Related to: On the Medium of Thought, John von Neumann, Early Isolation Tank Psychonautics: 1970s Trip Reports, Pseudo-Time Arrow, Thinking in Numbers, High-Entropy Alloys of Experience, A Single 3N-Dimensional Universe: Splitting vs. Decoherence, A New Way to Visualize General Relativity, Visual Quantum Physics, and Feynman’s QED Video Lectures (highly recommended!)
Interviewer presumably asks: What is it like to think about your work?
Well, when I’m actually doing my own things, that I’m working in the high, deep, and esoteric stuff that I worry about, I don’t think I can describe very well what it is like… First of all it is like asking a centipede which leg comes after which. It happens quickly and I am not exactly sure… flashes and stuff goes on in the head. But I know it is a crazy mixture of partial differential equations, partial solving of the equations, then having some sort of picture of what’s happening that the equations are saying is happening, but they are not as well separated as the words that I’m using. And it’s a kind of a nutty thing. It’s very hard to describe and I don’t know that it does any good to describe. And something that struck me, that is very curious: I suspect that what goes on in every man’s head might be very, very different. The actual imagery or semi-imagery which comes is different. And that when we are talking to each other at these high and complicated levels, and we think we are speaking very well and we are communicating… but what we’re really doing is having some kind of big translation scheme going on for translating what this fellow says into our images. Which are very different.
I found that out because at the very lowest level, I won’t go into the details, but I got interested… well, I was doing some experiments. And I was trying to figure out something about our time sense. And so what I would do is, I would count trying to count to a minute. Actually, say I’d count to 48 and it would be one minute. So I’d calibrate myself and I would count a minute by counting to 48 (so it was not seconds what I counted, but close enough), and then it turns out if you repeat that you can do very accurately when you get to 48 or 47 or 49, not far off you are very close to a minute. And I would try to find out what affected that time sense, and whether I could do anything at the same time as I was counting and I found that I could do many things, but couldn’t do other things. I could… For example I had great difficulty doing this: I was in university and I had to get my laundry ready. And I was putting the socks out and I had to make a list of how many socks, something like six or eight pair of socks, and I couldn’t count them. Because the “counting machine” was being used and I couldn’t count them. Until I found out I could put them in a pattern and recognize the number. And so I learned a way after practicing by which I could go down on lines of type and newspapers and see them in groups. Three – three – three – one, that’s a group of ten, three – three – three – one… and so on without saying the numbers, just seeing the groupings and I could therefore count the lines of type (I practiced). In the newspaper, the same time I was counting internally the seconds, so I could do this fantastic trick of saying: “48! That’s one minute, and there are 67 lines of type”, you see? It was quite wonderful. And I discovered many things I could read while I was… I could read while I was counting and get an idea of what it was about. But I couldn’t speak, say anything. Because of course, when I was counting I sort of spoke to myself inside. I would say one, two, three… sort of in the head! Well, I went down to get breakfast and there was John Tuckey, a mathematician down at Princeton at the same time, and we had many discussions, and I was telling him about these experiments and what I could do. And he says “that’s absurd!”. He says: “I don’t see why you would have any difficulty talking whatsoever, and I can’t possibly believe that you could read.” So I couldn’t believe all this. But we calibrated him, and it was 52 for him to get to 60 seconds or whatever, I don’t remember the numbers now. And then he’d say, “alright, what do you want me to say? Marry Had a Little Lamb… I can speak about anything. Blah, blah, blah, blah… 52!” It’s a minute, he was right. And I couldn’t possibly do that, and he wanted me to read because he couldn’t believe it. And then we compared notes and it turned out that when he thought of counting, what he did inside his head is that when he counted he saw a tape with numbers, that did clink, clink, clink [shows with his hand the turning and passing of a counting tape], and the tape would change with the numbers printed on it, which he could see. Well, since it’s sort of an optical system that he is using, and not voice, he could speak as much as he wanted. But if he wanted to read then he couldn’t look at his clock. Whereas for me it was the other way.
And that’s where I discovered, at least in this very simple operation of counting, the great difference in what goes on in the head when people think they are doing the same thing! And so it struck me therefore, if that’s already true at the most elementary level, that when we learn about mathematics, and the Bessel functions, and the exponentials, and the electric fields, and all these things… that the imagery and method by which we are storing it all and the way we are thinking about it… could be it really if we get into each other’s heads, entirely different? And in fact why somebody has sometimes a great deal of difficulty understanding when you are pointing to something which you see as obvious, and vice versa, it may be because it’s a little hard to translate what you just said into his particular framework and so on. Now I’m talking like a psychologist and you know I know nothing about this.
Suppose that little things behaved very differently than anything that was big. Anything that you are familiar with… because you see, as the animal evolves, and so on, as the brain evolves, it gets used to handling, and the brain is designed, for ordinary circumstances. But if the gut particles in the deep inner workings whereby some other rules and some other character they behave differently, they were very different than anything on a large scale, then there would be some kind of difficulty, you know, understanding and imagining reality. And that is the difficulty we are in. The behavior of things on a small scale is so fantastic, it is so wonderfully different, so marvelously different than anything that behaves on a large scale… say, “electrons act like waves”, no they don’t exactly. “They act like particles”, no they don’t exactly. “They act like a kind of a fog around the nucleus”, no they don’t exactly. And if you would like to get a clear sharp picture of an animal, so that you could tell exactly how it is going to behave correctly, to have a good image, in other words, a really good image of reality I don’t know how to do it!
Because that image has to be mathematical. We have mathematical expressions, strange as mathematics is I don’t understand how it is, but we can write mathematical expressions and calculate what the thing is going to do without actually being able to picture it. It would be something like a computer that you put certain numbers in and you have the formula for what time the car will arrive at different destinations, and the thing does the arithmetic to figure out what time the car arrives at the different destinations but cannot picture the car. It’s just doing the arithmetic! So we know how to do the arithmetic but we cannot picture the car. No, it’s not a hundred percent because for certain approximate situations a certain kind of approximate picture works. That it’s simply a fog around the nucleus that when you squeeze it, it repels you is very good for understanding the stiffness of material. That it’s a wave which does this and that is very good for some other phenomena. So when you are working with certain particular aspect of the behavior of atoms, for instance when I was talking about temperature and so forth, that they are just little balls is good enough and it gives us a very nice picture of temperature. But if you ask more specific questions and you get down to questions like how is it that when you cool helium down, even to absolute zero where there is not supposed to be any motion, it’s a perfect fluid that hasn’t any viscosity, has no resistance, flows perfectly, and isn’t freezing?
Well if you want to get a picture of atoms that has all of that in it, I can’t do it, you see? But I can explain why the helium behaves as it does by taking my equations and showing that the consequences of them is that the helium will behave as it is observed to behave, so we now have the theory right, but we haven’t got the pictures that will go with the theory. And is that because we are limited and haven’t caught on to the right pictures? Or is that because there aren’t any right pictures for people who have to make pictures out of things that are familiar to them? Let’s suppose it’s the last one. That there’s no right pictures in terms of things that are familiar to them. Is it possible then, to develop a familiarity with those things that are not familiar on hand by study? By learning about the properties of atoms and quantum mechanics, and practicing with the equations, until it becomes a kind of second nature, just as it is second nature to know that if two balls came towards each other they’d mash into bits, you don’t say the two balls when they come toward each other turn blue. You know what they do! So the question is whether you can get to know what things do better than we do today. You know as the generations develop, will they invent ways of teaching, so that the new people will learn tricky ways of looking at things and be so well trained that they won’t have our troubles with picturing the atom? There is still a school of thought that cannot believe that the atomic behavior is so different than large-scale behavior. I think that’s a deep prejudice, it’s a prejudice from being so used to large-scale behavior. And they are always seeking to find, to waiting for the day that we discover that underneath the quantum mechanics, there’s some mundane ordinary balls hitting, or particles moving, and so on. I think they’re going to be defeated. I think nature’s imagination is so much greater than man’s, she’s never gonna let us relax.
From the blog Visual Quantum Physics (same as gifs above):