hackandthink

Thanks, nice explanation.

"However, by taking advantage of two classical bits and an entangled qubit pair" Yes one needs entanglement. https://qiskit.org/textbook/ch-algorithms/teleportation…

"one can send two classical bits to teleport one qubit" How do you do this? (it goes against my intuition of a qubit as state in a hilbert space)

This won't happen and the paper does not speculate in any way about it. But they are vague about the implications and I'm generally unsure about the practical relevance of quantum protocols …

Thanks, I'm not confused anymore.

I am confused: "From a proof-theoretic perspective, Heyting’s calculus is a restriction of classical logic in which the law of excluded middle and double negation elimination have been removed&qu…

"The well-ordering theorem together with Zorn's lemma are the most important mathematical statements that are equivalent to the axiom of choice" This is all crazy stuff, but it would be…

OK, original poster doesn't speak about computable numbers: "consider the set of numbers that cannot be described using any finite collection of symbols" But I have a hard time acceptin…

I would pick Chaitin's constant. It is not only transcendantal like Pi, it is even uncomputable, so it would be part of his counterexample set. (Pi is computable, so you can describe it with an a…

Banach-Tarski from a constructivist/intuitionistic point of view: "So it really seems that when we switch to constructive theory, it actually does something even better, it eliminates this p…

I fully agree. Every judge and laywer should understand: base rate fallacy and cold hits. (and everyone should understand: Simpson's paradox, Regression toward the mean, NHST problems )

Probability is hard to understand and it means different things in different contexts. (is it only about knowledge or is it out there in the world) If it is hard for Andrew Gelman it may be too hard f…

Thanks for the link to the excellent article. Emmanuel Todd seems to me quite reasonable for a French intellectual. He analyzes the German confusion and helplessness quite aptly. (I don't underst…

"Why Small Modular Reactors Can’t Compete With Renewable Energy" "So the physics of thermal efficiency are important. So is modularity and manufacturability. There’s an optimizing curve…

Racial issues are part of military history: "Secondly, racial tensions between white and black soldiers and marines increased after the assassination of Martin Luther King Jr. in April 1968."…

The title of the post promises to much. "In a Moment, Mathematicians Merge Probability and Number Theory" - I really expected some deep connections between Probability and Number Theory. I d…

thanks

Thanks. I'm somewhat lost, but it seems to work Gödel like. The statement is true (equation has no solution) but we can't prove it.

My understanding: There's no algorithm to decide. But for any equation we can be lucky to find a solution or a proof that there's no solution. But this doesn't prove that there is an eq…

A nice article with a nice equation: 42 = -80538738812075974^3 + 80435758145817515^3 + 12602123297335631^3 Douglas Adams would rejoice. (checked it in bc) Some Background from Wikipedia: https:/…

Laziness enables doing computing/statistics with stochastic processes with infinitely many points. (e.g. Gaussian process regression) https://dl.acm.org/doi/pdf/10.1145&…