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Take two people Sam (average human) and Jack.

Jack says to Sam "I'm going to show you some skittles (or other object) and I want you to tell me as quick as you can how many I'm holding." He opens his hands and there are three. Sam can instantly tell there are three. Then Jack shows five to Sam, who takes a little longer, as he knows there are around 4/5 but can't tell so has to count.

As the number of skittles increases, Sam takes longer and longer to answer to the point where he needs to count the skittles one at a time to be sure, and sometimes to even recount them.

Why is it that we can instantly if we are looking at three maybe four objects but any more than this we cant? It gets harder and harder to estimate?

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The answer to this question is complicated, but assume it's not for the moment. The easy answer is that our eyes can detect patterns we're familiar with and "produce" an answer in the form of a number. Unfamiliar patterns do not produce this 'number'.

Take a die. We are immediately aware of the number of dots in the typical arrangement of one to six. We need expend no counting to do so. If the skittles are arranged in the familiar die pattern, we will have no problem knowing if there are 4 or 6 skittles.

Given a pair of dice, any gambler can tell you what number any two faces adds up to without counting the spots. Do it long enough, and your brain is on auto-recognize. In your example, if Sam is a gambler, and the skittles are arranged like the spots on two dice, again, no problem telling between 2-12 skittles.

If you arrange things in a comfortable pattern, this can go on into the hundreds.

enter image description here

The above was easily recognized by you as nine, I presume.

enter image description here enter image description here

Someone good with pattern recognition will know that the above left is 25 dots. However, they will not know that there are 25 dots in the above right.

So, the easy answer is that the eye can grasp high numbers of things if they are presented in a familiar pattern. The normal mind, however, is not able to do so with higher numbers arranged in a random pattern. And, random is how most things present themselves. So, we need to count.

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    $\begingroup$ While this is interesting, this sounds like pure conjecture. Do you have sources for this information? $\endgroup$ – gravityassist Dec 5 '14 at 1:11
  • $\begingroup$ @gravityassist - I hope you realize that by eyes, I don't mean the retina. $\endgroup$ – anongoodnurse Dec 5 '14 at 1:22
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    $\begingroup$ I didn't make that assumption. I just wanted op to have that information. Still doesn't change the fact that you have no sources to back up your answer. $\endgroup$ – gravityassist Dec 5 '14 at 1:35
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    $\begingroup$ Ahh so its not neccesarily amount of objects but the pattern they are arranged? $\endgroup$ – Srb1313711 Dec 8 '14 at 10:31
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This question appears to be related and the top answer lists a number of sources:

https://psychology.stackexchange.com/questions/3475/what-is-the-maximum-number-of-objects-an-average-human-being-can-recognize-at-on

Summed up, the average human can apparently recognize the exact number of up to 3-4 items almost instantly, but for anything above that either needs a counting mechanism that somewhat linearly grows with amount of items (which for 4-8ish can still be super fast, so you wouldn't necessarily notice the difference yourself) or there needs to be a familiar pattern which helps you determine the number more quickly.

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  • $\begingroup$ I have modified your answer, in particular substituting number for amount. Amount should only be used for non-countable objects in English, which in this specific instance is particularly pertinent. As an aide memoire — "amount of sugar (non-countable), number of lumps (countable)". $\endgroup$ – David Jan 25 at 13:10

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