Phys 87: Thinking Like a Physicist
Meets Wed. 3–3:50 PM in MHA 2623 Fall quarter, 2016
This Freshman Seminar is meant to free the minds of our
students so that they approach problems with flexibility,
intuition, and quantitative estimates. You think that's π you're
Students in physics classes often have problems transitioning from the lower
division courses into upper division courses. Many reasons
contribute, but one observation is that students have developed a
habit of solving problems by pattern-matching. This can come in the
form of equation-hunting or relying on exposure to essentially
identical problems from the past.
Human beings are powerfully adept at pattern recognition, and this
versatile tool can get us rather far—all the way to
upper-division physics. At this point, concepts begin to rule, and
students must have a well-stocked toolbox of mathematical techniques
at the ready—and know which tools to grab for the problem at
hand. Sure, identifying relevant concepts and applicable tools also
constitutes a type of pattern matching, but at a higher, more flexible
- Equation-hunting and formula-wedging are increasingly prevalent in
physics majors: historically more characteristic of engineering
- Over-reliance on pattern matching
- Stiff and formal relationship with numbers (relax, and let
π = 3 = 10/3 = sqrt(10))
- Difficulty adopting concept-driven, first-principles approach
- Under-developed intuition; infrequent application of symmetry
- Infrequent use of sanity checks, unit checks, estimation for scale
- Lacking intuition on basic units: how much is a N, J, W, C, F,
One may only speculate, but here are some thoughts:
- The educational system places emphasis on testing
- Many secondary education teachers don't really "get it"
- Changing population of majors: pragmatic, STEM-driven job-seekers
who don't want to be left out of the emerging world
- Increasingly inaccessible world: urban environment with x-box and wifi vs.
farm/woods, repair/dissection of simple equipment
- What I call the "Dora the Explorer Syndrome"—where
emphasis is on the idea, not on challenges and practical
feasibility of implementation. Kids come away thinking any
hair-brained idea constitutes a victory.
So let's try re-programming the way students approach problems
before reaching the upper-division whiplash moment. That's
what this Freshman Seminar aims to do. No guarantees that this will
be successful, but let's try building comfort and versatility in
thinking about problems so that students have better intuition and
alternate ways to sanity-check their answers. Among the approaches,
- Learn that there are often various ways to skin the cat
- Learn to ask: "How do I know if this is
right?"—and to answer on your own wihtout the aid
of an outside source (like answers in the back of a book, or online
solutions to a problem)
- Build estimation skills to assist sanity checks
- Apply intuition to anticipate the outcome, and apply feedback to
refine intuition when it is found to be off
- Check for symmetries or end-runs to potentially save time
- Check symbolic results in limiting cases to verify proper behavior
- Identify reliable, basic concepts (e.g., conservation laws) and
build your own formulas from there
- Encourage exploration and daily life problem creation/solving
Famous physicists like Fermi and Feynman frequently forged
formidable feats 'festimation. Less alliteratively, good physicists
tend to have well-developed estimation abilities. Seldom are these
skills learned in classes, but "learned on the mean
streets," as my colleague George Fuller puts it. Maybe it's a
selection effect: those who are good at estimation are more likely to
succeed in physics/science.
For me personally, I learned at least as much in my
explorations outside of class as I did in the formal classroom. I
almost always had some problem I was chewing on, and my eagerness to
understand and make progress drove new discovery. What's more,
because I had problems in mind (some of which I got stuck trying to
solve), when new concepts and tools became available in the classroom,
I would think, "Aha! That's the piece I've been waiting
for!" and I could return to the problem and do it less clumsily
than before. By having context in mind already, I had carved out
space waiting to be filled by classes. By exploring the problem
before and after new techniques came along, I owned the
material. It was personal. It meant something to me.
Examples of problems that occupied me during high school and college
appear in the list below (not chronological). I'm sure I am forgetting
numerous lesser problems, but these are the ones that stand out in memory.
And yes, my tendency to actually carry out these schemes brands me as an
experimentalist. But just because kid-me did some stupid things does not
mean that adult-me condones these activities!
- Why is the time between successive new moons not always
29.530589 days?—led to a successful science fair project
- In the process of working out the above problem, I needed
essentially instantaneous changes in some quantities, so I invented
the derivative to accomplish this. Granted, it was a crude
quantitative construct formed by differencing two values as the
independent variable (e.g., time) suffered a quantitatively very small
change. Later that year when derivatives were introduced in my math
class, you can imagine my excitement and personal connection. That
whole "limit as delta-x approaches zero" business? Totally understood
why. I owned it.
- What math describes the distance between lines of longitude on the
lunar map hanging over my desk?—when I first encountered the
sine function as a junior in high school, I had another Eureka moment:
I had been waiting on the sine, and had an immediate friend.
- What is the circumference of an ellipse?— the
formula for area is easy. The circumference is an introduction to
elliptic integrals, unbidden.
- Is the trajectory of a thrown rock a parabola or the end of a
very long ellipse?—and how to reconcile the math that says
parabola with the intuition that says ellipse?
- How does gravity vary as a function of latitude? Can I
reproduce the curve shown in my undergrad textbook by a combination of
Earth's oblate shape and centrifugal force?
- How should I throw a water balloon from the back seat of a
roller coaster to hit the front car as we go around a loop?
Elliptic integrals again?!
- Can I compute Sun and Moon positions accurately enough to
produce an eclipse track to kilometer accuracy?—associated
with my journey to the 1991 solar eclipse.
- Can I measure the radius of the Earth myself armed with a
theodolite?— yes, to about 10%. Variations in atmospheric
refraction limited accuracy.
- Can I use the same theodolite plus a timing signal get my
position on the Earth using star sightings?— yes: could tell
whether I was in my yard or my neighbor's, after a few weeks of
- What is the "muzzle velocity" of a three-man
sling-shot?—based on measuring "hang time" and
figuring in drag
- Building a telescope also exposed me to many practical
problems requiring thought, calculation, solutions, design,
A word on emulation
The lesson should not be to copy what I did. Emulating a rock star's
visible behavior is not effective (and will probably land you in jail!).
Countless hours practicing and honing the basic skills is where it's at
(which is utterly boring to most people). Concert pianists spent years
perfecting excruciatingly uninteresting scales before spinning off
masterpiece performances. Emulation is not in itself a likely path to
success. Rather, find your own interests and ask your own questions. Let
your curiosity guide you. Plunge in to solve problems or go as far as you
can while you wait on pieces to fall in place. Don't be afraid to explore.
It's stumbling into the dark that lets you build a picture of what you
can't see by staring into that darkness.