Mr. James Smith's procedures are not caricature of reasoning; they are
caricature of blundering. The old way of proving that 2 = 1 is solemn
earnest compared with his demonstrations. As follows:[388]
Let x = 1
Then x^2 = x
And x^2 - 1 = x - 1
Divide both sides by x - 1; then x + 1 = 1; but x = 1, whence 2 = 1.
When a man is regularly snubbed, bullied, blown up, walked into, and put
down, there is usually some reaction in his favor, a kind of deostracism,
which cannot bear to hear him always called the blunderer. I hope it will
be so in this case. There is nothing I more desire than to see _sects_ of
paradoxers. There are fully five thousand adults in England who ought to be
the followers of some one false quadrature. And I have most hope of 3-1/8,
because I think Mr. James Smith better fitted to be the leader of an
organized infatuation than any one I know of. He wants no pity, and will
get none. He has energy, means, good humor, strong conviction, character,
and popularity in his own circle. And, most indispensable point of all, he
sticks at nothing;
"In coelum jusseris, ibit."[389]
When my instructor found I did not print an acceptance of what I have
quoted, he addressed me as follows (_Corr._, Sept 23):--
"In this life, however, we must do our duty, and, when {242} necessary, use
the rod, not in a spirit of revenge, but for the benefit of the culprit and
the good of society. Now, Sir, the opportunity has been thrown in your way
of slipping out of the pillory without risk of serious injury; but, like an
obstinate urchin, you have chosen to quarrel with your opportunity and
remain there, and thus you compel me to deal with you as schoolmasters used
to do with stupid boys in bygone days--that is to say, you force me to the
use of the critic's rod, compel me to put you where little Jack Horner sat,
and, as a warning to other naughty boys, to ornament you with a dunce's
cap. The task I set you was a very simple one, as I shall make manifest at
the proper time."
In one or more places, as well as this, Mr. Smith shows that he does not
know the legend of little Jack Horner, whom he imagines to be put in the
corner as a bad boy. This is curious; for there had been many allusions to
the story in the journal he was writing in, and the Christmas pie had
become altered into the Seaforth [pi].
Mr. Smith is satisfied at last that--what between argument and punishment
he has convinced me. He says (_Corr._, Jan. 27, 1866): "I tell him without
hesitation that he knows the true ratio of diameter to circumference as
well as I do, and if he be wise he will admit it." I should hope I do, and
better; but there is no occasion to admit what everybody knows.
I have often wished that we could have a slight glimpse of the reception
which was given to some of the old cyclometers: but we have nothing, except
the grave disapprobation of historians. I am resolved to give the New
Zealander a chance of knowing a little more than this about one of them at
least; and, by the fortunate entrance into life of the _Correspondent_, I
am able to do it. I omit sober mathematical answers, of which there were
several. The following letter is grave earnest:
"Sir,--I have watched Mr. James Smith's writings on this subject from the
first, and I did hope that, as the more {243} he departs from truth the
more easy it must be to refute him, [this by no means always true] some of
your correspondents would by this time have done so. I own that I am unable
to detect the fallacy of his argument; and I am quite certain that '[Pi]'
is wrong, in No. 23, where he declares that Mr. Smith is 'ignorant of the
very elements of mathematical truth.' I have observed an immense amount of
geometrical reasoning on his part, and I cannot see that it is either fair
or honest to deny this, which may be regarded as the 'elements' of
mathematical truth. Would it not be better for '[Pi]' to answer Mr. Smith,
to refute his arguments, to point out their fallacies, and to save learners
from error, than to plunge into gross insult and unmanly abuse? Would it
not be well, also, that Professor De Morgan should favour us with a little
reasoning?
"I have hitherto seen no attempt to overthrow Mr. Smith's arguments; I
trust that this will not continue, since the subject is one of immense
importance to science in general, especially to nautical science, and all
that thereto belongs.
Yours, etc.,