The first thing I learned in my Physics undergraduate studies was Maths. Calculus. Scalar fields and vector fields, their derivatives and integrals, and differential equations of all kinds and flavours. Non-cartesian coordinate systems, transformations between them, fourier transformations. And a nice toolbox for beating the not-so friendly integrals.
Even for classical mechanics, that's the foundation.
If you want to talk about Quantum Physics you also need linear algebra, in particular Hilbert spaces and operators. And distributions.
If you don't understand the Maths, you are left with talking about interpretations. Especially in Quantum Physics, that means you are left with basically nothing.
Without Maths, you are not doing Physics. You are doing Metaphysics.
I almost feel that math ought to be learned through physics. At least, I remember my physics instructor explaining math concepts in a mich more terse and understandable way than my math professors.
I have a PhD in physics, and this is exactly how I learned the material. I mean, really learned it. I did fine in plain math classes, but never quite connected with the material.
Calculus and linear algebra both really only 'clicked' when applying them in my physics classes.
Physics is like the "word problems" we'd have in elementary sho, but for advanced math.
With no offense intended to mathematicians, a lot of the higher level material in my pure math courses tends to be of the "How many angels can dance on the head of a pin?" type. Debating the finer points of details that are mostly irrelevant minutia, yet which are given just as much text space as serious results that actually do things.
Physics' real-world origin prevents a lot of that sort of thing, and places emphasis on a practicality I find deeply appealing. Cauchy-Riemann equations are important, here's where they come from, here's what they do, bam done.
Although, there have been many cases where results from Pure Mathematics have found to elegantly describe phenomena in Physics, often years after the initial result which might have been regarded as the equivalent of "angels dancing on a pinhead" by physicists of the time.
Let's forget about the pure/applied divide. That's not what I am getting at and I want to make my language very clear. Let's instead talk about "maths for its own sake" and "maths for x" (physics, computer science, what have you).
Calculus is a nasty kind of maths to study for its own sake. It's not intuitive, and it's shaped by motivations that aren't at all clear until you've learned its applications.
Stuff like abstract algebra or graph theory on the other hand are - to me - "quite nice". They're certainly much more intuitive than anything in calculus world.
So, basically I agree with you - in high school, maths (by which we really mean geometry and calculus) should be hand in hand with physics. I mean that is its reason for being in the curriculum, to prepare future engineers. People who want to study "real maths" can learn something easier to grasp, and maybe a bit more profound.
Love your edit - rare to see that sort of honest self-criticism. On reddit it takes the form of '[deleted]' which I think is far lest honest than a retraction.
I don't know about any of that, but I know most people can understand how a computer works without understanding binary, transistors, quantum mechanics, or maths.
Superficial means of the surface. The surface of a computer is made up of materials such as glass, plastics, alloys, liquid crystals and light-emitting diodes, and paints. There are many levels that make up a computer and how it functions. You can't say you only know what is on the surface if you understand how it works multiple levels down.
If you meant 'they don't REALLY understand it', neither do physicists. There are many layers that make up a computer, and most physicists only understand the very bottom ones, and they can hardly use a computer as a result.
Just because there are some parts you don't full grasp doesn't mean you don't know how the thing works. If that were true, all physicists would only have a 'superficial' knowledge, because even they don't completely understand how the universe works.
Can anyone who's read the Feynman Lectures comment on how good they are? I started reading them, but after a few chapters I didn't feel that I was actually learning physics. I get the feeling that the Feynman Lectures are like Knuth's Art of Computer Programming: few people have read it, but it's widely known as being amazing. I'd be interested in hearing if this is correct.
The material in the Feynman lectures is deceptively deep. When he originally gave the lectures at Caltech, they were not all that well received. They were aimed at undergraduates, but the undergraduates -- some of the brightest in the country -- would end up stumbling out of the lecture hall looking like they'd been hit by a bus.
On the other hand, the lectures were quite popular among grad students and faculty members, if that tells you anything.
This stumbling out of the hall sounds like folklore. There are contradictory claims about how well the students took the lectures. (I attended Feynman's last lecture for Caltech freshmen, in the 80s -- a reprise of the volume 1 lecture on general relativity -- and saw nobody reacting like that. Admittedly we weren't going to get tested on it.)
For a few years at the beginning of my PhD, when I typed 'f' into the URL bar of my browser, www.feynmanlectures.caltech.edu/III_toc.html was the autocomplete instead of www.facebook.com. They are genuinely amazing once you have already studied some physics because they are so basic, yet so deep.
I may be biased (physics postdoc), but I think a lot more people have read (as in properly read, not just skimmed or cherry picked) the Feynman lectures than TAOCP. They're very approachable to anyone who understands basic real analysis and fairly short. They do start slow, though, that part is true.
I do think there's a bit of a misconception in that people think the Feynman lectures will teach them all there is to know about physics, at least in summary. That's false, if you want comprehensive coverage (of classical physics, mostly), try Landau-Lifshitz. The Feynman lectures are an idiosyncratic, fairly shallow treatment of selected parts of physics, produced by an extremely original mind. They're invaluable for the peculiar perspective they offer more so than anything else.
The first half-dozen lectures are not representative. They're sort of easing into the picture before getting started tackling problems.
I'd recommend giving volume 1 a shot to anyone comfortable with freshman calculus and willing to work at it. Like SICP, it might change the way you think. Much as I love SICP, the Feynman lectures are greater.
> Physicists and physics students are referred to as 'he' not out of sexist motivation, but is a reflection of the plain fact that at that period of history almost all physicists and physics majors were male.
If all the students in my class but one are male, and I say "if any student in my class wants to pass, then he should come to office hours", then it seems to me that I am being sexist. In fact, I'd go so far as to guess that sexist language about a group is more, not less, harmful when there are fewer women in the group.
I don't think sexism in '50's-era work means that it should be shunned or ignored, but this kind of apologia seems both unnecessary and unjustified. (Why not just "I have not edited the pronouns in the original"?)
The interesting thing is that in languages with more explicit gender marking than English, and with no less claim to feminism than the US, this does not seem to be an issue. For example, in French, to use your example, if there were 50 female students and one male student in the class you would still refer to them using the male plural pronoun (http://www.cafebabel.co.uk/society/article/sexist-grammar-th...).
I don't speak French, and am curious about this example.
If you have 50 women in a room, do you use the female plural pronoun?
In other words, are you saying that all it takes is one man in the room to make it male plural? Honestly (and I'm no gender theorist) this seems fairly sexist too. It's essentially saying psychologically that the man in the room takes precedence over any number of women.
Yes, in Portuguese (my native language) it is the same.
For instance, "amigos" means "friends" with at least one male (the example of 50 women in a room and 1 man). "amigas" would be "friends" with only women/females.
There is in Brazilian Portuguese (probably in other pt speaking countries as well) a movement of people pushing for the usage of letter-tokens to turn gender-specific words into gender-neutral. In this case, they would use "amigxs" or "amig@s".
I wonder if that's connected to gender-marking languages like French randomly gendering most nouns? It seems like that could weaken the significance of a words' grammatical gender...
Besides, isn't the more likely reason it was used simply because 'he' is the traditional gender-uncertain pronoun of choice for English? Perhaps someone who was an adult in 1996 could enlighten me whether the pronoun battles and use of 'they' instead of 'he' or 's/he' or 'he or she' were even half as heated as today.
"He" (and "men" rather than "people" or "humanity" or other substitutes) was the "neutral" or "collective" or "universal" pronoun of the English language until very recently. My recollection is that the academic debate began sometime in the 70s during the rise of feminism (when I was a teenager) and the popular debate began sometime during the 80s. I suspect that it was not common to suggest substituting pronouns for extant writings until the 90s or maybe 00s.
For a time, some used "he or she" (perhaps some still do) to avoid offending activists, and others tried the use of "one," though most attempts were awkward.
Incidentally, "gender" referred to words, and "sex" referred to people and animals. In other words, forms used to collect personal information always requested "sex" (M or F), never "gender." I don't recall when that change occurred, but probably sometime in the 90s.
I'm not trying to incite anyone, just observing that using "gender" to refer to living beings and substituting "he or she" or "she" or "one" or other constructions for the "universal he / men" are very recent phenomena, forty years or less.
> "He" (and "men" rather than "people" or "humanity" or other substitutes) was the "neutral" or "collective" or "universal" pronoun of the English language until very recently.
For what it's worth, and without meaning to argue with the claim about common useage, E. Nesbit, who wrote (at least) in the very early 20th century (a quick Google shows me her "5 children and It" was published in 1902), already used the jarring-to-me but eminently logical 'it' as a gender-neutral pronoun.
I agree that's not a good implication to make. The question was about understanding why the editorial comment would be made at all at the time, what the motivation for it was, and why the supposed reasoning for using the pronoun was the user being in a particular environment and time instead of the simpler explanation of pronoun tradition. A plausible candidate would be the ideological battles for the correct usage of pronouns that I've seen in my own adulthood, which isn't to say all ideological issues are bad for being ideological.
> As a check on his aptitude, a serious-minded student will take courses in several different departments to find out in what field he can do the best work. This is quite distinct from finding out where he can get the best grades...
edit: wording
Interesting, "[...] in what field he can do the best work" is given as the prime criterion, and not "in what field he can earn the most money" which is given a lot of value today.
Arguably, doing the "best work" leads to financial reward, but focus on the latter inevitably sabotages the former. What a strange paradox!
If you really want to study physics, and you don't want to get a degree, this is about as good as it gets.