linkstream2 microblog

https://www.britannica.com/biography/John-von-Neumann/Princeton-1930-42
QT:{{”
Never much like the stereotypical mathematician, he was known as a wit, bon vivant, and aggressive driver—his frequent auto accidents led to one Princeton intersection being dubbed “von Neumann corner.” “}}

https://en.wikipedia.org/wiki/Lise_Meitner

QT:{{”
At that point we both sat down on a tree trunk (all that discussion had taken place while we walked through the wood in the snow, I with my skis on, Lise Meitner making good her claim that she could walk just as fast without), and started to calculate on scraps of paper. The charge of a uranium nucleus, we found, was indeed large enough to overcome the effect of the surface tension almost completely; so the uranium nucleus might indeed resemble a very wobbly unstable drop, ready to divide itself at the slightest provocation, such as the impact of a single neutron. But there was another problem. After separation, the two drops would be driven apart by their mutual electric repulsion and would acquire high speed and hence a very large energy, about 200 MeV in all; where could that energy come from? Fortunately Lise Meitner remembered the empirical formula for computing the masses of nuclei and worked out that the two nuclei formed by the division of a uranium nucleus together would be lighter than the original uranium nucleus by about one-fifth the mass of a proton. Now whenever mass disappears energy is created, according to Einstein’s formula E = mc2, and one-fifth of a proton mass was just equivalent to 200 MeV. So here was the source for that energy; it all fitted![98]
“}}

https://en.wikipedia.org/wiki/Ergodic_theory#Mean_ergodic_theorem
QT:{{”
A central concern of ergodic theory is the behavior of a dynamical system when it is allowed to run for a long time. The first result in this direction is the Poincaré recurrence theorem, which claims that almost all points in any subset of the phase space eventually revisit the set. Systems for which the Poincaré recurrence theorem holds are conservative systems; thus all ergodic systems are conservative. More precise information is provided by various ergodic theorems which assert that, under certain conditions, the time average of a function along the trajectories exists almost everywhere and is related to the space average. Two of the most important theorems are those of Birkhoff (1931) and von Neumann which assert the existence of a time average along each trajectory. For the special class of ergodic systems, this time average is the same for almost all initial points: statistically speaking, the system that evolves for a long time “forgets” its initial state. Stronger properties, such as mixing and equidistribution, have also been extensively studied.
“}}

https://en.wikipedia.org/wiki/Reinhold_Bertlmann

QT:{{”
In 1978 Bertlmann went to CERN, where he worked together with J. S. Bell.[1] Bertlmann always wore socks of different colours. In 1981 Bell wrote the article “Bertlmann’s socks and the nature of reality”, where he compared the EPR paradox with Bertlmann’s socks: if you observe one sock to be pink you can predict with certainty that the other sock is not pink. Thus you might assume that quantum
entanglement is just the same. However, this is a non-admissible simplification, and Bell in his article explains why.[2]
“}}

https://en.wikipedia.org/wiki/Fat_Man

QT:{{”
Oppenheimer brought John von Neumann to Los Alamos in September 1943 to take a fresh look at implosion. After reviewing Neddermeyer’s studies, and discussing the matter with Edward Teller, von Neumann suggested the use of high explosives in shaped charges to implode a sphere, which he showed could not only result in a faster assembly of fissile material than was possible with the gun method, but which could greatly reduce the amount of material required, because of the resulting higher density.[8] The idea that, under such pressures, the plutonium metal itself would be compressed came from Teller, whose knowledge of how dense metals behaved under heavy pressure was influenced by his pre-war theoretical studies of the Earth’s core with George Gamow.[9] The prospect of more-efficient nuclear weapons impressed Oppenheimer, Teller, and Hans Bethe, but they decided that an expert on explosives would be required. Kistiakowsky’s name was immediately suggested, and Kistiakowsky was brought into the project as a consultant in October 1943.[8]
“}}

https://en.wikipedia.org/wiki/Eigenfunction

QT:{{”
In the study of signals and systems, an eigenfunction of a system is a signal f(t) that, when input into the system, produces a response y(t) = λf(t), where λ
“}}

https://en.wikipedia.org/wiki/Paul_Dirac#:~:text=Dirac%20was%20known%20among%20his,was%20one%20word%20per%20hour.
QT:{{”
Dirac was known among his colleagues for his precise and taciturn nature. His colleagues in Cambridge jokingly defined a unit called a “dirac”, which was one word per hour.
“}}

https://en.wikipedia.org/wiki/Heligoland

QT:{{”
Werner Heisenberg (1901–1976) first formulated the equation underlying his picture of quantum mechanics while on Heligoland in the 1920s. While a student of Arnold Sommerfeld at Munich in the early 1920s, Heisenberg first met the Danish physicist Niels Bohr. He and Bohr went for long hikes in the mountains and discussed the failure of existing theories to account for the new experimental results on the quantum structure of matter. Following these discussions, Heisenberg plunged into several months of intensive theoretical research but met with continual frustration. Finally, suffering from a severe attack of hay fever, he retreated to the treeless (and pollenless) island of Heligoland in the summer of 1925. There he conceived the basis of the quantum theory.
“}}

https://plato.stanford.edu/entries/russell-paradox/

QT:{{”
John von Neumann’s (1925) untyped method for dealing with paradoxes, and with Russell’s paradox in particular, is simple and ingenious. Von Neumann introduces a distinction between membership and non-membership and, on this basis, draws a distinction between sets and classes. An object is a member (simpliciter) if it is a member of some class; and it is a non-member if it is not a member of any class.
“}}

https://en.wikipedia.org/wiki/Russell%27s_paradox

QT:{{”
Informal presentation Most sets commonly encountered are not members of themselves. For example, consider the set of all squares in the plane. This set is not itself a square in the plane, thus it is not a member of itself. Let us call a set “normal” if it is not a member of itself, and “abnormal” if it is a member of itself. Clearly every set must be either normal or abnormal. The set of squares in the plane is normal. In contrast, the complementary set that contains everything which is not a square in the plane is itself not a square in the plane, and so it is one of its own members and is therefore abnormal. Now we consider the set of all normal sets, R, and try to determine whether R is normal or abnormal. If R were normal, it would be contained in the set of all normal sets (itself), and therefore be abnormal; on the other hand if R were abnormal, it would not be contained in the set of all normal sets (itself), and therefore be normal. This leads to the conclusion that R is neither normal nor abnormal: Russell’s paradox.
“}}