i fell for it.
solve this math problem and ill be ur bubble box bitch 4ever
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Elbirn Content Aficionado
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Psyche he/theySurvivor
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after some reading i've decided that these answers are as useless as the one i linked to earlier!
do you guys not know how to type in english- Psyche
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Psyche he/theySurvivor
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let's try working through an example!- GreyICE
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Man, what you have wandered into is a piece of shit called a differential equation. I passed Diff Eq with a C, and I'm quite proud of that C. I worked harder for that C than I did for a lot of the As I got and I was in engineering. The guy next to me was on his fifth year, and had failed exactly two classes for his civil engineering degree. Differential Equations. Twice.
A differential equation is an equation such that the input of the equation is the function of the output. There are small, small islands of solveable differential equations. They are afloat in an infinite ocean of ones that we cannot possibly solve. I don't mean that we haven't solved. There are mathematical proofs that many parts of the ocean are utterly impossible to solve. Other parts of the ocean have solutions that would require several decades to understand. Even looking at them too long makes your head start to hurt. I didn't believe in the Lovecraft until I saw them, but it was then I realized that there were concepts so alien that understanding the language they were formed in was an impediment to understanding and that ignorance could be a shield from madness.
TLDR: Fucking simulate it you prick, I don't have the time or the knowledge to tell if you've managed through sheer dumb luck to stumble onto one of the rare islands where the fucking equation is solveable, but I doubt it severely. Or find a mathematics PhD with spare time. But don't expect the explanation to be anything other than Cthulu speakShowThat which is done out of love always takes place beyond good and evil
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Yeah hilariously a lot of the equations we use a lot are completely impossible to solve. Like Navier-Stokes. Describes everything from how water moves in pipes to how airplanes fly. Not the littlest inkling as to how we might go about solving it. Like... no hope. Not one bit of it.
Solveable equations are nice and fun and what you usually find in textbooks, but they're a small and select subset.ShowThat which is done out of love always takes place beyond good and evil
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In post 28, Psyche wrote:let's try working through an example!
Ok, like there are many explanations already so here's a worked example.
Here's the transition matrix from your first post:
http://www.wolframalpha.com/input/?i=ei ... 0.5%5D+%5D
You need to transpose the matrix, think of using the equations like:
next state is R = 0.6 * R + 0.5 * B
next state is B = 0.4 * R + 0.5 * B
Then look at the eigenvectors of this matrix. The one you want is the one that can be a valid state with all positive probabilities, so it's (0.780869, 0.624695).
Wolfram alpha has helpfully given you a unit vector as its result. But for your probability vector, you want the components to sum to one. So calculate. (0.780869, 0.624695)/((0.780869 + 0.624695) to make this happen and you get:
(0.55555, 0.444444) and which is the long-term steady state of your transitions. So you'd expect 5/9 red and 4/9 blue.- Kagami
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I don't understand, you were provided an exact solution that can be computed in O (numsteps*numcolors^2) time for the finite case and also a solution for the infinite case.In post 27, Psyche wrote:after some reading i've decided that these answers are as useless as the one i linked to earlier!
do you guys not know how to type in english- Kagami
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by useless i don't mean totally useless; merely as useless as the answer i already had!
i was complaining about having to think- Psyche
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mole's post makes everything crystal clear though!
it's basically a clearer version of the answer that the dudes at stackexchange gave me!
i bet i could explain this to a third grader!- Kagami
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Keep in mind, the eigenvector solution isn't entirely complete. There can be multiple steady states, corresponding to multiple valid eigenvectors.
In that case, you have to consider the probability of falling into each one. Conveniently, since they're nonnegative and orthogonal, they must be non-overlapping.Last edited by Kagami on Sat Jun 18, 2016 10:03 am, edited 1 time in total. - Kagami
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