THE
USEFULNESS OF USELESS KNOWLEDGE 547
mathematical work of the eighteenth
and nineteenth centuries was the "Non-
Euclidian Geometry." Its inventor,
Gauss, though recognized by his con-
temporaries as a distinguished mathe-
matician, did not dare to publish his
work on "Non-Euclidian Geometry" for
a quarter of a century. As a matter of
fact, the theory of relativity itself with all
its infinite practical bearings would have
been utterly impossible without the work
which Gauss did at Gottingen,
Again, what is known now as "group
theory" was an abstract and inapplicable
mathematical theory. It was developed
by men who were curious and whose
curiosity and puttering led them into
strange paths; but "group theory" is
to-day the basis of the quantum theory of
spectroscopy, which is in daily use by
people who have no idea as to how it
came about.
The whole calculus of probability was
discovered by mathematicians whose
real interest was the rationalization of
gambling. It has failed of the practical
purpose at which they aimed, but it has
furnished a scientific basis for all types of
insurance, and vast stretches of nine-
teenth century physics are based upon it.
From a recent number of
Science
I quote
the following:
The stature of Professor Albert Einstein's
genius reached new heights when it was dis-
closed that the learned mathematical physicist
developed mathematics fifteen years ago which
are now helping to solve the mysteries of the
amazing fluidity of helium near the absolute
zero of the temperature scale. Before the
symposium on intermolecular action of the
American Chemical Society Professor F. Lon-
don, of the University of Paris, now visiting
professor at Duke University, credited Professor
Einstein with the concept of an "ideal" gas
which appeared in papers published in
1924
and
1925.
The Einstein
1925
reports were not about
relativity theory, but discussed problems seem-
ingly without any practical significance at the
time. They described the degeneracy of an
"ideal" gas near the lower limits of the scale of
temperature. Because all gases were known
to be condensed to liquids at the temperatures
in question, scientists rather overlooked the
Einstein work of fifteen years ago.
However, the recently discovered behavior of
liquid helium has brought the side-tracked
Einstein concept to new usefulness. Most
liquids increase in viscosity, become stickier and
flow lesseasily, when they become colder. The
phrase "colder than molasses in January" is the
layman's concept of viscosity and a correct one.
Liquid helium, however, is a baffling excep-
tion. At the temperature known as the "delta"
point, only 2.19 degrees above absolute zero,
liquid helium flows better than it does at higher
temperatures and, as a matter of fact, the liquid
helium is about as nebulous as a gas. Added
puzzles in its strange behavior include its
enormous ability to conduct heat. At the delta
point it is about 500 times as effective in this
respect as copper at room temperature. Liquid
helium, with these and other anomalies, has
posed a major mystery for physicists and
chemists.
Professor London stated that the interpreta-
tion of the behavior of liquid helium can best be
explained by considering it as a Bose-Einstein
"ideal" gas, by using the mathematics worked
out in
1924-25,
and by taking over also some
of the concepts of the electrical conduction of
metals. By simple analogy, the amazing
fluidity of liquid helium can be partially ex-
plained by picturing the fluidity as something
akin to the wandering of electrons in metals to
explain electrical conduction.
Let us look in another direction. In
the domain of medicine and public health
the science of bacteriology has played for
half a century the leading role. What is
its story? Following the Franco-Pros-
sian War of 1870, the German Govern-
ment founded the great University of
Strasbourg. Its first professor of anat-
omy was Wilhelm von Waldeyer, subse-
quently professor of anatomy in Berlin.
In his
Reminiscences
he relates that among
the students who went with him to Stras-
bourg during his first semester there was
a small, inconspicuous, self-contained
youngster of seventeen by name Paul
Ehrlich. The usual course in anatomy
then consisted of dissection and micro-
scopic examination of tissues. Ehrlich
paid little or no attention to dissection,
but, as Waldeyer remarks in his
Remi-
mscences:
I noticed quite early that Ehrlich would work
long hours at his desk, completely absorbed in
microscopic observation. Moreover, his desk
gradually became covered with colored spots of
every description. As I saw him sitting at work
one day, I went up to him and asked what he