
How the brain 'approximates' without counting - dnetesn
https://medicalxpress.com/news/2019-08-brain-approximates.html
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l3s2d
Tangentially related, there was an interesting Reddit post on this a few years
ago:
[https://www.reddit.com/r/askscience/comments/2ayhkp/if_someo...](https://www.reddit.com/r/askscience/comments/2ayhkp/if_someone_asks_me_how_many_apples_are_on_the/)

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Unklejoe
Cool. It kind of reminds me of how problems are often solved in an FPGA.

You can only have so much combinatorial logic before you need to break the
problem up into multiple stages. The subitizing thing seems like solving the
problem in one step with combinatorial logic, whereas counting is like
breaking the problem into multiple stages.

It makes sense that the brain can only do so much combinatorial computation
before the problem needs to be broken up into smaller pieces, incorporating
memory.

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Razengan
Something related that I've always been curious/uncomfortable about:

Can you count without using a language?

Try this: Clap your hands or tap on something an arbitrary number of times.
Can you tell how many times you did it without "saying" one, two, three in
your head?

Even if you pay attention to it, it seems impossible to count without
language.

At least not a stream of sensory inputs; small clusters of around 10 or fewer
things seem easily countable from just looking at a "snapshot."

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anotheryou
I can't turn it off, but I know I can very well do math without words or
numbers in my head.

Geometry is the best example, anythig beyond the basics has no good common
names and still you can do it in your head.

If you slice through a pair of carrots, how many pieces of carrots are there
afterwards? (do this simple thing in your head an than read on)

I slice them imaginary and than start counting what I'm left with. The part
where I go from 2 carrots to 4 carrot parts happens without words. Anyone
doing it differently? You of course have to be self-observing enough to say
more than "I just know" :).

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n0on3
That might as well be a shortcut, as in your brain has done 2*2 so many times
that you have an immediate path for that fixed answer... if this is the case
there's no actual calculation performed, as in you can't do the same thing for
"what if you slice 73 carrots in half"...

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anotheryou
I'm kinda shure I do it visually :)

But yea, get's more difficult with 73. But even there I might determine
"visually" that cutting across a row of carrots halfs each of them. So the 2
in 73*2 ist still determined without words.

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rahimnathwani
The book 'Teach your baby math' suggests that toddlers can learn to recognise
how many dots are shown to them, up to at least 200.

I haven't fully explored this, but made a simple web app to implement part of
the training system in the book. It shows you (or your child) a number of
dots, and says the number out loud.

[https://dots.twilam.com/](https://dots.twilam.com/)

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taneq
Very few humans can directly perceive more than maybe 10 individual items in a
group without counting. If you're telling me you can show a toddler a group of
157 dots and have them say "157", I don't believe you.

(Maybe they can learn to recognize _a particular grouping_ of dots in a book,
but that's a different question.)

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rahimnathwani
I have read reports online of people succeeding with this method using paper
flashcards.

However, like you, I wonder:

\- are these reports true?

\- even if they are true, has the child just memorised a small section of each
particular grouping?

Of course, this trick wouldn't work if a parent is using my online tool, as
the patterns of dots are pseudo-random, so the same number is unlikely to have
the same representation on subsequent views.

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jpadif
This is among other things is what the book Thinking, Fast and Slow by Daniel
Kahneman is about.

Totally recommended read.

~~~
lern_too_spel
Many of the studies cited in that book have been toppled by the replication
crisis in psychology.

~~~
alanbernstein
Is there a consolidated source explaining this? Say, if I wanted to read the
book, but avoid learning false factoids?

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lern_too_spel
Here are a few examples: [https://jasoncollins.blog/2016/06/29/re-reading-
kahnemans-th...](https://jasoncollins.blog/2016/06/29/re-reading-kahnemans-
thinking-fast-and-slow/)

I would just avoid factoids from psychology altogether for the next few years
while the researchers in that field sort everything out.
[https://www.theatlantic.com/science/archive/2018/11/psycholo...](https://www.theatlantic.com/science/archive/2018/11/psychologys-
replication-crisis-real/576223/)

Worse, some of the famous studies aren't merely underpowered or based on
nonrepresentative samples (like college kids) or sloppily executed — some
famous studies are outright fraudulent.
[https://www.vox.com/2018/6/13/17449118/stanford-prison-
exper...](https://www.vox.com/2018/6/13/17449118/stanford-prison-experiment-
fraud-psychology-replication)

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powersurge360
I haven't yet read this and won't until after work but I did click through and
notice it didn't mention subitizing.

Subitizing is pretty cool and it's the name for how you can look at items and
instantly know how many there are if it's less than some small number
(approximately 5 iirc).

Here's a wiki article on it for anyone interested:
[https://en.wikipedia.org/wiki/Subitizing](https://en.wikipedia.org/wiki/Subitizing)

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Cerium
Interesting! I was having a conversation last weekend with a friend when I
asked "How many objects can you count without counting, you just know the
answer". I didn't know the name for it. For me the answer is three, four if
they are in a good arraignment, five is almost always a group of three and
two.

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perl4ever
If I see a five-pointed star, or a five spoked wheel, I don't have to count to
know how many. Probably same goes for six, or a hexagon. Maybe seven.

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leetbulb
I believe that's recognizing a shape and knowing an attribute.

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neilv
How does this perception mechanism fit in with how people conceptualize or
register numbers?

A friend was telling me that when she thinks of a number, a particular
visualization of it automatically comes into her mind. From how she described
it, I recall thinking it sounded like an accidental approximation of something
like a logarithmic scale, but less direct and less precise than it had to be.
I knew her pretty well, and, other than this visual, she didn't appear
atypical (was social, smart and educated, but no savant superpowers, nor any
unusually low limits).

I was wondering whether she had a normal human conception of numbers, and
somehow just had a little extra introspection on that. Or maybe this visual
was an independent mechanism (perhaps learned in childhood). Or maybe she
conceived of numbers differently than most people.

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pawelk
> A friend was telling me that when she thinks of a number, a particular
> visualization of it automatically comes into her mind. From how she
> described it, I recall thinking it sounded like an accidental approximation
> of something like a logarithmic scale

Sounds like spacial-sequence synesthesia. When I think of numbers I see them
at specific points on a logarithmic(-ish) scale as well. I don't think it
gives me any advantage in mental math / counting / estimating, but I can not
disable it and try to experience numbers any other way. I have only learned
it's not common in my early adulthood, until then I have just assumed that's
the way everyone's mind works.

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ricklamers
I wonder if they take into account the idea that you have some prior reference
for expected object counts.

I felt like this is an important mechanism at play when I read the classroom
example. If I saw a picture of a classroom for 2 seconds and am then asked to
estimate the chair count, in my head it goes something like: mean #chairs in
classrooms in my experience * fullness of the classroom in picture (e.g. .5-2
range) = count estimate.

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toxik
But if I show you a bunch of made up widgets you never saw before, you’d still
be able to guess.

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gcbw3
reading articles on scientific paper is such as waste of time.

This is describing the _introduction_ of the paper, i'd guess.

Since in cogsci the Gestalt effect/theory is widely accepted. What i believe
the paper did (but i can't ready it) is to 'reverse engineer' the effect in
some part of the brain and came up with an estimate of the number the process
will 'estimate' based on your vision focal point into the collection of items.

...but who knows.

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moate
[https://www.pnas.org/content/early/2019/08/13/1819956116z](https://www.pnas.org/content/early/2019/08/13/1819956116z)

Here's an abstract for you. This link was provided in the article. Reading
articles on scientific papers can be helpful if you like...read...and check
the links/references. You know, the same way you might want to check the
annotations in a scientific paper.

~~~
gcbw3
Thanks! couldn't find it at first.

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kontorlaore
I think it's more than just estimating the count of objects.

We also "approximate" for example a spatial distribution - think about how
when running through rough terrain, you instantly know which path to choose to
encounter fewer rocks. You are certainly not focusing and counting each
individual rock.

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Mirioron
The image in the article is really an example of a spatial distribution and
fits very well. There's really no way to count which color there is more of in
some area of the image, but you can still estimate which one there is more of.
I'm not even sure how we could numerically assess that without guesstimation.

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emilfihlman
Eh? That is one of the easiest things you can do with parallel/analog/fpga
computing. You simply sum (and this does not mean compute summing, it just
happens) the signals that respond in a certain way. It doesn't require much.

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Mirioron
Sure, with _computing_ , but if you didn't have access to such technology?

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emilfihlman
I mean, just looking at our eyes: it's a field of evenly spaced measurement
devices that send a direct signal to out brain. Ie we have a "parallel
transmission of pixels".

You then just check what colour has the strongest (most) signals.

Or do you mean something else? Like how to do that consciously or something
and not like, how it's possible?

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jimktrains2
Our rods and cones are no where near uniformly distributed, even after
accounting for the blood vessel running around the retina.

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emilfihlman
If so, just add another layer that biases the result based on actual
distribution.

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amflare
So if I understand it correctly, the tl;dr is that we don't like "counting"
items in our peripheral vision, so we approximate by mentally tallying how
many "snapshots" it takes to see all the items in question?

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hosh
I wonder what is the implication for this for people on the ASD spectrum.

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curious_fella1
How does that affect this?

