[thedoc]

Say you had three eggs on the table, by simply looking at them you can tell that there are three eggs (without counting one, two, three etc...). My question is, how many eggs or any other objects does there have to be until you have to start counting them?
Asked by Chemistry4me

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[thedoc]

We put this to Dr Roy Allen, School of Psychology, University of Aberdeen:
He’s talking about subitising and subitising is our apparent ability to instantly apprehend the quantity of a small group of objects without needing to consciously count each one individually. Unfortunately this is a research topic which has quite a heated debate about it. A lot of people argue that subitising as such doesn’t exist at all and that really is some form of fast counting which is conscious. It’s very difficult to research into subitising simply because you have to eliminate conscious counting. The only way to do that is to present stimuli very quickly, very short periods of time. Something like 50ms and then ask people to give their impression of the quantity of objects that they actually see. This particular person’s question is quite difficult to answer because as long as the objects are present for a long length of time there’s always the possibility that they might also be counting as well as subitising. The answer to the question is probably 3 or 4 in the true sense of subitising. We probably do this by some form of pattern recognition. There’s some correlation between quantity and particular shape. For example, a triangle – three objects is always a triangle or almost invariably a triangle; two objects always form the ends of a straight line.

[syhprum]

Round about seven seems to be my after that I have to start counting them.

[DoctorBeaver]

I have a suspicion the answer may be akin to how many quanta of information can be stored in short term memory. Most people can remember 7 items, numbers, letters, etc. However, items can be aggregated so that it appears we can store more.

If, for instance, you try to remember the numbers 0 1 2 5 9 7 1 6 8 2 1 you would probably struggle. But put in the form of a phone number - 01259 716821 - it becomes easier because you have aggregated the dialling code reducing the amount of discrete numbers from 11 to 7. It may be that we can instinctively tell when there are 7 items, but more than that would need to be counted or aggregated (i.e. seeing 2 groups of 4 items each).

I have seen no research on this subject so all this is just an educated guess (or, more accurately, a stab in the dark).

[Chemistry4me]

I went to a kindergarden and asked the kids to count pens, I noticed that nearly every time they took three pens at once by just looking. For example, if I said that I wanted 12 pens, they'll take three, then another three, then another three etc... Obviously the number will change as we get older but I presume that for kids it will be around 3-4.

[dentstudent]

The other method would be how many are recognisable in a line. If you can recognise 7 for example, then it follows that you can recognise 7 X 7, and therefore "know" that there are 49 without counting. It's a question of the spatial distribution of the items that need counting.

[chris]

Is it just that with small numbers of objects you could them so quickly that you don't notice yourself doing it; larger numbers of objects take longer to count and hence are more likely to reach consciousness?

Chris

[BenV]

I wonder if there's a tie in with learning to count in the first place?  You can't instinctively know that there are 6 items until you have learned to count to six, so even if you can instinctively know the size of a small group, must you go through the process of mentally marking how many according to the numbers you have learned, in other words, counting them?

[dentstudent]

I wonder if there's a tie in with learning to count in the first place?  You can't instinctively know that there are 6 items until you have learned to count to six, so even if you can instinctively know the size of a small group, must you go through the process of mentally marking how many according to the numbers you have learned, in other words, counting them?

Ben, I'm not sure that I agree with that statement. My eldest boy "knows" that there are 5 fingers on a hand without having to count to 5. Perhaps there are 2 "learning to count" methods - the first being the incremental 1,2,3,4..., the second being "people (generally) have 5 fingers per hand, so two hands are 10". I'm sure that there is a great deal of cross-over between the two methods, and that we perhaps teach counting using both without realising, but I'm not sure that you have to be able to count incrementally to be able to determine how many "fingers"  there are. Of course, this method is not without it's short-comings. There are people with fewer and more fingers than 5.

[dentstudent]

But I can see that you would need to know how many hands you were holding up. But then you can also learn that (most) people have 2 hands....

[Raghavendra]

i have the answer

  "It should not be small nor greater.. If it is visible it can be counted until and unless our eye is visible. Directly"

[Chemistry4me]

Sorry, what was that? You have the answer? I don't think you've understood the question raghavendra   

[DoctorBeaver]

I went to a kindergarden and asked the kids to count pens, I noticed that nearly every time they took three pens at once by just looking. For example, if I said that I wanted 12 pens, they'll take three, then another three, then another three etc... Obviously the number will change as we get older but I presume that for kids it will be around 3-4.

The other method would be how many are recognisable in a line. If you can recognise 7 for example, then it follows that you can recognise 7 X 7, and therefore "know" that there are 49 without counting. It's a question of the spatial distribution of the items that need counting.

Examples of aggregation.

[RD]

http://www.sciencemuseum.org.uk/antenna/neurobotics/smart/115.asp

[DoctorBeaver]

I got 2 spot on (no pun intended) & a total of 5 within 5 which, apparently, makes me better than anyone in the experiment.

[RD]

You're in savant league Dr B...

two savant twins to instantaneously count matches spilled on the floor (one said "111"; the other said "37, 37, 37").

http://discovermagazine.com/2002/feb/featsavant/

[RD]

Either I'm getting in touch with my inner savant ...



or I'm getting better with practice.

http://www.sciencemuseum.org.uk/antenna/neurobotics/smart/115.asp

[DoctorBeaver]

Either I'm getting in touch with my inner savant ...



or I'm getting better with practice.

I think it's a case of getting used to how crowded the area is.

[Chemistry4me]

Yes, that was quite tricky!

[RD]

.






Yes I cheated on this test.

[Chemistry4me]

How? You took photos and then went back and counted them?

I saw that!

[Chemistry4me]

Come on! Spill the beans!

[RD]

How? You took photos and then went back and counted them?

No counting necessary, just forgery.

[DoctorBeaver]

How? You took photos and then went back and counted them?

No counting necessary, just forgery.

An example of lateral thinking 

[amaterasu]

many birds seem to possess such a number sense, too.
i've read that they can somehow distinguish 2 from 3.  for instance, if a nest contains 4 eggs and 1 of them could be taken safely, but when 2 are removed the bird generally deserts the nest.

our number sense isn't all that great either, actually.
interestingly, cardinal number implies no counting.  you need a number system to create a counting process and only humans seem to be capable of doing so.