The Best Color Scale? Not Rainbow

Image from Borland and Taylor (2007).

Even though rainbow color maps look pretty, Borland and Taylor (2007; pdf) argue that they’re rarely the best choice for showing data.

The rainbow color map confuses viewers through its lack of perceptual ordering, obscures data through its uncontrolled luminance variation, and actively misleads interpretation through the introduction of non-data-dependent gradients.

–Borland and Taylor (2007): Rainbow Color Map (Still) Considered Harmful in IEEE Computer Graphics and Applications.

They recommend the much more boring (but visually useful) greyscale and bi-colored schemes, for things like temperature maps and so on where the data is continuous.

A pretty, but not very informative, rainbow color scale.

Starting Algebra too Early?

There’s been a push for students to take algebra earlier and earlier, yet there are some serious pedagogic arguments that early algebra might not be a great idea for many, if not most, students. A fascinating paper by Clotfelter et al., (2012) (pdf) showed pretty clearly that for a large number of students, taking algebra earlier actually resulted in worse performance in not just algebra, but the follow-up classes as well (geometry and pre-calculus for example), compared to students who waited to take the subject. Indeed the Charlotte-Mecklenburg School District (the district studied in the article) actually reversed their policy of having students take algebra in 8th grade.

Students affected by the acceleration initiative scored significantly lower on end-of-course tests in Algebra I, and were either no more likely or significantly less likely to pass standard follow-up courses, Geometry and Algebra II

— Clotfelter et al., (2012): The Aftermath of Accelerating Algebra: Evidence from a District Policy Initiative (pdf) via NY Fed.

The argument for early algebra comes from the correlation between early algebra and better performance on standardized tests, and more advanced math classes in high school. But the authors here indicate that forcing students to take algebra early does not result in the same outcomes.

The argument against early algebra is based on the research that shows formal thinking develops during adolescence, and the belief that to do well in algebra requires the abstract thinking skills that are seated in the maturing prefrontal cortex. Until students are ready for the abstract thinking required (which happens at different times for each student), they will struggle with algebra.

Algebra provides an essential foundation for further mathematics, which is why it is my strong preference that students progress by demonstrating mastery of the topics at their own pace rather than struggling through the class.

Letter Spacing and Readability (particularly for dyslexia)

Letter spacing. Read this.

Two European researchers have demonstrated that increasing the spacing between letters help students with dyslexia read faster, bumping up their reading ability by about a year. Their app for testing your best reading spacing, DYS, is free.

Robert Lee Hotz has the details.

Unlike having to use expensive fonts, like dyslexie, letter spacing is very easy to change on a webpage, and anyone should be able to change the preferences on their browser; for Mozilla Firefox you can change the letter-spacing using User CSS (which is not quite as easy as changing it in the preferences).

ᔥ Hotz, 2012.

About Fire (Flames Really)

Ben Ames explains the science of flames.

It skims over pyrolysis; chemiluminescence, where the chemical reaction (combustion/oxidation) produces excited atoms and molecules that need spit out (emit) blue light to get to their ground state); and the incandescent light emission of microscopic soot particles which produce the yellow parts of the flame.

I’m not sure who the guy chained to the rock is. It might be Prometheus, who stole fire from the gods, but I don’t remember him being sent into hell in the myth.

Observing the Venus Transit

Shadow of the planet Venus during it's transit of the Sun on June 5th, 2012 at approximately 18:00 Central Time. Photograph taken from the MH Solar Observatory in St. Louis, MO, USA.

It’s pretty amazing how ecstatic seeing a simple circle with a little blobby dot can make a person feel. Following Ron Hipschman’s instructions, I installed a small aperture (~0.5 mm) solar projector at the newly established Muddle Home Solar Observatory (MHSO). The kids and I used it, and SunAeon’s app, to observe Venus transiting the Sun. It was, in a word, awesome.

The MHSO's small aperture (pinhole), solar projector.

For us the transit occurred late in the day, so by the end we had trees getting in the way.

Trees beginning to obscure the Sun.

If it seems odd that the trees are at the top of the image, it’s because the images in pinhole projectors are inverted. If I flip it around the right way, the image would actually look like this.

Corrected (inverted) image from the pinhole projector.

Reasons to Study Algebra: Economics


I hope you think that I am an acceptable writer, but when it comes to economics I speak English as a second language: I think in equations and diagrams, then translate.

— Krugman (1996): Economic Culture Wars in Slate

I sometimes get the question: Why do I have to learn algebra? Followed by the statement: I’m never going to have to use it again. My response is that it’s a bit like learning to read; you can survive in society being illiterate, but it’s not easy. The same goes for algebra, but it’s a little more complex.

Paul Krugman argues for the importance of algebra for anyone thinking about economics, the economy, and what to do about it. Even at the basic level, economists think in mathematical equations and algebraic models, then they have to translate their thoughts into English to communicate them. People who are not familiar with algebra are at a distinct advantage.

There are important ideas … that can be expressed in plain English, and there are plenty of fools doing fancy mathematical models. But there are also important ideas that are crystal clear if you can stand algebra, and very difficult to grasp if you can’t. [my emphasis] International trade in particular happens to be a subject in which a page or two of algebra and diagrams is worth 10 volumes of mere words. That is why it is the particular subfield of economics in which the views of those who understand the subject and those who do not diverge most sharply.

— Krugman (1996): Economic Culture Wars in Slate

P.S. In the article, he also points out the importance of algebra in the field of evolutionary biology.

Serious evolutionary theorists such as John Maynard Smith or William Hamilton, like serious economists, think largely in terms of mathematical models. Indeed, the introduction to Maynard Smith’s classic tract Evolutionary Genetics flatly declares, “If you can’t stand algebra, stay away from evolutionary biology.” There is a core set of crucial ideas in his subject that, because they involve the interaction of several different factors, can only be clearly understood by someone willing to sit still for a bit of math.

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