One of this naval officer's fellow sufferers was a farm labourer, who took it into his head that the Lord Chancellor had offered £100,000 reward to any one who should square the circle. So Hodge went to work and squared it, and then hied him to London, blissfully dreaming of sudden wealth. Hearing that De Morgan was a great mathematician, he left his papers with him, including a letter to the Lord Chancellor, claiming the £100,000. De Morgan returned the papers with a note, saying that no such prize had ever been offered, and gently hinting that the worthy Hodge had not sufficient knowledge to see in what the problem consisted. This elicited from the rustic philosopher a long letter, from which I must quote a few sentences, so characteristic of the circle-squaring talent and temper:—
Doctor Morgan, Sir. Permit me to address you
Brute Creation may perhaps enjoy the faculty of beholding visible things with a more penitrating eye than ourselves. But Spiritual objects are as far out of their reach as though they had no being Nearest therefore to the brute Creation are those men who Suppose themselves to be so far governed by external objects as to believe nothing but what they See and feel And Can accomedate to their Shallow understanding and Imaginations
... When a Gentleman of your Standing in Society ... Can not understand or Solve a problem That is explicitly explained by words and Letters and mathematacally operated by figuers He had best consult the wise proverd
Do that which thou Canst understand and Comprehend for thy good.
I would recommend that Such Gentleman Change his business
And appropriate his time and attention to a Sunday School to Learn what he Could and keep the Litle Children form durting their Close
With Sincere feelings of Gratitude for your weakness and Inability I am
Sir your Superior in Mathematics.
X. Y.
A few days after this elegant epistle there came to De Morgan another from the same hand. Hodge had sent his papers to some easy-going American professor, whose reply must clearly have been too polite. It is never safe to give your crank an inch of comfort; it will straightway become an ell of assurance. This American savant, crows Rusticus, "highly approves of my work. And Says he will Insure me Reward in the States I write this that you may understand that I have knowledge of the unfair way that I am treated in my own nati County I am told and have reasons to believe that it is the Clergy that treat me so unjust. I am not Desirious of heaping Disonors upon my own nation. But if I have to Leave this kingdom without my Just dues. The world Shall know how I am and have been treated
"I am Sir Desirous of my Just dues
"X. Y."
A cynical philosopher once said that you cannot find so big a fool but there will be some bigger fool to swear by him; and so our agricultural friend had his admiring disciple who felt bound to break a lance for him with the unappreciative De Morgan:—
"He has done what you nor any other mathematician as those who call themselves such have done. And what is the reason that you will not candidly acknowledge to him ... that he has squared the circle shall I tell you? it is because he has performed the feat to obtain the glory of which mathematicians have battled from time immemorial that they might encircle their brows with a wreath of laurels far more glorious than ever conqueror won it is simply this that it is a poor man a humble artisan who has gained that victory that you don't like to acknowledge it you don't like to be beaten and worse to acknowledge that you have miscalculated, you have in short too small a soul to acknowledge that he is right.... I am backed in my opinion not only by Mr. Q. a mathematician and watchmaker residing in the boro of Southwark but by no less an authority than the Professor of mathematics of ... College United States Mr. Q and I presume that he at least is your equal as an authority and Mr. Q says that the government of the U. S. will recompense X. Y. for the discovery he has made if so what a reflection upon Old england the boasted land of freedom the nursery of the arts and sciences that her sons are obliged to go to a foreign country to obtain that recompense to which they are justly entitled."[46]
Ordinarily, the aim of the paradoxers is to achieve renown by doing what nobody ever did. Hence the fascination exercised upon them by those apparently simple problems which already in ancient times were recognized as "old stickers," the quadrature of the circle, the trisection of angles, and the duplicature of the cube. The ancients found these geometric problems insolvable, though it was left for modern algebra to point out the reason, namely, that no quantities can be geometrically constructed from given quantities, except such as can be formed from them algebraically by the solution of quadratic equations; if the algebraic solution comes as the root of a cubic or biquadratic equation, it cannot be constructed by geometry. Against this hopeless wall the crowd of paradoxers will doubtless continue to break their heads until the millennium dawns.
Sometimes, however, our crank has a practical end in view, as in the numerous attempts to discover "perpetual motion," or, in other words, to invent a machine out of which you can get indefinitely more energy than you put in. It is not strange that many thousands of dollars have been wasted in this effort to recover Aladdin's lost lamp. The notorious Keely motor is but one of a host of contrivances born and bred of crass ignorance of the alphabet of dynamics. But perpetual motion is not the only form assumed by wealth-seeking crankery. In 1861 a Captain Roblin, of Normandy, having ascertained to his own satisfaction, from the prolonged study of the zodiac of Denderah, the sites of sundry gold-mines, came forward with proposals for a joint stock company to dig and be rich. The labours of Herr Johannes von Gumpach were of a more philanthropic turn. He published in 1861 a pamphlet entitled "A Million's Worth of Property and Five Hundred Lives annually lost at Sea by the Theory of Gravitation. A Letter on the True Figure of the Earth, addressed to the Astronomer Royal." Next year this pamphlet grew into a stout volume. It maintained that a great many shipwrecks were occasioned by errors of navigation due to an erroneous conception of the shape of the earth. Since Newton's time, it has been supposed to be flattened at the poles, whereas the amiable Gumpach calls upon his fellow-creatures to take notice that it is elongated, and to mend their ways accordingly.