This.
Think of learning math as learning a new language. If you are literate in the language, you can read it. If not, you can’t. Of course, the math language tends to be quite condensed.
I loaned my copy to a friend who took it back to the States with him, so I can’t dust it off to check, but my recollection was that he claimed he couldn’t read blueprints for the life of him. While he was duly modest, I don’t see him with false modesty either.
IIRC, it was a fairly complex system and his stated level of understanding was low enough, that I thought it was believable.
Also, I had something similar happen. A week in my freshman year, a friend recommended the calculus for math majors instead of the calculus for engineers which I was enrolled. I attended one day, and they were studying matrices, which we weren’t yet. My friend wasn’t there, so I took notes for him. I hadn’t had any of the previous sessions, so I had no idea what was going on, but I dutifully took notes.
After a large number of blackboards filled with matrices, for which I was completely clueless as to their meaning, I couldn’t read one of instructor’s scribbled numbers and asked what that one was. She clarified it, then thought, went back to the previous matrix, then the previous one, made a correction which changed another number and then finally the number I happened to pick was also corrected. The instructor thanked me and said I was correct.
The look on the other students’ faces was priceless. Unlike our massive weed-out pre-engineering monstrosities, the math major course had less than a dozen students (for a freshman class!) and they must have recognized that I was new. As it was, I elected to stay with the engineering-oriented class and didn’t attend
I can completely believe that a random question can just happen to be the one which was incorrect. Granted, Feynman did win the Nobel price and I wasn’t even on scholarship, so there would be a couple standard deviations in intelligence between us, but I can see where even the gods can be lucky.
Sure, I was just being careful to define our terms due to potential ambiguities. 
Ever heard “The part was so easy I could have phoned it in!”? That’s what “nailed it” means to me.
Oh, sure, it’s possible that Feynman was just phenomenally lucky-- It does happen, after all. But given the fact that he was indisputably a friggin’ genius polymath, I find it the simpler hypothesis to assume that he was performing an act of genius. I’m not saying that he actually fully comprehended the schematic, but he probably had at least some level of intuitive understanding of it, at least enough to make a significantly better-than-average stab at a component that happened to be interesting.
This thread is gold. 
I think that the actual excerpt makes it clear that he had no clue:
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I’m completely dazed, Worse, I don’t know what the symbols on the blueprint mean! There is some kind of a thing that at first I think is a window. It’s a square with a little cross in the middle, all over the damn place. I think it’s a window, but no, it can’t be a window, because it isn’t always at the edge. I want to ask them what it is.
You must have been in a situation like this when you didn’t ask them right away. Right away it would have been OK. But now they’ve been talking a little bit too long. You hesitated too long. If you ask them now they’ll say “What are you wasting my time all this time for?”
What am I going to do? I get an idea. Maybe it’s a valve.
I take my finger and I put it down on one of the mysterious little crosses in the middle of one of the blueprints on page three, and I say “What happens if this valve gets stuck?” –figuring they’re going to say “That’s not a valve, sir, that’s a window.”
So one looks at the other and says, “Well, if that valve gets stuck–” and he goes up and down on the blueprint, up and down, the other guy goes up and down, back and forth, back and forth, and they both look at each other. They turn around to me and they open their mouths like astonished fish and say “You’re absolutely right, sir.”
So they rolled up the blueprints and away they went and we walked out. And Mr. Zumwalt, who had been following me all the way through, said, “You’re a genius. I got the idea you were a genius when you went through the plant once and you could tell them about evaporator C-21 in building 90-207 the next morning,” he says, “but what you have just done is so fantastic I want to know how, how do you do that?”
I told him you try to find out whether it’s a valve or not.
Exactly. You can see an expert using this technique here. He’s using his familiarity and expertise with the subject to evaluate an entire section of the process all at once.
Your conscious mind can have no clue, but if you are used to looking at graphs all day long, then your subconscious mind can pattern match which may lead you to a revelation which seems like it was lucky or genius.
I’m another supporter of the “foreign language” analogue. If you don’t know the language, it’s gibberish. If you do, you can read it and understand it. Doesn’t matter if it’s Russian or Group Theory. Some people know these things, others don’t.
You’re right. But in this case it was a blueprint, not a graph, and Feynman said he had zero experience reading blueprints.
Oh, crap. It’s a zombie, isn’t it?
I saw that right away.
I assume this thread came up again because there’s another similar current one, in which somebody linked to this one.
There’s a famous joke about big-ass equations (or big ass-equations?) like that. You can stop reading this post now if you already know it.
This famously smart-ass professor (or smart ass-professor?) walks into the classroom and proceeds to write one of those infamously big-ass-equations on the board. Then he turns to the class and says: “Now, to begin today’s lecture, I think you’ll all agree that this equation, which I’ve written here, is obvious. . . .”
But then he suddenly paused, and a furrow crossed his brow. He turned toward the board and stared at the equation for a minute. Then, turning back to the class, he confessed: “Uh. . . If you will excuse me for a moment, I shall have to think this over again.” And with that, he abruptly left the classroom.
Five minutes later, the students are still waiting patiently for him to return. Ten minutes later, still waiting, maybe not so patiently. Fifteen minutes later, some students start to leave, but some hang tight and wait. . .
THIRTY MINUTES later, the professor strides back into the classroom, all smiles, and declares: “Yes, yes, I was right all along. It IS obvious!”
(Credit: I first read a version of this anecdote in the sci-fi-ish novel Stand on Zanzibar by John Brunner (1968), but it’s a well-known tale, of which I’ve seen many variant tellings.)
My old calculus prof related a similar story – when he was in school, the textbook they were using reduced a long and difficult equation to a shorter and more elegant one in a single step, declaring that the derivation was “of course, obvious.” My professor related that it wasn’t obvious to him, and upon coming to class the next day found his professor filling the chalkboards with an ugly derivation. He finished, turned to the class, and said “I just wanted to show you what was ‘obvious’!”
This topic also puts me in mind of another of Feynman’s stories. As a student, he used to enjoy arguing with the math students, and would poke fun at the way they’d declare that any step or result that they didn’t want to discuss in detail was “trivial.” He annoyed them with his conclusion that, to a mathematician, “trivial” means “already proven.”
My Calc I prof gave me a little pamphlet to read once, which described some higher-order number system that its author had invented (in which each integer n was replaced by the exponential e[sup]n[/sup] and operations analogous to + and * are introduced, showing that an entire Calculus can be developed that closely mimics conventional Calculus). In it, he uses the phrase “it turns out . . .” a lot. The first usage has a footnote to the effect that " ‘It turns out that…’ means ‘it can be proved that…’ "
In the book What Is The Name Of This Book? (Amazon Listing ; Full Text (PDF)), Raymond Smullyan tells this story that was going around back in his days at Princeton:
When I was in high school, I and a friend collected “universal justifiers” from math textbooks.
We only really found two good ones, but they seemed quite popular. They were:
"It is clear from the diagram that . . . " and "Simplifying, we get . . . "
Except in this case, the blueprint (or at least, that portion of it) was a graph. Now, Feynman’s ignorance of blueprints meant that he didn’t know for sure that it was a graph, or even, if it was a graph, what it was a graph of. It could just as easily have been wiring instead of plumbing, for instance. But even if it had been wiring instead of plumbing, his question would still have been a good one (albeit using a peculiar word), because points of single connectivity in a graph are interesting, no matter what the graph is.
Forgive the ignorance, but how can a blueprint be a graph? A blueprint is a visual representation of a concrete object, while a graph is a visual representation of abstract data.
And how can a graph have a symbol that represents a window? Now, I can see how a blueprint — like for a building or something — could have a symbol that represents a window. But I guess I’m really missing something about graphs.
I have often seen graphs included in blueprints as the can be used to provide clarity to a given variable included in the drawing or simply as documentation. There is no hard fast one size fits all print. You may send one type to a machine shop and a completly differnt type to a customer. What ever makes the point you are trying to make clearer can and should be included.
For clarity, here, by “graph” I don’t mean a plot of something on the Y axis versus something on the X axis, but a representation of a network of nodes which are connected together in various ways (in this case, valves connected by pipes, but it could have been almost anything). And the graph didn’t represent a window; it had a symbol on it which looked sort of like a window, but which turned out to represent a valve.