Three at a Glance

There's an experiment on the left, and I'd like you to try it before I tell you what it's for. It takes about a minute.

You'll see the word "Ready." One second later a group of dots will appear. There might be any number of them from 2 to 7. They won't stay long. They'll vanish very quickly, in about the time you need to blink. The question is, can you tell when there are three of them?

If there are exactly three dots, tap the screen or click the mouse. Otherwise do nothing.

If you'd like to see what this looks like before trying it, click Preview on the left. You can press Stop at any time. Also, it helps if you focus on the center of the square and let yourself just notice how many dots there are.

When you are ready, press Tap on 3.

Done? Then tap Graphs, and you'll see how well the experiment worked. On the top graph, the copper colored dots show the number of times you picked three correctly. The bottom graph shows how long you took to do it.

What the experiment was for

The experiment was designed to find out one thing: when you saw three dots, were you counting them, or just seeing them?

Here's how it was set up. The flash was short, about a fifth of a second, which is not long enough to count three things. The groups of three came mixed in with groups of two, four, five, six and seven, in no pattern, so you couldn't guess when the next three was coming. And the screen wrote down not only whether you tapped, but how long after each flash you tapped, to the thousandth of a second.

If you had been counting, you'd have missed most of the threes, and the ones you caught, you'd have caught late. Look at the graphs. You caught the threes, and you caught them fast, and a two or a four hardly ever fooled you. You weren't counting. There wasn't time. You saw three the way you see red: all at once, without working anything out.

Experiment 2 is a different version of the experiment. It lets you try with any number you like up to 7. Most people find that as the numbers get larger, recognizing them takes more time and they are more likely to make mistakes.

Under the graph for Experiment 2 there's a knob that makes the dots stay longer. Turn it up until you can catch the larger numbers every time. Then look at your times. The taps come later now, and the reason is that you're counting, and counting takes time. It takes about a quarter of a second for each dot. So you've just measured how fast you count, which is something almost nobody knows about themselves.

So your brain has two different ways of finding out how many. One is instant, and it works up to about four. The other is counting: it takes time, and it works for any number. They feel like the same thing. The clock shows they aren't.

Six, in two colours

Experiment 3 uses six again, and this one is surprising.

Tap Two colours. The dots flash for the same short moment, but now some are red and some are blue. When there are six, three are red and three are blue. Tap when you see six.

You'll catch them. In a single heap, six is too many to see at a glance. In two colours, it isn't. The colour splits the six into two threes. You can see three, so you see three-and-three, and that's six. You never counted. Two glances, both instant.

This is why the six on a die is two rows of three, and the five is a four with a dot in the middle. Six dots in a heap have to be counted. Six dots as three and three, you see at once. Whoever first arranged the spots on dice that way, thousands of years ago, had noticed that a heap of six is hard to see and a row of three is easy, and built the die around it. Nobody knows who it was. Dice are older than writing.

Red, and a triangle

Colour did something in that last experiment, so now let's try colour by itself.

In Experiment 4, tap One red dot. Dots flash, all blue, except that sometimes one of them is red. Tap when you see a red one. The screen will change how many dots there are, from four up to twenty. Watch your times.

It takes you no longer to find the red dot among twenty than among four. The red one doesn't have to be found; it's simply there, the way a light is there in a dark room. Whatever finds red isn't looking through the dots one at a time. It sees the whole screen at once.

Tap One triangle among squares. Same experiment, but now the dots are all squares, and sometimes one of them is a triangle. Tap when you see a triangle.

Nobody can tell you what will happen this time, because it depends on the shapes, and on you. Some shapes jump out the way red does. Some have to be hunted for, and then twenty take longer than four. Whether a triangle among squares jumps out is a question you can answer and I can't. The graph will say. If twenty squares take you longer than four, that extra time is the hunting, and you've measured it.

Where it's done

Tap the brain on the left. Three places light up.

One is a fold near the top of the brain, above your ears and a little toward the back, called the intraparietal sulcus. Say "intra-pa-RYE-etal," or just say IPS. It answers how many, fast, without counting. Another is a patch low down at the back, which answers what colour. The third is a strip along the very back, where seeing starts; it draws the edges that make a triangle a triangle.

So three different questions, how many, what colour, and what shape, are answered in three different places, and all three answer before you've had time to think. You don't need to remember the names. I'm telling you because "how many" has an address in your head, and "red" has a different one.

Older than counting

You were born able to see how many.

Here is how we know. Show a baby a few hours old a picture of four things while she hears four sounds, and she looks at that picture longer than at a picture of twelve things. Show her twelve things while she hears twelve sounds, and it's the other way round. She can't count. She can't do much of anything yet. But she can tell four from twelve, and a few days later she can tell two from three.

Colour came later. A newborn can see red before any other colour, and the rest of the colours arrive over her first few months.

Animals can see how many, too. Guppies can tell a group of three fish from a group of four, and they swim toward the bigger group. Once the groups get past four, the guppies stop being able to tell. Honeybees can be trained to fly past exactly three landmarks to find sugar. Crows can do it. And a lioness, hearing strange lions roar in the dark, counts the roars, compares them with the size of her own pride, and walks toward the roars if her side is bigger and stays put if it isn't. Nobody taught her. She can hear three.

So seeing three is older than counting, and older than words. Counting is a trick people invented to reach past four. What you measured today is what was there before the trick.

The man who counted beans

In 1871 the English logician and economist, William Stanley Jevons was curious about how many objects he could see at a glance — without counting. So he put a small box on a black tray, took a handful of beans, and threw some into the box without looking at how many. Then he glanced at the box, guessed the number, and counted the beans out properly to check.

He did this 1,027 times.

He was right every time at three and four. At five he was wrong about one throw in twenty. At ten he was wrong half the time. He wrote it up for a science magazine, on one page, and it may be the first experiment anyone ever did to study their own brain by throwing beans in a box.

His experiment was fair for the same reasons yours was. He didn't know the number before he looked. He glanced once and didn't let himself look again. And he wrote down every throw, the misses along with the hits. That is what makes an experiment fair: you set it up so you can't fool yourself, and then you believe what it shows you.

He needed 1,027 throws and a whole afternoon. You did it in a minute, with a clock he didn't have. The most he could see at a glance was four. That seems to be true of just about all of us.