George Simon Ohm was born in Erlangen, Holy Roman Empire (100 km from the Czech border) on March 16th, 1789. He died in Munich, Kingdom of Bavaria (200 km from the Czech border) at the age of 65. When he was just four months old, he could have stormed the Bastille but he decided not to.His father was officially uneducated but he was actually one of the most widely respected autodidacts. Georg's mother died when he was ten years old. Among seven siblings, only three survived to adulthood: sister Elizabeth Barbara, Georg Simon, and his younger brother Martin Ohm who would become a famous mathematician (during their lifetime, maybe more famous than Georg Ohm). Martin Ohm figured out what \(a^b\) was for \(a,b\in\CC\); I loved this problem when I was 8 years old or so.
Imagine that it's just 200 years ago – and 4/7 of the children were dying before they reached adulthood. Medicine and related fields have made an amazing progress since Ohm's time. On the other hand, one could be worried that this cruel fate of the children was still imposing some "creative" natural selection on the mankind that became absent sometime in the 20th century. So far, things look fine but who knows what the people will think about this issue in 2100.
Georg Simon Ohm most famously worked as a high school teacher – that's when he discovered his Ohm's law\[
U = RI.
\] I can't forget the joke about the three Ohm's laws: \(U=RI\), \(I=U/R\), \(R=U/I\). I guess that many people, especially among the girls, wouldn't view this as a joke.
Note that the unit "one ohm" of resistance is denoted by the capital Omega, \(\rm\Omega\), because the letters starts almost like Ohm's name. Ohm made the discovery in 1827, when he was 39 and when he was playing with the electrochemical cell invented by Alessandro Volta. Ohm's law is clearly paramount for all electric circuits but sadly enough, electric circuits only began to be a hot topic more than 50 years later. Imagine how rich he would be if he could collect royalties from Ohm's law patents today.
Ohm's career involved various teaching jobs – including those at universities (not the most famous ones) – that were paying so little that he almost starved to death. And that's true despite the fact that he was hired by no one else than the Prussian king at one moment. The king loved Ohm's book and work. Some low-brow colleges that used to employ Ohm didn't so they fired him, and so on.
Johann Dirichlet was among Ohm's students.
There's another law that Ohm proposed, the so-called Ohm's other law or Ohm's acoustic law. Using a modern language, it says that the human ear is a Fourier analyzer that measures \(|\tilde f(\omega)|^2\) for all accessible frequencies \(\omega\).
This statement, known to be partly false, is pretty fascinating. For example, it implicitly says that the relative phases don't matter. For example, look at the graphs of the functions \(\sin(x)+\sin(2x)\) and \(\sin(x)+\cos(2x)\). The graphs of the position of the speaker as a function of time look very different (the second graph is time-reversal-symmetric but the first one is far from it, for example) but because the amplitudes have the same absolute values, we can't hear the difference between these two sounds.
When I was a kid, I played the piano and I was very confused by certain basic things. For example, when I was 7, I was convinced that if you play "C" and "E" at the same moment, the ear must hear the tone in between, "D", if I pick a prominent example. That's of course rubbish – each frequency has its independent "account" – as I understood a year later (even though I surely had to "hear" this fact – hear chords – a long time earlier). But it was still confusing to me why we can't hear the differences between the functions above, for example, and why interference never cancels the same tone coming from two sources etc. You're welcome to offer your opinion.
Ohm's acoustic law answers most of these questions. Nevertheless, musicians have generally hated this law from the beginning – it became a major reason why musicians distrust physicists. It has to be wrong, they feel and hear (?). Well, I am sure that the law "ears are Fourier analyzers" can't be quite true. On the other hand, I haven't found any coherent description by the musicians that would clarify what they really dislike about the law.
Well, I would say that the ear only hears some frequencies, from \(20\) to \(20,000\,{\rm Hz}\) or so; frequencies outside this interval are simply eliminated (gradually). Moreover, it must be able to partly determine the phase of the cycle for low enough frequencies. And it must suffer from limitations of the resolution with which the frequencies may be distinguished; good musicians generally have a more precise sense of hearing. And the brain of course can't remember too much information about the function \(|\tilde f(\omega)|^2\) so it compresses it in some way – determines the loudest components (frequencies) and/or describes the remaining sound as "some sort of noise" etc. Otherwise I am not really able to think about other limitations that the law could have.
Can you help me? My guess is that the dissatisfied musicians must misunderstand some Fourier maths even if their ear is subconsciously doing a good job in the Fourier analysis. And artists may always hate science for "making things dull" (not true!). So I would guess that the opposition is ultimately irrational but I am ready to be proved wrong.
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