Podcasting & Education

I just finished listening to a pod-conference (did I just make that up?) between the SASIC teachers, exploring ways to use podcasting and other technologies in and out of the classroom. Im disappointed I wasnt able to join in on the live discussion, but as a podcast listener myself (Im especially crazy about radiolab), Im pretty excited about the possibilities that are opened by using these innovations.

I think a radiolab-esque sort of format (merging stories and discussion into segments around a central theme, while mixing in music, interviews, and other noise-scapes) would be a great way for students to present a project, sort of like a cross between journalism and art. But like anything of substance, it definitely takes a good deal of time and effort, so I will try to see what I can do and look forward to seeing what others can produce as well.

Its not a question of if technology will transform the classroom, the better questions are how and when.

Google+ for educators

I came across this article at a site called ReadWriteWeb discussing the educational potential for  Google+, the new social networking site by Google that is currently in the testing, or beta, phase (limited to a certain amount of invites).

This site should be a bit similar to facebook and/or twitter, except you will be connecting to other people in separate groups, or circles. So, for instance, people will probably have a circle for family, one for friends, one for co-workers, one for fellow hobbyists, etc., and educators could presumably have a circle for each of their classes, one with their colleagues, departments, and so on.

I will have to wait and see Google+ for myself to make any conclusions about it, but I have a feeling that within a couple generations from now post-facebook communities like these are going to start having some big impacts on education, if not other parts of our lives too.

Jackson Pollock - Artistic Physicist?

I came a cross a good article that suggests that Jackson Pollock, one of the first and most influential artists in abstract painting, may have had an intuitive sense for the physical and mathematical sciences that shows up in his works.

Pollock chose the type of paints that he used very carefully, seeking specific desired effects, textures, and colors. The researchers studying his paintings believe that his paint drippings exhibit certain properties of fluid dynamics that he might have been only subconsciously aware of, such as what is called a "coiling" effect on viscous liquids (thick slow moving liquids like honey, or thick paints).

This video demostrates the coiling phenomenon on a viscous liquid being poured slowly onto a moving belt. The zig-zags you see it start to make arent because the pouring container is moving, it is stationary, it starts doing this because the belt starts moving slower. So if Pollock slowly dripped a thick, viscous paint, it would land in a way that creates seemingly random patterns.

This makes sense, as Pollocks works are a kind of controlled chaos, seeming to be simultaneously random and yet also carefully and intricately designed. The researchers studying his paintings also suggest that his compositions show similarities to fractal geometry, which our minds see as pleasant as it is evident in the beauty of nature, such as clouds, snowflakes, mountains, and plant life.

For more of Jackson Pollock's works, click here.

A Brief Explanation of Math & Music

The connection between math and music is profound and pretty extensive, but here are some of the basics. It started with Pythagoras - yes, the same guy with the triangle theorem - a Greek man in the year 500 B.C. who had an entire philosophy, kind of a religion, with a large number of followers. His philosophies are considered among the most influential in history, and they believed, among other things, that everything in existence is composed of numbers.

So, probably also a fan of music, he tried to figure out the numbers in music. He experimented with a monochord, which is basically like a single guitar string, and found that by changing the length of the string (like holding down a guitar string) has a direct effect on the note that sounds.

For instance, putting your finger on the exact middle of a string on a guitar (the 12th fret), you are changing the length of the string to half the length that it is normally, the ratio for is 1/2 (or 1 to 2) since it is half. At this point, these two notes are the same, except one is an octave higher. Since sound is a wave in the air - like a wave in the water, except we cant see it - and the frequency determines what note it is, the frequencies of the notes behave in the same way that that the length of the string does. If you play the open (or full length) "A" string on a guitar, its frequency is 440 Hertz and is the "A" note - but then if you put your finger on the middle of the string, its still an "A" note, except an octave higher, and its frequency will be 880 Hertz. So, 2 times 440 = 880 and the ratio of the string lengths is 1/2!

The same can be said for the other notes in the scale. For instance, the ratio of string length from the same open "A" string to the "E" note (7th fret) is 3 to 2 (or 3/2) and the frequency of the "E" note is 660 Hertz. So, thats 660 to 440, or 660 divided by 440, which is equal to 3/2!!

For some reason our ears recognize these ratios without thinking about it, because simple ratios (such as 2/1 and 3/2 and 5/4) are the notes that sound pleasant to us - and our scales are built around these - whereas complicated ratios sound painful and grating to us.

So, many instruments after Pythagoras were built around his mathematical ratios. But there was a problem - it was hard to switch keys on these instruments (Like from the key of C to the key of E) because the relative ratios just didnt add up right. Along came Sebastian Bach who devised a way of dividing the frequencies into what he called the "well-tempered scale." Bach used this system to write songs in which he could easily switch between many different keys in the same song. But the sacrifice that he made for this ability was that the notes were no longer the pure mathematical ratios, but were instead close approximations.

This "well-tempered scale" was eventually developed into the "even-tempered scale," in which all the 12 half steps in the octave are the same distance apart. This "even-tempered scale" is the system that our modern "fretted" instruments use, like the piano and guitar, and this is what allows our music writers so much freedom in composition, though the notes you hear are only approximations of the pure notes that your ears want to naturally hear.

Profound theorems:

Theorem 1. A sheet of writing paper is a lazy dog.

Proof: A sheet of paper is an ink-lined plane. An inclined plane is a slope up. A slow pup is a lazy dog. Therefore, a sheet of writing paper is a lazy dog.

Theorem 2. A peanut butter sandwich is better than eternal happiness.

Proof: A peanut butter sandwich is better than nothing. But nothing is better than eternal happiness. Therefore, a peanut butter sandwich is better than eternal happiness.

The Wisdom of the Crowd

In this excerpt from The Wisdom of Crowds by James Surowiecki, a brief story of British scientist Francis Galton is told about his witnessing of a contest that challenged people to guess the weight of an ox. Much like the guessing games that you might see in a mall that ask you to guess the number of gumballs in a giant container, the person with the closest guess to the actual weight of the ox won a prize.

Now Mr. Galton was a pretty skeptical person, believing that the majority of people were uneducated and therefore were a detriment to society and/or a democracy. Most of the people entering the contest were not experts on ox weights, so he was curious to take a look at the results of the contest, stating “The average competitor was probably as well fitted for making a just estimate of the dressed weight of the ox, as an average voter is of judging the merits of most political issues on which he votes."

But what he found was surprising... he took the average of all the 800 or so guesses and, it came to 1,197 lbs., which is an almost exact match to the correct answer of 1,198 lbs.!! Much like a colony of ants can achieve much more than any single ant can alone, the entire group of humans averaged as a whole had better insight than any single person.

This is routinely proven time and again in any contest of this kind - following the rule that the greater the number of people participating, the more accurate the average guess will be (so only a handful of people is probably not big enough). This makes me wonder about the collective power that we have as a species, and about how much goes to waste or unnoticed.

Being a democracy consisting of mainly 2 parties of political ideologies, both seem to push toward either extreme, repelling like opposite poled magnets, and these extremes are usually how they are represented in the media. But if we could train ourselves as a society to see the power of the average, I think we might find that the answer is almost always a compromise found somewhere in the middle.

I dont know how much faith I put into polling, but if only we could express the big, dividing issues of the day into a mathematical vote, and go with the average, maybe we would be better off, or at least cut through some of the bureaucracy tying down our representatives. Or maybe that's what American Idol already is, a sophisticated test to see if the masses can come to the right conclusion in the end... nah...