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12.7.13




Now I am embarrassed to admit it, but in high school I did very little math. I was at the time getting very involved in the violin and so spent as little time on math courses as possible. So after many years of work in the violin and  in Talmud, when I stated math again I was starting at an extremely elementary level. I did not know Algebra or even how to divide fractions--zilch. But I found a small introductory book to Elementary Math in used book store and after my morning prayers by the Western Wall, I used the method of the Ari'zal [Isaac Luria] of saying the words forwards and backwards. I would read one page forwards and understand nothing. But then I would say the words on the page  backwards and somehow the idea went into my head.

So I applied to Hebrew University and got a high enough score on the Collage entry Exam [Psychometric test] to be accepted. But then I had to run to the USA  So in New York I started the collage entry idea all over again. I applied to Brooklyn College but they did not have an idea of starting a semester in the middle of a year and I had made up my mind to go  for Rosh HaShannah to Uman, Ukraine]. So I applied instead to New York University. [At the time I did not know this is an Ivy League School.]
At any rate, at that time I majored in Physics. But this involved a certain amount of math also. But in any case I was still doing the reading the words forwards and backwards and everything was going fine. I would read the words forwards and under stand zero. Then I would read the words backwards and it would miraculously enter my head.

The whole thing feel apart when I stated differential equations.{Also Chemistry.} At that point the saying the words backwards just got to be an hindrance and not a help. So  I started in math and physics just saying the words and going on.

I should perhaps admit here that this does not seem to work very well with Tosphot. when it comes to Tosphot it is very helpful to have a smart learning partner

But even with that I admit that the only way I have ever made any progress with Tosphot [of R Akiva Eiger and the Pneii Yehoshua for that matter is by sitting on the same Topshot for weeks at a time.]

But for Tosphot you really need a learning partner because he requires two different types of talent.One is analytic ability. Another is deep thinking.
Without both it is hard to see the depths of Tosphot and his rigorous logic..

I mathematics I for a time used a few methods.  I also discovered an idea  to repeat what you learn in German. I have found this helpful when it comes to higher mathematics. For some reason when I read higher Mathematics in English something just does not click. But when I read the same thing in German or Russian I find it makes sense. For one interesting example I read about tensors for sometime in English nothing made sense. Then one day I opened up the Wiki in German on tensors and right away at the beginning of the page they have this nice little diagram which makes the whole thing makes sense instantly. Like they say in Hebrew "Chaval Al Hazman"--what a waste of time do do anything else!

I don't have a lot of ideas about Physics I admit since most of my efforts on it are spent trying to catch up with missed time. But one thing I should mention while philosophers today take materialism as their staring point and assume the existence of matter, in Physics matter has been disappearing for a long time. The first person to get rid of it to some degree was Gell Man. Quarks are point particles. String theory did in materialism completely. Now all there is is space time. And space time as we know from Kant is on the level of the thing in itself of which we have no ability to conceive of. We can simply put it into the equations but we don't know what it is. [String Theory today is basically expressed the language of Homology and Homotopy. That means it is about holes in spaces and about deforming spaces. And it is not quantum physics. Quantum physics people tried for years to make it fit with gravity with no luck. And I myself worked on a GUT with a Russian Physicist which was more promising than the others. People gave up. String theory is modified Relativity. It is just taking the idea of Kaluza Klein and expanding  them.]