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Mathematics

[L&FP 39:] Implication logic is pivotal to understanding how we think as duty-bound rational creatures

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 whatever reason, p being so is sufficient for q to also be so. This compound proposition does NOT assert that p, only that p is sufficient for q. Similarly, q is NECESSARY for p, i.e. if q can be false and p true, q is not implied by p. As a bare structure, this is termed material implication, fleshing out the why of the implication Read More ›

Gregory Chaitin’s take on: Was math invented or discovered?

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. " Read More ›

Gregory Chaitin on true randomness

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? Read More ›

Kurt Gödel was unhappy with atheism and finally he blasted one fashionable type to smithereens

More scandalous still, Gödel was not a Darwinist: “I believe that mechanism in biology is a prejudice of our time which will be disproved.” Read More ›

Sabine Hossenfelder asks, Do complex numbers exist?

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. Read More ›

Gregory Chaitin (of Chaitin’s number fame) muses on what makes the great mathematicians stand out

Chaitin offers some thoughts on Georg Cantor and Srinivasa Ramanujan as well, both of whom thought that their math discoveries were divinely inspired. Read More ›

Semi-circles and right angle dilemmas . . .

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 Yates shares his seven-year-old daughter’s maths homework to Twitter The question asked students whether a semi-circle had ‘two right angles’ or not The maths lecturer, from Oxford, admitted that he was stumped by the problem  People were left baffled by the question and came up with conflicting answers  By Kate Dennett For Mailonline Published: 17:40 GMT, 25 February 2021 | Updated: 17:40 GMT, 25 February Read More ›

Jonathan Bartlett: Antiracism in Math Promotes Racism and Bad Math

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" Read More ›

Chronicles of the war on math: Why math is racist

Wethinks that the big winners are teachers who can’t teach, protected by unions. The big losers are kids who leave school innumerate and must cope with a workplace that no longer needs innumerate people. We have machines now. Read More ›

Fun: Why is a human body halfway between the mass of a proton and the sun?

That’s what they say, anyway, at Wolfram Math: “The human body has a mass that, more or less, is halfway between the mass of the proton (~1.672×10 ² kg) and the mass of the Sun (~1.988×10³ kg). A value very close to the mass of an average human body is the geometric mean of those two values”