## Monday, 8 June 2009

### Fool me once, Fool me Everytime?

Concurrency is the term, I think; you see an idea and then wham, bam, bang, it comes at you several more times. Well, right now it seems to be illusions and our inability to believe our own lying eyes.
Several nights ago I was flipping through the new Ted blogs and they had one by Dan Ariely, the author of "Predictably Irrational." If you teach Stats or any of social science, you need to watch this one, but it is about 17 minutes long, so here is the part about what I'm talking about.

He shows the picture at the top...Then he shows the two tables with a red line on each one, and finally he rotates the line so that you can see (at least if you believe he didn't shrink the line as he rotated it), that the two tables are both the same length. Now take the lines away... admit it, the table on the left looks longer. I even cut a copy of each table from the video, put them side by side on my smart board, then rotated one and drew parallel lines through the two red lines... the same.... rotate it back???? ARRRGGGHHHHH!

I just found another note on this one and it says that,"This is Roger Shepard’s “Turning the Tables” illusion. This optical illusion appeared in the Jan. 2003 issue of Discover Magazine." And here is a
link to a java applet at Rice University where you can turn and superimpose the shapes with your mouse to show they really are the same...

Ok, so two days later I'm flicking through some blogs and the folks over at 360 have a really nice one about illusions (go see it)... and they had a similar visual example they called the Sander illusion [I did a wiki-lookup and found,"The Sander illusion or Sander's parallelogram is an optical illusion described by the German psychologist Friedrich Sander (1889-1971) in 1926. However, it had been published earlier by Matthew Luckiesh in his 1922 book Visual Illusions"]

It is two parallelograms that have equal length diagonals... only they DON'T look equal. You can measure, and sure enough, spot on, as the British folk say.

Take away the ruler, BAM, the diagonals look different again. And I wondered WHY?? What is it that makes it look longer...

Sooooooooo I built one. I laid out a Geogebra spred that would allow me to adjust the angle of the two parallelograms, and the bases of them, while keeping the diagonals the same (a little hidden circle).. So try it your self, survey your class.. is there an angle that makes it seem the MOST different? Does it matter if we adjust the bases??? Here, for you to try, (if I did this right) is a JavaG-bra that will allow you to move a few points around and compare. And just to show I have only my arm up my sleeve, the picture on the left shows the hidden circle in the construction. It seems that the diagonal shape gives the illusion of perspective, and the longer box seems to go "deeper" into the picture... at least that's what it looks like to me, but hey, you can't believe what I see.