We al learn to do division
“If there are 6 cakes and 3 children, how many cakes does each child get” Division is about sharing
But it does not always work
“It there are 2 sharks and 8 people in a pool, how many people does each shark get?” Division can not answer that question.
Because that example is not about sharing , it is about competition
Whether division works depends on what are called the “Rules of Engagement”
We all learnt to multiply
“If 10 children each bring 2 apples, how many apples are there?” Multiplication is about pooling Multiplication is the inverse of division
It is amazing how these simple arithmetical calculations parallel human activity.
only humans share. Animals , by and large, compete, excpet perhaps in feeding young
only humans make common pools. Animals do store food, but for individual use. Insects store food communally.
Only humans do arithmetic
Arithmetic is not something genetically inherited. … each generation has to be taught it. It is cultural inheritance , not DNA.
Sharing is not something genetically inherited. … kids have to be taught to share. If left untaught, they will compete.
Where did all this start?
How did our maths come to be so linked to our community skills?
Are there any Cultural Anthropologists who can shed light on this, or is it lost in pre-history?
My wife and I just had a big discussion about this, so what is the point!!! The 3R’s were taught, when, I was in school, not really sure, on what is being taught now!!!
“only humans share. Animals , by and large, compete, excpet perhaps in feeding young” : not true; look at pets in a house when cats and dogs eat from each other’s food and leave some for the others.
Check Marcel Mauss’s theory of gift
Traditional societies kept it… until the age of smartphones probably.
I think it is related to the brain hemisphere problem, as described by MacGilchrist here:
(except for his late New age bend –which certainly helps him pay his children university fees- the guy should be taught in schools)
Regardless of the method of teaching, the point is these behaviours have to be taught. … both the arithmetic and the cultural skills .
I agree, modern education seems to neglect traditional skills… eg “dont bother with times table, learn to use a calculator”. I am not sure what the effect of that will be on our culture.
We did the three R’s too in English class - reuse, reduce, recycle… But if they taught us that then, not sure what went wrong and almost nobody cares about them.
I’ve read a few evolution “popular science” books - and Richard Dawkins goes to great length to argue that “altruism” isn’t confined to humans - and there’s a genetic / evolutionary benefit to altruism…
And a more recent read - was Richard Wrangham’s “The Kindness Paradox”… Highly recommended… His argument was that 2-300,000 years ago - humans “self domesticated” themselves - and he argues that bonobos have done it to…
You’ve also left off “empathy” - i.e. without being taught to be empathetic - humans can do it… Empathy can lead to sharing…
True, animal populations may indeed evolve altruism genetically. Humans seem to have left it to cultural inheritance.
I have a friend who lectures in creative writing. He wrote a book called “Ferocious Animals” it is short stories about kids of of control. There is no inbuilt sharing … it has to be taught.
Also what is that famous book about kids isolated on an island? I know “Lord of the Flies” … they descend into savagery.
Indeed. That drives at least some sharing. I cant think of a mathematical equivalent for feelings like empathy.
Empathy seems to be about being able to see another person’s point of view. It is a bit like having an object in a graph and being able to project its shape onto more than one axis. Objects look different when viewed from different angles… so Perspective Geometry maybe.
Way more complicated than simple arithmetic.
Simple example… whether a political party is viewed as right or left wing depends on whether the viewer is right or left wing… ie on the viewer’s perspective.
So is empathy about rotating the axes (or the object… it doesnt matter)?
Only a few “higher” (there’s no heirarchy in evolution) animals can achieve “theory of mind” - e.g. elephants can… and chimpanzees… and maybe some cetaceans…
I think some intelligent birds do it - or are “capable of it” - like corvids and some parrots…
I’m amazed how much brain processing power birds have - with such seemingly small brains… the old “bird brain” epithet is silly and redundant…
Darwin also said species change when domesticated… something to do with tameness and changes in the neural crest
Tameness would be a prerequisite for any form of cooperation.
Just so others can keep up…‘theory of mind’ is not some scientific theory… it is what an individual thinks about what other peoples minds are doing.
It is one thing to be aware of your own mind, and something else to try and second guess that other peoples minds exist and are different to yours.
Animals dont get that abstract
Yeah, and maybe cockatoos. They cooperate to solve problems.
I think that is only half right. Let me modify it
‘Empathy is about transformations’
A transform can be a rotation, or a shift of origin, or a scaling. All represent a shifting view of something… including the more abstract case of a shift from one mind’s view to another mind’s view.
I like this discussion.
Another question
What is the cultural significance of exponentiation?
I agree, we feed our visitors every morning around the same time, and they know when to come, if we are late, they sit on the windows sill and start to peck till I go feed them, process repeated at mid day and evening meal, when we return from holiday so do they the following morning.
Also if we eat in the back garden or front depending on the sun and weather, they know where to come and at what time
By “corvids and some parrots” I implied cockatoos - which are parrots… However - I think the African grey, and the New Zealand kea, are generally thought of as being the smartest parrots… I’ve seen video of kea solving complex problems that corvids (crows / ravens) struggled with…
But yeah - cockatoos are pretty smart, and semi-social : however pairs will often squabble over proximity and territory (e.g. a next tree hollow).
I had to put a brick on my bin lid a few weeks back - two corellas (little corellas - i.e. white cockatoo) were co-operating to try and get it open…
This is “separately learned” behaviour… i.e. sulphur crested cockatoos, which don’t occur naturally in Perth, are known to open rubbish bin lids in Sydney and on the east coast…
I must be really old-school educated! I do math in my head, even more difficult calculations like 37.7 / 2. Looking at 37, I find half of 30 = 15, then I look at 7, finding half = 3.5. Now I have 18 and .5, so I look at .7 where half is .35, as I add in .5 to get .85, so my answer is 18.85.
Note: I wrote this as I took the steps in my head, and I can do addition, subtraction, and multiplication similarly, simply by breaking the calculation into logical parts such as whole numbers and fractional components.
Math is fun, but try to convince a school kid of that!
