Mathematics

Stephen Wolfram has spent his life to date -- and will likely continue to do so -- developing amazing new computational technologies to empower scientists and academics to more efficiently and effectively compute their way through their research, and even help them to make a few discoveries along the way. Now, Wolfram and his company's decades worth of computational development are being reimplemented into a simple user interface that is accessible to anyone who can ask a question. In particular, the ultimate goal of Wolfram|Alpha is to -- simply! -- "make all systematic knowledge immediately…

Chaos is the disorder of a dynamical system but it is not completely unpredictable.   Researchers are convinced that locating the origin of chaos and watching it develop might allow science to predict, and perhaps counteract, outcomes. Like having a heart attack.  Writing in in the journal CHAOS, researchers say chaos models may someday help model cardiac arrhythmias (abnormal electrical rhythms of the heart) and help to understand the behavior of ventricular fibrillation, a severely abnormal heart rhythm that is often life-threatening, in order to mitigate it. One study found chaos…

I am playing with Coq and Isabelle now :) Formalizing the following: fun p(a) = if (p(a) % 2 = 0) then (p(a div 2)) else (a).The greatest divisor of a, which is power of two = p(a). I want to show that the number of multiplication-addition series always equals p(a+1) and gives odd result for odd, even result for even and follows the formula (((3/2)**(p(a+1)))*a+1)-1.This should be trivial by binary analysis. I want to show that because of this even-odd differentiation, 3n+1 series is never called more than twice in a row. This follows from upper. I want to show that for any even number, all…

It really isn't necessary for me to have an opinion on any topic at hand - it's so much easier to consult the latest poll to know how my fellow humans feel about an issue (and by extension, how I should feel about it too). Hermann Hesse writes that the bourgeoisie "substitute majority for power, law for force, and the polling booth for responsibility," so I should be able to substitute the results of an online poll for the firing of my own synapses.1 Dr. Rugbyologist writes in his article on statistical importance in architecture that "it is extremely important that we regularly convene…

How does a former math teacher in Texas keep winning the lottery?  Joan Ginther has hit four Texas Lottery jackpots and raked in $21 million since 1993 ($5.5 million, half of the Texas Lottery jackpot, that first time).  The last time she won was two years ago ($3 million prize from a scratch ticket).  And then two years before that ($2 million scratch ticket again).  And now $10 million in the $140 million Extreme Payout with a scratch ticket (errr ... again). The chances of that, if those are the only 4 she ever bought, are 1 in 18 septillion - 18,000,000,000,000,000,000…

(updated - more formal, removed some parts and improved general clarity) Over years, I come again and again back to Halting Problem and it's unsolvability ..now I have created a system, which is theoretically able to find halting problems in far larger class of systems than just FSM's. It's based on what I call topological identicalness of abstractions and abstraction of programs - it could, basically, prove somewhat different programs identical if they follow the same logic. It is not meant to be runnable on normal computer - it takes a lot of memory. It's, right now, a pure theory. When it…

Let's say we have 1D cellular automata, bounded at beginning. The following is solution for halting problem - mathematically unproven, somewhat open here and there, but basically very near to what I have seeked. As I have lately rephrased the problem itself and how to solve it, it's here:1. We can not, possibly, find a general solver, but we should look for what is possible. FSM solver has a weakness in that it can not solve theoretical algorithms - solving infinitely growing number, just an iteration, would take a very long time. This is a theoretical infinity we should be able to handle.2.…

The following is based on my idea that there are two main problems related to halting problem: That you can not check if program does not halt. You can always check if it does. That the finite state machine solution does not cope with infinities - it has no way to understand anything about that. It wont detect any infinitely growing program as hanging. Cellular Automata is more pure and mathematical thing than a computer - it does not have this messy differentiation between memory, processor, instruction set or code pointer. Thus it's far better machine to think about halting checkers -…

Consistent with the Standard Model of particle physics, there is postulated a Higgs field which determines those particles which are massive and those which are not. Photons are massless. Gluons also are thought to be massless, but they are not free particles, so their velocity or locus of interaction generally is assumed to be unobservable. What is the nature of the Higgs field? Well, because it determines rest mass, its effects must be Lorentz invariant. Therefore, it must be a differential field in which position is undefined. A similar "field" is that of the vacuum permittivity, which is…

In team sports it is often difficult to determine the value of an individual.   Some sports can do it easily enough, like baseball(1) or basketball, but during the World Cup, casual fans who hear commentators talk about the quality 'form' of a player are lost when the game is 0-0. Jordi Duch, Joshua S. Waitzman and Luís A. Nunes Amaral of Northwestern University say they may have an answer.   How so?  The impact of a player like Robinho of Brazil or Landon Donovan for the US is obvious yet somehow great teams, as we all know, are more than a sum of their individual parts(2) but…