I decided to investigate. I started by counting seconds—without looking at a clock, of course—up to 60 in a slow, steady rhythm: 1, 2, 3, 4, 5.… When I got to 60, only 48 seconds had gone by, but that didn’t bother me: the problem was not to count for exactly one minute, but to count at a standard rate. The next time I counted to 60, 49 seconds had passed. The next time, 48. Then 47, 48, 49, 48, 48.… So I found I could count at a pretty standard rate.
Now, if I just sat there, without counting, and waited until I thought a minute had gone by, it was very irregular—complete variations. So I found it’s very poor to estimate a minute by sheer guessing. But by counting, I could get very accurate.
[...]
For instance, when I put out the laundry, I had to fill out a form saying how many shirts I had, how many pants, and so on. I found I could write down “3” in front of “pants” or “4” in front of “shirts,” but I couldn’t count my socks. There were too many of them: I’m already using my “counting machine” − 36, 37, 38 - and here are all these socks in front of me − 39, 40, 41.… How do I count the socks?
I found I could arrange them in geometrical patterns—like a square, for example: a pair of socks in this comer, a pair in that one; a pair over here, and a pair over there—eight socks.
I continued this game of counting by patterns, and found I could count the lines in a newspaper article by grouping the lines into patterns of 3, 3, 3, and 1 to get 10; then 3 of those patterns, 3 of those patterns, 3 of those patterns, and 1 of those patterns made 100. I went right down the newspaper like that. After I had finished counting up to 60, I knew where I was in the patterns and could say, “I’m up to 60, and there are 113 lines.” I found that I could even read the articles while I counted to 60, and it didn’t affect the rate! In fact, I could do anything while counting to myself—except talk out loud, of course.
[...]
The next morning, over breakfast, I reported the results of all these experiments to the other guys at the table. I told them all the things I could do while counting to myself, and said the only thing I absolutely could not do while counting to myself was talk.
One of the guys, a fella named John Tukey, said, “I don’t believe you can read, and I don’t see why you can’t talk. I’ll bet you I can talk while counting to myself, and I’ll bet you you can’t read.”
So I gave a demonstration: they gave me a book and I read it for a while, counting to myself. When I reached 60 I said, “Now!” − 48 seconds, my regular time. Then I told them what I had read.
Tukey was amazed. After we checked him a few times to see what his regular time was, he started talking: “Mary had a little lamb; I can say anything I want to, it doesn’t make any difference; I don’t know what’s bothering you”—blah, blah, blah, and finally, “Okay!” He hit his time right on the nose! I couldn’t believe it!
We talked about it a while, and we discovered something. It turned out that Tukey was counting in a different way: he was visualizing a tape with numbers on it going by. He would say, “Mary had a little lamb,” and he would watch it! Well, now it was clear: he’s “looking” at his tape going by, so he can’t read, and I’m “talking” to myself when I’m counting, so I can’t speak!
The newspaper lines counting technique reminds me of counting territory in a go game. There are a few ways of doing this, some of them involving counting by 4s, which is quite fast when you can do it (I can’t). After I learned about this I got into the habit of counting everything by 2s, but thinking “1, 2, 3, 4, …” and doubling at the end rather than thinking “2, 4, 6, 8, …”. I keep track of the parity bit visually, if odd. In my experience this roughly doubles the speed I can count, say, people in a room without losing any accuracy.
Incidentally, chunks of even numbers work particularly well for go since dead stones effectively count double, one for the prisoner and one for the empty intersection underneath.
The Feynman story:
-- source
(The rest of the story is interesting as well.)
The newspaper lines counting technique reminds me of counting territory in a go game. There are a few ways of doing this, some of them involving counting by 4s, which is quite fast when you can do it (I can’t). After I learned about this I got into the habit of counting everything by 2s, but thinking “1, 2, 3, 4, …” and doubling at the end rather than thinking “2, 4, 6, 8, …”. I keep track of the parity bit visually, if odd. In my experience this roughly doubles the speed I can count, say, people in a room without losing any accuracy.
Incidentally, chunks of even numbers work particularly well for go since dead stones effectively count double, one for the prisoner and one for the empty intersection underneath.