Thursday, July 30, 2009
Friday, July 24, 2009
another post here, although written in spanish, has a number of interesting LOGO (or python turtle) example exercises.
"For each day that the high temperature in your hometown is at least 1 degree Fahrenheit above average, as listed by Weather Underground, you owe me $25. For each day that it is at least 1 degree Fahrenheit below average, I owe you $25."
He's trying to address recent statements by some conservatives, paraphrased as "It's cold this summer here in Minneapolis, so global warming must be wrong." That's a bit of a strawman, but from the Power Line blog post, there really is this sense of local vs global perspective.
Well, it's actually a pretty silly challenge to a pretty silly statement. No serious GW skeptic I've heard contests that their is warming on a global scale, but argues against the magnitude or, more commonly, the cause of the warming (human vs not). The statistical challenge here only addresses whether there is warming, and even there is rigged to win even if there were no real global warming, because of the urban heat island effect. Most of the thermometers started out in rural areas, or in fields outside of towns, and cities were built around them. Areas around pavement are warmer than the surrounding areas, so there would be a measured warming trend due to development, not due to atmospherics.
A better bet would involve predicting the global temperature for, say, 5 years from now (along with the uncertainty). Each side puts in their prediction, and pays $1 times the ratio of the posterior probabilities for the two models, P(M1)/P(M2). Would anyone take a bet like that?
Monday, July 20, 2009
Because supporters and opponents tend to break down along partisan lines. Democrats favor sampling because the people who are traditionally hardest to count are the urban poor, minorities, and immigrants, all of whom tend to live in Democratic strongholds and vote Democratic. These groups are often undercounted because they move so frequently and do not trust government employees asking questions. Republicans, by contrast, stress that the Constitution specifies an “actual enumeration” of the population, not an estimate. They also argue that statistical sampling is inferior to counting. “Anyone familiar with public opinion polling can tell you that statistical sampling carries a margin of error,” Republican Reps. Darrell Issa and Patrick McHenry recently wrote. “And error is the enemy of a full and accurate census.”
The notion that a national count is completely error free is ridiculous. I think everyone would agree that if you do a count, that you will not get everyone. It is known that mistakes are made, omissions occur, and that some people actively avoid the census. Because the census avoidance is not random, the omissions are biased in some way. One can argue in which ways the bias points, but the bias is there.
So what is the best plan of action in this case? You want to make an estimate of the number of people in the country. "Estimate" is the correct word, even for an enumeration, given the fact that the enumeration is known to be incomplete. The best thing to do, then, is to have a public and open statistical model of the process of sampling, with independent ways to confirm the validity of the model. If the model is simple, and open, it would be difficult to argue against. Without this approach, a "strict enumeration" is really an unstated statistical model where the assumptions are very difficult to see.
Sunday, July 19, 2009
In a strict way, this is an agnostic perspective. The description of the universe, as described by Laplace, does not need to use the concept of God in any way. This does not disprove the existence of God, or even deny God's existence. It merely states that the concept of God is not needed. This is the pure vision of science, and why science does not necessarily conflict with religion. However, there could be certain claims from specific religions that conflict with science. The 6000 year old Earth, part of some fundamentalist Christian beliefs, is one example. The God as the mystery in the Universe is not something that can conflict with science.
Saturday, July 18, 2009
In Chapter 10 he quotes Laplace:
"We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes."
and Mlodinow states that this is an expression of determinism. He then further states
But for Laplace's dream to hold true, several conditions must be met. First, the laws of nature must dictate a definite future, and we must know those laws. Second, we must have access to data that completely describe the system of interest, allowing no unforeseen influences. Finally, we must have sufficient intelligence or computing power to be able to decide what, given the data about the present, the laws say the future will hold.
He then criticizes it with the following three problems:
- society is not governed (as far as we know) by definite and fundamental laws in the way physics is
- like Lorenz, we cannot obtain the precise data necessary for making predictions
- human affairs are so complex that it is doubtful we'd be able to make the calculations anyway
He concludes "as a result, determinism is a poor model for the human experience." His point seems to be, in some ways, obvious and in other ways irrelevant.
Laplace was simply saying that "God" would not find anything random, because of complete knowledge. The connection between knowledge and inference, which probability theory affords, was worked out by Laplace in great detail and it known to use today as Bayesian inference. The structure of Bayesian inference describes randomness simply as the product of our ignorance of the model, the parameters, the initial conditions, the measurement details, etc... Laplace was simply saying that with perfect knowledge, there is no randomness. E.T. Jaynes would describe the "random process" as a mind-projection fallacy: you have ignorance of the system, so you attribute its unpredictable behavior as a product of the system itself. A rolled die is following Newton's Laws, deterministically, and detailed knowledge of the die and the roll and the surface should allow you to predict 100% of the time what it will do. We lack that knowledge, thus the behavior becomes unpredictable. We often then attribute that unpredictable behavior as a "random die", as if it were the die that contains the randomness and not our own ignorance.
Bringing in Lorenz, and chaos theory, is irrelevant here. Lorenz's systems were completely deterministic, and it is theoretically possible for a being to know the state of the system out to a sufficient number of decimal places to provide any particularly set level of uncertainty in the system. With the quantization of states, it then becomes possible to know *exactly* what state something is in. Of course, quantum mechanics is a two-edged sword in this example: it solves the chaos problem, but adds an inherent, physical, randomness to the system which is very peculiar.
The problem with Mlodinow, it seems, is that he hold human activity to be a bit too special. We are, after all, made up of atoms and would thus be governed by the laws of physics. Certainly it would be too complex to handle, for us, but Laplace was not talking about us in his quote, or at least not us right now or in the near future.
Friday, July 10, 2009
Wednesday, July 8, 2009
Imagine a woman named Linda, thirty-two years old, single, out-spoken, and very bright. In college she majored in philosophy. While a student she was deeply concerned with discrimination and social justice and participated in antinuclear demonstrations.
Linda is active in the feminist movement: 2.1Linda is a bank teller and is active in the feminist movement: 4.1Linda is a bank teller: 6.2
They presented a group of internists with a serious medical problem: a pulmonary embolism (a blood clot in the lung). If you have that ailment, you might display one or more of a set of symptoms. Some of those symptoms, such as partial paralysis, are uncommon; others, such as shortness of breath, are probable. Which is more likely: that the victim of an embolism will experience partial paralysis or that the victim will experience both partial paralysis and shortness of breath? Kahneman and Tversky found that 91 percent of the doctors believed a clot was less likely to cause just a rare symptom than it was to cause a combination of the rare symptom and a common one. (In the doctor's defense, patients don't walk into their offices and say things like "I have a blood clot in my lungs. Guess my symptoms."
- steak with no potatoes
- steak with potatoes
- clot with paralysis and shortness of breath
- clot with paralysis and no shortness of breath
Linda owns an IHOP franchiseLinda had a sex-change and is now LarryLinda had a sex-change and is now Larry and owns an IHOP franchise
- someone is claiming that the patient has an embolism
- the patient is claiming, or someone has measured, that she has partial paralysis
- the patient is claiming, or someone has measured, that she has shortness of breath
- they had the means to measure shortness breath in the patient, but there was none
- they did not have the means to measure shortness of breath
Tuesday, July 7, 2009
I've just finished the book "Euclid's Window" by Leonard Mlodinow, and really enjoyed it. The book describe the history of geometry from Euclid, Descartes, Gauss, and Einsten. During his coverage of Euclid he presents a simple proof of the Pythagorean Theorem that really resonated with me. I don't recall ever seeing a proof of it, or at least no memorable proof. This one uses a minimum of jargon and formality...you just draw the picture, discuss it for a bit, and you see it!
You start with a right triangle, like:
which, by eye, you can see that the total area of the square is the area of 4 triangles (just like our original) plus the area of the inner square, which is c*c (which reminds me that I have to figure out how to do superscripts and subscripts in this blog. :) )
The second construction is nearly the same as the first, and looks like:
which, again by eye (with a little shading to make it a bit more obvious), the total area of the square is the area of 4 triangles (just like our original) plus the area of the two inner squares, which are a*a and b*b. Therefore:
for any triangle for which you can make this construction, which are right triangles.