Uncommon Descent Serving The Intelligent Design Community
Category

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

There is a current conflict among researchers as to whether our number sense is biological or cultural (nature or nurture). But the conflict appears to miss the point: Elaborate number sense depends on the ability to abstract. If that ability is biological, where exactly is it? If it is cultural, it is an iteration of the ability to abstract. Read More ›

Sabine Hossenfelder: Is math real?

Hossenfelder: The physicists who believe in this argue that unobservable universes are real because they are in their math. But just because you have math for something doesn’t mean it’s real. You can just assume it’s real, but this is unnecessary to describe what we observe and therefore unscientific. Read More ›

Can only math solve the mystery at the heart of the universe?

Hartnett, quoting: "“This is [a] very embarrassing thing that we don’t have a single quantum field theory we can describe in four dimensions, nonperturbatively,” said Rejzner. “It’s a hard problem, and apparently it needs more than one or two generations of mathematicians and physicists to solve it.”" Read More ›

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 ›

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

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. Read More ›

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 ›

Eric Holloway asks, What is the essential feature of creative intelligence?

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. Read More ›

Gregory Chaitin: Why “impractical” things like philosophy are actually quite useful

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? Read More ›

Math paradoxes show us that the world we live in is not and cannot be purely naturalist

Robert J. Marks sometimes uses the paradox of the smallest “uninteresting” number to illustrate proof by contradiction — that is, by creating paradoxes Read More ›