7 ms·

Why the Human Brain Perceives Small Numbers Better

104 points by digital55 3y ago

apienx 3y ago
These guys claim to see distinct “neural signatures” depending on whether n is >4 or =<4. They can see neurons misfiring for the larger numbers. Is it hard-coded in our brains? My guess is no. You can probably train brains to instantly recognise patterns for numbers larger than 4, and I’d expect the observed effect would disappear for then trained individuals.
- tgv 3y ago
  It's a visual count. The visual system probably isn't optimized for counting. It identifies and tracks objects, but not many. I'm not surprised 4 is a common boundary, and I also wouldn't be surprised if it were somewhat hard-coded. It could well be limited by a "lower" layer. The experiment is artificial, so it might not represent counting in a more natural setting, where e.g. the objects might have features that distinguish them better. The article brushes over that.
- monocasa 3y ago
  There's a lot of evidence from other studies of being able to track about 4 simultaneous objects. It looks like (but we don't have concrete evidence quite yet) that somewhere (maybe higher level parts of the visual cortex, maybe something higher level like state scratch pads, maybe something else we haven't thought of) there's a four wide logical pathway. When we overload it, it seems that we sort of time slice whatever it is, jumping between the objects at roughly four at a time. In addition to performance tests, there's also the data point that there's a surprising amount of languages in pre agricultural societies that have words for 'one' through 'four', but anything else is some degree of 'many'. And yeah, you can train your brain to see larger sets if they're in a pattern that the middle parts of the visual cortex can train on, but the limit does seem to be around 4 visual symbols/tokens concurrently. Another place you see an interesting bandwidth limitation is that pretty much all languages have a pretty fixed semantic bits per secondnwhen spoken. Specifically around 39 bits per second. We can listen and hear faster but rates, but it's very difficult to speak faster. Similar to the above discussion the cute hack to go faster is to essentially give a single internal symbol to a larger sequence of syllables through training, not casting off the limitation but sort of hacking around it. https://www.science.org/doi/10.1126/sciadv.aaw2594 https://www.science.org/doi/10.1126/sciadv.aaw2594
  - dboreham 3y ago
    PCI lanes
- pixl97 3y ago
  Not sure if it's hard coded, but the brain is taking a lot of visual shortcuts because of the limited visual bandwidth you have. https://youtu.be/HU6LfXNeQM4?si=PRdZP_hdwdyJQkdP&t=521 https://youtu.be/HU6LfXNeQM4?si=PRdZP_hdwdyJQkdP&t=521 Your Brain: Perception Deception This section is interesting on how little we see in high definition, and how much mental processing it takes.
hiAndrewQuinn 3y ago
The rule of four comes in handy across all kinds of places. A command line argument that can be run with 4 or fewer distinct words/flags/etc is one I'm much more likely to try running than one with more.
- bee_rider 3y ago
  It even kinda works for something like tar. tar czvf output files The czvf is really four arguments I guess, but it expresses a single concept in some sense.
  - snakeyjake 3y ago
    The GNU Foundation wants to know your location and while you're using the "Old" option style. You will use "tar --create --gzip --verbose --file output files" and you will like it.
    - bee_rider 3y ago
      It turns out that “GNU/Stallman was right” applies only to matters philosophical.
cheschire 3y ago
There are four lights.
neoneye2 3y ago
Tetris games with 4 cells, is that easier that Tetris games with 5 or more cells?
Someone 3y ago
I find this unconvincing. FTA: “More than 150 years ago, the economist and philosopher William Stanley Jevons discovered something curious about the number 4. While musing about how the mind conceives of numbers, he tossed a handful of black beans into a cardboard box. Then, after a fleeting glance, he guessed how many there were, before counting them to record the true value. After more than 1,000 trials, he saw a clear pattern. When there were four or fewer beans in the box, he always guessed the right number. But for five beans or more, his quick estimations were often incorrect.” and “For example, some neurons are tuned to the number 3. When they’re presented with three objects, they fire more. Other neurons are tuned to the number 5 and fire when presented with five objects, and so on. These neurons aren’t exclusively committed to their favorites: They also fire for numbers adjacent to it. (So the neuron tuned to 5 also fires for four and six objects.) But they don’t do it as often, and as the presented number gets farther away from the preferred number, the neurons’ firing rate decreases” So, the experiment was about integers, not numbers in general, and the neurons don’t necessarily encode integers, but also could encode reals with noise/uncertainty. I think the latter decently describes the experimental data if the noise/uncertainty is around 20% of the value. Rounding such a signal to integers will be faultless for n < 4, and get increasingly worse the larger n is. In pseudocode: Round(n * (1 + gaussianRandom())) == n for small n, but not for larger n. To support a claim that we’re better at smaller integers, I think you’d have to show that the standard deviation for larger n goes up superlinearly. (An alternative way to phrase this is by claiming that these cells encode logarithms of numbers)
- ahoho 3y ago
  This was exactly my undergrad research topic! My knowledge is a bit out of date (perhaps this is in TFA), but the running theory is that there are two number systems. The first operates noiselessly and immediately for numbers under 4. The second works in the exact way you are describing, where the magnitude of errors are linear in the size of the set (the “analog magnitude” system). As I recall, there is substantial evidence supporting the idea of two separate systems rather than one. I don’t really follow your point about integers. We know the brain does object detection at a low level, so it makes sense that the number systems will operate over countable elements.
jacobgorm 3y ago
And yet GitHub still send me six digit one time codes, with no spaces to help my brain with chunking.
aragonite 3y ago
Relevant: https://en.wikipedia.org/wiki/Subitizing https://en.wikipedia.org/wiki/Subitizing Also, technically it's not that we perceive small number "better". We only perceive (i.e. subitize) the size of a small collection. We find out the size of a large collection by counting, but counting is not a kind of perception, any more than inference, computation, etc are kinds of perception.
- ooterness 3y ago
  For what it's worth, the upper limit for subitization varies quite a bit. The neurotypical limit is usually four, but can be raised with practice. Children with Down's Syndrome may not be able to subitize at all. Autistic savants can subitize up to thirty or more, with unconfirmed cases up to several hundred.
  - mike_hock 3y ago
    Monkeys can fucking subitize double-digit numbers, which makes you question whether we are actually the smartest species on the planet.
    - cscurmudgeon 3y ago
      No, it doesn’t. Why? No monkeys are discussing of subitization as a concept and how their species compares with others. Just because a kangaroo can jump higher than humans doesn’t mean it can go to the moon before humans. And, g factor. https://en.m.wikipedia.org/wiki/G_factor https://en.m.wikipedia.org/wiki/G_factor Even savants can have low IQ.
    - pixl97 3y ago
      Eh, we're doing that smartest/most intelligent thing that always has lead to problems in human perception. An adult Chimpanzee can rip your arms off. Pretty much all it's muscles are fast twitch. Of course you're going to have far better dexterity than the chimp, because you have a much better balance of muscle fibers. That's the thing about intelligence, it's about generalization, not specific ability. A CPU can count to a billion in a second, nothing about that speed means it's 'smarter' than you. This is also why we're going to have to come up with new metrics on abilities as we develop more general intelligence software to see how and where said software differs from humans.
hun3 3y ago
Maybe it could also explain why we decided on hexadecimal radix e.g., each digit has 2^4 possible values.
trebligdivad 3y ago
I'd love if these guys spoke to the Allen institute guys doing genetics of individual neurons; what is it that makes these neurons count particular values. Also, does anyone understand what the 'interface' is? Is this 'n' spikes within a given time, or spikes on different inputs?
layer8 3y ago
So the brain uses floating-point with only two bits for the mantissa. ;)
nayuki 3y ago
The headline would be fuel for anti-metric advocates. "Look! 1 pound is easier to mentally process than 454 grams." "3 cups is better than 710 mL."
- softg 3y ago
  Except here in the metric land when we want to buy a pound of something (or thereabouts) we ask for half a kilo. And the second can easily be 3/4 liters.
  - gumby 3y ago
    In northern Germany it’s fairly common to hear Pfund used in the market to mean 500 g.
- gumby 3y ago
  I don’t know if you intended this as a joke, but this is true and a good UX insight. For day to day activities, the US customary units are more humane. Foot, pound, cup, are simply common sizes that one encounters. Foot and cup break into convenient units (powers of two in small scale volume, convenient rationals like a half, two thirds, etc for both). A standard stair riser is 2/3 of a foot — 8 inches — for example. The US system is better in this way than the imperial system as the former’s pint, quart etc are more conveniently sized with better fractions. And, to your point: all this breaks down when the sizes get bigger (or tinier!) than you can physically “handle”. A yard/meter is pretty big (people don’t usually measure areas for rooms etc in yards) and beyond that metric becomes as good and most of the time easier. If only it hadn’t been designed around powers of 10! But this principle extends to other special case units. For example while I prefer to use metric screws technical reasons, the fractions of 2 in drill threads are much more intuitive. And you can see this principle breaks down for non-“intuitive” units: temperature is abstract, foot-pounds are not better than newton-meters etc. But use the right tool for the job. I mostly write Lisp and C++ code but it doesn’t mean I won’t sometimes reach for Python. Note: I was born in a (then) non-metric country and currently live in the remaining one, but have lived in metric land for a lot of my life and use them both all day long. So no bias.
jojojaf 3y ago
I didn't read the article but, small numbers are more immediately useful. Larger numbers are needed for describing more complex phenomena, and their construction relies on smaller numbers. So I find the explanation to the title of this article to be intuitively obvious; I don't see how it could be possible for a brain to evolve to perceive large numbers better than smaller ones
- Swenrekcah 3y ago
  Perhaps a fish or an insect might benefit more from knowing an accurate approximation of their or another school/swarm, than it would from knowing if there are 2 or 4 of them somewhere (since there seldom are so few).
- passion__desire 3y ago
  Brain systems do handle order of magnitude changes. E.g. going from dimly lit room [1-3] to bright sunlight. [1000-2000]
- atleastoptimal 3y ago
  [flagged]
  - willio58 3y ago
    I didn’t read either of your comments but I agree as well
    - dd36 3y ago
      Where am I?
      - notmuchserious 3y ago
        Maybe
        adhesive_wombat 3y ago
kzrdude 3y ago
What's the number of things that we can count instataneously and intuitively. What's your number in your opinion? It would appear as though it's three or four. I look over to some series of things, if it's exactly two or three, I know that pattern, if it's more, I have to make out groupings of two or three. I think even for four or five we might do this habitually?
- Drakim 3y ago
  For me it's four, my brain just instantly recognizes that there are four things, that instant pairing of pairings: oooo Five is a bit more iffy, I can obviously tell quickly that there are five things, but then it feels like it's my 3 and 2 pattern recognition kicking in plus some addition math: ooo oo. If you spread the objects out in a weird way where I don't see that 3+2 grouping then I have to count em.
- arketyp 3y ago
  Many years ago at a LAN party at my friend's house his father came in with a news article saying studies showed that gamers could develop a better sense for instantaneous assessment of count, up to 6 I vaguely recall. Anyhow I do remember reconsidering my aptitude, since for me it gets confusing with >= 5.
- ooterness 3y ago
  For what it's worth, the upper limit for subitization varies quite a bit. The neurotypical limit is usually four, but can be raised with practice. Children with Down's Syndrome may not be able to subitize at all. Autistic savants can subitize up to thirty or more, with unconfirmed cases up to several hundred.

104 points by digital55 3y ago

These guys claim to see distinct “neural signatures” depending on whether n is >4 or =<4. They can see neurons misfiring for the larger numbers. Is it hard-coded in our brains? My guess is no. You can probably train brains to instantly recognise patterns for numbers larger than 4, and I’d expect the observed effect would disappear for then trained individuals.

tgv 3y ago
It's a visual count. The visual system probably isn't optimized for counting. It identifies and tracks objects, but not many. I'm not surprised 4 is a common boundary, and I also wouldn't be surprised if it were somewhat hard-coded. It could well be limited by a "lower" layer. The experiment is artificial, so it might not represent counting in a more natural setting, where e.g. the objects might have features that distinguish them better. The article brushes over that.
monocasa 3y ago
There's a lot of evidence from other studies of being able to track about 4 simultaneous objects. It looks like (but we don't have concrete evidence quite yet) that somewhere (maybe higher level parts of the visual cortex, maybe something higher level like state scratch pads, maybe something else we haven't thought of) there's a four wide logical pathway. When we overload it, it seems that we sort of time slice whatever it is, jumping between the objects at roughly four at a time. In addition to performance tests, there's also the data point that there's a surprising amount of languages in pre agricultural societies that have words for 'one' through 'four', but anything else is some degree of 'many'. And yeah, you can train your brain to see larger sets if they're in a pattern that the middle parts of the visual cortex can train on, but the limit does seem to be around 4 visual symbols/tokens concurrently. Another place you see an interesting bandwidth limitation is that pretty much all languages have a pretty fixed semantic bits per secondnwhen spoken. Specifically around 39 bits per second. We can listen and hear faster but rates, but it's very difficult to speak faster. Similar to the above discussion the cute hack to go faster is to essentially give a single internal symbol to a larger sequence of syllables through training, not casting off the limitation but sort of hacking around it. https://www.science.org/doi/10.1126/sciadv.aaw2594 https://www.science.org/doi/10.1126/sciadv.aaw2594
- dboreham 3y ago
  PCI lanes
pixl97 3y ago
Not sure if it's hard coded, but the brain is taking a lot of visual shortcuts because of the limited visual bandwidth you have. https://youtu.be/HU6LfXNeQM4?si=PRdZP_hdwdyJQkdP&t=521 https://youtu.be/HU6LfXNeQM4?si=PRdZP_hdwdyJQkdP&t=521 Your Brain: Perception Deception This section is interesting on how little we see in high definition, and how much mental processing it takes.

hiAndrewQuinn 3y ago

The rule of four comes in handy across all kinds of places. A command line argument that can be run with 4 or fewer distinct words/flags/etc is one I'm much more likely to try running than one with more.

bee_rider 3y ago
It even kinda works for something like tar. tar czvf output files The czvf is really four arguments I guess, but it expresses a single concept in some sense.
- snakeyjake 3y ago
  The GNU Foundation wants to know your location and while you're using the "Old" option style. You will use "tar --create --gzip --verbose --file output files" and you will like it.
  - bee_rider 3y ago
    It turns out that “GNU/Stallman was right” applies only to matters philosophical.

cheschire 3y ago

There are four lights.

neoneye2 3y ago

Tetris games with 4 cells, is that easier that Tetris games with 5 or more cells?

Someone 3y ago

I find this unconvincing. FTA: “More than 150 years ago, the economist and philosopher William Stanley Jevons discovered something curious about the number 4. While musing about how the mind conceives of numbers, he tossed a handful of black beans into a cardboard box. Then, after a fleeting glance, he guessed how many there were, before counting them to record the true value. After more than 1,000 trials, he saw a clear pattern. When there were four or fewer beans in the box, he always guessed the right number. But for five beans or more, his quick estimations were often incorrect.” and “For example, some neurons are tuned to the number 3. When they’re presented with three objects, they fire more. Other neurons are tuned to the number 5 and fire when presented with five objects, and so on. These neurons aren’t exclusively committed to their favorites: They also fire for numbers adjacent to it. (So the neuron tuned to 5 also fires for four and six objects.) But they don’t do it as often, and as the presented number gets farther away from the preferred number, the neurons’ firing rate decreases” So, the experiment was about integers, not numbers in general, and the neurons don’t necessarily encode integers, but also could encode reals with noise/uncertainty. I think the latter decently describes the experimental data if the noise/uncertainty is around 20% of the value. Rounding such a signal to integers will be faultless for n < 4, and get increasingly worse the larger n is. In pseudocode: Round(n * (1 + gaussianRandom())) == n for small n, but not for larger n. To support a claim that we’re better at smaller integers, I think you’d have to show that the standard deviation for larger n goes up superlinearly. (An alternative way to phrase this is by claiming that these cells encode logarithms of numbers)

ahoho 3y ago
This was exactly my undergrad research topic! My knowledge is a bit out of date (perhaps this is in TFA), but the running theory is that there are two number systems. The first operates noiselessly and immediately for numbers under 4. The second works in the exact way you are describing, where the magnitude of errors are linear in the size of the set (the “analog magnitude” system). As I recall, there is substantial evidence supporting the idea of two separate systems rather than one. I don’t really follow your point about integers. We know the brain does object detection at a low level, so it makes sense that the number systems will operate over countable elements.

jacobgorm 3y ago

And yet GitHub still send me six digit one time codes, with no spaces to help my brain with chunking.

aragonite 3y ago

Relevant: https://en.wikipedia.org/wiki/Subitizing https://en.wikipedia.org/wiki/Subitizing Also, technically it's not that we perceive small number "better". We only perceive (i.e. subitize) the size of a small collection. We find out the size of a large collection by counting, but counting is not a kind of perception, any more than inference, computation, etc are kinds of perception.

ooterness 3y ago
For what it's worth, the upper limit for subitization varies quite a bit. The neurotypical limit is usually four, but can be raised with practice. Children with Down's Syndrome may not be able to subitize at all. Autistic savants can subitize up to thirty or more, with unconfirmed cases up to several hundred.
- mike_hock 3y ago
  Monkeys can fucking subitize double-digit numbers, which makes you question whether we are actually the smartest species on the planet.
  - cscurmudgeon 3y ago
    No, it doesn’t. Why? No monkeys are discussing of subitization as a concept and how their species compares with others. Just because a kangaroo can jump higher than humans doesn’t mean it can go to the moon before humans. And, g factor. https://en.m.wikipedia.org/wiki/G_factor https://en.m.wikipedia.org/wiki/G_factor Even savants can have low IQ.
  - pixl97 3y ago
    Eh, we're doing that smartest/most intelligent thing that always has lead to problems in human perception. An adult Chimpanzee can rip your arms off. Pretty much all it's muscles are fast twitch. Of course you're going to have far better dexterity than the chimp, because you have a much better balance of muscle fibers. That's the thing about intelligence, it's about generalization, not specific ability. A CPU can count to a billion in a second, nothing about that speed means it's 'smarter' than you. This is also why we're going to have to come up with new metrics on abilities as we develop more general intelligence software to see how and where said software differs from humans.

hun3 3y ago

Maybe it could also explain why we decided on hexadecimal radix e.g., each digit has 2^4 possible values.

trebligdivad 3y ago

I'd love if these guys spoke to the Allen institute guys doing genetics of individual neurons; what is it that makes these neurons count particular values. Also, does anyone understand what the 'interface' is? Is this 'n' spikes within a given time, or spikes on different inputs?

layer8 3y ago

So the brain uses floating-point with only two bits for the mantissa. ;)

nayuki 3y ago

The headline would be fuel for anti-metric advocates. "Look! 1 pound is easier to mentally process than 454 grams." "3 cups is better than 710 mL."

softg 3y ago
Except here in the metric land when we want to buy a pound of something (or thereabouts) we ask for half a kilo. And the second can easily be 3/4 liters.
- gumby 3y ago
  In northern Germany it’s fairly common to hear Pfund used in the market to mean 500 g.
gumby 3y ago
I don’t know if you intended this as a joke, but this is true and a good UX insight. For day to day activities, the US customary units are more humane. Foot, pound, cup, are simply common sizes that one encounters. Foot and cup break into convenient units (powers of two in small scale volume, convenient rationals like a half, two thirds, etc for both). A standard stair riser is 2/3 of a foot — 8 inches — for example. The US system is better in this way than the imperial system as the former’s pint, quart etc are more conveniently sized with better fractions. And, to your point: all this breaks down when the sizes get bigger (or tinier!) than you can physically “handle”. A yard/meter is pretty big (people don’t usually measure areas for rooms etc in yards) and beyond that metric becomes as good and most of the time easier. If only it hadn’t been designed around powers of 10! But this principle extends to other special case units. For example while I prefer to use metric screws technical reasons, the fractions of 2 in drill threads are much more intuitive. And you can see this principle breaks down for non-“intuitive” units: temperature is abstract, foot-pounds are not better than newton-meters etc. But use the right tool for the job. I mostly write Lisp and C++ code but it doesn’t mean I won’t sometimes reach for Python. Note: I was born in a (then) non-metric country and currently live in the remaining one, but have lived in metric land for a lot of my life and use them both all day long. So no bias.

jojojaf 3y ago

I didn't read the article but, small numbers are more immediately useful. Larger numbers are needed for describing more complex phenomena, and their construction relies on smaller numbers. So I find the explanation to the title of this article to be intuitively obvious; I don't see how it could be possible for a brain to evolve to perceive large numbers better than smaller ones

Swenrekcah 3y ago
Perhaps a fish or an insect might benefit more from knowing an accurate approximation of their or another school/swarm, than it would from knowing if there are 2 or 4 of them somewhere (since there seldom are so few).
passion__desire 3y ago
Brain systems do handle order of magnitude changes. E.g. going from dimly lit room [1-3] to bright sunlight. [1000-2000]
atleastoptimal 3y ago
[flagged]
- willio58 3y ago
  I didn’t read either of your comments but I agree as well
  - dd36 3y ago
    Where am I?
    - notmuchserious 3y ago
      Maybe
      - adhesive_wombat 3y ago

kzrdude 3y ago

What's the number of things that we can count instataneously and intuitively. What's your number in your opinion? It would appear as though it's three or four. I look over to some series of things, if it's exactly two or three, I know that pattern, if it's more, I have to make out groupings of two or three. I think even for four or five we might do this habitually?

Drakim 3y ago
For me it's four, my brain just instantly recognizes that there are four things, that instant pairing of pairings: oooo Five is a bit more iffy, I can obviously tell quickly that there are five things, but then it feels like it's my 3 and 2 pattern recognition kicking in plus some addition math: ooo oo. If you spread the objects out in a weird way where I don't see that 3+2 grouping then I have to count em.
arketyp 3y ago
Many years ago at a LAN party at my friend's house his father came in with a news article saying studies showed that gamers could develop a better sense for instantaneous assessment of count, up to 6 I vaguely recall. Anyhow I do remember reconsidering my aptitude, since for me it gets confusing with >= 5.
ooterness 3y ago
For what it's worth, the upper limit for subitization varies quite a bit. The neurotypical limit is usually four, but can be raised with practice. Children with Down's Syndrome may not be able to subitize at all. Autistic savants can subitize up to thirty or more, with unconfirmed cases up to several hundred.