# Jakub Konieczny

Oxford, United Kingdom

Age: 26

 15h awarded Curious 17h awarded Famous Question 2d comment Can Pascal's wager be made to work?The casino example is very valid, but I would already be interested in an argument that roughly "beaks even" (in that the expected utility of X is roughly 0 - as it actually is in casino). Somehow, this is the best I would hope for - even if we understood utility perfectly, you can't give a good estimate for the probability of god's existence. 2d comment Can Pascal's wager be made to work?Cort Ammon, I was writing the second comment before I saw yours, but it happens to partially answer it. I'm not asking that all terms in the expression that you mention be computed - I'm merely asking for sufficiently good estimates. 2d comment Can Pascal's wager be made to work?Note that to argue that the expected utility of a certain action is positive, there is no need even be able to evaluate utility of a single specific action. Pascal does not do it. Instead, he argues that utility of a certain action if God exists is infinite (or at least orders of magnitute larger than anything else involved) so that even rescaled by a factor like 1/1000000 it still dominates all the other terms which would appear. 2d comment Can Pascal's wager be made to work?I'm afraid we are talking at cross purposes here. In particular, I'm quite happy to keep things at a rather informal level, where Tarski's results will not be that much of an issue. I can hardly imagine formalising one's utility so much that these problems may arise. Surely, it is even harder to have a system that is somehow able to describe utility (which is connected to physical world, which is messy and complicated) but at the same time is too weak to include integer arithmetic. 2d comment Can Pascal's wager be made to work?Sure, infinite time multiplied by even a small improvement in utility per unit of time gives infinite utility. However, to make it work you need to assume that the god favours those who pretend to believe over those who do not believe but are generally good people, which I don't think is generally believed. So, there is infinite utility hanging in the balance, but it is not sure which strategy is more likely to give you this infinite improvement. 2d asked Can Pascal's wager be made to work? Nov 26 comment ErdÅ‘s and Szemerédi sums and producsActually, Solymosi's 4/3 have been slightly improved by Shkredov and Konyagin: arxiv.org/pdf/1503.05771.pdf Nov 25 answered How does aptitude at solving Olympiad problems relate to success at further mathematical studies? Nov 25 awarded Nice Question Nov 24 answered Pseudocode in Scientific Article Nov 24 comment Pseudocode in Scientific ArticleWhat kind of code are we talking about? What's the reason why you need to include it? Nov 22 comment Graph Isomorphism for non-mathematicianThat's an interesting perspective - thanks! Nov 22 comment Graph Isomorphism for non-mathematician@Jernej: Thanks! That's helpful, but not quite what I'm looking for (it seems to be aimed at beginner graph theoretists, I'm looking for something for laymen). Nov 21 asked Graph Isomorphism for non-mathematician Nov 20 comment Linear Algebra - finding matrix such that Ker A = ...Surely, you mean that \$Ker A\$ is supposed to be spanned by the vectors you mention. Is \$A\$ supposed to be a square matrix? I'm assuming yes. As long as you are willing to do some brute force computation, what you can do is the following. Let the 3 vectors you mention be \$v_1,v_2,v_3\$ nad pick \$v_4,v_5\$ so that \$v_i\$ are a basis. Next, pick \$u_i\$ so that \$u_1 = u_2 = u_3 = 0\$ and \$u_4,u_5\$ are linearly independent. You can now find (unique!) \$A\$ s.t. \$A v_i = u_i\$. This \$A\$ will do the trick. Nov 10 asked Naive Euclidean algorithm - average complexity? Nov 8 awarded Nice Question Nov 5 awarded Yearling