"Jewish Mathematics"?(mathenchant.wordpress.com)
mathenchant.wordpress.com
"Jewish Mathematics"?
https://mathenchant.wordpress.com/2024/04/17/jewish-mathematics/
25 comments
If you strip the context from this interesting article, you are also left with an interesting point. That is: there is value in different perspectives and approaches to a problem, yet the more different the perspective the harder it is to explain to others.
QM had to move forward as a slow-rolling wave for this reason (probably I thought of this case due to the horrifying example chosen by the author), while special and general relativity did not require that (instead GM was simply extremely hard to understand :-).
But the example I find most interesting is Newton introducing* calculus to England in order to address bugs in celestial mechanics and prove that the orbits were elliptical.
QM had to move forward as a slow-rolling wave for this reason (probably I thought of this case due to the horrifying example chosen by the author), while special and general relativity did not require that (instead GM was simply extremely hard to understand :-).
But the example I find most interesting is Newton introducing* calculus to England in order to address bugs in celestial mechanics and prove that the orbits were elliptical.
This is a very hacker news discussion, discussing the math at the beginning which is entirely tangent to the point of the article. While I am deeply disturbed by the rising antisemitism in America, that's one reason why I love spending time here at hacker news, where we can forget about that and focus on technology and progress, where knowledge is the only true source of authority.
If you are referring to the protests against israeli politics, that is not antisemitism. Or are you referring to something else?
Fixating on basic arithmetic in the intro and discarding the entire essay is considered a very hacker news discussion?
Yeah. Let's be honest, how many articles have you replied to without reading in full? And we love math around here.
the only "jewish math" you need to know that is useful is gematria
Jews have a rich tradition of finding deep meaning and significance in numbers, which goes far beyond gematria. The Torah is filled with intriguing examples, such as the seven days of creation, the 12 tribes of Israel, and the 40 days and nights of the Great Flood. Many Jewish rituals also incorporate symbolic numbers, like the 18 blessings in the Amidah prayer or the custom of giving monetary gifts in multiples of 18 (representing "chai" or life). From the cycles of the Jewish calendar to the 613 mitzvot, numbers permeate Jewish thought as a way to understand both the divine order and our human place within it.
The Torah itself might be a universal constant, such as PI, a hypothesis presented by Stan Tenan in this lecture from 1989.
https://m.youtube.com/watch?v=OJGW2UANWRE&list=PLgCDgIRQwOvK...
https://m.youtube.com/watch?v=OJGW2UANWRE&list=PLgCDgIRQwOvK...
That's fascinating, especially considering Old testament beliefs regarding the Transcendence of the Torah.
Useful I don't know (for some people, I suppose) but a great answer.
I did it like this:
7 1/4 - 3/4
= 7.25 - 0.75
= 6.5
= 6 and 1/2
I would have assumed that most people would do it this way when they see a fraction that can be expressed as an easy floating point but maybe not!
7 1/4 - 3/4
= 7.25 - 0.75
= 6.5
= 6 and 1/2
I would have assumed that most people would do it this way when they see a fraction that can be expressed as an easy floating point but maybe not!
Haha. I posted roughly the same thing as well. I wonder if those of us in fields like engineering that are used to ugly decimal numbers have a tendency to this direction.
Me too.
And it’s not one of the two ways the article claims people do math.
And it’s not one of the two ways the article claims people do math.
I just subtracted 1 and added a 1/4, barely giving it any thought. The example given is too simple for comparing methods.
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There also was a "German Physics" movement that tried to discredit relativity theory and quantum mechanics as essentially Jewish. Heisenberg was called a "white Jew" in a SS periodical. The movement didn't have much success, and Heisenberg eventually became the leader of the (unsuccessful) German effort to develop an atomic bomb.
I'm pretty sure he was not. From https://en.wikipedia.org/wiki/Werner_Heisenberg :
> When the German scientists heard about the Hiroshima bomb, Heisenberg admitted that he had never calculated the critical mass of an atomic bomb before. When he subsequently attempted to calculate the mass, he made serious calculation errors. Edward Teller and Hans Bethe saw the transcript, and drew the conclusion that Heisenberg had done it for the first time as he made similar errors as they had. Only a week later Heisenberg gave an impressive lecture about the physics of the bomb. He correctly recognized many essential aspects, including the efficiency of the bomb, although he still underestimated it. For Popp, this is proof that Heisenberg did not spend time on a nuclear weapon during the war; on the contrary, he avoided even thinking about it. ...
> The Farm Hall transcripts reveal that Heisenberg, along with other physicists interned at Farm Hall including Otto Hahn and Carl Friedrich von Weizsäcker, were glad the Allies had won World War II.[114] Heisenberg told other scientists that he had never contemplated a bomb, only an atomic pile to produce energy. ... On the failure of the German nuclear weapons program to build an atomic bomb, Heisenberg remarked, "We wouldn't have had the moral courage to recommend to the government in the spring of 1942 that they should employ 120,000 men just for building the thing up."[117]
> When the German scientists heard about the Hiroshima bomb, Heisenberg admitted that he had never calculated the critical mass of an atomic bomb before. When he subsequently attempted to calculate the mass, he made serious calculation errors. Edward Teller and Hans Bethe saw the transcript, and drew the conclusion that Heisenberg had done it for the first time as he made similar errors as they had. Only a week later Heisenberg gave an impressive lecture about the physics of the bomb. He correctly recognized many essential aspects, including the efficiency of the bomb, although he still underestimated it. For Popp, this is proof that Heisenberg did not spend time on a nuclear weapon during the war; on the contrary, he avoided even thinking about it. ...
> The Farm Hall transcripts reveal that Heisenberg, along with other physicists interned at Farm Hall including Otto Hahn and Carl Friedrich von Weizsäcker, were glad the Allies had won World War II.[114] Heisenberg told other scientists that he had never contemplated a bomb, only an atomic pile to produce energy. ... On the failure of the German nuclear weapons program to build an atomic bomb, Heisenberg remarked, "We wouldn't have had the moral courage to recommend to the government in the spring of 1942 that they should employ 120,000 men just for building the thing up."[117]
In 1942, Heisenberg became the director of the Kaiser Wilhelm Institute for Theoretical Phiysics, where research into nuclear physics was conducted (on a small scale) and a Uranmaschine (small experimental reactor) was built. At that point, Heisenberg indeed didn't believe anymore in the possibility of building a fission bomb. But a year before that, Heisenberg had told Niels Bohr that he believed that such a weapon was possible.
So, you're right: although there was an "atomic weapons program" in Germany, it became an "atomic energy program" quite early on, and that happened before Heisenberg became a leading figure in it. The Allies came to know this only after 1945.
From "Heisenberg's war : the secret history of the German bomb", Heisenberg realized in mid 1941 that what he thought was "safe" work in nuclear reactors could be used to produced bombs. https://archive.org/details/heisenbergswarse0000powe/page/11... and by that summer thought it was widely enough known to be a concern.
He hoped to "try to channel research in the direction of a power-producing machine" (https://archive.org/details/heisenbergswarse0000powe/page/11...)
"Whenever Heisenberg spoke of the visit [to Bohr] he always placed one question at the center of his concerns: what should the German scientists do? The dilemma was quite stark: if it would be wrong to give a bomb to Hitler, was it also wrong to ‘‘work’’ on bomb-related research? The answer was not easy. They might preserve their moral integrity by refusing to do research on fission, but in that event the Heereswaffenamt might only find other, more willing physicists to do the job. By continuing to work on the project, Heisenberg, Weizsicker and Wirtz would maintain a degree of control over its direction—so long as the military authorities made no decision to embark on a full-scale program to build a bomb. Any decision of that kind, Heisenberg knew, would deliver control of the project into military hands.”' - https://archive.org/details/heisenbergswarse0000powe/page/11...
By contrast, other Germans in 1942 were more enthusiastic. From https://archive.org/details/heisenbergswarse0000powe/page/13...
> In a report prepared for the Heereswaffenamt, Diebner and his associates—Friedrich Berkei, Werner Czulius, Georg Hartwig and W. Herrmann—claimed that a bomb might be built with an ‘‘explosive effect a million times greater than the same weight of dynamite’’ using either uranium-235 or the ninety-fourth element, produced in reactors.” By what route the general knowledge of plutonium reached Diebner and the Heereswaffenamt, and how long it took, is not known,” but it was discussed clearly in the report by Diebner’s group completed in February 1942. The report, Energiegewinnung aus Uran (‘‘Energy Production from Uranium’’), said 10 to 100 kilograms of fissionable material would be required for a bomb—the lower figure was in fact about right—and urged that the program be transformed into a major industrial project. The report did not minimize the effort required, confessing frankly that separation of U-235 was still beyond reach, and that the details of plutonium production remained to be worked out.
I believe your "Heisenberg indeed didn't believe anymore in the possibility of building a fission bomb" is best interpreted in the larger context of "in the timeframe the military wanted".
When you say "atomic weapons program" and "leader of the (unsuccessful) German effort to develop an atomic bomb", what specifically do you mean? "Diebner, throughout the life of the nuclear weapon project, had more control over nuclear-fission research than did Walther Bothe, Klaus Clusius, Otto Hahn, Paul Harteck, or Werner Heisenberg." says https://en.wikipedia.org/wiki/German_nuclear_program_during_... and https://archive.org/details/heisenbergswarse0000powe/page/14... gives more about what he did in developing that report.
He hoped to "try to channel research in the direction of a power-producing machine" (https://archive.org/details/heisenbergswarse0000powe/page/11...)
"Whenever Heisenberg spoke of the visit [to Bohr] he always placed one question at the center of his concerns: what should the German scientists do? The dilemma was quite stark: if it would be wrong to give a bomb to Hitler, was it also wrong to ‘‘work’’ on bomb-related research? The answer was not easy. They might preserve their moral integrity by refusing to do research on fission, but in that event the Heereswaffenamt might only find other, more willing physicists to do the job. By continuing to work on the project, Heisenberg, Weizsicker and Wirtz would maintain a degree of control over its direction—so long as the military authorities made no decision to embark on a full-scale program to build a bomb. Any decision of that kind, Heisenberg knew, would deliver control of the project into military hands.”' - https://archive.org/details/heisenbergswarse0000powe/page/11...
By contrast, other Germans in 1942 were more enthusiastic. From https://archive.org/details/heisenbergswarse0000powe/page/13...
> In a report prepared for the Heereswaffenamt, Diebner and his associates—Friedrich Berkei, Werner Czulius, Georg Hartwig and W. Herrmann—claimed that a bomb might be built with an ‘‘explosive effect a million times greater than the same weight of dynamite’’ using either uranium-235 or the ninety-fourth element, produced in reactors.” By what route the general knowledge of plutonium reached Diebner and the Heereswaffenamt, and how long it took, is not known,” but it was discussed clearly in the report by Diebner’s group completed in February 1942. The report, Energiegewinnung aus Uran (‘‘Energy Production from Uranium’’), said 10 to 100 kilograms of fissionable material would be required for a bomb—the lower figure was in fact about right—and urged that the program be transformed into a major industrial project. The report did not minimize the effort required, confessing frankly that separation of U-235 was still beyond reach, and that the details of plutonium production remained to be worked out.
I believe your "Heisenberg indeed didn't believe anymore in the possibility of building a fission bomb" is best interpreted in the larger context of "in the timeframe the military wanted".
When you say "atomic weapons program" and "leader of the (unsuccessful) German effort to develop an atomic bomb", what specifically do you mean? "Diebner, throughout the life of the nuclear weapon project, had more control over nuclear-fission research than did Walther Bothe, Klaus Clusius, Otto Hahn, Paul Harteck, or Werner Heisenberg." says https://en.wikipedia.org/wiki/German_nuclear_program_during_... and https://archive.org/details/heisenbergswarse0000powe/page/14... gives more about what he did in developing that report.
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7 1/4 - 3/4
How I did it 3/4 - 1/4 = 2/4 = 1/2 = .5
7 - .5 = 6.5 = 6 1/2
How I did it 3/4 - 1/4 = 2/4 = 1/2 = .5
7 - .5 = 6.5 = 6 1/2
Great article, many other cultures have versions of maths that are sometimes never taught, similar like vedic mathematics
7¼ - ¾ == (7¼ + ¼) - (¾ + ¼) == 7½ - 1 = 6½
is it not similar to what happens in the US?
https://m.youtube.com/watch?v=cTokizGa6zQ
https://m.youtube.com/watch?v=cTokizGa6zQ
It was sad to read the history here of antisemitism.