Quantum Mechanics and False Dichotomies

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?

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...

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... 

 Additional note (Jan 2021): My man Derek Muller explores these ideas in great depth: https://www.youtube.com/watch?v=dBap_Lp-0oc

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...

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...

Crackers, Entropy, and Time

Sebastien broke a cracker the other day.  Lately, he has been trying to put the broken ones back together before eating them.  This invariably frustrates him and he looks to me while making that pouty face.  I tell him "Sorry, you just can't fight entropy - it's always gonna win in the long run!"

All the different ways that cracker could break - so many possibilities.  Yet, only a very few, carefully lined up ways to put it back together.  Statistically, it's just not gonna happen with the two of us pushing the pieces together with our fingers.  Statistically, it's much more likely to remain broken, or, to break further as we try.  I know this from experience - he's just finding out the cruel nature of entropy for the first time.

We are going "forward in time" for the same reason: entropy.  The only thing giving a "direction" to time is that statistically crackers are more likely to break than they are to be made whole again.  Break a few more crackers and now you are 40 years old instead of 20 months old.

"Aha," Sebastien may be thinking, "I will cheat time by making a cracker factory in which we turn cracker crumbs into crisp new crackers!" 

That is all fine and well inside your factory, but the cost to the outside universe!  You will be dumping waste heat and sowing disarray with your discards at a rate exceeding your cracker making capacity.  Global entropy increases and time moves forward.

Sebastien scratches his head (very cute) and then thinks "What if I am very, very small and I don't interact at all with the rest of the universe?  Then can I cheat time?"

Hmm, he has a point there.  If you completely isolate yourself and don't break any crackers yourself then you may indeed have made time an irrelevant concept.  That's what's happening with different quantum states for subatomic particles when we say "we know they're in there somewhere but we don't know exactly where until we go looking for them".  Those isolated, non-cracker-breaking subatomic particles are not "buzzing around, skipping from state to state" - there is no sequence of events to them.  For time has no meaning to them and all their options stack up on top of each other into one big past-future-now stack called a "superposition".  No remembrances of things past and no excitement for the future in that world.

Maybe breaking crackers is a good thing? 

Deciduous/Evergreen

Struck again by sparse dark branches naked on a blue sky

A canvas upon which I sometimes project my thoughts

My younger self grasping for the imponderable

An older version of myself will someday do the same

This image threads together the stages of my life

Scattered white clouds; gentle swayings in the breeze

These lonely, dead branches will be/once were lushly green

At those times, I wonder about their future/past stark barrenness

Deciduous thoughts leading me to contemplate the Evergreen

But those trees are ever-changing

They will/were not always be here

Even the sky was not ever so

Am I pondering the Eternal

or the Changes that make me pine for it?