Trained primarily in physiology, Helmholtz wrote on many other topics, ranging from theoretical physics to the age of the Earth, and to the origin of the Solar System.

His first important scientific achievement, an 1847 treatise on the conservation of energy, was written in the context of his medical studies and philosophical background.

This was a rejection of the speculative tradition of Naturphilosophie and vitalism which was at that time a dominant philosophical paradigm in German physiology.

[4] Drawing on the earlier work of Sadi Carnot, Benoît Paul Émile Clapeyron and James Prescott Joule, he postulated a relationship between mechanics, heat, light, electricity and magnetism by treating them all as manifestations of a single force, or energy in today's terminology.

The physical sound needs to be increased exponentially in order for equal steps to seem linear, a fact that is used in current electronic devices to control volume.

Helmholtz had, in his early repudiation of Naturphilosophie, stressed the importance of materialism, and was focusing more on the unity of "mind" and body.

[9] In 1851, Helmholtz revolutionized the field of ophthalmology with the invention of the ophthalmoscope; an instrument used to examine the inside of the human eye.

His main publication, titled Handbuch der Physiologischen Optik (Handbook of Physiological Optics or Treatise on Physiological Optics; English translation of the 3rd volume here), provided empirical theories on depth perception, colour vision, and motion perception, and became the fundamental reference work in his field during the second half of the nineteenth century.

Bell failed to reproduce what he thought Helmholtz had done but later said that, had he been able to read German, he would not have gone on to invent the telephone on the harmonic telegraph principle.

Although he made no major contributions to this field, his student Heinrich Rudolf Hertz became famous as the first to demonstrate electromagnetic radiation.

Based on work on Maxwell's equations, Heaviside pronounced that longitudinal waves could not exist in a vacuum or a homogeneous medium.

[22] Despite the speculative associations of the latter, his philosophy of science is thoroughly indebted to his use of mathematical physics to supplant vitalism and articulate the general conservation of energy principle.

These developments inspired new readings of Kant[4] and contributed to the rise of late modern neo-Kantianism movement in philosophy.