Mathematics
The 3n + 1/ n/2 conjecture
Here is an example of how numbers can give us hard puzzles: The obvious point, for the naturals is that 3n + 1 converts an odd to an even and division by two pulls out an odd factor or else gets into the chain of powers of two, which has precisely one odd member, 1. Where, of course, conveniently, 3 * 1 + 1 is 4. Thus the halting loop. (The negatives bring in other loops on their side of zero.) So, the [pseudo-?]algorithm — does it always halt? — is searching for the ladder of powers of 2. Find it and you halt, fail and you explode into a halting fail. Or, is there another loop in the positive Read More ›
At Mind Matters News: Why animals can count but can’t do math
Sabine Hossenfelder: Is math real?
How do humans have a number sense?
Can only math solve the mystery at the heart of the universe?
L&FP 45: The Hypothetical Syllogism — a lecture
Here: This syllogism is of considerable practical importance: This raises the issue of denying the consequent, ~q. If p –> q and ~q, then as q is necessary for p, ~p. Where, p is sufficient for q, by reason of its core characteristics, the states of affairs associated with p, causal power, requirement of logic of being etc. Let us note, p –> q is equivalent in import to ~q –> ~p. (Let’s add, that denying the antecedent, thinking this falsifies the consequent also fails, p –> q does not mean there isn’t another way, say r, to get q. There’s more than one way to skin a cat-fish.) Connected to ID, Newton’s rules demand that causal adequacy be shown Read More ›
Is there a hole at the bottom of math?
L&FP, 42a: The limit on Mathematical knowledge
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 of rational, responsible faith, not utter certainty on the whole, once a sufficiently complex system is on the table. (Yes, first duties of reason obtain . . . here, there be dragons that love chick peas [Cicero . . .].) The defeasible [= defeat-able] framework for understanding knowledge extends to Mathematics. A fortiori to Computer Science and Physics, then onward across the spectrum of disciplines Read More ›
Granville Sewell on origin of life as a provably unsolvable problem
Then, they came for Sir Isaac . . .
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 teaching to explain the “global origins and historical context” of his theories, documents suggest. The plans form part of the engineering faculty’s efforts to “challenge long-standing conscious and unconscious biases” among students to tackle “Eurocentric” and “white saviour” approaches to science and maths, and promote “inclusive design”. When objectivity, core physical science and core Math are demonised through implicit, euphemistic tagging as racist, it is Read More ›