@oristarA,
oristarA wrote:1) Does “Science is the belief in the ignorance of experts” mean "“Science is the belief that experts are ignorant”?
Yes, but if you read the quote in context, you will find that Feynman is using the word
expert in a quasi-sarcastic way. He really means what I would call pseudo-experts.
Feynman wrote:We have many studies in teaching, for example, in which people make observations, make lists, do statistics, and so on, but these do not thereby become established science, established knowledge. They are merely an imitative form of science [...] The result of this pseudoscientific imitation is to produce experts, which many of you are. [But] you teachers, who are really teaching children at the bottom of the heap, can maybe doubt the experts. As a matter of fact, I can also define science another way: Science is the belief in the ignorance of experts.
When someone says, "Science teaches such and such," he is using the word incorrectly. Science doesn't teach anything; experience teaches it. If they say to you, "Science has shown such and such," you might ask, "How does science show it? How did the scientists find out? How? What? Where?"
It should not be "science has shown" but "this experiment, this effect, has shown." And you have as much right as anyone else, upon hearing about the experiments--but be patient and listen to all the evidence--to judge whether a sensible conclusion has been arrived at.
Source
As I understand Feynman, his message here is two-fold. For one, many so-called experts are in fact ignorant. Second, truth in science comes from evidence and logic, not from the authority of "expertise" real or imagined. And every person who puts in the necessary work can evaluate evidence and logic.
oristarA wrote:2) Does "it is difficult to get across a real feeling as to the beauty" mean "it is difficult to catch/enjoy a real feeling about the beauty"?
No --- not to catch or enjoy it for yourself, but to pass it on to others, your students for example.