[HN Gopher] Why the Human Brain Perceives Small Numbers Better
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Why the Human Brain Perceives Small Numbers Better
Author : digital55
Score : 86 points
Date : 2023-11-11 01:56 UTC (1 days ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| jojojaf wrote:
| 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
| atleastoptimal wrote:
| I didn't read the headline, but I agree.
| willio58 wrote:
| I didn't read either of your comments but I agree as well
| dd36 wrote:
| Where am I?
| notmuchserious wrote:
| Maybe
| adhesive_wombat wrote:
| Why?
| sethammons wrote:
| Not reddit; the thread should expect downvotes
| layer8 wrote:
| Sunday
| ilayn wrote:
| I'm scraping the web. You are right by the way.
| Swenrekcah wrote:
| 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 wrote:
| Brain systems do handle order of magnitude changes. E.g. going
| from dimly lit room [1-3] to bright sunlight. [1000-2000]
| kzrdude wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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.
| apienx wrote:
| 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 wrote:
| 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 wrote:
| 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
| dboreham wrote:
| PCI lanes
| pixl97 wrote:
| 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
|
| Your Brain: Perception Deception
|
| This section is interesting on how little we see in high
| definition, and how much mental processing it takes.
| hiAndrewQuinn wrote:
| 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 wrote:
| 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.
| cheschire wrote:
| There are four lights.
| neoneye2 wrote:
| Tetris games with 4 cells, is that easier that Tetris games with
| 5 or more cells?
| Someone wrote:
| 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 wrote:
| 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.
| pixl97 wrote:
| I was watching a NOVA episode about the human mind recently,
| and in the episode they were showing that the eyes only have
| a very limited 'high bandwidth' optical viewing area.
| Anything outside of this high bandwidth area has to be
| committed to memory. I wonder if anyone has researched if
| that corresponds with our ability to count.
| bee_rider wrote:
| I think this is a near-universal experience among people who've
| played a lot of Risk, but did everyone else collect their
| little dudes into units of 5, and then collect those up into
| further collections of five five-unit-squads? After that, 125
| units is too many to really be necessary at once.
| Aerbil313 wrote:
| There are arena in the brain which encode integers up to <small
| number I forgot>. Alex's Adventures In Numberland was a
| fascinating book.
| jacobgorm wrote:
| And yet GitHub still send me six digit one time codes, with no
| spaces to help my brain with chunking.
| aragonite wrote:
| Relevant: 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 wrote:
| 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 wrote:
| _Monkeys_ can fucking subitize double-digit numbers, which
| makes you question whether we are actually the smartest
| species on the planet.
| cscurmudgeon wrote:
| 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
|
| Even savants can have low IQ.
| pixl97 wrote:
| 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.
| bee_rider wrote:
| Humans just "do it in software."
| falsaberN1 wrote:
| Is it really four? Could have sworn it was five, since you
| got a "middle" to help managing the group or subgroup. At
| least I immediately bunch things in groups of five, so I
| always thought it was the correct one.
| _a_a_a_ wrote:
| It's deffo 4 for me. I can see 4 in one shot, if it's say 5
| or 6 or a bit higher I have to split the group and subitise
| each then sum them. YMMV and your mileage beats mine :)
| falsaberN1 wrote:
| Huh. Interesting. I thought it was one of those things
| like how we ended up with base 10 numbers because we have
| 5x2 fingers and that kinda stuff, but interesting to know
| I was off.
| Modified3019 wrote:
| I had a warehouse job for a while, essentially being my own
| independent mini-factory within a larger factory, cutting
| conduit and packaging things up for shipping out.
|
| Part of the job involved accurately counting hundreds or
| thousand of screws. I quickly found that visually grouping
| screws into groups of 4 on a large table was the fastest
| way to be 100% accurate. If I tried to do 5, sometimes I'd
| get a sort of confusion/uncertainty, not being quite clear
| if it was really 5, or 4 or 6, forcing me to check. I'd go
| on to group these little piles of 4, into larger groups of
| 4. So I got really good at counting in 4 and it's
| multiples, 16, 64, 256.
|
| I can definitely see 4 being generally optimal, unless one
| can expect perfect visual ordering, which is possible with
| text, but rare in the real world.
| hun3 wrote:
| Maybe it could also explain why we decided on hexadecimal radix
| e.g., each digit has 2^4 possible values.
| trebligdivad wrote:
| 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 wrote:
| So the brain uses floating-point with only two bits for the
| mantissa. ;)
| nayuki wrote:
| 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 wrote:
| 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 wrote:
| In northern Germany it's fairly common to hear _Pfund_ used
| in the market to mean 500 g.
| gumby wrote:
| 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.
| FunkyDuckling wrote:
| For room temperature I do like Fahrenheit, and feel it's
| pretty intuitive ... 100 is Hot, 0 is cold. 75 is pretty
| warm, 25 is pretty cold.
|
| It doesn't match the small number scale, but still feels
| better.
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