That "hole through the center of the Earth" question

I'm always asked these sorts of things.  Go figure.  I suppose it comes with the job, like the Air Force general based in New Mexico who continually deals with Area 51 speculation.

If you dug a hole through the center of the Earth, and jumped in, would you stay at the center because of gravity?

This experimentalist's answer:

No, because (a) the engineering barriers to digging said hole are insurmountable, and (b) if you weren't crushed, you'd be asphyxiated or, more likely, burnt.  Look up the temperature of Earth's core.

The theorist's answer:

Assume the hole is wide enough that there are no forces other than the gravitational interaction between you and the Earth.  The gravitational field INSIDE the Earth is zero at earth's center, always points toward Earth's center, and gets bigger as a linear function of distance from the center.  (The mathematics here are the same as when using Gauss's Law to determine the electric field inside a sphere of uniform charge density.  The 1/r² dependence only occurs outside the sphere.)

By definition, when an object experiences a linear restoring force, its motion is simple harmonic. Thus, you'd oscillate about the center of the Earth like an object attached to a spring.  If you jump in from Earth's surface, then, you'd speed up until you passed earth's center, after which you'd slow down, reaching the surface on the other side of the earth before you repeated the process ad infinitim.

"Does that make sense?" Don't take 'yes' for an answer.

I am at heart the most straightforward, literal person in the universe.  I mean what I say, and I say what I mean.  And I hear the words that people say, too often without considering the body language and social cues behind the words.

Consider the friendly sophomore from Norte Dame Academy, at the, I dunno, 1988 or so Kentucky State Latin Competition.  We met there and had been talking throughout day.  Her team's bus was leaving before the award ceremony.  She gave me her number, and said, "please call me tomorrow to tell me the results." So, the next day I dutifully called.  I gave her the results.  I congratulated her.  I said goodbye.  I never saw her again.  Sorry, Lisa.

Or, the wonderful woman in grad school who, after we had hung out together several afternoons, said "Can you come over to my apartment tonight?  My roommate will be out.  I'll cook you dinner." I accepted.  I thanked her for the yummy meal, and left.  Sorry, Michelle.

Or, and more pertinent to this blog, the diligent junior in the weekly problem solving sessions that my college paid me six bucks an hour to run.  I showed her how to solve a problem involving the work-energy theorem.  I asked her if the approach I suggested made sense.  She said, "yes."  I took her at her word.  Sorry, Alex.

I suspect that most readers are shaking their heads at the first two stories, wondering how I could be so clueless.  Had I recognized Lisa's or Michelle's body language and tone of voice, events would have turned out less dull, or at least differently.  And decades after the fact, I now have the perspective to recognize what I missed.  Most people wouldn't have misunderstood these cues in the first place, of course; I had to work consciously on interpreting social subtext, even though such interpretation comes naturally to others.

Over twenty-plus years of teaching, I've similarly had to continually analyze and re-evaluate my students' body language and tone of voice.  In 1994 I believed Alex when she told me she understood my explanation.  Why would she have said "yes" if the real answer was "no"?  In retrospect, there could be any number of reasons.  Among others:

(a) I'm a proud, diligent student, and I cannot admit to myself or (especially) to a peer that I don't get something; 

(b) I don't quite understand this right now, but I have irrational confidence that if I stare at the problem for another 20 minutes I'll magically see the light; or 

(c) I really wish Greg would shut up and stop explaining, and the only way I can tell him that without seeming rude is to pretend I understand.

Nowadays, when I explain something one-on-one to a student, I still ask, "does that make sense?"  But I'm ignoring the verbal content of the response.  I'm watching for and listening to body language and tone of voice.  Students often use words they don't mean.  Their tone usually gives their true thoughts away; it's practically impossible for a high school student to send false messages with body language.  

What am I looking for in response to "does that make sense?"

When I explain how to approach a physics problem, I always make the student go back to his seat and write up the solution in his own words.  So I'm watching how he leaves the vicinity of my desk.

The student who truly understands my explanation can hardly wait to get back to his seat to put his newfound knowledge into practice.  He usually moves with confident purpose.  Sometimes he'll have a bit of sheepishness about him, because he realizes he should have figured this out earlier.  

The student who's still confused walks much slower, with his eyes turned upward or downward.  He's in no rush, because either he's still thinking about what I said, or perhaps he's frustrated that I won't just tell him the right answer and he's throwing a wee tantrum.  

So, when the confident student comes back a moment later, I can move him along without thinking about it -- he's got it.  

But even if the less confident student comes back with a correct answer, I still push a bit.  I ask a few more questions to test for understanding.  I make him write each step of reasoning explicitly, even though I might have let the confident student slide by with some things implied.  I don't harass or embarrass, of course... I simply recognize that this student has shown me through his body language that I have to do more to help him.

Woodberry Forest Conceptual Physics Tournament -- want to be an "examiner"?

My school has for years given three sets of exams, one each trimester.  This year, though, we're limited to two written exams.  For the last trimester, we're encouraged to create a cumulative project of some sort in lieu of an exam.  Yay.

Thus, we are creating the Woodberry Forest Conceptual Physics Tournament.  This competition for our 9th graders, to be held at 1:00 on Sunday May 21 2017, replaces their final exam.*

*No, to be clear to all, we're not giving an A to the winner and an F to the person in last place.  That's silly.  We're just having a fun, competitive tournament, to determine a winner.  Judges aren't awarding grades.

How does this tournament work?

On May 2, I will reveal a slate of three problems to the 73 participants.  These problems will be old AP Physics 1 "paragraph response" questions.  Except, rather than just answer in a paragraph, the students will spend the month of May setting up experiments to provide evidence for their answers.  By tournament time, each student will be expected to be prepared to discuss the solution to two of the three problems, with both theoretical and experimental support.

At the tournament, each student will participate in two "physics fights."  Think of these physics fights like a miniature version of a graduate thesis defense.  Students will have a strict limit of three minutes to present their solution to the examiner.  An examiner then will engage each student in conversation about the problem for five minutes.  The students are judged by the examiner not only on the quality of their solution, but also on their ability to discuss the solution, to confidently hold a conversation with the examiner.

How do the students prepare?

Starting on May 2, all conceptual physics classes the rest of the year will be devoted to tournament preparation.  They'll set up experiments in class, they'll be assigned to write up their solution as homework, they'll practice presenting.  

Most importantly, my AP physics classes will spend their final weeks of the school year serving as mentors to the conceptual students.  I will assign each AP student to lead groups of three or four 9th graders.  The AP student will dive into the problems with the freshmen, helping to create and analyze experiments, helping the freshmen to understand the details of their presentations, and serving as mock-examiners in practice sessions.  This mentoring serves as the final project in lieu of the exam in the AP classes.

We need examiners.

The key, I think, to any class project is external assessment.  I and the other conceptual physics teachers will play the role of coach and advocate, always encouraging and helping the students to deepen their understanding of the problems and to improve their presentations.  Our relationship will be purely supportive, enthusiastic, positive.  

We can't then turn around and grill these same students as examiners!  That'd be like our football team's coaching staff refereeing the state finals.  Even -- especially -- if their officiating were fair, the coach-student relationship, both in practice and after the game, would be irrevocably compromised.

So we need examiners.  We can pay.

Would you like to come to Woodberry on May 21 to be an examiner?  My guess is we'd ask you to arrive at lunch time, like 12:00.  We would have a meeting of all examiners in our beautiful dining hall over lunch.  

Then we'd ask you to be the examiner for a couple of hours' worth of physics fights -- depending on how many examiners we get, you'd probably be asked to run 8-12 rounds.  Then, we will gather everyone into our auditorium for the top two participants to engage in a final physics fight for the championship.

In any case, my goal is to be done by 3:30, or possibly (it's our first time running this) 4:00 if there are logistical issues.  No later -- our students will be attending the final seated meal with their advisors that night followed by study hall, so we can't run late.

We will pay you $100 plus lunch (and even dinner, if you'd like to stick around) for your time.  (If you're coming from more than a few hours away, we can put you up on campus on Saturday or Sunday night.) I think you'd find that the camaraderie among the examiners and the engagement with the students will make the trip worthwhile.

Who's eligible as an examiner?

Certainly any physics teacher, or anyone with a physics / math / engineering background.  I'm inviting alumni whom I've taught in an AP or AP-equivalent course to come back to judge.  I'd also welcome any alumni of your advanced physics class, even if they're still seniors in high school.  As long as you can engage in conversation about physics at the AP level, as long as you can recognize good and bad physics, we'd love to have you.  When I run the USIYPT, I find the mixture of undergraduate / graduate / professor / high school teacher / industrial physicist / retired physicist on the juror panel allows some amazing relationships to develop.  I'd love to create a similar vibe here.

How can I sign up?

Send me an email, or contact me via Twitter, or call me -- my contact information is on the Woodberry Forest School faculty page.  I'll send you more information, including the three problems, and our current draft of the judging rubric.