| aminer68@gmail.com: Jun 07 03:53PM -0700 Hello, Read the following webpage from Yale school of management, it says: "Intelligence is about brain power whereas rational thinking is about control." Read the following carefully: Why a high IQ doesn't mean you're smart https://som.yale.edu/news/2009/11/why-high-iq-doesnt-mean-youre-smart So notice that i have "generalized" it more and i just said the following: I think i am more smart, and i think that Mensa IQ tests are not testing correctly intelligence, because they are lacking to test a very important thing in intelligence, it is what we call being "rigorous" in your thinking, i mean that there is humans that are genetically more rigorous thinking than others, and i am of the ones that are genetically more rigorous in thinking than average white european humans, and this genetically more rigorous in the thinking process is also part of human intelligence , but it is not tested by Mensa IQ tests, and this genetically more rigorous than average in the thinking process also permits you to be high quality thinking than average and it permits you to be efficiently selective of knowledge or of the thinking, that means it also permits you to know how to select what is high quality knowledge or what is high quality thinking. So as you will notice in the following that i am more rigorous in my thinking than average people, because notice how i am doing mathematics and speaking about the conditions required for the Markov chain to find its way to an equilibrium distribution, so that you understand more easily the PageRank Algorithm and so that you understand more easily the Markov chains, read again carefully my following thoughts to notice it: I was just reading the following webpage: PageRank Algorithm - The Mathematics of Google Search http://pi.math.cornell.edu/~mec/Winter2009/RalucaRemus/Lecture3/lecture3.html I think this webpage above is not rigorous mathematics, because you have to speak about the conditions required for the Markov chain to find its way to an equilibrium distribution, so read my following tutorial to understand: My name is Amine Moulay Ramdane, i will talk about Markov chains in mathematics.. In mathematics, many Markov chains automatically find their own way to an equilibrium distribution as the chain wanders through time. This happens for many Markov chains, but not all. I will talk about the conditions required for the chain to find its way to an equilibrium distribution. If in mathematics we give a Markov chain on a finite state space and asks if it converges to an equilibrium distribution as t goes to infinity, an equilibrium distribution will always exist for a finite state space, but you need to check whether the chain is irreducible and aperiodic. If so, it will converge to equilibrium. If the chain is irreducible but periodic, it cannot converge to an equilibrium distribution that is independent of start state. If the chain is reducible, it may or may not converge. So i will give an example: Suppose that for the course you are currently taking there are two volumes on the market and represent them by A and B. Suppose further that the probability that a teacher using volume A keeps the same volume next year is 0.4 and the probability that it will change for volume B is 0.6. Furthermore the probability that a professor using B this year changes to next year for A is 0.2 and the probability that it again uses volume B is 0.8. We notice that the matrix of transition is: 0.4 0.6 0.2 0.8 The interesting question for any businessman is whether his market share will stabilize over time. In other words, does it exist a probability vector (t1, t2) such that: (t1, t2) * (transition matrix above) = (t1, t2) [1] So notice that the transition matrix above is irreducible and aperiodic, so it will converge to an equilibrum distribution that is (t1, t2) that i will mathematically find, so the system of equations of [1] above is: 0.4 * t1 + 0.2 * t2 = t1 0.6 * t1 + 0.8 * t2 = t2 this gives: -0.6 * t1 + 0.2 * t2 = 0 0.6 * t1 - 0.2 * t2 = 0 But we know that (t1, t2) is a vector of probability, so we have: t1 + t2 = 1 So we have to solve the following system of equations: t1 + t2 = 1 0.6 * t1 - 0.2 * t2 = 0 So i have just solved it with R, and this gives the vector: (0.25,0.75) Which means that in the long term, volume A will grab 25% of the market while volume B will grab 75% of the market unless the advertising campaign does change the probabilities of transition. Thank you, Amine Moulay Ramdane. |
| aminer68@gmail.com: Jun 07 01:49PM -0700 Hello... Read again, i correct about more political philosophy about what is abstract reasoning.. I think i am more smart, and i think that Mensa IQ tests are not testing correctly intelligence, because they are lacking to test a very important thing in intelligence, it is what we call being "rigorous" in your thinking, i mean that there is humans that are genetically more rigorous thinking than others, and i am of the ones that are genetically more rigorous in thinking than average white european humans, and this genetically more rigorous in the thinking process is also part of human intelligence , but it is not tested by Mensa IQ tests, and this genetically more rigorous than average in the thinking process also permits you to be high quality thinking than average and it permits you to be efficiently selective of knowledge or of the thinking, that means it also permits you to know how to select what is high quality knowledge or what is high quality thinking. So as you will notice in the following that i am more rigorous in my thinking than average people, because notice how i am doing mathematics and speaking about the conditions required for the Markov chain to find its way to an equilibrium distribution, so that you understand more easily the PageRank Algorithm and so that you understand more easily the Markov chains, read again carefully my following thoughts to notice it: I was just reading the following webpage: PageRank Algorithm - The Mathematics of Google Search http://pi.math.cornell.edu/~mec/Winter2009/RalucaRemus/Lecture3/lecture3.html I think this webpage above is not rigorous mathematics, because you have to speak about the conditions required for the Markov chain to find its way to an equilibrium distribution, so read my following tutorial to understand: My name is Amine Moulay Ramdane, i will talk about Markov chains in mathematics.. In mathematics, many Markov chains automatically find their own way to an equilibrium distribution as the chain wanders through time. This happens for many Markov chains, but not all. I will talk about the conditions required for the chain to find its way to an equilibrium distribution. If in mathematics we give a Markov chain on a finite state space and asks if it converges to an equilibrium distribution as t goes to infinity, an equilibrium distribution will always exist for a finite state space, but you need to check whether the chain is irreducible and aperiodic. If so, it will converge to equilibrium. If the chain is irreducible but periodic, it cannot converge to an equilibrium distribution that is independent of start state. If the chain is reducible, it may or may not converge. So i will give an example: Suppose that for the course you are currently taking there are two volumes on the market and represent them by A and B. Suppose further that the probability that a teacher using volume A keeps the same volume next year is 0.4 and the probability that it will change for volume B is 0.6. Furthermore the probability that a professor using B this year changes to next year for A is 0.2 and the probability that it again uses volume B is 0.8. We notice that the matrix of transition is: 0.4 0.6 0.2 0.8 The interesting question for any businessman is whether his market share will stabilize over time. In other words, does it exist a probability vector (t1, t2) such that: (t1, t2) * (transition matrix above) = (t1, t2) [1] So notice that the transition matrix above is irreducible and aperiodic, so it will converge to an equilibrum distribution that is (t1, t2) that i will mathematically find, so the system of equations of [1] above is: 0.4 * t1 + 0.2 * t2 = t1 0.6 * t1 + 0.8 * t2 = t2 this gives: -0.6 * t1 + 0.2 * t2 = 0 0.6 * t1 - 0.2 * t2 = 0 But we know that (t1, t2) is a vector of probability, so we have: t1 + t2 = 1 So we have to solve the following system of equations: t1 + t2 = 1 0.6 * t1 - 0.2 * t2 = 0 So i have just solved it with R, and this gives the vector: (0.25,0.75) Which means that in the long term, volume A will grab 25% of the market while volume B will grab 75% of the market unless the advertising campaign does change the probabilities of transition. Thank you, Amine Moulay Ramdane. |
| aminer68@gmail.com: Jun 07 01:42PM -0700 Hello, More political philosophy about what is abstract reasoning.. I think i am more smart, and i think that Mensa IQ tests are not testing correctly intelligence, because they are lacking to test a very important thing in intelligence, it is what we call being "rigorous" in your thinking, i mean that there is humans that are genetically more rigorous thinking than others, and i am of the ones that are genetically more rigorous in my thinking than average humans, and this genetically more rigorous in the thinking process is also part of human intelligence , but it is not tested by Mensa IQ tests, and this genetically more rigorous than average in the thinking process also permits you to be high quality thinking than average and it permits you to be efficiently selective of knowledge or of the thinking, that means it also permits you to know how to select what is high quality knowledge or what is high quality thinking. So as you will notice in the following that i am more rigorous in my thinking than average people, because notice how i am doing mathematics and speaking about the conditions required for the Markov chain to find its way to an equilibrium distribution, so that you understand more easily the PageRank Algorithm and so that you understand more easily the Markov chains, read again carefully my following thoughts to notice it: I was just reading the following webpage: PageRank Algorithm - The Mathematics of Google Search http://pi.math.cornell.edu/~mec/Winter2009/RalucaRemus/Lecture3/lecture3.html I think this webpage above is not rigorous mathematics, because you have to speak about the conditions required for the Markov chain to find its way to an equilibrium distribution, so read my following tutorial to understand: My name is Amine Moulay Ramdane, i will talk about Markov chains in mathematics.. In mathematics, many Markov chains automatically find their own way to an equilibrium distribution as the chain wanders through time. This happens for many Markov chains, but not all. I will talk about the conditions required for the chain to find its way to an equilibrium distribution. If in mathematics we give a Markov chain on a finite state space and asks if it converges to an equilibrium distribution as t goes to infinity, an equilibrium distribution will always exist for a finite state space, but you need to check whether the chain is irreducible and aperiodic. If so, it will converge to equilibrium. If the chain is irreducible but periodic, it cannot converge to an equilibrium distribution that is independent of start state. If the chain is reducible, it may or may not converge. So i will give an example: Suppose that for the course you are currently taking there are two volumes on the market and represent them by A and B. Suppose further that the probability that a teacher using volume A keeps the same volume next year is 0.4 and the probability that it will change for volume B is 0.6. Furthermore the probability that a professor using B this year changes to next year for A is 0.2 and the probability that it again uses volume B is 0.8. We notice that the matrix of transition is: 0.4 0.6 0.2 0.8 The interesting question for any businessman is whether his market share will stabilize over time. In other words, does it exist a probability vector (t1, t2) such that: (t1, t2) * (transition matrix above) = (t1, t2) [1] So notice that the transition matrix above is irreducible and aperiodic, so it will converge to an equilibrum distribution that is (t1, t2) that i will mathematically find, so the system of equations of [1] above is: 0.4 * t1 + 0.2 * t2 = t1 0.6 * t1 + 0.8 * t2 = t2 this gives: -0.6 * t1 + 0.2 * t2 = 0 0.6 * t1 - 0.2 * t2 = 0 But we know that (t1, t2) is a vector of probability, so we have: t1 + t2 = 1 So we have to solve the following system of equations: t1 + t2 = 1 0.6 * t1 - 0.2 * t2 = 0 So i have just solved it with R, and this gives the vector: (0.25,0.75) Which means that in the long term, volume A will grab 25% of the market while volume B will grab 75% of the market unless the advertising campaign does change the probabilities of transition. Thank you, Amine Moulay Ramdane. |
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