Numberness Is Learned

Philosophy Forums Psychology and Mind
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A remarkable things observed in raising my kids is that the concept of quantity, of number-ness, is not innate.

I had thought it would be as easy to teach kids the names of numbers as it is to teach them the names of other things. ‘Mom’ and ‘dad’ are easy, as are names for e.g. specific toys. They learn these by associating the sound with the thing, which is always roughly the same thing.

They also learn general nouns, like ‘dog’ and ‘ball’, and accurately apply them to members of a category. This takes a little longer, but perhaps not as long as you’d expect, and it’s striking that once they understand the concept they rarely make mistakes like calling a cat a dog. ‘Dog’ is a pretty complex concept, having a diverse range of size and shape and color and behavior. But kids get the idea of a dog readily.

They can also name abstract concepts, like ‘tired’ and ‘hungry’ and ‘hurt’, or ‘big’ and ‘small’.

I had expected that number would be similar, but it seemed much harder to convey. showing them three blocks and three balls and saying ‘three’, the kind of thing that works well for other concepts, did not seem to come naturally. This would make sense if when I show them three things, they don’t see it as particularly different from four things or five things. Certain pre-industrialized languages have much courser quantity words, limited to something like ‘one’, ‘a few’, ‘many’, and ‘a lot’.

This blindspot is hard to understand for someone who has long left that style of thought, but I can somewhat inhabit it by considering that, early on, numbers are effectively like another alphabet: they have an order, but the order is just the order, it’s arbitrary. So if I consider the statement “there are C balls”, that seems weird and counterintuitive, but is probably similar to how young children begin to understand “there are 3 balls”.

I think I get even closer to this by thinking about doing math like that, considering an equation like,
H + C = K
In terms of ordering it’s correct: K is C letters after H. But it feels weird and arbitrary and non-number, which is probably how everything about numbers feels to early language learners.

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Just because language is learned doesn’t mean we don’t have an innate capacity to communicate.

And just because we never got a firm grasp on quantity doesn’t mean 2+2 stops equaling 4.

Weirder than what you just said is the fact that some people do not have a mind‘s eye that visualizes things.

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Learning the concept of quantities would probably be a higher-order conceptual terrain. Because it is so abstracted from real immediate sensory experience. It involves pure thought, conception as such.

There are stages of concept development that kids go through, much of it implicitly and not formally taught but rather indirectly picked up on through observation of the world around them. The first stage is when infants learn “objects exist”. That is the most basic level, at least according to the theory and system I know of. Part of the function of Peekaboo games with infants is they are learning this concept. An object is present, then you put it behind your back. To their little mind, it no longer exists. But POOF you bring it back. Do this over and over, and they will develop the rudimentary conceptual understanding that Objects Exist.

Later they learn that objects are different, objects have a name, objects have a function, and it goes up from there.

But the whole numerical thing is interesting. Asking “How many?” could only make sense after they have learned how to count and distinguish at least between 1 and 2. I would start there. Pick one ball, put it on the table. Tell them “This is one ball”. Then remove it and put two coins on the table, tell them “This is two coins”. Repeat this until they can successfully answer the question “How many?” with regard to either 1 or 2 things, first with the balls and coins but then expanded to other novel items.

Once 1 and 2 are grasped, they have the basic concept of quantity, albeit indirectly and probably not yet very well understood or remarked upon linguistically. But phrasing it as a question “how many?” seems to point directly to the abstraction which is the pure concept of numbers as such. Add a third thing and then they will learn to distinguish between 1, 2 and 3. And so on and so on. Just my guess but it seems like it could work well.

Once this level is grasped, you can start associating the word “number” with either “1”, “2” or “3” things. As in, “Yes you are right, there are 3 balls. The number of balls here is 3. 3 is a number.” You are right this is basically like teaching them another language entirely. But good thing kids are usually super smart and pick up on stuff like this after just a little exposure and successful repetition.

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I think that’s right, it was just surprising to see something so fundamental be so absent.

A related concept that I learned in the past couple years is “subitizing”, the rapid recognition of small quantities of objects, e.g. you look at 4 things and immediately know that there are 4 of them without counting. It’s something most people learn from experience, but some schools explicitly teach it in preschool and kindergarten.

I think that may be where my surprise comes from: for me, to look at 4 things is just to see that there are 4 of them, it’s a fundamental part of my experience of the world. Kids see colors and shapes and size, and later objects and categories, but the number-ness that we see when we subitize is not there – or maybe just limited, Wiki says even babies can subitize 1-3 things, so maybe I was just starting at too high a number when I was trying to teach my kids about numbers.

Yeah, this stuff fascinating.
Another weird one I came across is that not everyone ‘hears’ when they’re reading. Like they can read and absorb the information, but they’re directly turning the shapes into ideas, instead of shapes->sounds->ideas. My wife does it, and it makes her a much faster reader than me, but I remember what I read better.

The diversity of human experience is cool and underappreciated.

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I read about subitizing recently. There’s this weird thing about items being split between both visual fields that helps remember more items.

Are you talking about when they’re reading aloud? Pardon my confusion, I am tired and I’m going to sleep.

Sometimes I read aloud because I have zero attention span. It keeps me on task. I notice when I get distracted faster. It’s not because the content doesn’t keep my attention, but because my brain goes off on 5000 different related rabbit trails. Sometimes reading aloud doesn’t even help with that.

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2 posts were split to a new topic: Hearing What You Read

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It may be learned in humans, but what about animals? Bees can count - wild, but supported by evidence. Do you suppose they had to learn, or do you suppose there’s something instinctual about it for them?

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I think more or less is pretty much basically understood.
But numbering and conscious quantification is learned.
When an ape swings from branch to branch they certainly ahve to quantitfy the distance, and that their effort is at least adequate for the jump.
My dog even knows to take the bigger treat.
So I think what you are saying is limited.

Think of Baldrick when Blackadder tries to teach hi to count.
Here are two beans, and here are two more. Put them together and what do you have?
Answer “Some Beans!”

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How many beans do you have if you have all the beans?

How many beans don’t you have if you have no beans?

If you have one bean, do you have all the beans, or do you just have some beans?

And that’s why everyone is all messed up about quantity.

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Bees can count? Lol.

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…does this count as counting?
https://youtu.be/-7ijI-g4jHg?feature=shared

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This is remarkable..
You might still argue that a chimp has to learn numberness, but you cannot deny that they outperform humans

https://www.youtube.com/shorts/k-eltEACEQM