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Monthly Archives: March 2011
Hilbert with Ladders, 2004 by Don Relyea (Source: http://www.donrelyea.com)
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Tagged abstract algebra, art, complex numbers, curves, Hilbert space, mathematics
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Noncommutative distances between industries
The distance from your house to the grocery must be the same as the distance back, but 20thcentury mathematicians speculated about circumstances where this might not be the case. Very smallscale physics is noncommutative in some ways and so is … Continue reading
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Tagged Abelian, asymmetric, asymmetry, business, business school, commutativity, distance, investment banking, marketing, math, mathematics, maths, metric, nonAbelian, noncommutative, noncommutative, PR, quantum field theory, quantum physics, quasimetric, quasimetrics, symmetric, symmetry
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You know what’s surprising? Rotations are linear transformations. I guess lo conocí but no entendí. Like, I could write you the matrix formula for a rotation by θ degrees: But why is that linear? Lines are straight and circles bend. When you rotate something … Continue reading
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Tagged facts, image, intuition, linear algebra, linear mapping, math, mathematics, maths, matrix, projection, rotation, tensor, unintuitive, why
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When economists use maths to describe people, it’s somehow clearer when they’re less accurate. People tried to model the entire world and failed — but the logic of simple metaphors means … more. Below is a good example. The main question motivating the paper below is: would school vouchers improve the educational system, and would they increase inequality? A Complicated Endogenous Jargony Title by G. Glomm and B. Ravikumar PAPER SUMMARY The paper studies the difference between private and public systems of education. The public system means that everyone pays taxes to finance schools and the quality of schools is the same for everyone. The private educational system means that people choose how much to pay for education and the quality of schooling depends on the amount of money a student’s parent puts into it. The model used on the paper is an overlapping generations model. In the first period agents allocate a unit of time between studies (i.e. acquiring human capital) and leisure. In the second period agents get income equal to their human capital. The main findings of the paper are the following: First, inequality declines faster with the public system of education. Second, private education results in higher per capita income unless the initial inequality is not very high. Third, if income distribution is skewed to the left, then majority voting will result in the choice of the public education system. end of excerpt METAPHORS AND FAIRY TALES Alright, so what does that mean? We took a mathematical model which resembles reality. It is wildly inaccurate; much more inaccurate than assuming the sun is a point mass for instance. But … the conclusion still does seem to say something. But what? And what, precisely, can you do with the knowledge gained from reading the above? Does it prove anything about real school vouchers? Does it even make a valid suggestion about real school voucher policy? It’s not exactly an iftheworldwerelikethis story and it’s certainly not a here’showitisandhere’swhatitmeans story. More like a mathematical fairy tale? Or something. This ambiguity and vagueness are actually what made me return to mathematics after years away from it. It’s exciting to think that logic and maths might apply to relevant, contentious questions like political disputes. It’s also cool how economists rely on judgment to construct assumptions, “pure logic” to reach conclusions, and then judgment again to apply the conclusions.
School vouchers’ effect on economic inequality.
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Tagged economics, education, logic, mathematics, overlapping generations model, politics, theory
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http://www.bbc.co.uk/emp/9player.swf?revision=10344_10570 The Taiping “Heavenly Kingdom” historical mèmes: appropriating convenient parts of a foreign, exotic religion for one’s own needs. Buddhism in USA over the last 25 years; Christianity in China 100 years ago. sex is bad smoking, drinking is bad … Continue reading
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Tagged China, Christianity, facts, history, religion, revolution, Taiping Rebellion, xenophilia
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Hot Showers
You know what’s really nice about the U.S. of A.? Being able to take hot showers with lots of water, for pretty much as long as you like. Thanks, prosperity.
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Tagged amenities, appreciating things, capitalism, comfort, gratitude, heat, hedonic treadmill, technology, utility theory, warmth, wealth
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“The anchovies were nowhere near the sardines and the tuna. That’s because they were near the pizza toppings. But it was only a problem because this was a threedimensional grocery store. If it had been a thirtydimensional grocery store they could … Continue reading
Not saying I agree with this classification … but consider it a more topologically complex alternative to the ≅ℝ² picture of {positive vs negative affect} ⨯ {high/low energy} used in the “Miller mood map”. I’m not even sure if that’s the correct term for the ≅ℝ² story … Continue reading
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Tagged affect, emotions, feelings, graph theory, math, mathematics, maths, mood, personality, psychology, sentiment, submission, topology
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