonies and the Six Nations; when every thing had been settled to the satisfaction of both sides, and nothing remained but a mutual exchange of civilities, the English Commissioners told the Indians, they had in their Country a College for the instruction of youth who were there taught various languages, Arts, and Sciences; that there was a particular foundation in favor of the Indians to defray the expense of the education of any of their sons who should desire to take the benefit of it. And now if the Indians would accept of the offer, the English would take half a dozen of their brightest lads and bring them up in the best manner; The Indians after consulting on the proposal replied that it was remembered some of their youths had formerly been educated in that College, but it had been observed that for a along time after they returned to their Friends, they were absolutely good for nothing being neither acquainted with the true methods of killing deer, catching beaver or surprising an enemy. The proposition however, they looked on as a mark of the kindness and good will of the English to the Indian Nations which merited a grateful return; and therefore if the English Gentlemen would send a dozen or two of their children to Onondago the great Council would take care of their education, bring them up in really what was the best manner and make men of them…

I pray God long to preserve to Great Britain the laws, manners, liberties and religion notwithstanding the complaints so frequent in your public papers, of the prevailing corruption and degeneracy of your people; I know you have a great deal of virtue still subsisting among you, and I hope the Constitution is not so near a dissolution, as some seem to apprehend; I do not think you are generally become such slaves to your vices, as to draw down that
Justice
Milton speaks of when he says that sometimes nations will descend so low from reason, which is virtue, that no wrong, but justice, and some fatal curse annexed deprives them of their
outward
liberty, Their
inward
lost.—Paradise Lost.

In history we find that piety, public spirit and military prowess have their flows, as well as their ebbs, in every nation, and that the tide is never so low but it may rise again; but should this dreaded fatal change happen in my time, how should I even in the midst of the affliction rejoice, if we have been able to preserve those invaluable treasures, and can invite the good among you to come and partake of them! O let not Britain seek to oppress us, but like an affectionate parent endeavor to secure freedom to her children; they may be able one day to assist her in defending her own whereas a mortification begun in the foot may spread upwards to the destruction of the nobler parts of the body. I fear I have extended this rambling letter beyond your patience, and therefore conclude with requesting your acceptance of the enclosed pamphlet from, Sir,

Your most humble servant,

B. Franklin