Holloway: To discover the principle of all principles would cut off the very limb we are sitting upon. That is why the very nature of creative intelligence, though we can catch glimpses of it, will remain forever outside our grasp.
Chaitin reflects on the fact that if he had to do practical work 60 years ago, there wouldn’t be practical research today based on the Omega number. But that raises a question: If materialism were true, why does theoretical stuff matter so much?
His takehome point: “Common Core is not as radical as the New Math of the 1950s, but both make the fatal error of prioritizing the thoughts of adults over those of students.”
Robert J. Marks sometimes uses the paradox of the smallest “uninteresting” number to illustrate proof by contradiction — that is, by creating paradoxes
And what were you doing during the COVID-19 lockdowns? 😉
Decades ago, Gregory Chaitin reminds us, mathematicians were not forced by the rules of the academic establishment to keep producing papers, so they could write key books.
In recent months we have had several forum threads, which naturally tend to throw up onward topics worth headlining. Here, I will headline some observations on implication logic in deductive and in inductive reasoning. However, first, the core of the logic of implication. Algebraically, p => q is analysed as ~[p AND ~q]. Interpreted, for Read More…
Chaitin, best known for Chaitin’s unknowable number: “Some mathematics, I think, is definitely invented, not discovered. That tends to be trivial mathematics … But other mathematics does seem to be discovered. That’s when you find some really deep, fundamental mathematical idea, and there it really looks inevitable. “
One suspects that disliking Newton wouldn’t mean embracing widespread innumeracy. But the trend to deplatforming major math and science figures will likely end no other way. Why study what one is taught to despise?
Chaitin: You see, with the normal coin tosses, actually every possible finite sequence of heads and tails in a sense is equally random, because they were all generated by tossing a fair coin. But some of them, all heads has a lot of structure, all tails have a lot of structure, alternating heads and tails have a lot of structure. I was looking at something that ignored how the sequence is generated and just looked at it and said, is there structure here or isn’t there?
More scandalous still, Gödel was not a Darwinist: “I believe that mechanism in biology is a prejudice of our time which will be disproved.”
The people who don’t think complex numbers really exist would probably not be happy with quantum mechanics being even more non-local without them. But of course, if complex numbers really do exist, then immaterial things really exist. Not a good time to be a hard core materialist.
Chaitin offers some thoughts on Georg Cantor and Srinivasa Ramanujan as well, both of whom thought that their math discoveries were divinely inspired.
Daily Mail reports on a class assignment for seven year olds that happened to be set for the daughter of a Mathematics Lecturer at Oxford. Maths lecturer is left baffled by his seven-year-old daughter’s geometry homework and turns to Twitter for help – so can YOU work out if it’s true or false? Dr Kit Read More…
Bartlett: … one thing that is helpful for parents, students, and teachers is for students to show their work. I know it can be hard to get students to do this. My own children hate to do it. However, being explicit about the steps in their reasoning is important for a number of reasons. First, showing their work helps students with harder problems… So, what does Equitable Math say about this practice? According to their published guide, “White supremacy culture shows up in math class when students are required to show their work”