[jrapdx3]

The problem in discussing this subject is the idea of "intuition" itself because the term doesn't have an unambiguous definition. Meaning varies from one instance to another, even one moment to the next, and disputes arise from imprecise communication.

In the example, I think what Feynman is describing, we commonly call "visualization", to be able to "see" the problem in imagination. That is no less a form of abstraction that is often vital to problem-solving. Of course, not every problem yields to this approach but it is a powerful feature of our basic cognitive tool set.

Einstein wrote that his early success in formulating his idea of special relativity was the outcome of his intuition about the physical properties of light, etc. he studied. Later on, the mathematical abstractions became more powerful, and at that point intuition about the "physical" nature of phenomena was insufficient for understanding.

But I think there are forms of intuition that apply to very abstract ideas, or what seem to be so to us. I once heard a physicist say "we never really understand higher mathematics, we just get used to it". Feynman would probably have agreed with that sentiment.

"Getting used to it" is really the equivalent of developing an intuition about the subject. I remember first learning about programming recursive functions, mind boggling in the beginning. After a while, it began to "sink in", that is, it became intuitive, I no longer had trouble "seeing" how it worked. The key is familiarity, something once strange is now digestible.

So there's nothing binary about intuition, it covers many forms of thought, and incorporates reasoning about emotion, having a "feel" for the problem in question. There are limits to our abilities, at the highest level it's genius, but there are no clear boundaries.

[abdullahkhalids]

I agree that there are various patterns of thought that can be labelled intuition. I would like to add on that you have to practice to develop any of these different types intuition. This is I think what Feynman is saying and he is emphasizing the type of intuition (run the experiment in your head) that is very useful for physicists.

In every field there is probably a different type of intuition that is useful. In abstract math maybe 'getting used to it' very fast is very useful. In geometric math maybe being able to visualize objects in space is useful. In programming maybe seeing the run of the code in your head is useful.

[reagency]

You don't see the code run in your head, though. You get a feel for how this design pattern works at a glance (intuition), or you carefully step through the code like a debugger.

[ViViDboarder]

This was reaffirming. I spend several hours last night unable to sleep trying to solve a problem. As you describe: I had a design and kept throwing scenarios at it and debugged it.

[stuxnet79]

> "we never really understand higher mathematics, we just get used to it"

Correct me if I am wrong but I believe this statement is attributed to Von Neumann. It has really stuck with me over the years, just because of how true it is.

I agree that what is important is self-consistency, precision and rigor. Intuition is for the birds. Like you have stated it is ambiguous and often deceptive. Mathematical abstractions enable us to circumvent these pitfalls.