A Budget of Paradoxes, Volume IIDe Morgan, Augustus
Philosophy
A Budget of Paradoxes, Volume II
De Morgan, Augustus
Circle-squaring; Perpetual motion; Science -- Miscellanea; Trisection of angle
"For this Mr. Smith cared nothing: he persisted in the publication, and the
book is before us. Mr. Smith has had so much grace as to conceal his kind
adviser's name under E. M., that is to say, he has divided the wrong among
all who may be suspected of having attempted so hopeless a task as that of
putting a little sense into his head. He has violated the decencies of
private life. Against the will of the kind-hearted man who undertook his
case, he has published letters which were intended for no other purpose
than to clear his poor head of a hopeless delusion. He deserves the
severest castigation; and he will get it: his abuse of confidence will
stick by him all his days. Not that he has done his benefactor--in
intention, again--any harm. The patience with which E. M. put the blunders
into intelligible form, and the perseverance with which he tried to find a
cranny-hole for common reasoning to get in at, are more than respectable:
they are admirable. It is, we can assure E. M., a good thing that the
nature of the circle-squarer should be so completely exposed as in this
volume. The benefit which he intended Mr. James Smith may be {107}
conferred upon others. And we should very much like to know his name, and
if agreeable to him, to publish it. As to Mr. James Smith, we can only say
this: he is not mad. Madmen reason rightly upon wrong premises: Mr. Smith
reasons wrongly upon no premises at all.
"E. M. very soon found out that, to all appearance, Mr. Smith got a circle
of 3-1/8 times the diameter by making it the supposition to set out with
that there was such a circle; and then finding certain consequences which,
so it happened, were not inconsistent with the supposition on which they
were made. Error is sometimes self-consistent. However, E. M., to be quite
sure of his ground, wrote a short letter, stating what he took to be Mr.
Smith's hypothesis, containing the following: 'On AC as diameter, describe
the circle D, which by hypothesis shall be equal to three and one-eighth
times the length of AC.... I beg, before proceeding further, to ask whether
I have rightly stated your argument.' To which Mr. Smith replied: 'You have
stated my argument with perfect accuracy.' Still E. M. went on, and we
could not help, after the above, taking these letters as the initials of
Everlasting Mercy. At last, however, when Mr. Smith flatly denied that the
area of the circle lies between those of the inscribed and circumscribed
polygons, E. M. was fairly beaten, and gave up the task. Mr. Smith was left
to write his preface, to talk about the certain victory of truth--which,
oddly enough, is the consolation of all hopelessly mistaken men; to compare
himself with Galileo; and to expose to the world the perverse behavior of
the Astronomer Royal, on whom he wanted to fasten a conversation, and who
replied, 'It would be a waste of time, Sir, to listen to anything you could
have to say on such a subject.'
Public-domain text, read in full here on John Shaqi.
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