Science, Entropy (relative) and Education

Workout notes early morning:
rotator cuff (pulley, dumbbell), pullups (4 sets of 10, 3 shoulder grip), rows (15 x 180, 15 x 200, 10 x 220), bench 10 x 135, 4 x 180, 3 x 180, 3 x 180, sit ups (5 sets of 20), push backs (3 sets of 10), abductors (3 sets of 10), incline (10 x 135, 8 x 135), pull downs (3 sets of 10 x 160), curls (3 sets machine, 70-80) military (3 sets of 10 on the machine; 10 x 90, 10 x 80, 10 x 80)

later (after Barbara’s foot appointment) swimming: 500 free, 10 x (25 fist, 25 free), 10 x (25 3g, 25 free) 10 x (25 kick, 25 free; 6 front, 2 side, 2 sfs), 4 x (25 fly, 25 free)

Tomorrow: “fun” obstacle race at Wildlife Prairie Park. 3 mile (4.8 km) run with obstacles.

Cool Picture
Our ancestors or relatives:

Why our intuition is so difficult to combat: (article by Jonah Lehrer in the New Yorker)

A new study in Cognition, led by Andrew Shtulman at Occidental College, helps explain the stubbornness of our ignorance. As Shtulman notes, people are not blank slates, eager to assimilate the latest experiments into their world view. Rather, we come equipped with all sorts of naïve intuitions about the world, many of which are untrue. For instance, people naturally believe that heat is a kind of substance, and that the sun revolves around the earth. And then there’s the irony of evolution: our views about our own development don’t seem to be evolving.

This means that science education is not simply a matter of learning new theories. Rather, it also requires that students unlearn their instincts, shedding false beliefs the way a snake sheds its old skin.

To document the tension between new scientific concepts and our pre-scientific hunches, Shtulman invented a simple test. He asked a hundred and fifty college undergraduates who had taken multiple college-level science and math classes to read several hundred scientific statements. The students were asked to assess the truth of these statements as quickly as possible.

To make things interesting, Shtulman gave the students statements that were both intuitively and factually true (“The moon revolves around the Earth”) and statements whose scientific truth contradicts our intuitions (“The Earth revolves around the sun”).

As expected, it took students much longer to assess the veracity of true scientific statements that cut against our instincts. In every scientific category, from evolution to astronomy to thermodynamics, students paused before agreeing that the earth revolves around the sun, or that pressure produces heat, or that air is composed of matter. Although we know these things are true, we have to push back against our instincts, which leads to a measurable delay.


What is more interesting is that when we see something that IS true scientifically but goes counter to our “built in” biases, something specific happens in our brains. Here, some physics students were shown a video of spheres of different masses falling at the same speed. They knew that the video was correct but:

But it turned out that something interesting was happening inside their brains that allowed them to hold this belief. When they saw the scientifically correct video, blood flow increased to a part of the brain called the dorsolateral prefrontal cortex, or D.L.P.F.C. The D.L.P.F.C. is located just behind the forehead and is one of the last brain areas to develop in young adults. It plays a crucial role in suppressing so-called unwanted representations, getting rid of those thoughts that aren’t helpful or useful. If you don’t want to think about the ice cream in the freezer, or need to focus on some tedious task, your D.L.P.F.C. is probably hard at work.

According to Dunbar, the reason the physics majors had to recruit the D.L.P.F.C. is because they were busy suppressing their intuitions, resisting the allure of Aristotle’s error. It would be so much more convenient if the laws of physics lined up with our naïve beliefs—or if evolution was wrong and living things didn’t evolve through random mutation. But reality is not a mirror; science is full of awkward facts. And this is why believing in the right version of things takes work.

On a similar vein, what about entropy and evolution? Sean Carrol in Cosmic Variance writes:

The first is a bit of technical background you can ignore if you like, and skip to the next paragraph. It’s the idea of “relative entropy” and its equivalent “information” formulation. Information can be thought of as “minus the entropy,” or even better “the maximum entropy possible minus the actual entropy.” If you know that a system is in a low-entropy state, it’s in one of just a few possible microstates, so you know a lot about it. If it’s high-entropy, there are many states that look that way, so you don’t have much information about it. (Aside to experts: I’m kind of shamelessly mixing Boltzmann entropy and Gibbs entropy, but in this case it’s okay, and if you’re an expert you understand this anyway.) John explains that the information (and therefore also the entropy) of some probability distribution is always relative to some other probability distribution, even if we often hide that fact by taking the fiducial probability to be uniform (… in some variable). The relative information between two distributions can be thought of as how much you don’t know about one distribution if you know the other one; the relative information between a distribution and itself is zero.

The “next paragraph” is also pretty interesting; surf to the blog and read it.

I’ll focus on the first one. Here is John Baez’s post. The idea is roughly this: the idea about entropy is “relative”; that is, there is no “ether” state to measure it against. So when you do a calculation (often in the form of an integral), you are integrating with respect to something. What you are integrating with respect to matters! This amounts to having a choice for a measure (as opposed to the usual Lesbegue measure, for example).

We are also lead to the Bertrand paradox which is roughly this: if you inscribe an equilateral triangle in a circle and then you take a random chord (line connecting two points of the circle), what is the probability that the chord is longer than the sides of the triangle? Answer: it depends on HOW you choose “randomly”. It turns out that there is a way of making the “best random choice” (using the principle of “maximum ignorance” which means, roughly that your answer and method should be invariant with respect to things like translation and scaling.) And this “best way of making a random choice” conflicts with at least MY intuition!

Education: this is one reason I feel a bit guilty about following college football. There is a defensive lineman who is “close” to graduating from a major university. But:

Even with the help of his academic advisers, Mr. Cathey has still struggled. The university would not provide the names of his professors, saying it didn’t want to expose faculty members to scrutiny. But papers from various courses Mr. Cathey has taken—which he provided to The Chronicle, in part to illustrate his improvement during college­—show a student who has had trouble completing basic assignments. For a developmental-writing class his first year, he submitted a two-page paper, titled “Some Important Womens,” in which he was asked to describe common issues or challenges facing characters in several books.

“Fannie Hou Hammer, Irma Muller and Aurthor Mayo-Raggie are important people with struggles, detonations, and failure that surround their environment,” he wrote in his introductory paragraph. “Then I give you my points on, ‘what I thinks the point that I thought it was making?”

Dasmine Cathey: 4 Academic Papers (Browse the documents)

Joseph Jones, an associate professor of English and director of the university’s first-year composition program, says many students with little exposure to analytical writing commit even more “surface” spelling and grammatical errors than they might normally as they try to articulate complicated ideas.

Without commenting on Mr. Cathey, he says instructors are encouraged to evaluate students on a variety of factors, including their improvement.

“On an absolute scale, you might think maybe this student doesn’t deserve to pass a class,” he says. “But over 15 weeks, if you see a certain improvement and can project a trajectory over the next couple of years that she’ll be an adequate college student, you might make a different call.”


For one assignment, he had to look at the covers of 10 magazines he had never read and describe their target markets. “Ladies if you looking for a maganize thats is tagering just you and all about you. Then this one is for you,” he said about Woman’s World. “Telling the ladies how to eat. What diet to be no for your body, and more.”

In addition to the grammatical problems, he misspelled “magazine” 13 times, but the professor didn’t mark him down for it. In fact, she praised him for his conversational style.

“This is a beginning class where we try to get students to discover the media and start expressing themselves in writing,” Ms. Justice says. “If this had been a writing class, I’m sure he wouldn’t have passed because spelling and words are so much more important there.”[…]

Later in the article, the player gets help writing his resume. He DOESN’T KNOW what degree plan he is in:

Finally, she asks about his degree, which he hasn’t listed.

“What’s your major?” she asks.

“Sports management.”

“Is that a bachelor of science or arts?” she says.

He doesn’t know, so he walks a few steps away to ask Ms. Connell.

“Do I have a bachelor of science or arts?” he says.

Ms. Connell comes out of her office and heads toward Ms. Rusboldt. “He has a bachelor of liberal studies in interdisciplinary studies,” she says.

Mr. Cathey sits back down, a staff member by each side. He taps out, “Bachelor of Liberal Studies.”

Oh boy.


June 8, 2012 - Posted by | college football, education, evolution, mathematics, science, social/political, swimming, weight training

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