Indeed. That was the remarkable insight of Kurt Gödel (1906–1978), which destroyed formerly triumphant positivist philosophy. When you get to the bottom of the universe (if you do), it’s mostly questions, not answers.
Here, a video series explores Godel’s incompleteness results: The core point is that Hilbert’s scheme collapsed, nicely summarised. The Godel incompleteness results and the Turing machine halting challenge made Mathematics irreducibly complex. So, Mathematics, too, is a venture of knowledge as warranted, credibly true (so reliable) belief, which must be open to correction. An exercise Read More…
Sewell: I cannot think of anything in all of science that can be stated with more confidence than that a few unintelligent forces of physics alone could not have rearranged the basic particles of physics into Apple iPhones.
Newton. The latest year zero reset target, as Telegraph reports: Sir Isaac Newton has been labelled as a potential beneficiary of “colonial-era activity” in draft plans to “decolonise” the engineering curriculum at Sheffield University. Students learning about the mathematician and scientist’s three laws of motion, the core of modern physics, could see changes in their Read More…
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.”