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Mathematics is an useful model for reality.However, most inventions that claims that use mathematics are only inspired by mathematics. Sometimes the mathematics was created after the fact. Encryption...
Russel's paradox is defining "the set of all sets that don't contain themselves". You can show that such construct leads to a contradiction. Read the wiki link for details. I started this article as a...
In my 5'th grade, the new professor of Mathematics told us a puzzle: there is a jug with water staying in the desert, and a bird wants to drink some water. However, the jug have a tight neck, like the...
This article contains my personal reflections on irrational numbers, especially the informational property of their infinite strings of decimal - strings that often look close to random at a shallow l...
Please check my informal introduction to "Kolmogorov complexity" if you are not familiar with the subject. In this article I will approach some less discussed ramifications of it and hopefully some ne...
I define intelligence as the capacity of one entity to create complex internal representations that can be used to predict about it's environment the likely outcome from a particular configuration or...
"P equals NP?" is a million dollars unsolved problem. Introduction "P" is the class of problems where we have algorithms that solves the problem in polynomial time. "NP" is the class of problems havin...
In a temperate musical octave, there are 12 possible sounds. However, in a certain melody, usually, only 7 of them are used. When you see, for example, "Symphony...in Do major", you should expect that...
We have this requirement: "Create the smallest program that will print the full text of the play Othello by William Shakespeare". I should warn you that the requirement hides a trick and you will hate...
I will argue below that sorting of a big array, using only comparison, is inherently harder than solving the problem of choosing the best next move on a chess game. One could say that it is not fair t...