Bach & Other Genuises

Albert Einstein and JS Bach

Teddy Kaufman wrote (April 22, 2006):
Einstein, the most prominent genius of the 20^th century was born on 14 March 1879 in Ulm, Württemberg, Germany and died 51 years ago on 18 April 1955 in Princeton, New Jersey, USA. He was awarded the following most prestigious prizes:
Nobel Prize - Awarded 1921
Fellow of the Royal Society - Elected 1921
Royal Society Copley Medal - Awarded 1925
Fellow of the Royal Society of Edinburgh - Elected 1927
AMS Gibbs Lecturer - 1934

Additional non-scientific works are: About Zionism (1930), Why War? (1933), My Philosophy (1934), and Out of My Later Years (1950) .

When Einstein arrived in the United States in 1933 after fleeing the Nazi Germany, he brought with him his violin in addition to his stunning scientific accomplishments and world wide fame.

He was a very talented violin player who was involved with some amateur chamber ensembles in Berlin during the early thirties, Mostly he loved Bach's Partitas and Sonatas. Einstein's gifts inevitably resulted in his dwelling much in intellectual solitude and, for relaxation, music played an important part in his life. He made no secret of how much music meant to him.

Following are some of his quotations related to music:
"I took violin lessons from the age 6 to 14, but had no luck with my teachers for whom music did not transcend mechanical practicing. I really began learning only when I was 13 years old, mainly after I had fallen in love with Mozart's sonatas".
(When asked about his theory of relativity ): "It occurred to me by intuition, and music was the driving force behind that intuition, My didiscoveryas the result of musical perception ... If I were not a physicist, I would probably be a musician. I often think in music. I live my daydreams in music. I see my life in terms of music".
" He often told me that one of the most important things in his life was music. Whenever he felt he had come to the end of the road or into a difficult situation in his work, he would take refuge in music and that would usually resolve all his didifficulties( Bernard Mayor , quoted in - http://www.LearnToReadMusic.org ).

To me, both geniuses Bach and Einstein exhibited several aspects in common: Originality, productivity, talent,curiosity, inspiration and, mathematics, Bach with his enormous and prolific musical output is to my mind, one of the most prominent composers during the last four centuries. As far as I understand, Bach used numerology/cabalistic symbolism , and the "golden section" as well as the Fibonacci succession (1, 1, 2, 3, 5, 8, 13 etc., in which each number in the succession is the sum of the two previous ones). Also, it has been postulated that Bach worked like an architect, joining the two different parts of a musical piece into one harmonious whole before the actual process of composition started. Moreover, the symmetry of his music, was probably influenced by Gottfried Liebniz (Inventor of the calculus, 1646 - 1716 ) who claimed that "Music is a secret arithmetical exercise and the person who indulges in it does not realize that he is manipulating numbers."

The mathematical aspects of Bach's music are of great interest to me. Hence, comments on this issue from our list members would be most appreciated.

Julian Mincham wrote (April 23, 2006):
Teddy Kaufman wrote:
< To me, both geniuses Bach and Einstein exhibited several aspects in common:
Originality, productivity, talent,curiosity, inspiration and, mathematics,>
To this pair I would add Isaac Newton who similarly exhibited these qualities. I think, from memory, that some comparisions are made in Wolff's book JSB the Learned musician between these two.

(However,I am writing this 10,000 miles from home and consequently away from my books and scores and cannot verify any references---for this reason I will exhibit restraint and not take up the tempting invitation to discuss Bach's mathematical characteristics).

All three men transcend their time and culture, contributing unique insights into nature and the human condition.

Richard wrote (April 23, 2006):
Teddy Kaufman wrote
< To me, both geniuses Bach and Einstein exhibited several aspects in common: >
OK for the Music, Bach , etc, but the moral positions of Einstein can be criticized....

A. Sparschuh wrote (April 26, 2006):
Isaac Newton, Albert Einstein and JS Bach math skills

Teddy Kaufman wrote:
< To me, both geniuses Bach and Einstein exhibited several aspects in common:
Originality, productivity, talent,curiosity, inspiration and, mathematics,>
The actual controversy about JSBs W.F.Bach's math skills is discussed in:
http://listserv.albany.edu:8080/cgi-bin/wa?A2=ind0604&L=HPSCHD-L&P=R14330&I=-3
like in Einstein's case, some outfashioned scholars allege still wrongly, that Bach would hadn't liked maths too.

Julian Mincham wrote:
< To this pair I would add Isaac Newton who similarly exhibited these qualities. I think, from memory, that some comparisions are made in Wolff's book JSB the Learned musician between these two… >
Wolff overtook that comparison in citing Schubart 1784/5, cf: Dokumente Vol.3 #903 p.409 line 10:
"Was Newton als Weltweiser war, war Bach als Tonkünstler"
transl:
"What Newton was as world-sage, was Bach as tone-artist"

Newton played pretty well the viola, and invented for instance in tuning theory the 612-division of the octave.
Lit: new Grove 2^nd Ed. Vol.17 p.815-4

Tom Hens wrote (April 27, 2006):
A. Sparschuh wrote:
< The actual controversy about JSBs W.F.Bach's math skills is discussed in:
http://listserv.albany.edu:8080/cgi-bin/wa?A2=ind0604&L=HPSCHD-L&P=R14330&I=-3 >
That's not a discussion, that just points to a message on another mailing list by yourself. Where's the evidence that Bach was interested in mathematics at all? All claims I've ever seen wanting to link Bach with "mathematics" seem to be about extremely elementary arithmetic, the kind one is supposed to have mastered by the time one is ten or so.

Julian Mincham wrote (April 27, 2006):
Tom Hens wrote:
< Where's the evidence that Bach was interested in mathematics at all? All claims I've ever seen wanting to link Bach with "mathematics" seem to be about extremely elementary arithmetic, the kind one is supposed to have mastered by the time one is ten or so. >
Yes, I would be interested to see evidence of this as well. My understanding is that Bach was interested in NUMBERS (and their symbolic values) rather than MATHEMATICS as such. Numbers such as 7 and 14 clearly had symbolic interest for him as did the number obtained by adding up those associated with letters of a person's name (A=1, B=2 etc). Consequently he fashioned various compositions around such numbers which gave the works a sort of numerical complexity which many other composers may not have applied to the same degree. I suspect it was this from which Bach's 'mathematical' reputation arose.

William Rowland (Ludwig) wrote (April 27, 2006):
[To Tom Hens] The State of Mathematics during the time of Bach. First of all; most people could only do the most elementary math and that includes most Organbuilders who worked more by rote and feel than anything scientific.

Bach might have known about Algebra, Plane Geometry and Trigonometry and particularly about Geometry as it was part of the Classics regieme in the Pedagogy of the age. As an Educator of the times; he was expected to know math since he had charge of boys to teach in his choir. He would have known little to nothing about The Calculus which Newton had invented/ was discovered sometime during the black plague while he was on sabbatical from Cambridge at his parents house when the legendary apple hit him on the head. Newton did not publish his Principia until 1687. By the time of Newtons death in 1727; Bach would have most certainly would have heard of the Calculus from the circles that he traveled in that included University Dons but whether or nohe acquainted himself with this advances of Mathematics at that time is unknown.

If would not be surprizing if Bach or any of his children had difficulties with Math a common problem among those in the arts of that time and even today. It is said that Beethoven when it came to Math was a dummy while Mozart tended to be brilliant in theory but in practice a very poor manager of money.

Eric Bergerud wrote (April 27, 2006):
[To Ludwig] I hung out with PhD track math students in my grad days at Berkeley: all nuts of course, but wonderful guys. Nice to know if someone has figured out the precise difference between math and arithmatic - they used to quibble about stuff like that. (Normally, of course, I didn't have a clue about what they quibbled about. A little unfair really: several of them were very keen history buffs and could easily keep up with me.)

Anyway, if someone was pursuing a PhD in music at a top school today, what kind of math requirements would they be looking at? Enough to jawbone with Stephen Hawking or only Pascal?

William Rowland (Ludwig) wrote (April 27, 2006):
[To Eric Bergerud] Today's Phd Music major probably would need a through grounding in acoustics and physics as well as Boolerian Algebra, Calculus and in addition to Hawking--- Kip Thorne and have knowledge of string theory (no that is not the Pythagorean Theory of a mono-chord). Perhaps the Boolerian component would be more stressed because of computers. There are methods of composition which use math as a methodology of composing (and also used in painting works of art on canvass). Supposedly Bach used these methods---if we are to accept what some one the list have stated. I have yet to learn them.

String theory goes beyond Einstein's theory of relativity and gets into some very strange oddball physics that a beautiful mind might have considered. While Einstein's theory states that we can not travel faster than the speed of light (and at that speed we would stay permanently fixed at the age we began traveling);

String theory states that we can travel faster than the speed of light by making use of wormholes and that there more than three dimensions in time and space ---as many as 11 or 12 (although theoretically according the the series of Fibonacci numbers there should be 13. If I have lost you here let me know please.). It is weird because in string theory you can go past the date that you died and go back in time before you were born and when we combine that with game theory ---it becomes some rather powerful stuff. String theory goes beyond Hawking (who now rejects some of his thinking some 30 years ago)so that we can see before time and after the time that the Big Bang occurred. All matter is the result of a nuclear particle called a Neutrino---without the Neutrino the present cosmos could have never existed because it is the only known particle that can engage in nuclear fusion or the binding of atoms together thus turning Hydrogen into Helium and up the scale of Elements on the periodic chart to we get to the theoretical element I call Ultimatum which is the heaviest and most unstable element ever created and responsible for the Big Bang.

William Herschel, the Great Astronomer and minor composer of Haydn's time(his compositions sound like Haydn-Mozart combined), was probably the first of professional musicians who really got into the Math thing after he and his sister, Caroline, (an excellent astronomer and optician in her own right(discoverer of comets and other bodies) but not recognized until the women's right movement)became the best telescope makers and opticians the world had ever seen until that date--even in these days of computers doing optical work---their work in optics still is some of the best that humans have ever produced. They did this as a manner of relaxing from all the stress of playing for the Court of George III and like Bach as Kapellmeister in Bath. Caroline in her younger years was a very promising beauty. Unfortunately, Caroline like Beethoven came down with smallpox and it left her rather hideously scared. The family decided because her physical attributes had been destroyed that she probably would never be married and so she ended up as William's housekeeper and remained so even after William married and had a son who like Bach's sons is equally as famous as his father.

William Rowland, composer et al
amateur astronomer.
Teacher of Einstein's great grandaughter, Julie.

Bradley Lehman wrote (April 27, 2006):
< Anyway, if someone was pursuing a PhD in music at a top school today, what kind of math requirements would they be looking at? Enough to jawbone with Stephen Hawking or only Pascal? >
None. When I was in five years of master's/doctoral work at Michigan, in music and musicology, there was zero requirement of any math courses or demonstrable proficiency. Not even the requirement to recognize a Pascal's triangle or run a Sieve of Eratosthenes.

I remember that in a music theory course or two we discussed the Golden Proportion very briefly and especially in analysis of Bartok's music; but nothing more advanced in math than that. Just look rather mechanically at the music about 62% of the way through the piece and see that something interesting or momentous happens there. So? (Just because it's a good satisfying place to put a climax to a piece of music....the same type of thing can be post-rationalized back into binary dance movements the way Bach wrote them, too. Reach the most remote key areas soon after the double-bar repeat...and post-rationalize that this also led into the place to put the hairiest bits of development section in classical sonata form, too, through Mozart/Haydn/Beethoven/Schubert.....)

That proportion itself is easily understandable by watching the half-hour film "Donald in Mathmagic Land" that I saw several times in elementary school: Amazon.com
...and have watched many times since then, as well, because it's so good!

As for reading about string theory (superstring theory) in leisure time, I'm enjoying Brian Greene's books The Elegant Universe and The Fabric of the Cosmos.

Vladimir Skavysh wrote (April 27, 2006):
[To Ludwig] I would not make haste myself to recommend that String Theory be taught to students seeking Ph.D. in music. Firstly, one would first have to get a Ph.D. in mathematics (or theoretical physics) to really understand the theory. Secondly, and more importantly, there are practically no reasons to think that String Theory is correct. Aside from quantum gravity, the theory's predictions differ greatly from what experiments have already shown, all recent experiments that have planned to verify the predictions of String Theory produced null results, and the philosophical basis upon which the theory lies is shaky at best. During the next decade, a series of new experiments are planned to occur which will decide once and for all whether the theory is wrong or not--and I say the theory is going down.

From the point of view of ontology, however, the theory is indeed interesting and anyone could benefit from studying this ontology.

William Rowland (Ludwig) wrote (April 27, 2006):
[To Vladimir Skavysh] Thank you for your reply.

I am aware that String theory is somewhat a very controversial topic and many like you debate the existence of the implications of string theory and if this is all a bunch of foolish nonsense of a beautiful mind. I myself am opened minded about it.

One does not necessarily have to have a Phd to understand string theory. It has been explained in the United States so that Middle School students can understand the general theory. The US Public Broadcasting Program NOVA science series has an excellent television program on string theory that does a good job of explaining it. (Excuse the unintended spam but he cost for dvd copy is 20.00 USA and by the way this science program does some excellent programing about science and music et al). OF course it does not get into the complicated maof String theory.

Please contact me off list and give me the details of the experments and the journal citations please as I wish to learn more. I make this request because I fear the we are getting to the limits of off topic subjects. This list is after all about J.S. Bach not Theorectical astrophysics or other such related topics.

James P. Spencer wrote (April 28, 2006):
Ludwig wrote:
< Today's Phd Music major probably would need a through grounding in acoustics and physics as well as Boolerian Algebra, Calculus and in addition to Hawking--- Kip Thorne and have knowledge of string theory (no that is not the Pythagorean Theory of a mono-chord) Perhaps the Boolerian component would be more stressed because of computers. etc etc >
It's boolean algebra (and logic), not boolerian, and the rest of this isn't a whole lot more accurate.

It's really hard to see why a music major would need to know anything about Hawking's work which, setting aside his popular works (which is what he is really known for - quite rightly so - but which contain almost nothing in itself which is very original), is focused primarily on black holes and the quantum mechanics of black holes.

It's similarly hard to see why a music major would need to know anything about string theory, your description of which sounds like pieces of pop science badly understood. Certainly string theory is not about traveling faster than the speed of light and it certainly doesn't postulate that "all matter is the result of a nuclear particle call a Neutrino." On the contrary, in it's basics, string theory postulates that all matter is the result of vibrations of Plank length one dimensional strings vibrating in multiple dimensions (which would seem to be the only apparent relationship to music). I have no idea what your comment about "theoretically according to the series of Fibonacci numbers there should be 13;" the number isn't some arbitrary value, it's forced by the math, math which despite my engineering background, I don't profess to understand but which would not be of any value to a musician. (The extra dimensions in which the strings vibrate are, if they exist at all, wrapped far too tightly on themselves to have any practical interest in terms of generating sound.)