121–130 of 281 posts
> I have attempted to deliver [these lectures] in a spirit that should be recommended to all students embarking on the writing of their PhD theses: imagine that you are explaining your ideas to your former smart, but ignorant, self, at the beginning of your studies! -Richard Feynman
s/smart/dumb
:)
My response is that for every 100 of these types of papers, one of them may prove to be pivotal or inspirational in something truly groundbreaking and functionally useful. For this reason, I am all for 100 different people spending their time doing things like this, because eventually one of them will make an impact that is greater than 100x the efforts of 100 normal men. It's just a different kind of "brick in the w…
Great point. I think this applies to scientific research in general, which is why the constant emphasis on only funding research with clear and immediate economic payoff seems a bit shortsighted. In reality, chances are that most research won't lead to anything significant - but the 1% that does will have outsized impact that will more than pay for the rest. And we don't know which 1% this will be in advance.
Although there have been a few Fouriers across history, the most compelling brilliant scientists had one foot in applied science working on theory in the spare time. Euler, Gauss, Faraday, Langmuir. Most of the best basic science had goals "to explain something pressing" (which is not the same as "do something because there will be no payoff") anyways, like Planck, Einstein, Peter Mitchell.
There's something to be gained about cutting your teeth on problems with results, instead of just lollygagging about in theoryland.
Feynman talked about this in an exercise where he described the motion of spinning discs - a very "applied" problem, and remarked that later those insights proved useful in a separate, unrelated problem.
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> I don't see comments helping me... I don't know why people say this type of thing, as if there's some choice you have to make between good names and comments. You can have both, and there are absolutely times when comments are necessary . Too many comments may be a "smell", but code that doesn't require any comments at all is very unlikely.
> there are absolutely times when comments are necessary . I'll have to take your word for it, because I've yet to run into that situation.
Which way does the returned force vector point? Towards mass A, or towards mass B?
2) Vector3 UnitVectorWithDirection(Vector3 originalVector);
What does this function do when the magnitude (length) of originalVector is zero?
3) float ArcTan(float x);
What is the allowable range of values for x?
...
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In Germany you get to your advanced courses for the last two years of High school. I picked Math and Physics. We did a bunch of linear regression(with maple?) i believe. And some manual differential equations. I was one of the best in that class, but when I asked what we need this stuff for the other people in the class looked at me and said the following: "if you ask this question you're in the wrong class" I went o…
> Why can't we just provide a simple real life example first and then go on explaining the details? This. People learn differently, in my case, if I can't get the 'Why' first, I'm not that excited to learn it. I guess making 'simple' real life examples in many cases is hard. I also tend to learn things much better if they came from a real problem/need I have. There was a good discussion about a 'project based univers…
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Comments are incredibly useful for that bit of code that you spent hours trying to make it work and you couldn't figure out a way to name things well or to improve it. That's where a comment is priceless.
The downside of course is that comments aren't compiled/run - so they often become out of date. "Often" might actually be an understatement. I can't tell you how many times I've been reading a comment that runs quite contrary to what the code really does. You then end up reading the code to reason about it anyway, paying two taxes. After too many of those experiences, you just end up going straight to the code as the…
I certainly am.
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> Up through my first differential equations class I found almost everything trivial to learn Mankind hasn't yet figured out a good way to teach the first Differential Equations course. The first serious Calculus course introduces some level of rigor and formalism, but this alone is not sufficient for Diff Eqs. And the DE courses are typically leaning towards applications, so they tend to succumb to the "fiddle these…
This point is more thoroughly explained under section 7 here: https://web.williams.edu/Mathematics/lg5/Rota.pdf
TLDR: The author independently re-discovered what you may know as Old Code Syndrome. I think that's because mathematical papers place too much value on terseness and abstraction over exposition and intuition. This guy's basically in the position of a fairly new developer who's just been asked to do non-trivial update of his own code for the first time. All those clever one-liners he put into his code made him feel sm…
Over the years, I've stopped and started about 3 pretty major personal projects and through that I progressively got better at writing and documenting code in a way that make it easy to pick back up after a long break.
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In Germany you get to your advanced courses for the last two years of High school. I picked Math and Physics. We did a bunch of linear regression(with maple?) i believe. And some manual differential equations. I was one of the best in that class, but when I asked what we need this stuff for the other people in the class looked at me and said the following: "if you ask this question you're in the wrong class" I went o…
> I was one of the best in that class, but when I asked what we need this stuff for the other people in the class looked at me and said the following: "if you ask this question you're in the wrong class" I am always so disappointed when I hear people express this. Being able to place an effort in a broader context is so helpful in being able to approach the work well. A few teachers in the Literature department in hi…
I used to know a math lecturer, and his attitude was very much that it was his job to throw proofs at his students, and the bright ones would put the rest together for themselves.
He wasn't even remotely interested in the less bright ones, and certainly not in presenting the material in a way that made it easier for them to follow.
Digital has real potential here, because you can build animations and virtual math labs to explore concepts and give them a context, and suddenly math becomes practical and not just an excuse for wrangling abstract symbols for the sake of it.
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> there are absolutely times when comments are necessary . I'll have to take your word for it, because I've yet to run into that situation.
1) Vector3 computeNewtonianGravity(float massA, Vector3 positionA, float massB, Vector3 positionB); Which way does the returned force vector point? Towards mass A, or towards mass B? 2) Vector3 UnitVectorWithDirection(Vector3 originalVector); What does this function do when the magnitude (length) of originalVector is zero? 3) float ArcTan(float x); What is the allowable range of values for x? ...
1) Vector3 calcNewtonianGravityToB(float massA, Vector3 positionA, float massB, Vector3 positionB);
2) Vector3 unitVectorWithDirection(Vector3 originalVector_mayBeZero); vs. Vector3 unitVectorWithDirection(Vector3 originalVector_throwsIfZero); (if in a supporting language, throws declaration would also clarify).
3) float ArcTan(float x_throwsIfZero); or float ArcTan(float x_returnsNaNIfNot0to1), etc.
This assumes:
(a) You're not working in a language or environment that supports range constraints in the first place, cause if you are then that's ideal.
(b) You're working on personal code or a small team. If you're writing code for public consumption you have no choice but to add detailed API documentation if you want to be successful, even if it's not DRY.
> I have attempted to deliver [these lectures] in a spirit that should be recommended to all students embarking on the writing of their PhD theses: imagine that you are explaining your ideas to your former smart, but ignorant, self, at the beginning of your studies! -Richard Feynman
After spending the last five years trying to explain math to a general technical audience, I'd agree with this, but with one minor change: s/smart/dumb :)
Quantum mechanics is the worst. I dislike a lot of the "popular science" language and analogues used to describe it, but the real (academic) pedagogical material is completely inappropriate for regular people. I'm worried that I'll be an inscrutable physicist before I grok it well enough to explain to a highschooler, though.