“Science is the belief in the ignorance of experts”?

1) Does “Science is the belief in the ignorance of experts” mean "“Science is the belief that experts are ignorant”?

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"?

Context:

“Science is the belief in the ignorance of experts.”
―Richard Feynman

“To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature... If you want to

learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.”
―Richard Feynman

The subject "What Is Science" is not my choice. It was Mr. DeRose's subject. But I would like to say that I think that "what is science" is not at all equivalent to "how to teach science," and I must call that to your attention for two reasons. In the first place, from the way that I am preparing to give this lecture, it may seem that I am trying to tell you how to teach science--I am not at all in any way, because I don't know anything about small children. I have one, so I know that I don't know. The other is I think that most of you (because there is so much talk and so many papers and so many experts in the field) have some kind of a feeling of lack of self-confidence. In some way you are always being lectured on how things are not going too well and how you should learn to teach better. I am not going to berate you for the bad work you are doing and indicate how it can definitely be improved; that is not my intention.

'I have a small child, so I know that I don't know how to teach science to them.'

As a matter of fact, we have very good students coming into Caltech, and during the years we found them getting better and better. Now how it is done, I don't know. I wonder if you know. I don't want to interfere with the system; it is very good.

'I have a small child, so I know that I don't know how to teach science to them.'

Only two days ago we had a conference in which we decided that we don't have to teach a course in elementary quantum mechanics in the graduate school any more. When I was a student, they didn't even have a course in quantum mechanics in the graduate school; it was considered too difficult a subject. When I first started to teach, we had one. Now we teach it to undergraduates. We discover now that we don't have to have elementary quantum mechanics for graduates from other schools. Why is it getting pushed down? Because we are able to teach better in the university, and that is because the students coming up are better trained.

FBM wrote:

'I have a small child, so I know that I don't know how to teach science to them.'

Ironically, I failed to get the meaning of another "one" below:
"we had one"? "we had one course in elementary quantum mechanics"?

Quote:

Only two days ago we had a conference in which we decided that we don't have to teach a course in elementary quantum mechanics in the graduate school any more. When I was a student, they didn't even have a course in quantum mechanics in the graduate school; it was considered too difficult a subject. When I first started to teach, we had one. Now we teach it to undergraduates. We discover now that we don't have to have elementary quantum mechanics for graduates from other schools. Why is it getting pushed down? Because we are able to teach better in the university, and that is because the students coming up are better trained.

Why is it getting pushed down? Because we are able to teach better in the university, and that is because the students coming up are better trained.

In the context, does "why is it getting pushed down" refer to "why is the course getting pushed down from graduate school to undergraduate school"?

Cool.
In the context, does "why is it getting pushed down" refer to "why is the course getting pushed down from graduate school to undergraduate school"?

Quote:

Why is it getting pushed down? Because we are able to teach better in the university, and that is because the students coming up are better trained.

After some time, I was reminded of a little poem:

A centipede was happy quite, until a toad in fun
Said, "Pray, which leg comes after which?"
This raised his doubts to such a pitch
He fell distracted in the ditch
Not knowing how to run.

All my life, I have been doing science and known what it was, but what I have come to tell you--which foot comes after which--I am unable to do, and furthermore, I am worried by the analogy in the poem that when I go home I will no longer be able to do any research.

The speaker went on:

Quote:

After some time, I was reminded of a little poem:

A centipede was happy quite, until a toad in fun
Said, "Pray, which leg comes after which?"
This raised his doubts to such a pitch
He fell distracted in the ditch
Not knowing how to run.

All my life, I have been doing science and known what it was, but what I have come to tell you--which foot comes after which--I am unable to do, and furthermore, I am worried by the analogy in the poem that when I go home I will no longer be able to do any research.

Does "Not knowing how to run" refer to "losing his ability to run (at least for the time being)"?
That is, the centipede was tortured by the problem that he lost his ability of running temporarily. And the speaker would also be troubled as to losing his ability to research (for the time being)?

Exactly. By teaching how to do science/research, he has to think about things that otherwise were automatic for him, which may put him into the same difficulty as the centipede.

Quote:

In the context, does "why is it getting pushed down" refer to "why is the course getting pushed down from graduate school to undergraduate school"?

Yeah, that's what it means, Oris. And then he gives you the answer.