Dot Counting Estimation Game

About Dot Flash

Dot Flash shows a square filled with scattered dots for less than two seconds and then takes it away. You slide to the number of dots you think you saw. The dots are placed at random without overlapping, so there is no pattern to count, only an impression of how many there are.

The numbers grow with the level. On level 1 there are between about 8 and 40 dots, and the field is visible for roughly one and a half seconds. On level 10 you may see up to about 300 dots for under a second. The slider is logarithmic because with a big swarm the question is not whether it was 120 or 121, but whether it was nearer 100 or 150.

How to play

1. Look at the field when it appears, with a soft gaze, as if you were looking at a flock of birds. Do not start counting.
2. When the dots disappear, a slider shows up. Move it to the number that feels right. It runs from 3 to 400.
3. Lock in before the 10 second answer timer ends.
4. The real number is shown on the slider, so you can see how far off you were and in which direction.

A field of dots appears for a moment. Slide to how many you think there were. Do not try to count them one by one, there is no time. The slider is logarithmic.

How scoring works

The score depends on the ratio between your answer and the real number, on a logarithmic scale, so 60 when the answer is 40 is as wrong as 27 would be. A perfect answer scores 100 and the score reaches 0 at a factor of about 2.2 on level 1 and 1.6 on level 10. On the top level 20 percent off still earns about 60 points.

The number of dots is drawn on a logarithmic scale between 8 and 40 on level 1 and between 20 and 300 on level 10, so every size range appears. The flash lasts 1.6 seconds on level 1 and 0.7 seconds on level 10, which is too short for counting more than a few dots.

What it trains

The game trains the approximate number system, the brain's built-in ability to judge numerosity without counting. It is shared with many animals and appears in human babies, and it is the basis of our first feeling for amounts: more or less, much or few.

Practice can sharpen the ability. In everyday life it supports quick judgements of crowd size, a full or empty parking lot, how many items are on a shelf or how many people are in the room.

Tips for a higher score

• Look at the field as a whole, not at individual dots. Counting attempts take longer than the flash and usually spoil the impression.
• Divide the field into quarters and judge one quarter. Multiply by four. This works well when the dots are spread evenly.
• Use the density: a tightly packed field has many dots and a loose one has few. Compare it with fields you remember from earlier rounds.
• Small numbers up to about four can be seen at once without counting. A swarm of ten or more must be estimated.
• Check the feedback. After a few rounds your sense of 50, 100 and 200 dots will calibrate.

The idea behind it

Researchers call the ability to judge numerosity the approximate number system. In a well-known 2008 study published in Nature, Justin Halberda and colleagues showed that the sharpness of this sense, in 14-year-olds, was related to their earlier maths scores, although the question of cause and effect is still debated. Adults can usually distinguish two sets that differ by about 15 percent.

Stanislas Dehaene popularized the idea in his 1997 book The Number Sense. Experiments with infants show that six-month-old babies can tell apart sets with a ratio of 1 to 2, and that this improves to about 2 to 3 around the age of nine months. The fact that the error grows in proportion to the number is another case of Weber's law.

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