Question of the Week

How many objects can you instinctively count?

Sun, 25th Jan 2009

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Question

Chemistry4me asked:

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?

Answer

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 Chinese AbacusA 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.

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Round about seven seems to be my after that I have to start counting them. syhprum, Tue, 20th Jan 2009

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). DoctorBeaver, Tue, 20th Jan 2009

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. Chemistry4me, Tue, 20th Jan 2009

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. dentstudent, Wed, 21st Jan 2009

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 chris, Wed, 21st Jan 2009

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? BRValsler, Wed, 21st Jan 2009



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, Wed, 21st Jan 2009

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....

dentstudent, Wed, 21st Jan 2009

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"

raghavendra, Wed, 21st Jan 2009

Sorry, what was that? You have the answer? I don't think you've understood the question raghavendra  Chemistry4me, Wed, 21st Jan 2009





Examples of aggregation. DoctorBeaver, Fri, 23rd Jan 2009

http://www.sciencemuseum.org.uk/antenna/neurobotics/smart/115.asp RD, Sat, 24th Jan 2009

I got 2 spot on (no pun intended) & a total of 5 within 5 which, apparently, makes me better than anyone in the experiment. DoctorBeaver, Sat, 24th Jan 2009

You're in savant league Dr B...

http://discovermagazine.com/2002/feb/featsavant/
RD, Sat, 24th Jan 2009

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 RD, Sat, 24th Jan 2009





I think it's a case of getting used to how crowded the area is. DoctorBeaver, Sat, 24th Jan 2009

Yes, that was quite tricky! Chemistry4me, Sun, 25th Jan 2009

.






Yes I cheated on this test. RD, Sun, 25th Jan 2009

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

I saw that! Chemistry4me, Sun, 25th Jan 2009

Come on! Spill the beans! Chemistry4me, Sun, 25th Jan 2009



No counting necessary, just forgery. RD, Sun, 25th Jan 2009



No counting necessary, just forgery.


An example of lateral thinking  DoctorBeaver, Sun, 25th Jan 2009

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.
amaterasu, Sun, 25th Jan 2009



a cuckoo will remove an egg from a nest before adding its egg, so presumably the host bird can notice an addition.
RD, Mon, 26th Jan 2009


I've tried this 5 times, sometimes I am a long way off but other times I am right on the dot, am I meant to be getting fluctuating results like these? Chemistry4me, Tue, 27th Jan 2009

I would have thought your guesses would get better DoctorBeaver, Tue, 27th Jan 2009

Well...um... Chemistry4me, Tue, 27th Jan 2009

hey guys...i listened to the podcast where i gathered our brains take apart various sections of the items in the form of shapes like triangles, and we attempt to count them from there.

What i want to know is that in the days of medieval war or even now perhaps, when the look out/ leader spies the advancing enemy from a distance, they were able to work out how many ranks, and a number estimate of how many soldiers there were...was it this same method used or were they 'smarter' and thus more quite capable of such a feat? SETF, Tue, 3rd Feb 2009

They probably would have had more time that 50ms, so they can 'count' or do some multiplication/calculations, e.g 25 x 20 etc... Chemistry4me, Wed, 4th Feb 2009

~2 out of 5. erickejah, Fri, 13th Feb 2009

What is 2 out of five? Did you mean the test? Chemistry4me, Fri, 13th Feb 2009

Interesting discussion!
One thing not being brought to the fore is the Innate counting thing.
Counting is a learned thing! When counting is irrelevant in a "PRIMITIVE" culture, things about counting suddenly seem very different then in societies of "WEIRD" (Western Educated  Industrialized Rich Democratic.....as  termed by anthropologist Joe Henrich) people.
To illustrate I copy below an excerpt from the 12 february 2009 Nature Journal to illustrate:

From the article:
Darwin 200: Human nature: the remix

Dan Jones

There is evidence that humans have not just one innate number system, but two. The 'analogue estimation' system evaluates quantities in an approximate manner by relating them to imprecise notions such as 'amount of stuff' or 'extent of imaginary line'. The second system is more exact, but can initially, and innately, keep track of only three or four items11.

The exact number system can handle larger numbers, but this requires cultural learning and elaboration (the analogue system seems to function in much the same way across cultures). Some societies, such as the Pirahã; of the Amazon, have little need for large exact numbers (they do not trade or keep accounts), and use only 'one', 'two' and 'many'. The Pirahã also perform poorly at lining up groups of three or more objects (nine nuts, say, with nine batteries), or estimating when the last of 15 beans has been removed from a tin. Without the cultural demand for trading in large numbers, they have neither developed the concept nor invented the words12.

Cross-cultural studies also suggest that a basic grasp of geometric concepts, such as points, lines and parallelism, is a universal component of human cognition, or at least found in disparate cultures13. A similar story holds for how people relate numbers to space, but with an interesting twist. Western adults tend to order clusters of dots (grouped in 10, 100 and 1,000), along a linear scale, so that the distance between the group of 10 and 100 is much smaller than the gap between 100 and 1,000. Western infants, by contrast, group numbers on a logarithmic scale, with the gap between 100 and 1000 the same as that between 10 and 100. Cross-cultural studies among the indigenous Amazonian Mundurucú revealed that both children and adults order numbers logarithmically. Together with the results from Western infants, this suggests that the logarithmic system could be an innate and universal aspect of mathematical thinking, one that gets tweaked in Western populations through formal education in certain mathematical tools and techniques to produce a switch to the linear system14. wannabe, Fri, 27th Feb 2009

Thanks for that wannabe
The last paragraph was quite interesting. Chemistry4me, Fri, 27th Feb 2009

yepyep erickejah, Sun, 8th Mar 2009



Yep, up to three seems to be normal with people that don't have mathematics. "The Hadza people, hunter-gatherers in Tanzania, for example, have words only for "one," "two," and "three"; anything more is "many." And I've heard/read that about other tribes too before. And Animals seems to be able to count too, just as amaterasu tells.
http://www.hno.harvard.edu/gazette/2002/03.14/01-thinking.html yor_on, Tue, 17th Mar 2009



Aye? What is this for? Chemistry4me, Tue, 17th Mar 2009

Me being crosseyed?

Swear to I didn't see that.
Aliens?

Sh* I'm gonna get abduct...


---------

I'll take it away..
Now nobody will know...

Am I clever or what. yor_on, Tue, 17th Mar 2009



loool.. I didn't see that "Yes I cheated on this test" at first ..
Farah jarjous, Tue, 24th Mar 2009

get out of here




I think it's a case of getting used to how crowded the area is.
gurpal, Wed, 22nd Jul 2009

Genius Dot Test is a simple iPad application that tests your ability to quickly estimate large numbers of objects. It uses three different skill levels (the highest goes up to 1000 objects), and tracks your progress over time. It's on iTunes if you are interested: https://itunes.apple.com/us/app/genius-dot-test/id988222365?mt=8 locksleyu, Wed, 6th May 2015

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