Imaginary Numbers via Veritasium

 Veritasium gives the background of imaginary numbers and their connection to the physics of reality:

https://www.youtube.com/watch?v=cUzklzVXJwo

y = x^x

Today, just this interesting video on the innocent-looking function y = x^x:

http://screencast.com/t/m4fmGwmkrT9

"the wonders of the world of algebra"

Sir Roger... and algebra:

Currently lacking time for longer posts, so just another quotation today, this time from the eminent Roger Penrose remarking on his introduction to algebra as a youngster (taken from his Foreward to Mircea Pitici's "The Best Writing on Mathematics 2013"):

"My earliest encounter with algebra came about also at an early age, when, having long been intrigued by the identity 2 + 2 = 2 X 2, I had hit upon 1.5 + 3 = 1.5 X 3. Wondering whether there might be other examples, and using some geometrical consideration concerning squares and rectangles, or something -- I had never done any algebra -- I hit upon some rather too-elaborate formula for what I had guessed might be a general expression for the solution to this problem. Upon my showing this to my older brother Oliver, he immediately showed me how my formula could be reduced to 1/a + 1/b = 1, and he explained to me how this formula indeed provided the general solution to a + b = a X b.  I was amazed by this power of simple algebra to transform and simplify  expressions, and this basic demonstration opened my eyes to the wonders of the world of algebra."

A Post, a Rant, and a Video

A few more links today in case you've missed them:

Evelyn Lamb continues the recent spate of commentary on pi with her take on pi and big (I mean B-I-I-I-G) numbers here:

http://blogs.scientificamerican.com/roots-of-unity/2013/04/17/big-numbers-are-big/

Wonderful rant from Grant Wiggins on the never-ending-wrangle over teaching high-school algebra:

http://grantwiggins.wordpress.com/2013/04/10/my-100th-post-so-why-not-bash-algebra/

And Keith Devlin weighs in, as well, on the teaching of algebra, in this 4-minute video:

Algebra... the Discussion Continues

If you missed it today, the Diane Rehm Show (NPR) did an hour with Andrew Hacker and other guests on the issue of "Is Algebra Necessary" which Hacker raised to the forefront in a recent NY Times op-ed. The podcast is available here:

http://thedianerehmshow.org/shows/2012-08-29/algebra-necessary

You can hear the frustration/aggravation in Dr. Hacker's voice as he defends his position against the backlash he created. If anything, he may be stating his case more staunchly now than in the original article. Clearly the arguments can go back-and-forth for a long time; several of the listeners' call-in comments/experiences are interesting as well. I still find fault with Hacker's overall take, but I respect his ability to stand his ground.

In the end, he says he is simply asking that we "re-think" our insistence on algebra as a "requirement" for all high school graduates. I wouldn't completely oppose that... so long as we also "re-think" the insistence on various English, literature, history, art and music requirements as well.

It's Not Necessary…

to beat a dead horse, but I will link to yet one more response to the NY Times "Is Algebra Necessary?" piece which drew a lot of fire (ire?) earlier in the month. This one from Jennifer Ouellette that I missed a week-or-so ago:

http://blogs.scientificamerican.com/cocktail-party-physics/2012/08/14/make-us-do-the-math/

A bit therefrom:

"I spent ten years training in jujitsu, yet I have yet to use my skills to defend myself from a real-world attack. So I guess those ten years were a waste, right? Wrong! The most important lessons I gleaned from martial arts had to do with learning to fail: getting my ass kicked and getting back up, again and again and again, until I mastered a given skill. Why wasn’t I willing to do the same for math?
All we’d end up teaching kids with Hacker’s strategy is avoidance. I was a master of avoidance. But learning to buckle down and do unpleasant things that don’t come easily to us prepares us for life…

"There’s a lot to be said for confronting fear and anxiety head-on, and fighting through a wall rather than throwing up one’s hands in defeat."

…I dare say we haven't heard the last on this topic.