But all this begs the question. Why should we believe Gauss's law?
No one has the resources to verify the whole of science through first-hand experience so at some point you have no choice but to trust someone.
No one has the resources to verify the whole of science through first-hand experience so at some point you have no choice but to trust someone.
Because experiments show that it's correct.
> No one has the resources to verify the whole of science through first-hand experience
Courses in science commonly include actual experiments, either done by the professor while students watch, or done by the students themselves in labs, precisely to give the students first-hand experience in the scientific phenomena being studied in the course.
> at some point you have no choice but to trust someone
You may have to trust other people for first-hand observations of things you didn't observe yourself. But that isn't what's involved here. Here the student had a theoretical law whose consequences she was perfectly capable of working out for herself. She did not have to trust anyone for that.
In this particular case, the student even saw the problem with Feynman's statement: her letter says, in reference to the statement in Feynman's book that turned out to be wrong: "This was confusing, as it seemed to contradict all your previous statements." So why did she base her exam answer on the statement she found "confusing"? She should have thought it through for herself.
Even the beginner doesn't have to "trust" that calculus works. He can verify for himself that using calculus to manipulate equations in the theory yields predictions which are confirmed by experiment.
The main area where I see that "trust" would be required in science is reporting of raw data directly obtained from experiments that other people run. Yes, everyone else has to trust that the person who is reporting that data actually ran the experiment they claim to have run and recorded that exact data from that experiment in its entirety--that they didn't make up the data, or massage it, or cherry pick only certain runs, etc. That is why, when scientists are found to have violated this trust, the penalties are typically severe.
Other than that, though, you don't have to "trust" anything in science blindly. Whether a particular set of data is consistent with a particular set of theoretical predictions is something that can be verified independently. And since theoretical predictions are just mathematical derivations from certain stated axioms, those can also be verified independently. So no one ever has to just take someone else's word about those things.
The US educational system seems to regard some of the foundational elements of STEM will enormous trepidation (I've known US high school students headed for STEM majors at quality universities who haven't studied calculus for more than a year (typically just covering differentiation, not integration)). Combined with it's greater breadth of educational goals, both in grade school and even for a bachelors, it's not really surprising that there will be students (in the US at least) who begin college level physics without fully understanding the tools (or history) of the subject.
You always have to stop somewhere. Any given one of your assumptions may be verifiable in principle, but you won’t have the time and wherewithal to verify all of them. Science as it’s actually practiced is a huge pyramid of trust.
The verification issue comes about when you need to run the experiments yourself to prove that your equations don't just match with fudged data.
You can pretty much prove that calculus works from a purely logical basis (I might be using incorrect terminology here but you get the point, pure math is self-proving.).
Right, but it’s pretty clear from your use of terminology here that you personally haven’t studied the foundations of calculus deeply. Which is 100% fine. You understand roughly why it works and you trust that specialists have checked it out more thoroughly.
A lot of people on this thread keep pointing out that various things can be verified. But they are saying this precisely because they themselves have not verified the things in question and yet trust that it is possible to do so. The point is that this is perfectly reasonable in most contexts. You do not have to take on the burden of proving for yourself every mathematical theorem that you make use of.
There are shades between full formal verification of literally everything and then "trust the elders". You can know a little bit about a lot and use that as a sort of statistical verification because you're basically running a monte carlo sim to find holes in the logic, if you find no holes then you can reasonably assume that the rest is true and that's not based on trust.
It's a bit like having a 500-dimensional jigsaw puzzle, once you show that most of the pieces fit together the other ones have nowhere to go any more except to fit.
Another relevant details is that "the class was a survey course for non-majors".
>She also clearly refused to believe her professor when he explained the problem to her.
There's nothing in the letter to support this conclusion. But in any case, you can't coherently criticize the student both for believing Feynman and for not believing her professor! I thought the point was that she wasn't supposed to 'believe' anyone.
And yes, of course the student was hoping that Feynman might have turned out to be right after all so that she could get some extra points on the test. So what?
And he answered that question.
> I thought the point was that she wasn't supposed to 'believe' anyone.
I am presuming that her professor actually showed her why she was wrong, instead of asking her to take his word for it.
> And yes, of course the student was hoping that Feynman might have turned out to be right after all so that she could get some extra points on the test. So what?
You don't get it. Gauss's law is a very very elementary law (usually taught in high school). Her professor would have most definitely explained why he took off points from her exam. There are two explanations now as to why she included that PS: i) she didn't understand her professor's explanation, and hence also did not understand Gauss's law properly, ii) she was grade grubbing. I cannot sympathize with her for (i) since she most definitely did not make an effort to understand her professor's simple argument, yet she found the time to write a letter to Feynman. Also, W&M is a large research university with multiple physics professors and graduate students and it's unlikely that no one would have been able to help her with this. So she clearly didn't try hard enough to understand Gauss's law and that's not Feynman's fault. And I really cannot sympathize with her if it's case (ii).
b) William and Mary, although close to Thomas Jefferson lab, is not an R1
b) Also doesn't make any difference. I'm familiar enough with W&M to know that (i) it has a full-fledged graduate program and (ii) professors there collaborate extensively with JLab in both theory and experiment, though I admit that I don't know if that was the case when this student wrote the letter.
You don't have to "believe" the axioms. You can test them, by testing whether the experimental predictions derived from them are confirmed or not.
This particular incident had nothing to do with the validity of Gauss's law, which is nothing but a restatement of Coulomb's law in electrostatics, and something that has been extensively verified in experiments. Feynman's presentation of Gauss's law is crystal clear. The issue in question was an application of Gauss's law. Feynman likely goofed up (like most of us do) because he didn't think twice and went by his intuition. And he was absolutely right to criticize the student -- saying that something is written in famous book X written by famous author Y is completely irrelevant in science if you cannot make a good argument for why it is right. This is different from many social "sciences" where people often make such claims.
I think Feynman was getting on a favorite hobby horse about not trusting authority and reading the letter a little uncharitably.