<p>The ability to discretize numbers seems to depend on having words for discrete numbers. But humans seem to be able to estimate, regardless of linguistic constraints. </p>

<p>As a cool counterexample to "typical educated adults" as evidence for exact, symbolic representation of number, the <a href="http://www.spiegel.de/international/spiegel/brazil-s-piraha-tribe-living-without-numbers-or-time-a-414291.html" rel="nofollow">Pirahã</a> people of Brazil do not have words for numbers and do not seem to possess any numerical concepts beyond "few" or "many." So, it's not a given that humans universally represent number, but even the Pirahã seem to have ability to estimate, suggesting that your intuition may be correct and it's meaningful differences that are universally represented. </p>

<p>Gordon, P. (2004) <a href="http://www.sciencemag.org/content/306/5695/496.abstract" rel="nofollow">Numerical Cognition Without Words: Evidence from Amazonia</a>. <i>Science</i> (306), 496-499.</p>

CC BY-SA 3.0
2013-02-15T03:17:34.083Z
2013-02-18T02:18:02.680Z
2013-02-18T02:18:02.680Z
Amyunimus
<p>One common way of framing numerical cognition is in terms of a "mental number line". This mental number line is thought to have a logarithmic scale, so perceived differences are inversely proportional to their magnitude. For example, the difference between 6 and 7 is perceived as bigger than the difference between 76 and 77. This is just a variant of the Weber-Fechner Law, which applies in many perceptual domains (sound loudness, object weight, light brightness, etc.). So people don't exactly put numbers into discrete bins, but small differences begin to blur together for larger numbers. </p>

<p>In typical, educated adults there is also thought to be an explicit symbolic or linguistic representation of numbers that captures their exact value and allows us to do exact calculations.</p>

<p>For theories of numerical cognition, one good place to start is:</p>

<p>Feigenson, L., Dehaene, S., &amp; Spelke, E. (2004). <a href="http://pbs.jhu.edu/research/feigenson/Feigsenson%20Deheane%20Spelke%202004.pdf">Core systems of number</a>. <em>Trends in cognitive sciences</em>, 8(7), 307-314.</p>

CC BY-SA 3.0
2013-02-07T15:40:33.283Z
Note that one has to be careful with Weber-Fechner type laws when there is [not a natural system of units](http://cogsci.stackexchange.com/a/1772/29). Although in the case of the number line we do have a natural system, but I meant for things like loudness and brightness.
Artem Kaznatcheev
CC BY-SA 3.0
2013-02-07T13:59:15.000Z
2013-02-07T13:59:15.000Z
Dan M.
<p>It seems reasonable to me that humans discretize numbers: this number is bigger than than number, or when faced with a series of numbers that range from 0 - 100, 50 is "middling", 10 is "low" and 90 is "high". It doesn't seem to me that the brain would place much value in the difference between 76 or 77.</p>

<p>I ask this in the context of scoring in games: many games present scores to players as numbers, but it seems to me the numbers themselves are meaningless, and actually translate to mental buckets where you can say "this is a good score" or "this is a bad score". Players don't actually perceive the numbers. This would indicate that games that use grading systems like A-F would be better communicators of player performance.</p>

<p>Is there any research to back up this theory? I'm coming up short, but I can't believe no-one has tried to answer this question.</p>

CC BY-SA 3.0
2013-02-04T23:34:40.773Z
Related, and nearly a duplicate: http://cogsci.stackexchange.com/questions/1118/why-do-participants-prefer-to-give-input-values-that-are-round-numbers
Chuck Sherrington
CC BY-SA 3.0
2013-02-18T11:32:55.797Z
I am not familiar with any research on this topic, but for myself I like to see my progress as often as possible. I also want to know if I got better since the previous try. So a scale of 0-100 would be much more meaningful than a scale of A-F. Even though I also have tendency to round numbers (this seems natural to me - we do use categorization in other domains so why not with numbers..), I would much rather appreciate score with finer scale. Especially in a game where I can see my score changing over time. A-F would not change that often and I wouldn't get feedback on my progress.
Oriesok Vlassky
CC BY-SA 3.0
2013-02-20T03:52:46.897Z
Just to note, players often compete for those points, and it is very important to them to know the exact outcome in order to win.  All top 10 boards are based on those points.
nycynik
<measurement><cognitive-modeling>
Do humans mentally discretize numbers?
cflewis
# Do humans mentally discretize numbers?

(Asked by: username_0 on 2013-02-04)

It seems reasonable to me that humans discretize numbers: this number is bigger than than number, or when faced with a series of numbers that range from 0 - 100, 50 is "middling", 10 is "low" and 90 is "high". It doesn't seem to me that the brain would place much value in the difference between 76 or 77.

I ask this in the context of scoring in games: many games present scores to players as numbers, but it seems to me the numbers themselves are meaningless, and actually translate to mental buckets where you can say "this is a good score" or "this is a bad score". Players don't actually perceive the numbers. This would indicate that games that use grading systems like A-F would be better communicators of player performance.

Is there any research to back up this theory? I'm coming up short, but I can't believe no-one has tried to answer this question.

**Tags:** measurement, cognitive-modeling

> **Comments:**
> **username_1**: Related, and nearly a duplicate: http://cogsci.stackexchange.com/questions/1118/why-do-participants-prefer-to-give-input-values-that-are-round-numbers  
> **username_2**: I am not familiar with any research on this topic, but for myself I like to see my progress as often as possible. I also want to know if I got better since the previous try. So a scale of 0-100 would be much more meaningful than a scale of A-F. Even though I also have tendency to round numbers (this seems natural to me - we do use categorization in other domains so why not with numbers..), I would much rather appreciate score with finer scale. Especially in a game where I can see my score changing over time. A-F would not change that often and I wouldn't get feedback on my progress.  
> **username_3**: Just to note, players often compete for those points, and it is very important to them to know the exact outcome in order to win.  All top 10 boards are based on those points.  

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## 2 answers

### Answer by username_5 on 2013-02-07. Score: 7 | Accepted answer

One common way of framing numerical cognition is in terms of a "mental number line". This mental number line is thought to have a logarithmic scale, so perceived differences are inversely proportional to their magnitude. For example, the difference between 6 and 7 is perceived as bigger than the difference between 76 and 77. This is just a variant of the Weber-Fechner Law, which applies in many perceptual domains (sound loudness, object weight, light brightness, etc.). So people don't exactly put numbers into discrete bins, but small differences begin to blur together for larger numbers.

In typical, educated adults there is also thought to be an explicit symbolic or linguistic representation of numbers that captures their exact value and allows us to do exact calculations.

For theories of numerical cognition, one good place to start is:

Feigenson, L., Dehaene, S., & Spelke, E. (2004). [Core systems of number](http://pbs.jhu.edu/research/feigenson/Feigsenson%20Deheane%20Spelke%202004.pdf). *Trends in cognitive sciences*, 8(7), 307-314.

> **Comments:**
> **username_6**: Note that one has to be careful with Weber-Fechner type laws when there is [not a natural system of units](http://cogsci.stackexchange.com/a/1772/29). Although in the case of the number line we do have a natural system, but I meant for things like loudness and brightness.  

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### Answer by username_4 on 2013-02-15. Score: 5

The ability to discretize numbers seems to depend on having words for discrete numbers. But humans seem to be able to estimate, regardless of linguistic constraints.

As a cool counterexample to "typical educated adults" as evidence for exact, symbolic representation of number, the [Pirahã](http://www.spiegel.de/international/spiegel/brazil-s-piraha-tribe-living-without-numbers-or-time-a-414291.html) people of Brazil do not have words for numbers and do not seem to possess any numerical concepts beyond "few" or "many." So, it's not a given that humans universally represent number, but even the Pirahã seem to have ability to estimate, suggesting that your intuition may be correct and it's meaningful differences that are universally represented.

Gordon, P. (2004) [Numerical Cognition Without Words: Evidence from Amazonia](http://www.sciencemag.org/content/306/5695/496.abstract). *Science* (306), 496-499.


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