HERMANN LUDWIG FERDINAND VON HELMHOLTZ
BY: J. J O'CONNOR AND E. F. ROBERTSON
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Hermann Ludwig Ferdinand von Helmholtz Born:
31 Aug 1821 in Potsdam, Germany Died: 8 Sept
1894 in Berlin, Germany by: J. J O'Connor
and E. F. Robertson Hermann Ludwig Ferdinand
von Helmholtz
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Hermann von Helmholtz's father was August
Ferdinand Julius Helmholtz while his mother
was Caroline Penn. Hermann was the eldest
of his parents four children. His childhood
had a strong influence on both his character
and his later career. In particular the views
on philosophy held by his father restricted
Helmholtz's own views.
Ferdinand Helmholtz had served in the Prussian
army in the fight against Napoleon. Despite
having a good university education in philology
and philosophy, he became a teacher at Potsdam
Gymnasium. It was a poorly paid job and Hermann
was brought up in financially difficult circumstances.
Ferdinand was an artistic man and his influence
meant that Hermann grew up to have a strong
love of music and painting. Caroline Helmholtz
was the daughter of an artillery officer.
From her Hermann inherited [1]:-
... the placidity and reserve which marked
his character in later life.
Hermann attended Potsdam Gymnasium where
his father taught philology and classical
literature. His interests at school were
mainly in physics and he would have liked
to have studied that subject at university.
The financial position of the family, however,
meant that he could only study at university
if he received a scholarship. Such financial
support was only available for particular
topics and Hermann's father persuaded him
that he should study medicine which was supported
by the government.
In 1837 Helmholtz was awarded a government
grant to enable him to study medicine at
the Royal Friedrich-Wilhelm Institute of
Medicine and Surgery in Berlin. He did not
receive the money without strings attached,
however, and he had to sign a document promising
to work for ten years as a doctor in the
Prussian army after graduating. In
1838 he began his studies in Berlin. Although
he was officially studying at the Institute
of Medicine and Surgery, being in Berlin
he had the opportunity of attending courses
at the University. He took this chance, attending
lectures in chemistry and physiology.
Given Helmholtz's contributions to mathematics
later in his career it would be reasonable
to have expected him to have taken mathematics
courses at the University of Berlin at this
time. However he did not, rather he studied
mathematics on his own, reading works by
Laplace, Biot and Daniel Bernoulli. He also
read philosophy works at this time, particularly
the works of Kant. His research career began
in 1841 when he began work on his dissertation.
He rejected the direction which physiology
had been taking which had been based on vital
forces which were not physical in nature.
Helmholtz strongly argued for founding physiology
completely on the principles of physics and
chemistry.
Helmholtz graduated from the Medical Institute
in Berlin in 1843 and was assigned to a military
regiment at Potsdam, but spent all his spare
time doing research. His work still concentrated,
as we remarked above, on showing that muscle
force was derived from chemical and physical
principles. If some vital force were present,
he argued, then perpetual motion would become
possible. In 1847 he published his ideas
in a very important paper Uber die Erhaltung
der Kraft which studied the mathematical
principles behind the conservation of energy.
Helmholtz argued in favour of the conservation
of energy using both philosophical arguments
and physical arguments. He based many ideas
on the earlier works by Sadi Carnot, Clapeyron,
Joule and others. That philosophical arguments
came right up front in this work was typical
of all of Helmholtz's contributions. He argued
that physical scientists had to conduct experiments
to find general laws. Then theoretical argument
(quoting from the paper):
... endeavours to ascertain the unknown causes
of processes from their visible effects;
it seeks to comprehend them according to
the laws of causality. ... Theoretical natural
science must, therefore, if it is not to
rest content with a partial view of the nature
of things, take a position in harmony with
the present conception of the nature of simple
forces and the consequences of this conception.
Its task will be completed when the reduction
of phenomena to simple forces is completed,
and when it can at the same time be proved
that the reduction given is the only one
possible which the phenomena will permit.
He showed that the assumption that work could
not continually be produced from nothing
led to the conservation of kinetic energy.
This principle he then applied to a variety
of different situations. He demonstrated
that in various situations where energy appears
to be lost, it is in fact converted into
heat energy. This happens in collisions,
expanding gases, muscle contraction, and
other situations. The paper looks at a broad
number of applications including electrostatics,
electrostatics, galvanic phenomena and electrodynamics.
The paper is an important contribution and
it was quickly seen as such. In fact it played
a large role in Helmholtz's career for the
following year he was released from his obligation
to serve as an army doctor so that he could
accept the vacant chair of physiology at
Königsberg. He married Olga von Velten on
26 August 1849 and settled down to an academic
career.
On one hand his career progressed rapidly
in Königsberg. He published important work
on physiological optics and physiological
acoustics. His received great acclaim for
his invention of the ophthalmoscope in 1851
and rapidly gained a strong international
reputation. In 1852 he published important
work on physiological optics with his theory
of colour vision. However, experiments which
he carried out at this time led him to reject
Newton's theory of colour. The paper was
rightly criticised by Grassmann and Maxwell.
Helmholtz was always prepared to admit his
mistakes and indeed he did just this three
years later when he published new experimental
results showing these of his 1852 paper to
be incorrect.
A visit to Britain in 1853 saw him form an
important friendship with William Thomson.
However, on the other hand, there were problems
in Königsberg. Franz Neumann, the professor
of physics in Königsberg was involved in
disputes concerning priority with Helmholtz
and the cold weather in Königsberg had a
bad effect on his wife's delicate health.
He requested a move and, in 1855, was appointed
to the vacant chair of anatomy and physiology
in Bonn.
In 1856 he published the first volume of
his Handbook of physiological optics, then
in 1858 he published his important paper
in Crelle's Journal on the motion of a perfect
fluid. Helmholtz's paper Uber Integrale der hydrodynamischen Gleichungen,
welche den Wirbelbewegungen entsprechen began by decomposing the motion of a perfect
fluid into translation, rotation and deformation.
Helmholtz defined vortex lines as lines coinciding
with the local direction of the axis of rotation
of the fluid, and vortex tubes as bundles
of vortex lines through an infinitesimal
element of area. Helmholtz showed that the
vortex tubes had to close up and also that
the particles in a vortex tube at any given
instant would remain in the tube indefinitely
so no matter how much the tube was distorted
it would retain its shape.
Helmholtz was aware of the topological ideas
in his paper, particularly the fact that
the region outside a vortex tube was multiply
connected which led him to consider many-valued
potential functions. He described his theoretical
conclusions regarding two circular vortex
rings with a common axis of symmetry in the
following way:-
If they both have the same direction of rotation
they will proceed in the same sense, and
the ring in front will enlarge itself and
move slower, while the second one will shrink
and move faster, if the velocities of translation
are not too different, the second will finally
reach the first and pass through it. Then
the same game will be repeated with the other
ring, so the ring will pass alternately one
through the other.
This paper, highly rigorous in its mathematical
approach, did not attract much attention
at the time but its impact on the future
work by Tait and Thomson was very marked.
For details of the impact of this work, particularly
Helmholtz's results on vortices, see the
article Topology and Scottish mathematical
physics.
Before the publication of this paper Helmholtz
had become unhappy with his new position
in Bonn. Part of the problem seemed to revolve
round the fact that the chair involved anatomy
and complaints were made to the Minister
of Education that his lectures on this topic
were incompetent. Helmholtz reacted strongly
to these criticisms which, he felt, were
made by traditionalists who did not understand
his new mechanical approach to the subject.
It was a somewhat strange position for Helmholtz
to be in for he had a very strong reputation
as a leading world scientist. When he was
offered the chair in Heidelberg in 1857,
he did not accept at once however. When further
sweeteners were put forward in 1858 to entice
him to accept, such as the promise of setting
up a new Physiology Institute, Helmholtz
agreed.
Helmholtz suffered some personal problems.
His father died in 1858, then at the end
of 1859 his wife, whose health had never
been good, died. He was left to bring up
two young children and within eighteen months
he married again. On 16 May 1861 Helmholtz
married Anna von Mohl, the daughter of another
professor at Heidelberg [1]:-
Anna, by whom Helmholtz later had three children,
was an attractive, sophisticated woman considerably
younger than her husband. The marriage opened
a period of broader social contacts for Helmholtz.
Some of his most important work was carried
out while he held this post in Heidelberg.
He studied mathematical physics and acoustics
producing a major study in 1862 which looked
at musical theory and the perception of sound.
In mathematical appendices he advocated the
use of Fourier series. In 1843 Ohm had stated
the fundamental principle of physiological
acoustics, concerned with the way in which
one hears combination tones. Helmholtz explained
the origin of music on the basis of his fundamental
physiological hypotheses. He formulated a
resonance theory of hearing which provided
a physiological explanation of Ohm's principle.
His contributions to the theory of music
are discussed fully in [8].
From around 1866 Helmholtz began to move
away from physiology and move more towards
physics. When the chair of physics in Berlin
became vacant in 1870 he indicated his interest
in the position. Kirchhoff was the other
main candidate and because he was considered
a superior teacher to Helmholtz he was offered
the post. However, when Kirchhoff decided
not to accept Helmholtz was in a strong position.
He was able to negotiate a high salary as
well as having Prussia agree to build a new
physics institute under Helmholtz control
in Berlin. In 1871 he took up this post.
Helmholtz had begun to investigate the properties
of non-Euclidean space around the time his
interests were turning towards physics in
1867. Bernardo in [9] writes:-
In the second half of the 19th century, scientists
and philosophers were involved in a heated
discussion on the principles of geometry
and on the validity of so-called non-Euclidean
geometry. ... Helmholtz's research on the
subject began between 1867 and 1868. Moving
from the observation that our geometric faculties
depend on the existence, in nature, of rigid
bodies, he presumed he had given a proof
that Euclidean geometry was the only one
compatible with these bodies, maintaining,
at the same time, the empirical, not a priori,
origin of geometry. In 1869, after Beltrami's
letter ... he realized he had made a mistake:
the empirical concept of a rigid body and
mathematics alone were not enough to characterize
Euclidean geometry. The following year, fully
sharing the mathematical itinerary that,
through Gauss, Riemann, Lobachevsky and Beltrami,
led to the creation of the new geometry,
he proposed to spread this knowledge among
philosophers while at the same time criticizing
the Kantian system. This marked the beginning
of a heated philosophical discussion that
led Helmholtz in 1878 to try to appease the
criticisms of the Kantian a priori.
A major topic which occupied Helmholtz after
his appointment to Berlin was electrodynamics.
He discussed with Weber the compatibility
of Weber's electrodynamics with the principle
of the conservation of energy. In fact the
argument was heated and lasted throughout
the 1870s. It was an argument which neither
really won and the 1880s saw Maxwell's theory
accepted. Helmholtz attempted to give a mechanical
foundation to thermodynamics, and he also
tried to derive Maxwell's electromagnetic
field equations from the least action principle.
R Steven Turner writes in [1]:-
Helmholtz devoted his life to seeking the
great unifying principles underlying nature.
His career began with one such principle,
that of energy, and concluded with another,
that of least action. No less than the idealistic
generation before him, he longed to understand
the ultimate, subjective sources of knowledge.
That longing found expression in his determination
to understand the role of the sense organs,
as mediators of experience, in the synthesis
of knowledge.
To this continuity with the past Helmholtz
and his generation brought two new elements,
a profound distaste for metaphysics and an
undeviating reliance on mathematics and mechanism.
Helmholtz owed the scope and depth characteristic
of his greatest work largely to the mathematical
and experimental expertise which he brought
to science. ... Helmholtz was the last great
scholar whose work, in the tradition of Leibniz,
embraced all the sciences, as well as philosophy
and the fine arts.
Article by: J J O'Connor and E F Robertson.
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