Hinton - The Fourth Dimension.pdf

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THE FOURTH DIMENSION
It is a long step from Gauss’s serenity to the disturbed
and passionate life of Johann Bolyai—he and Gauss,
the two most interesting figures in the history of mathematics.
For Bolyai, the wild solider, the duellist, fell
at odds with the world. It is related of him that he was
challenged by thirteen officers of his garrison, a thing not
unlikely to happen considering how differently he thought
from everyone else. He fought them all in succession—
making it his only condition that he should be allowed
to play on his violin for an interval between meeting each
opponent. He disarmed or wounded all his antagonists.
It can be easily imagined that a temperament such as
his was one not congenial to his military superiors. He
was retired in 1833.
His epoch-making discovery awoke no attention. He
seems to have conceived the idea that his father had
betrayed him in some inexplicable way by his communications
with Gauss, and he challenged the excellent
Wolfgang to a duel. He passed his life in poverty,
many a time, says his biographer, seeking to snatch
himself from dissipation and apply himself again to
mathematics. But his efforts had no result. He died
January 27th, 1860, fallen out with the world and with
himself.
METAGEOMETRY
The theories which are generally connected with the
names of Lobatchewsky and Bolyai bear a singular and
curious relation to the subject of higher space.
In order to show what this relation is, I must ask the
reader to be at the pains to count carefully the sets of
points by which I shall estimate the volumes of certain
figures.