Links for 2022-12-03
We might well end the flu and colds in the next few decades. Using mRNA for flu vaccine looks promising, animal trials show it provides generalized flu protection. https://statnews.com/2022/11/24/experimental-flu-vaccine-developed-using-mrna-seen-as-potential-game-changer
“How could AI become as curious as humans? We're presenting a simple and scalable generalization of curiosity-driven exploration to help agents tell the difference between “noise” and “novelty - and stay robust in uncertain environments.” https://arxiv.org/abs/2211.10515
Introducing DeepNash - the first AI to master Stratego, a game of hidden information which is more complex than chess, Go and poker. https://www.deepmind.com/blog/mastering-stratego-the-classic-game-of-imperfect-information
“Could AI help people with a wide range of views find agreement? Our team fine-tuned a 70 billion parameter language model to generate statements that could bring consensus among groups with diverse opinions.” https://arxiv.org/abs/2211.15006
AI experts are increasingly afraid of what they’re creating https://www.vox.com/the-highlight/23447596/artificial-intelligence-agi-openai-gpt3-existential-risk-human-extinction
Feuerbach’s nine-point circle theorem https://www.johndcook.com/blog/2022/11/24/feuerbach/
“This theorem is surprising because out of a triangle with no symmetry pops a triangle with three-fold symmetry.” https://www.johndcook.com/blog/2022/11/30/unexpected-symmetry/
A geometric proof of the impossibility of angle trisection by straightedge and compass https://terrytao.wordpress.com/2011/08/10/a-geometric-proof-of-the-impossibility-of-angle-trisection-by-straightedge-and-compass/
Escher sentences: “More policewomen visited the headquarters than he did.” https://en.wikipedia.org/wiki/Comparative_illusion
Garden-path sentences: “The old man the boat.” https://en.wikipedia.org/wiki/Garden-path_sentence
“Generally, speaking, the use of obscenities in books was close to zero before 1960, and didn't really get off the ground until the 1970s.” https://jabberwocking.com/raw-data-what-popular-obscenity-has-grown-the-most/
The Twitter Files, Part One: How and Why Twitter Blocked the Hunter Biden Laptop Story https://threadreaderapp.com/thread/1598822959866683394.html
Richard's paradox: https://en.wikipedia.org/wiki/Richard%27s_paradox
The paradox begins with the observation that certain expressions of natural language define real numbers unambiguously, while other expressions of natural language do not. For example, "The real number the integer part of which is 17 and the nth decimal place of which is 0 if n is even and 1 if n is odd" defines the real number 17.1010101... = 1693/99, whereas the phrase "the capital of England" does not define a real number, nor the phrase "the smallest positive integer not definable in under sixty letters" (see Berry's paradox).
There is an infinite list of English phrases (such that each phrase is of finite length, but the list itself is of infinite length) that define real numbers unambiguously. We first arrange this list of phrases by increasing length, then order all phrases of equal length lexicographically, so that the ordering is canonical. This yields an infinite list of the corresponding real numbers: r_1, r_2, ... . Now define a new real number r as follows. The integer part of r is 0, the nth decimal place of r is 1 if the nth decimal place of r_n is not 1, and the nth decimal place of r is 2 if the nth decimal place of r_n is 1.
The preceding paragraph is an expression in English that unambiguously defines a real number r. Thus r must be one of the numbers r_n. However, r was constructed so that it cannot equal any of the r_n (thus, r is an undefinable number). This is the paradoxical contradiction.
Note that this paradox is not about whether the defined subset of real numbers is countable. The problem here is the self-referential character of the metalanguage, not countability. Diagonalization is used to highlight this problem rather than prove that the set in question is uncountable. Richard's paradox is self-referential since the defined phrase refers to all phrases that define real numbers, including itself.