He was imprisoned because he wasn't going to have any of that bystander effect: when he saw things he disagreed with, he spoke out. As a pacifist, he had much to disagree with as he lived through the February and October Revolutions in 1917; and then as an exile in Berlin (1919-1934), Vienna (1934-1938) and Yugoslavia. He was able to nip across borders, often at the last minute, because he had assets and married well. In the infinitely corruptible system that ran the Third Reich, if you had money you had a far far better chance than the dispossessed. But der Mann caught up with him eventually and he spent many long years in concentration camps as a political prisoner. His aristocratic wife managed to stay outside the wire and she eventually winkled him out of his last camp and across the border to Switzerland.
In the camps he had few assets and certainly not the infinite supply of pencils and paper that a mathematician needs to think deep thoughts. To keep himself sane, he developed a system of mental arithmetic which enabled him to carry out any arithmetic operation in his head. This Trachtenberg System was, after the war, expanded into a book and used in an Institute in Zurich to empower people by polishing their math skills. He found that this could have astonishing knock-on consequences for competence in other areas and self-esteem.
Trachtenberg loved numbers, they were his pals. And he used to talk to his friends in the camps and came up with nifty ways in which their natural relationships helped him carry out arithmetic operations on them. All in his head because paper was a currency in the camps and couldn't be wasted on diaries, or sums or stuff not essential for survival. I had hoped that I wouldn't have to explain how the Trachtenberg system works - I'd just point you at a brilliant youtube vid. But no - all the top-hitting Trachtenberg videos are earnest, didactic, boring and/or presented in a nearly impenetrable accent. Here's a taster: the rule for multiplying a big number by 6 just using your ability to add one digit numbers in your head.
Rule for 6x: to each "number" (digit to operate upon) add half the "neighbour" (the digit to the right); if the number is odd add another 5. If the neighbour is odd discard the fractional part when you half it: half of 5 is 2, half of 7 is 3 etc.
The challenge: 0443052 x 6
2 First number (2) has no neighbour: pop it down
'12 5 is odd: 5 + 5 + half neighbour (1): 5+5+1=11 enter 1 the ' is a "carry"
312 0 plus half of 5 (2) and add the carry: 0+2+1=3
8312 3 is odd so add 5, neighbour is 0: 3+5+0=8
58512 4 plus half of 3 (1): 4+1=5
658312 4 plus half of 4 (2) so 4+2=6
2658312 0 plus half of 4 (2) so 0+2=2
Check the answer on your calculator. Trachtenberg has similar systems for multiplying by 11, 7, 5, 4. etc. doing 718 x 592 and then moves on to square roots and internal consistency checks, like casting out 9s. It's fun, you should check it out; when armageddon starts next week, there won't be no calculators, there will just be the sound of a banjo.
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