usic. He was
fond of comparing the two, and often quoted Leibnitz: "Music is an
occult exercise of the mind unconsciously performing arithmetical
calculations." For him, so he assured his friends, music was a species
of sensual mathematics. Before he left St. Petersburg to settle in Balak
as its Kapellmeister he had studied at the University under the famous
Lobatchewsky, and absorbed from him not a few of the radical theories
containing the problematic fourth dimension. He read with avid interest
of J. K. F. Zoellner's experiments which drove that unfortunate Leipzig
physicist into incurable melancholia. Ah, what madmen these! Perpetual
motion, squaring the circle, the fourth spatial dimension--all new
variants of the old alchemical mystery, the vain pursuit of the
philosophers' stone, the transmutation of the baser metals, the
cabalistic Abracadabra, the quest of the absolute! Yet sincere and
certainly quite sane men of scientific training had considered seriously
this mathematic hypothesis. Cayley, Pobloff had read, and Abbot's
"Flatland"; while the ingenious speculations of W. K. Clifford and the
American, Simon Newcomb, fascinated him immeasurably. He cared
little--being idealist and musician--for the grosser demonstrations of
hyper-normal phenomena, though for a time he had wavered before the
mysterious cross-roads of demoniac possession, subliminal divinations,
and the strange rappings that emanate from souls smothered in hypnotic
slumber. The testimony of such a man as Professor Crookes who had
witnessed feats of human levitation greatly stirred him; but in the end
he drifted back to his early passions--music and mathematics.

Zoellner had proved to his own satisfaction the existence of a fourth
dimension, when he turned an India-rubber ball inside out without
tearing it; but Pobloff, a man of tone, was more absorbed in the
demonstration that Time could be shown in two dimensions. He often
quoted Hugh Craig, who compared Time to a river always flowing, yet a
permanent river: If one emerged from this stream at a certain moment and
entered it an hour later, would it not signify that Time had two
dimensions? And music--where did music stand in the eternal scheme of
things? Was not harmony with its vertical structure and melody's
horizontal flow, proof that music itself was but another dimension in
Time? In the vast and complicated scores of Richard Strauss, the
listener has set in motion two orders of auditions: he