Science Forums: Cap'n Refsmmat - Viewing Profile - Science Forums

Today I've upgraded the mathematics support on the SFN Blogs. We now use MathJax to display nicely-typeset equations directly in the browser, rather than generating fuzzy images which didn't always match with your blog themes. The MathJax output should look much, much nicer, and fits in with the surrounding text much better.

Your previous equations should already work perfectly with MathJax. In future posts, you can take advantage of new features, like using the LaTeX syntax for display equations:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

to get display-size nicely-typeset equations. For mathematics within a paragraph, you can still use the $latex x^2$ syntax you're used to, or LaTeX-style \( x^2 \) syntax.

Let me know if you encounter any problems.

(Incidentally, these changes will soon be making their way to SFN!)

I'm currently reading Against Method, a book by Paul Feyerabend, which makes an interesting argument against a theme we commonly cite on SFN. The so-called scientific method, Feyerabend writes, is both a poor description of how science has actually been conducted over centuries and a poor framework to adopt if one were to enforce its rules. Strictly following the scientific method would only prevent discoveries, says Feyerabend.

I haven't finished the book, but so far, Feyerabend has made interesting points. For example, we on SFN often argue that new hypotheses must be able to explain phenomena that older theories already can, and must make testable predictions which can demonstrate their superiority to current theories. But many times new theories not only provide new explanations but change the nature of the evidence, meaning they cannot be evaluated on the basis of their agreement with current theories. For example, when Galileo argued that the Earth was in motion around the Sun, contemporary accepted theories held that it was impossible for the Earth to be in motion: if it was, then a stone dropped from a tall tower would travel in a wide arc as the Earth sailed past underneath it.

Galileo convinced his audience not by making predictions which agreed with current "experimental data" -- data points showing that the Earth must be stationary -- but by arguing that our perceptions were misleading, and by introducing the ad hoc idea of inertia which made relative motion work. His hypothesis did not explain the same phenomena the old theory did -- it denied the phenomena existed.

It's a fascinating and well-written book, and I recommend it to members interested in the scientific method and the historical progression of science. I'm curious to see what other arguments Feyerabend has against the scientific method as I finish the book.

So I've been working on a little project over my winter break: re-aligning the terminal Poisson amplifiers on my VX equipment. I've gotten pretty far -- the T-pulses are easily collimated to a five-gram tolerance -- but I've been having a bit of trouble with sticky girdle springs keeping the Albertson flange from rasterizing. At this rate, I'll never be able to get the phase detractors to properly control the flux through the Poisson amplifiers.

I was thinking of using some homeomorphic walnut oil to lubricate the springs, but I was worried that the extra inductance would cause a phase loop and blow out the monad. Should I be worried, or will the type unifier prevent that?

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I just got back from tutoring students at a local high school. It was an event for students specifically taking AP classes, which culminate in an exam which is accepted for credit by many universities. The students are generally high school seniors -- 17 or 18.

Every student had a TI-89 calculator which they used to solve every problem. At one point, a student was working out some arithmetic and encountered this:



She paused, looked uncertain, and said "well, I don't know that off the top of my head" and reached for her calculator.

I'd ask other students "okay, now solve that equation for t" and they'd stare at me blankly, before reaching for their calculator to type "solve(4.9t^2 = 10, t)".

They had trouble with basic physics concepts. For example, a force that acts perpendicular to the direction an object travels does no work -- it doesn't contribute to the object's motion. (For example, if a block slides along the ground and you push straight down on the block, you're not doing work on it.) They were utterly surprised when their calculator gave them zero.

Many didn't get the concept of inverse sines and cosines, despite having done trigonometry for months.

You can see why I'm worried about the state of education. Most of this is basic algebra and arithmetic, and yet these high-school seniors couldn't do it without their TI-89s. They had passed their state standardized tests, passed their algebra classes, gotten into an advanced placement course -- and they can't multiply fractions.

What can we, as people in the science community, do? What can educators do to change this? We can't just make the tests harder -- they'll all fail. There's something structurally wrong with how we teach high schoolers.

I'm curious to hear if anyone else has had similar experiences as well.