Month: February 2012

Frames of Reference

A wonderful set of physical demonstrations of the different perspectives that come from different frames of reference. Excellent for physics, and maybe math too, because it does point out coordinate systems.

[- Leacock (1960): Frames of Reference, Presented by Ivey and Hume, via the Internet Archive.]

From the Coriolis Interactive Model.

The discussion of non-inertial (accelerating) frames of reference is particularly good, and would tie in well with the coriolis model demonstration.

Of course, different perspectives are important in the geometry of social interactions also.

(thanks to Mr. D. for the link to the video).

Master and Apprentice

Handmade Portraits: The Sword Maker from Etsy on Vimeo.

This video, contains some fascinating reflections from, Korehira Watanabe, one of the few remaining traditional sword makers in Japan.

Particularly intriguing is Watanabe’s somewhat counter-intuitive need to keep exploring new challenges in swordmaking, so that he might keep the ancient traditions alive. He’s also very interested in instilling the same type of drive in his disciple, with the hope that his disciple will someday surpass him.

I personally find this to be a quite appropriate perspective for a teacher.

Wavelengths of Light Illustration

The wavelength of red light compares to the size of an E.Coli bacterium. Violet light's wavelength is even smaller.

A few of the steps along the Scale of the Universe flash app include the wavelengths of different colors of light. It’s a great way to show the show the relative sizes of these waves.

Scale of the Universe: 62 Orders of Magnitude (1062)

Scale of the Universe 2, by Cary and Michael Huang. WARNING: look out for ads on the site.

In a modern variant on the Powers of Ten video, Cary and Michael Huang have created an excellent flash game that spans the scale of the universe, from the smallest, only hypothesized particles, through atomic, human, planetary, and galactic scales (to name a but a few), to the size of the universe itself. It goes further than the Cell Size and Scale flash app.

The link is here, but look out for an advertisement that takes up the game window, which will eventually let you through (or you can click the “Skip Ad” link on the bottom right of the ad).

Will the New Arab Democracies Survive?

The key countries at the heart of the Arab Spring: Tunisia, Egypt, and Libya. Image adapted from Wikimedia Commons User:Danalm000.

What are the chances that the revolutions of the Arab Spring succeed at creating democracies? According to a regression model created Jay Ulfelder: maybe.

[T]he probability that each of those new democracies would make it to their sixth birthday…:

  • Tunisia: 82%
  • Egypt: 48%
  • Libya: 89%

Ulfelder’s blog post is worth the read. It’s an excellent (if somewhat technical) example of how to do (and write up) some quick research, and how the ability to blog is changing the way scientists share ideas, and get feedback (check out the comments section).

FOIL: Multiplying Factors

FOILing.

Multiplying out two factors can be a little tricky. The FOIL mnemonic is a quick method when you have two terms in each factor, such as in:

(a + b)(a + b)

FOIL stands for:

  • Firsts,
  • Outer,
  • Inner,
  • Lasts.

It applies to the multiplication of the binomial cube.

Multiplying out factors using FOIL.

Another way of showing the process — step by step — would be like this:

Multiplying factors using FOIL.

After FOILing you combine the similar terms:

Combining like terms to get the final result.