11 Matching Annotations
1. May 2023
2. oeis.org oeis.org
1. Related to this note:

Haris Neophytou wants to apply a "primality sieve" (namely the sieve of Eratosthenes) to this list. I think it's so he can construct the primes that divide the order of the monster group $$M$$

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3. oeis.org oeis.org
1. Trying to follow an argument given here: https://youtu.be/mFZs7uGwNBo?t=3413

The sequence A002267 is claimed by Haris Neophytou to be the 1st 15 "super singular prime numbers" (ie, the primes that divides the order of the Monster Group). The order is the number of elements in the group.

Note that the last 3 elements [47, 59, 71] multiply to give the number of dimensions in which the Monster group exists: 196,883.

Neophytou believes A002267 gives a different way of looking at the monster group $$M$$.

Around 1:02:45, Neophytou says he'll start from A002822...

(a list of numbers, $$m\text{,}$$ such that $$6m - 1$$ and $$6m + 1$$ are twin primes)

... and construct "the minimal order of the monster" (what?)

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4. Apr 2023
5. www.popularmechanics.com www.popularmechanics.com
1. Only small tidbits of math remain unresolved for Rubik’s Cube. While God’s number is 20, it’s unknown exactly how many of the 43,252,003,274,489,856,000 combinations require a whole 20 moves to be solved.

We've got solutions for the number of configurations there are to solve a Rubic's cube with from 1 move up to 15, but we don't know how many cube configurations there are that can be solved with 16-20 moves.

• Example: the number of positions that require exactly one move solve them is 18, which is counted by multiplying the six faces and each of the three ways they can be twisted.

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6. Jan 2023
7. ncatlab.org ncatlab.org
1. In particular Erwin Schrödinger is said (Wigner (1981)) to have spoken of the Gruppenpest (German for “plague of group theory”) which ought to be abandoned. In his autobiography John Slater, an MIT physicist, claimed: It was at this point that Wigner, Hund, Heitler, and Weyl entered the picture with their “Gruppenpest”: the pest of the group theory… The authors of the “Gruppenpest” wrote papers which were incomprehensible to those like me who had not studied group theory, in which they applied these theoretical results to the study of the many electron problem. The practical consequences appeared to be negligible, but everyone felt that to be in the mainstream one had to learn about it. Yet there were no good texts from which one could learn group theory. It was a frustrating experience, worthy of the name of a pest. I had what I can only describe as a feeling of outrage at the turn which the subject had taken… As soon as this [Slaters] paper became known, it was obvious that a great many other physicists were as disgusted as I had been with the group-theoretical approach to the problem. As I heard later, there were remarks made such as “Slater has slain the ‘Gruppenpest’”. I believe that no other piece of work I have done was so universally popular.

Gruppenpest, a word of German origin, which has also entered into English to mean "the plague of group theory" and group theorists (mathematicians) who were applying abstract algebra to physics and quantum mechanics in the mid-twentieth century.

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8. inference-review.com inference-review.com

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9. docdrop.org docdrop.org
1. Woit, Peter. Quantum Theory, Groups and Representations: An Introduction. Revised and Expanded version [2022]. Springer, 2017. https://www.math.columbia.edu/~woit/QM/qmbook.pdf.

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10. Aug 2022
11. www.nytimes.com www.nytimes.com
1. MacFarquhar, N. (2021, March 26). Far-Right Extremists Move From ‘Stop the Steal’ to Stop the Vaccine. The New York Times. https://www.nytimes.com/2021/03/26/us/far-right-extremism-anti-vaccine.html

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12. Sep 2021
13. www.nytimes.com www.nytimes.com
1. This is the theory of the extended mind, introduced more than two decades ago by the philosophers Andy Clark and David Chalmers. A 1998 article of theirs published in the journal Analysis began by posing a question that would seem to have an obvious answer: “Where does the mind stop and the rest of the world begin?” They went on to offer an unconventional response. The mind does not stop at the usual “boundaries of skin and skull,” they maintained. Rather, the mind extends into the world and augments the capacities of the biological brain with outside-the-brain resources.

Where does the mind stop and the rest of the world begin?

There seems to be a parallel between this question and that between the gene and the body. Evolution is working at the level of the gene, but the body and the environment are part of the extended system as well. Link these to Richard Dawkins idea of the extended gene and ideas of group selection.

Are there effects to be seen on the evolutionary scale of group selection ideas with respect to the same sorts of group dynamics like the minimal group paradigm? Can the sorts of unconscious bias that occur in groups be the result of individual genes? This seems a bit crazy, but potentially worth exploring if there are interlinked effects based on this analogy.

2. One last resource for augmenting our minds can be found in other people’s minds. We are fundamentally social creatures, oriented toward thinking with others. Problems arise when we do our thinking alone — for example, the well-documented phenomenon of confirmation bias, which leads us to preferentially attend to information that supports the beliefs we already hold. According to the argumentative theory of reasoning, advanced by the cognitive scientists Hugo Mercier and Dan Sperber, this bias is accentuated when we reason in solitude. Humans’ evolved faculty for reasoning is not aimed at arriving at objective truth, Mercier and Sperber point out; it is aimed at defending our arguments and scrutinizing others’. It makes sense, they write, “for a cognitive mechanism aimed at justifying oneself and convincing others to be biased and lazy. The failures of the solitary reasoner follow from the use of reason in an ‘abnormal’ context’” — that is, a nonsocial one. Vigorous debates, engaged with an open mind, are the solution. “When people who disagree but have a common interest in finding the truth or the solution to a problem exchange arguments with each other, the best idea tends to win,” they write, citing evidence from studies of students, forecasters and jury members.

Thinking in solitary can increase one's susceptibility to confirmation bias. Thinking in groups can mitigate this.

How might keeping one's notes in public potentially help fight against these cognitive biases?

Is having a "conversation in the margins" with an author using annotation tools like Hypothes.is a way to help mitigate this sort of cognitive bias?

At the far end of the spectrum how do we prevent this social thinking from becoming groupthink, or the practice of thinking or making decisions as a group in a way that discourages creativity or individual responsibility?

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14. May 2020
15. www.annualreviews.org www.annualreviews.org
1. Edelmann, A., Wolff, T., Montagne, D., & Bail, C. A. (2020). Computational Social Science and Sociology. Annual Review of Sociology, 46(1), annurev-soc-121919-054621. https://doi.org/10.1146/annurev-soc-121919-054621

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16. Sep 2016
17. www.aei.org www.aei.org
1. First, according to Trumbull, Olson underestimates diffuse groups’ ability to develop compelling narratives about how they serve the public interest. In fact, weak, diffuse groups have a paradoxical political advantage: precisely because they are weak and diffuse, the public sees them as less self-interested and thus comparatively trustworthy. Second, Olson also underestimates the power of ideological motivation, rather than just money and concentration, to spur activism. Third, “diffuse interests can be represented without mobilization,” thanks to activism by politicians and government officials who take up their cause. (FDR started a federal pension program at a time when “retirees,” as a self-identified social class, did not yet exist. The program created the constituency, rather than the other way around.) Fourth, weak or diffuse interests can link up with concentrated groups to amplify their effectiveness, as when consumers align with exporters to oppose trade protections or when free-speech advocates join with political parties to oppose campaign-finance limits.