GPS and Louis Malle

Last summer, while we were travelling, I used a GPS device extensively for the first time.  Normally, I have a fairly decent sense of direction; take a look at a map and then keep track of where I am and I don't even sweat when I have to take a detour.

But, with GPS, I didn't prep, I didn't track, and I was completely lost all the time.  Of course, it didn't matter - because we had GPS! 

The double edge sword of technology - it makes our lives easier but it insulates us from reality.  Since I was uninvolved with the navigation, my brain just didn't engage and I was lost until the GPS device came to life.  I remember gently mocking friends about a year ago (before I used GPS) when I saw them pulled over in the parking lot after meeting them for a meal.  "Just waiting to find a few satellites" they said.  "Weirdos!" I thought.

All this reminds me of one of my favorite moments in Louis Malle's "MyDinner with Andre":  when they are talking about electric blankets.  On one side they are such a boon - they keep you warm no matter what the outside temperature is.  On the other hand, the potential empathy that might have been brought about by the cold is gone.  Is the person next to you cold?  Are there people who are cold and can't find shelter in the world? 

GPS: my enabler and my disabler.

Physics Rap Part Deux

Newtonamania

Lean in close - I ain't gonna hurt ya
All I wanna do is talk inertia.
what it is is a property of motion
Measured by mass, big like the ocean -
Could be small, like your IQ quotient
hoverin' near zero / Newton is my hero

Your natural state
is to sail sweetly
not come to stop
oh-so-neatly
Aristotle was wrong
Galileo was right -
to stop takes a fight
Wooo - this rap's outta sight!

"Look at me -
How fast I go!"
Universe don't care;
No  - no - no.
If V is constant -
then A is zero / Newton is my hero

Listen up, follow my flo -
To the moon we shall go.
Little ole "g" is smaller you see.

On the moon, weight is puny
Tiny tiny forces, kind of cartoon-y
Stubbed your toe, kind of lame -
Forget your mass is the same?
Shame shame shame-
So lighten up dear-o / Newton is my hero


What's up with all these crazy crazy forces?
Like U2 - riding wild horses:
Speed it up or slow down,
Twist or turn - you still a clown!
All that changin'  V over delta t?
It's force over mass quite simple-y
Nothing to fear-o / Newton is my hero
Hurt and confused, need amelioration?
You got forces, but no ex-celioration?
For you - might be big conundrum;
Simple equilibrium - humdrum humdrum:
Net force is zero / Newton is my hero

I push you - you push me
We're a happy family
With a pair of forces
one for each
We push equal opp'sitely

Standing on giants' shoulders
Seein' further over boulders
Keep these laws near-o /Newton is your hero

A New Twist on an Old Grading Paradigm

"You all have A's at this point" is a not uncommon opening day remark in school.  I am not one of the teachers who say that because I don't think of grades this way (I think of it is as an accumulation of effort and performance as the year goes along).  However, I do like to a play a little game with this concept near the end of the first marking period.  Here's how it usually plays out:

Me: "I have been thinking of a new way to do grades"
class looks slightly intrigued
Me: "I was thinking of starting everyone off with 100's and take away points rather than adding them"
some students looking serious, some looking disturbed
Me: "As the years goes on and as you make less than perfect scores the 100 would go down"
some students (seeing where this is headed) look distraught, some still going along
Me: "And then that fateful day would come when you would get down to the 89 and know that the A was never coming back"
all students looking horrified but some now realizing it is a joke
Me: "What do you think, sound like a good idea?"

Plato's Cave and The First Science Lesson

If you are not familiar with the allegory (or just want a refresher), click here for a three and half minute intro to it. This should be the first lesson in science.  Forget the scientific method or proper measuring technique or interpreting graphs:

We experience directly only narrow slices of the rich universe we live in:

Colors we see: red through blue

(but nature goes much lower than red and higher than blue)

Temperatures we feel:  from about -20 degrees Celsius to 100 degrees 
(but nature goes as low as -270 and up to the 100's of billions in Supernova explosions)

Speeds we experience:  from zero to 350 m/s (the speed of sound)
(but nature goes as high as 3,000,000 m/s - the speed of light)

Timescales we notice: 0.2 seconds (human reaction time) to 80 years 
(but nature goes from 10^-44 (the Planck unit of time) seconds to 15 billion years (the age of the universe))

sounds we hear: from 20 Hz to 20,000 Hz
(but nature creates pitches into the billions of Hz)

Distances we can experience directly: .000001  to 10,000  meters
(but nature goes from 10^-35 (the Planck unit of length) to 10²⁶ (the size of the observable universe))

We really are just stumbling around in the dark without science to help us out!

Rules, Impulse Control, and Dune

In years past I have shared with some of my student my "three rules for life":

1. Don't Rush
2. Balance
3. Live within your means

Of course, as I usually point out, all three of these are really all about balance.

The "Don't Rush" rule is about balance in time:  Enjoy the stage of life you are in. If you keep rushing to get to the next stage... well, we all know what the final stage is, don't we?

"Balance" I usually explain in terms of short term happiness vs. long term goals, selfishness vs. living for others, planning vs. carpe diem etc.
Rule #3 is self-explanatory but useful to point out in a society consumed by debt.

Lately though, I've been thinking about replacing the short list with "Impulse Control".  There is a great scene in Frank Herbert's Dune where the main character must survive a trial of pain (the gom jabbar): his hand is placed in a box where the nerves are stimulated with incredible pain but he must leave his hand inside as he knows the test giver will kill him if he pulls it out.  Rational intelligence over animal instinct.   Impulse Control. 

Revolutions, Islands, and the Melting Pot Names

Bemelmans can't count!

I grew up with Madeline and her two straight lines in her house covered in vines, but I never discovered an error until reading the book to my daughter.

After visiting Madeline in her recovery room (a bed with a crank!), the eleven remaining girls go back to their old house to break their bread, brush their teeth and go to bed.  In that three picture sequence (bread-brush-bed), the number of girls goes from 12 to 11 to 11.  Careful inspection reveals Madeline sitting at Miss Clavel's left at the dinner table but absent subsequently.  Perhaps Madeline went home with the other girls but upon eating dinner, suffered a relapse and was rushed back the hospital before the brushing of the teeth?

Also, is it just me or does Madeline's curly red hair look suspiciously blond and straight in several pictures?

'Tis a child's story, I know.  Maybe the Hollywood movie filled in the gaps?  I doubt it.

Subtraction and the Number Line

5-3

or

Five minus three

or

Five take away three

Same thing? Only if you are counting! If you believe in numbers as abstractions (which you do if you believe in the number zero, the concept of infinity, or negative numbers), then 5-3 is NOT Five take away three!

Lately, my friend PS and I have been discussing the wrongness of this idea of subtraction as "taking away". The conversation started with a TMBG video we show our kids about Zeroes and resurfaced recently when he fell asleep at a kindergarten curriculum night looking at the number line. Years ago I read a book called Where Mathematics Comes From which has really informed my thinking about math concepts. Out of these influences I have decided that we should throw out the old ways of "5 take away 3 leaves us with 2" to be replaced with the correct "marching 5 units to the right along the number line and then marching 3 units to the left leaves us exactly 2 units to the right of where we started".

(image from ehow.com)

The idea of subtraction as an act of "taking away" is sloppy thinking which most people get away with because they don't have to think things through. Not, that is, until they get to vectors in physics. What we find is that students think of negative acceleration as always meaning slowing down. This is because they think of negative meaning "taking away". The fact is if you are already heading in the negative direction, a negative acceleration will speed you up! (imagine going in reverse in your car and then stepping on the gas) Only now will the student begin to think of negative signs properly - as an indication of direction along the number line NOT as an act of taking away.

There is no subtraction.  There are only positive and negative and these mean: "going to the right" and "going to the left" respectively.

"5 - 3" is short hand for "(+5) then (-3)"

If this were how students were taught to think of the minus sign then when we introduce them to negative accelerations they will think "that is an acceleration directed to the left as opposed to the right" and kinematics would be a lot easier for them (and for us to teach).

Learning is only hard when there is a lot of unlearning to do first.