"Those who cannot learn from history are doomed to repeat it."
--- common paraphrase of George Santayana
"Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime."
--- common paraphrase of Anne Isabella Thackeray Ritchie
Have you ever gotten the impression that the introductory physics textbook you are forced to use is a charlatan,
that maybe it was designed by physicians and engineers purposely to make physics look boring,
so that anyone with any imagination would be driven away?
Generally such a book looks much more like a history book, and
apparently the author thinks that the only way to learn from the mistakes of history is to repeat them.
(Let's hope he didn't write the lab manual, too.)
Or maybe he is just a disgruntled physicist, who thinks that, well, he had to learn it that way,
so, by golly, that's the way you're going to have to learn it, too.
This type of approach has several important drawbacks, even for
The course is taught basically like this:
- Such books give no hint of how a scientist really thinks.
If you learn anything in school, it should be how to think.
Memorization is less useful: You can always look it up.
- The science of tomorrow is not the science of yesterday.
Even biologists should know quantum mechanics and special relativity,
which are relevant to things like
molecular biology and particle-beam cancer treatment.
The new ideas of tomorrow, in any branch of science, will
not come from just old physics.
- College degrees have breadth requirements for a good reason.
Breadth does not mean teaching outside topics as if they were inside.
This has the consequences:
- Give a few examples in class.
- Give the same examples on homework.
- Discuss the same examples in recitation sections. (I.e., do the homework problems for them.)
- Give the same examples on the exam.
I almost forgot the most important point: Every problem gives numerical values to all quantities, and answers must be given in numerical values. So every problem is not only a test on units, but also on how well one can use a calculator, which on an exam means a hand-held calculator (but not a smartphone, which is too smart). This teaches every student:
- They complete the course thinking it was very clear, the instructor was wonderful, & they really learned something.
- If you give them a truly different example to work out, they can't do it.
- If you ask them anything about any of the fundamental equations/principles the examples are applications of, they don't know it.
- Anything they learned can be produced more easily, efficiently, & accurately by an app on their phone.
- By the next semester they've forgotten everything.
- Arithmetic is more important than algebra. Plug in numbers as soon as possible so you can lose sight of what you're doing. (Something similar is happening to grad students, who now use Mathematica™ to do all algebra & integrals.)
- Use only 1970's technology. 1960's technology (slide rules) or worse yet, doing arithmetic in your head, is obsolete. But 1980's technology (personal computers) is cheating.
Here is a list of some of the things I have found in such books given to me as the "TA" of such courses:
Here's some more stuff I found in a similar textbook for pre-med students:
The concept of symmetry as an invariance of nature is nowhere even mentioned. Symmetry appears only as a property of particular solutions or problems. Linear symmetry is not distinguished from cylindrical symmetry. Rotations as transformations are thus not given, not even when discussing angular momentum. No indication is given how dot products and cross products relate to rotational invariance.
The introductory chapter of the book includes a discussion of units,
but nowhere is mentioned the fact that the whole point of units is
that you can choose whatever units are most convenient, such as using
the (reduced) mass of the electron as a unit of mass in atomic physics.
The book begins with "handyman physics": fulcrums, pulleys, etc.
Who are we trying to attract to physics, carpenters?
(This is why I didn't get interested in physics until I was 8, instead of at 5.
By then I learned from Crackerjacks and cereal that the good stuff is at the back, not in the front.
But you can't teach a course that way.)
Particle physics is tacked on the end (although a few particles themselves appear earlier, and collide).
Special relativity appears near the end, if at all, and after electromagnetism and optics.
(Ever hear of nonrelativistic light?)
Of course, that means in practice it won't be covered in the course.
Galilean relativity isn't covered until just before special relativity.
So students never get a chance to learn about symmetry.
- Vectors are done with unit vectors "i, j, k" (even in upper-division undergraduate courses), which are really quaternions. Why are we teaching them quaternions when we haven't even taught them complex numbers yet? Does anybody really use them anymore? If so, what is the unit vector for time in 4-vectors? (In this old quaternion notation it would be 1, but I'm sure nobody has used that since Maxwell.) Obviously this notation was already out of date in 1905, so why do we still teach 19th-century notation in the 21st century?
Newton's laws are discussed before conservation of energy and momentum.
Ironically, conservation of energy is used before Newton's laws
for the special case of constant acceleration (i.e., gravity),
but only as a subsidiary condition and not by name.
Scattering is discussed, and later the center of mass, but nowhere is the center-of-mass frame discussed!
(I guess you can ignore most modern accelerators.)
Centrifugal force is said to be misleading or incorrect, as demonstrated by a drawing of what would happen if an object were released from circular motion. In fact, the drawing is incorrect, since it illustrates only the centrifugal force, and ignores conservation of angular momentum, as if there were an angular friction. No wonder it took so long for Einstein to invent general relativity.
Electrodynamics is apparently about circuitry.
(What are these stupid constants "ε0" and "μ0"?)
Complex numbers don't appear till the end of quantum mechanics (itself toward the end of the book). Sin's, cos's, and complicated trigonometric identities abound, especially for electromagnetism. (On the other hand, quaternions are OK? See above.)
Ampere's law is given first in its original incorrect form
(with little hint given that it is wrong),
then corrected much later.
Maxwell's equations appear in full only in integral form, not differential (except in an appendix),
even though a partial version of the differential equations is applied to radiation.
The gradient appears only in a footnote (the divergence & curl only in the appendix).
Refraction of light is claimed to have no explanation in terms of particles,
quoting Newton's failure. Of course it does: As we know from quantum mechanics,
Newton's mistake was to confuse phase and group velocities.
For special relativity, Lorentz transformations come before 4-vectors.
Minkowski space isn't even mentioned.
Planck's constant is introduced in its original form, as "h";
" ħ" does not even appear.
- Although forces are often given as vectors, only the magnitude of the force is given in the equation for Coulomb's law: The radial unit vector never appears; it is only described in words.
- Derivatives & integrals are repeatedly used, but almost never by name. "Δ" is always used instead of "d", and "∑" instead of "∫". Solutions to differential equations are given (e.g., for circuits) without the equations.
- Dot products and cross products are frequently used, but never by name. In specific applications, dot products are written either with cos θ or with the projection of one vector on the other, but never with both, nor is the equivalence indicated. The right-hand rule appears to work differently in different cases.
- Maxwell's equations are called "Maxwell's predictions", and written only in words. Ampere's law is never corrected.
- A relativistic cube is said to appear "rectangular". If they had even only watched a little popular science on TV, they would know it appears as a rotated cube.