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I'm thinking about a species that is at the intelligence level of proto-humans. They have limited language but can still discuss concrete things with a little bit of abstraction. For instance, their language has non-locality (they can talk about things that are not right in front of them) but not abstractions like "beauty".

I'd like them to not be able to comprehend numbers, but I think that's wrong. If I'm not mistaken, some non-human species have at least some concept of number.

I'm thinking something like this: they are able to recognize one and communicate about a single thing as a single thing (there is a single rabbit at the river). They are able to understand groups, and perhaps have some words for small groups that they can readily subconsciously count. So perhaps they have a word for "pair" and "few" (for 3) but can't group anything above 3 into anything other than "group" - "there is a group of rabbits" might mean anything from four to a million.

The problem I'm having is how to relay this convincingly. With words for pair and few it is clear that they can distinguish some number of things. Why wouldn't they be able to distinguish more? What is preventing them from creating a simple counting system, and what consequences would that have on their ability to communicate?

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    $\begingroup$ Are you aware that there are human languages with limited numeral capabilities? Something like "one, two, many". $\endgroup$ – L.Dutch Jul 10 at 14:33
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    $\begingroup$ See Pratchett's Monstrous Regiment and how Trolls count - "One", "Two", "Many", "Lots" $\endgroup$ – ivanivan Jul 10 at 14:38
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    $\begingroup$ @L.Dutch: The canonical example is the Pirahã language, spoken by a small isolated tribe in Brazil. The language does not have any words for numbers; it has words meaning "few" and "many" (with the threshold being more than two is "many" when adding objects to a pile, but when subtracting objects from a pile less than five is "few"). Practice shows that Pirahã children who learn Portuguese (the standard language of Brazil) have no problem learning to count and to use numbers... $\endgroup$ – AlexP Jul 10 at 15:52
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    $\begingroup$ Fun science fact, monkeys cannot count higher than 6. If they see 5 scientists enter an observation post and 4 leave, they know they are being watched. However if 7 scientists enter and 6 leave, they think they are alone. $\endgroup$ – Harper Jul 10 at 23:03
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    $\begingroup$ @ivanivan Let me stop you right there. Trolls don't count like that! They count in a quartianary system! It goes: "One, two, three, Many... Many 1, many 2, many 3, Many Many... Many many 1, many many 2, many many 3, many many many... Many many many 1, many many many 2, many many many 3, LOTS. (might be from a different Terry Pratchett book). $\endgroup$ – Demigan Jul 11 at 6:47
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Four is a good limit. Most even semi-sentient things should understand something sliced twice is "quartered" into four, for example.

If you read any paragraph of well-written text, you are very unlikely to find one which has a specific number larger than four, other than in threads like this where numbers are being explicitly described.

In normal speech, we use numbers very rarely. We give far vaguer terms, instead. This is unlikely to be an issue for you.

Consider comparing opposing forces:

  • There's just a family of them, we can take them.
  • There are rather a lot of them, this might be risky.
  • There are more of them than us, but we might hold if we dig in.
  • There are a lot more of them than us, they'll overrun us.
  • The plains are crawling with them, we must run now!

Many of our collective terms have a built-in size limits which are approximate, non-numeric, but very well-understood by everyone who uses them. People are grouped as self, family, clan, tribe, nation, race. Property as desk, room, household, street/block, village, town, county, country, continent, planet, solar system, galaxy, universe. A pod of dolphins is up to a few dozen individuals; above that it's a group, then a supergroup for when it's up in the hundreds. Same with distance: a thumb, foot, pace, walk, long walk. Money: a farthing, ha'penny, penny, tuppence, shilling, quarter, pound...

Time goes in moments, heartbeats, breaths, morning/dawn/afternoon/evening/dusk/night (do we have a name for these day-parts?), *day/yesterday/tomorrow, moon, season, year, reign, epoch. You don't need dates like "1986", you just need "towards the end of the glam-rock era", "a few years before millennials started being born".

Containers and ingredient quantities are a pinch, thimble, teaspoon, tablespoon, cup, fist-sized, head-sized, crate,... you never need to measure an ingredient as "a head-sized lump plus two pinches", you're good so long as you're within 20-50%. So as long as your measures are within a couple of sizes of each other, you can make it work just by using them. Which is basically how cooking in America works, in fact, with tsp, tbsp, floz, cup, pint, quart, gallon... replace those with "apple sized" and such, and you've got something which works for any society.

Even generic terms, like a couple, few, several, lots, plethora, lots'n'lots, a shitload, countless, overwhelming ...have comparable (if overlapping) sizes.

Before you knew what a score or a gross or a dozen or a hogshead was, you got some sense of the scale of the thing from context. "I only asked for a few score of them, but they gave me a whole gross! How can I ever carry that many eggs home?"

So, give them a plethora of vague measurements, rather than numbers. If they have reason for more specific numbers in the dialog you are writing for them, then that means they have a need to measure stuff more carefully than their approximate grouping nouns permit them to. That in turn means they are at a technological stage where that matters, and your rationale for having them not use numbers no longer holds up, and probably needs reexamining in the context of your world.

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MAKE SPIKY CLUBS FAST!!!

Hello, not-tribe-member. Urk name Urk. Many moons ago, Urk in bad way. Urk kicked out of cave by Thag. Thag bigger than Urk, Thag take Urk spiky club, Urka (Urk wo-man). Urk not able kill deer, must eat leaves, berries. Urk flee from wolves.

Today, Urk big chief. Urk have best cave, many wives, many spiky clubs. Urk tell how.

WHAT DO: make one spiky club and take to cave places below. Add own cave place to bottom of list, take cave place off top. Put new message on walls many caves. Wait. Many clubs soon come! This not crime! Urk ask shaman, gods say okay.

HERE LIST:

1) Urk First cave Olduvai Gorge

few) Thag (not that Thag, other Thag) old dead tree by lake shaped like mammoth

few) Og big rock with overhang near pig game trail

Many) Zog river caves where river meet big water

Urk hope not-tribe-member do what Urk say do. That only way it work.

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    $\begingroup$ Greetings Urk. Me Og. Og think Urk idea inspire new building shape. Big on bottom. Pointy on top. Og think want one for Og tomb. Not this day, many moon from this day. Urk object if Og use idea? $\endgroup$ – cobaltduck Jul 11 at 15:50
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    $\begingroup$ As entertaining as this is, maybe it should actually try to answer the question? $\endgroup$ – GreySage Jul 11 at 17:16
  • $\begingroup$ @GreySage At least "many" people seem to think it does. :^) Heh heh. I got a "nice answer" badge and everything. $\endgroup$ – puppetsock Jul 12 at 13:39
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If you aren't familiar with it, I suggest you read "Watership Down" by Richard Adams. Its characters are rabbits who are asserted to be able to count to four, but all greater numbers are eqivalent. There is a word in their language which is sometimes translated as "five" and sometimes as "a thousand". The author is consistent about it, and the dialog around numbers feels natural to me. (Besides, it's a good read IMO.)

Also, look at how counting develops in early childhood. For a while before they can count -- age 2, maybe -- kids can handle one-to-one correspondence. They can, for instance, put get out one cup for each plate, though they may need to physically pair the objects to get it right. They may or may not be able to put out a cup for each person in the family -- one-to-one correspondence between physical objects and a list of people, some of whom aren't present. That's considerably harder.

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You can miss the counting ability, if you can still compare the relative size of sets.

To give an example, you don't need to know that a basket contains 20 apples and another basket 40 apples, if you can tell which basket has more apples than the other.

More often than not what matters is the relative size, not the absolute size. Other examples:

  • Is that group of attackers bigger or smaller than the group I am in?
  • which of those herds of preys is the biggest?
  • which pond contains more water?
  • kids not yet taught to count money preferring 20 5 cents coins to 2 1 Euro coins

Summing up, make sure they can convey the concept of bigger and smaller.

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Take a quick glance at a close group of 5 things.

Your brain can just tell, without really trying, that there are 5 things there, right? It's even easier with four or three, especially if the objects are arranged in familiar patterns, like a square or a quincunx (i.e., the pattern of dots for the number 5 on a die).

Now, take a quick glance at a group of 20 things.

Unless they were specially arranged into quickly-recognizable subgroups (say, a square of quincunxes), you almost certainly couldn't just intuit their number.

Now, try it with a hundred and two things. I don't care how they're arranged, there is no way (unless you are an autistic savant) that you are absolutely sure there weren't just 101, or actually 103, items in that group without some careful conscious counting. How they are arranged (i.e., in a nice grid with obvious small remainders, vs. randomly scattered) can make that conscious process easier or harder, but you definitely won't just automatically know.

So, the structure of your brain prevents you from intuitively understanding groups of more than about 7 things at a time, maybe up to 20 in special cases. You are only able to handle larger precise quantities because your brain does have some fairly sophisticated abstraction abilities, and you were taught the cognitive technologies of counting and arithmetic. Even after you are taught those technologies, though, most people have no real concept of, e.g., the difference between a thousand and a million--they are just "big numbers"; your ability to distinguish them is purely a matter of abstract formal symbol manipulation. You were taught those cognitive technologies because you live in a civilization which places value on keeping track of precise quantities--e.g., for tracking debts and commerce.

So, how do you keep your sub-humans from developing counting?

  1. Make them incapable of the necessary level of abstraction. Sounds like you've already done that, if they can't even comprehend "beauty".

  2. Make it irrelevant and unnecessary to them. Once you have more than 3 of something, why does it matter exactly how many there are? "Many" is enough.

As for consequences for their ability to communicate... well, obviously, they wouldn't be able to communicate precise large quantities. But if that isn't important to them, who cares? It just won't come up. Now, the difference between exactly 4 rabbits and exactly 1 million rabbits may indeed be relevant for things like organizing hunting parties, but exact numeric quantities aren't--they could simply say "small group of rabbits" vs. "big, big, group of rabbits!" and get the necessary point across. Or simply focus on what the necessary consequences are: e.g., rather than saying "there's a group of 5 lions coming", just say "we need many fighters to defend from a group of lions!"--and if there's a whole pride of lions coming, who cares exactly how big it is, just say "we gotta move the village, 'cause we can't fight that group of lions!"

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It's not possible for your creatures to not be able to comprehend large vs small groups.

Even bees can do this.

Waggle Dance: Purpose is to explain the distance, direction and desirability of a nectar source farther than 10 meters. In this dance, the bee makes two semi-circles and then runs the diameter of the circle. The straight side of the semi-circle shows direction, the running speed shows distance and the intensity shows the nectar’s sweetness and quantity.

Heck, bees can also do math. Including understanding the concept of zero. Bees have tiny brains and no expressive symbolic language, though they can retain symbols presented from human researchers and they have precise communication skills with other bees.

Ants are also able to communicate that a food source requires more workers to carry, but it's unclear if they can convey quantity beyond "I need backup."

This isn't limited to social animals with "hive minds."

Scientists have found that animals across the evolutionary spectrum have a keen sense of quantity, able to distinguish not just bigger from smaller or more from less, but two from four, four from ten, forty from sixty. (ref)

After giving countless examples of animals counting, distinguishing group size, and doing math, they conclude:

It’s not out of the question that you could have been wandering around 15,000 years ago and encountered a few of the last remaining Neanderthals, pointed to yourself and said, ‘one,’ and pointed to them and said, ‘three,’ and those words, in an odd, coarse way, would have been understood.

I challenge your assumption that it is possible for these proto-humans not to be able to distinguish between large and small groups or to do other basic counting and math skills. If they have any language at all, they will have words, or at least gestures or intonation, that convey size. It may not be with precision. They don't have to have any sort of writing system. But it will exist.

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Humans do not automatically count. In fact even up to the medieval era and probably beyond many people never had any numerical education. In fact it might still be practiced in large area's of Africa (1).

The idea is to simply tie a knot for every count. You've got 18 cows? Well you have one knot per cow (or in case of more advanced area's like wild-west ranches they might tie 1 knot per 10+ cows because of the volume of cows they had to count). You can also keep track of the amount of months pregnant, baskets of fruit collected etc this way without having any concept of actual numbers. "How many banana's you want?", hold up a rope with knots, "this many".

1: https://books.google.nl/books?id=X7SPDwAAQBAJ&pg=PA81&lpg=PA81&dq=counting+cattle+with+knots&source=bl&ots=WGXqVjXqKW&sig=ACfU3U2z9E3zBmLCMjm0lVf0FKEMNkCoJQ&hl=en&sa=X&ved=2ahUKEwix1rmW_KrjAhXDb1AKHcgnCNcQ6AEwFHoECAUQAQ#v=onepage&q=counting%20cattle%20with%20knots&f=false

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    $\begingroup$ One system I've seen in use is counting animals with pebbles. Some horses were being moved to another pasture, and the farmer (rancher?) had a few pebbles in one hand. As each horse went through, he moved one to the other hand. When the first hand was empty, all his horses had gone through. $\endgroup$ – Nic Hartley Jul 11 at 19:30
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What are they seeking ?

Your species seems to have evolve language for some stuff but not for others. As we currently know it, the first human written stuff ever was probably accounting, who exchange how much to whom. Which is exactly what your species doesn't give a damn about.

So they are probably eating enough, living well enough, and don't need to exchange stuff. Or they are definitely enjoying a anarchic heaven where there is enough of everything for everybody, and sharing is not even an action but a state of things.

So they speak only to go on adventures, describing what there is and what could be, sharing previous discoveries and geography, describing the world with "few/enough/many/too much" stuff, no notion of distance other than a day of walk.

So, basically, they just don't care. like hippies with an unlimited amount of pizzas, beers and no idea of what scarcity even mean.

Why would they care about number then?

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    $\begingroup$ I like that. Rather than counting, just talk about the numbers in terms of quality - "there are enough rabbits at the river", for what? For (dinner, making a coat whatever, it's in context). Or "there are not enough" or "there are not many" to mean "we need more". +1 $\endgroup$ – Michael Stachowsky Jul 10 at 14:42
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They might start referring to a group of something by the outcome you can get out of it. A single rabbit is a snack. Twenty rabbits is a feast.

This has the effect that the same term can account for different numbers. Two deer may make up a feast. They're not really concerned with the number of souls that are being taken, they only think about the amount of food there is to be had.

This can be achieved with any measurement you want. A cup of water is a sip. A bolt of leather ranges from a rag to a rug. Things weigh between a stone and a boulder.

This sort of communication can convey enough meaning to get the general idea across.

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