From PHYS-L W. Beaty 1999
> Question: How strong is your mathematical background?Undergrad engineering at U of Rochester, partial diff-equs, linear algebra, nothing higher. And this all mostly unused after twenty years.
> It seems you read a lot and write a lot, but you seem to > give short shrift to the equations.Oh, most definitely. In part, this is from a longstanding dose of Math Anxiety which I've never entirely defeated. But this just provided the seed. My avoidance of symbol-based reasoning is also a very intentional philosophy: If I want to communicate with people who speak English, then I must speak in English and finally THINK exclusively in English. My understanding of "Latin" might sometimes help, but more often it will interfere with English-think.
To really explain physics to the general public, I cannot rely on
anything resembling symbolic mathematical reasoning. It would cause me to
tell people "You cannot understand this, you don't have enough math
skills." The truth actually would be: "I cannot explain these
concepts in English, I am
hobbled by long usage of a crutch composed of mathematical concepts."
"A man of true science uses but few hard words, and then only when none will answer his purpose; whereas the smatterer in science thinks that by mouthing hard words he understands hard things."After "descending" from the symbological heights of university-level science training, and learning once again to talk physics with the unwashed masses, I rapidly perceived the unmistakable power in such an approach. Currently I commit the massive Physics-heresy of taking mathematics down from its high pedestal, and instead elevating something else, a thing which is very close to Pure Thought. Maybe describe it as "self-constructing conceptual networks." It's like picture-puzzles which, after being constructed in part, will magically attract the rest of the pieces and assemble themselves without help. Then we call it "AHA," "sudden insight," etc.
[Hey, I finally encountered a term for the above. It's called
"Babylonian" thinking. From The Character of Physical Law,
Babylonian minds elevate concept-nets and metaphor above all else... as
opposed to "Greek"
or "Euclidian" thinking which puts the equations far above concepts.]
There are plenty of math-based physics experts about. Why should I pursue
what everyone else pursues, when alternate paths might exist, paths which
lead to extremely useful viewpoints? "Everybody knows" that math is the
only route to physics. But study the misconceptions of textbook authors,
and you'll rapidly find that the greatest enemy of any scientist or
educator is the phrase "everybody knows."
> > I think we really should be discussing this on PHYS-L. Those people > > are sharp. If I've made a glaring error, they will find it quick. > > Well, most of my friends are embarrassed when they make a mistake. They > *really* hate screwing up in public, and they find it painful to back > down in public.I originally was just the same way: a huge flaming narcissist. In my longrunning observations of popular misconceptions (and also because of my fascination with the history and sociology of science,) I've come to the conclusion that avoidance of public embarrassment is a widespread mental disease among scientists. I have to constantly fight to eliminate it from myself. The "disease" is based upon dishonesty and a need to shield our egos from embarrassment-damage. Shielding ourselves from embarrassment has nothing to do with Scientific Integrity (see Feynman's CARGO CULT SCIENCE for wisdom about Scientific Integrity.) Shielding ourselves from embarassment leads to defensive twistedness in our reasoning; a shameful state for anyone hoping to tackle natures mystery.
The need to be right all the time is the biggest bar to new ideas. It is better to have enough ideas for some of them to be wrong, than to be always right by having no ideas at all. - Edward de BonoRather than courting dishonesty in order to avoid embarrassment, I conclude that we should do the exact opposite: constantly pursue embarrassment in order to avoid dishonesty. Even stronger advice: we should strive to burn every trace of dishonesty and habitual ass-covering from our thinking processes. Trial and error is vastly accelerated if we think aloud, while simultaneously a group of friendly colleagues points out our pitifully embarrassing blunders. This sort of thing can short out a large number of psychological ploys which we commonly use both to flee from embarrassment, and to preserve our misconceptions against attack. And the process of open criticism can almost instantly destroy our own cherished misconceptions, as long as we can avoid the usual response of retreating into defensiveness and into a reinforcement of our desire to Always Be Right. If we want to pursue trial and error, we should, in a certain sense, intentionally purse error. Or a better way to say it: intentionally exhibit our shameful flaws so the whole world can see. Over time, like magic, our flaws then become less and less. If instead we carefully hide them, then they can fester and infect many other parts of our thinking.
Don't get me wrong, I'm not saying that these things are EASY to do, or
that I'm always successful in doing them myself. I'm simply saying that
we would all benefit greatly if we could constantly strive in that
> Therefore (applying the golden rule) I try to avoid telling > people "you screwed up" in public. If this discussion *had* been on the > list, I would have tried to take it off-line, so as to reduce the chance > of hurt feelings.I request that you hurt my feelings, at least in regards to my falling into physics errors and misconceptions. I want to immediately know why I'm wrong, and don't spare any bit of the gruesome details. And it's better done in public, so others can defeat their similar demons.
People who wish to avoid the embarrassment of suddenly perceiving serious
personal mistakes while several hundred physics experts look on, need not
use listservers or newsgroups. Me, I recommend that everyone in the
Sciences make a habit of seeking out this sort of embarrassment. Don't
avoid it, instead develop a taste for it. Become embarrassment-gourmets.
Do the equivalent of pursuing the rare and exotic libation which
inexperienced children described as "rancid grape juice." The pursuit of
fermented fruit juice has rewards which the inexperienced children don't
I am convinced that this "pursuit of embarrassment" was a major component
of Richard Feynman's genius. He really, truly, didn't care what other
people thought. Most of us just don't get it. We give lip-service to
Scientific Integrity and/or Feynman's methods, but when it comes down to
actually employing them, we'd rather keep silent in order to maintain our
self-image as experts. We (amateur) scientists should instead be like
little kids who poke at things without a thought to looking like idiots:
we should be the very opposite of the self-declared experts who maintain
an exhalted and carefully defended image of our own perfection. Little
kids can see the mysteries. Little kids have a chance to defeat their
misconceptions by themselves, and to see very obvious things to which the
highly trained experts are blind. In addition, the highly trained experts
have a chance of acquiring massive misconceptions which they will fiercely
defend against all attack, because to relinquish their misconceptions
would damage their expertise in the eyes of their colleagues and in the
eyes of themselves.
Yes, this is yet another Physics Sermon. Please put your donations in
the tray as it passes among the pews! :)
"In science it often happens that scientists say, "You know that's a really good argument; my position is mistaken," and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time someting like that happened in politics or religion." - Carl Sagan
Some non-math physics books