We just finished up our unit on Quantum Mechanics in physics. I was going on and on about Bohr's Principle of Complementarity (Is it a wave or a particle?). I was getting all fired up and calling their attention to the fact that we are limited by our linguistic repetoire. I called our feeling that we must choose between describing fundamental particles "waves" OR "particles" a false dichotomy (we think we are so smart with our fancy words but nature doesn't care - waves and particles are just anthropocentric words; nature does what nature does). As I smugly stepped back to admire my sophisticated grasp of the problem, a couple of students spoke up. "You're beating a dead horse, Mr. Rideout - we get it, move on."
Of course, they are correct, everyone know language is fallible - Bohr himself said it himself long ago (1920):
"We must be clear that when it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images and establishing mental connections."
But, what I would like to leave my student with is this additional quote from Bohr:
"Anyone who is not shocked by quantum theory has not understood it"
This is the precise opposite of most of physics - usually once you understand some principle of physics you think, how could it be anything but this way?
Monday, May 24, 2010
Monday, May 17, 2010
Numeracy and Home Ownership
Recently, The Economist Magazine had a little blurb on a study regarding subprime mortgage borrowers who lost their houses.
It turns out that those who did better on a simple math test regarding percentages and interest rates were much more likely to hold onto their house during the downturn (even after normalizing for income & type of loan, etc). Take the test here.
What good is all that math you take in school? Well, it may allow you to be a home owner one day...
It turns out that those who did better on a simple math test regarding percentages and interest rates were much more likely to hold onto their house during the downturn (even after normalizing for income & type of loan, etc). Take the test here.
What good is all that math you take in school? Well, it may allow you to be a home owner one day...
Thursday, May 13, 2010
Art and Science of Illusions
In the last few years I have taken to doing a very short unit on human vision and illusions after finishing up basic optics in physics. Mostly I focus on how much processing goes on in our brain when we "see". I emphasize that what we think we "see" is really the result of a LOT of signal processing and assumptions built up from experience.
In the neuroscience community, it has become something of a fad to construct optical illusions that illustrate this point. The embedded video below is getting a lot of press for winning an award recently and is a fantastic illustration of this fact of human vision.
Look at the angles of those ramps and that very high central pillar. Those balls are rolling up hill! We know gravity pulls things down, but our brains use these clues about the construction of the ramp to make us think the balls are rolling up hill.
Take a careful look at around the 30 second mark and the "trick" is revealed. The "long" pillar is not vertical and the ramps are not angled the way you thought they were...
These types of illusion bring to mind M.C. Escher and, indeed, there is a whole school of thought about Art and Physics (see Shlain's book of the same title) which posits that Artists start seeing and playing with perception in a new way that just precedes what scientists are about to do in the scientific arena. When society is ready for the next level of abstraction, artists lead the way and the more cautious, constructionist scientists follow. If this is so, then perhaps we are about to have a breakthrough in theoretical physics based on our new understanding of the illusory nature of our own perception...
In the neuroscience community, it has become something of a fad to construct optical illusions that illustrate this point. The embedded video below is getting a lot of press for winning an award recently and is a fantastic illustration of this fact of human vision.
Look at the angles of those ramps and that very high central pillar. Those balls are rolling up hill! We know gravity pulls things down, but our brains use these clues about the construction of the ramp to make us think the balls are rolling up hill.
Take a careful look at around the 30 second mark and the "trick" is revealed. The "long" pillar is not vertical and the ramps are not angled the way you thought they were...
These types of illusion bring to mind M.C. Escher and, indeed, there is a whole school of thought about Art and Physics (see Shlain's book of the same title) which posits that Artists start seeing and playing with perception in a new way that just precedes what scientists are about to do in the scientific arena. When society is ready for the next level of abstraction, artists lead the way and the more cautious, constructionist scientists follow. If this is so, then perhaps we are about to have a breakthrough in theoretical physics based on our new understanding of the illusory nature of our own perception...
Additional note (Jan 2021): My man Derek Muller explores these ideas in great depth: https://www.youtube.com/watch?v=dBap_Lp-0oc
Sunday, May 9, 2010
Placebos, Diets, and the Power of Avoiding Negative Things
After a recent piece on the radio about another diet craze (Paleo Diet), a thought that has been bouncing around in my head for a while crystallized (at one point in the piece, a guy on the paleo diet said something like "I am allergic to eggs, so now that I am on this diet - I am much better off" and I remember thinking "well, couldn't he just avoid eggs without this diet?"):
All diet plans seem to work because they force you to pay attention to what you are putting in your body. That can only be a good thing, right? Then, it is just a matter of finding the diet plan that works for you in the sense that you to stay with it so that you pay attention for a long period of time! That might explain why different diets work for different people - even though the diets are antithetical to each other (think no carbs and all-carbs!).
Maybe this is what's up with the placebo effect in medicine. As long as you think about getting better and think that you are - you are paying attention (in a positive way) to your body and that can only help things along...
I'm not really talking about the power of positive thinking here - I'm talking about the avoidance of eating random things or engaging in activities not conducive to healing. I AM on a diet, I AM taking medicine that WILL make me feel better are thoughts that may not heal you on their own, but they certainly could help you make better decisions...
All diet plans seem to work because they force you to pay attention to what you are putting in your body. That can only be a good thing, right? Then, it is just a matter of finding the diet plan that works for you in the sense that you to stay with it so that you pay attention for a long period of time! That might explain why different diets work for different people - even though the diets are antithetical to each other (think no carbs and all-carbs!).
Maybe this is what's up with the placebo effect in medicine. As long as you think about getting better and think that you are - you are paying attention (in a positive way) to your body and that can only help things along...
Sunday, May 2, 2010
Arabic (?) Numerals
My entire life, I have thought of our numeral system as Arabic Numerals - that is how I was taught. Now, I find out that these numerals are Arabic in the sense that turkeys are "from turkey" - which is to say, not really. I was skimming the book "The Babylonian Theorem" by Peter Rudman from the local library (I tend to check out too many books to read and skim the nonfiction ones for fun - sloppy; I know, I know) when I read something along the lines of "when they invented the zero in India". Huh? I thought zeros were from the Arabic civilization.
Turns out the west found out about this cool system of numerals from the Arabs who got it from the Indians, but I was only taught one layer deep... Check out these pics from Wikipedia:
(First Century AD Indian numerals)
I am immediately struck by the the first three characters being the same as in Chinese:
(chinese chart clipped from http://mathematics.gulfcoast.edu/leolusk/4_1.htm - see comments)
I've been pondering the roman numerals being for 1-2-3 being vertical strokes (I II III) whereas the chinese ones being horizontal for some time now, but what I didn't realize until today is that our western hindu-arabic 2 and 3 are formed by connecting the 2 or 3 horizontal lines from the ancient Indian script.
Here's another picture from Wikipedia showing a phone with modern Western and Easter Arabic numerals :
The French may think that their turkey are from India ("D'ind" - see link above on turkeys), but really their zero's are. As a convoluted bonus we say "love" for zero in tennis because it sounds like "l'oeuf" (egg) in French. Wonder what they say for zero in tennis in India...
Turns out the west found out about this cool system of numerals from the Arabs who got it from the Indians, but I was only taught one layer deep... Check out these pics from Wikipedia:
(First Century AD Indian numerals)
I am immediately struck by the the first three characters being the same as in Chinese:
(chinese chart clipped from http://mathematics.gulfcoast.edu/leolusk/4_1.htm - see comments)
I've been pondering the roman numerals being for 1-2-3 being vertical strokes (I II III) whereas the chinese ones being horizontal for some time now, but what I didn't realize until today is that our western hindu-arabic 2 and 3 are formed by connecting the 2 or 3 horizontal lines from the ancient Indian script.
Here's another picture from Wikipedia showing a phone with modern Western and Easter Arabic numerals :
The French may think that their turkey are from India ("D'ind" - see link above on turkeys), but really their zero's are. As a convoluted bonus we say "love" for zero in tennis because it sounds like "l'oeuf" (egg) in French. Wonder what they say for zero in tennis in India...
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