How natural is numeracy?(aeon.co)
aeon.co
How natural is numeracy?
https://aeon.co/essays/why-do-humans-have-numbers-are-they-cultural-or-innate
15 comments
The book "Where Mathematics Comes From"[1] by Lakoff and Núñez makes a lengthy, detailed argument that numeracy is evolved, not universal. I didn't find myself agreeing with everything in it, but I no longer take it for granted that math is a universal concept.
[1] https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From
[1] https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From
Can you explain what you mean by evolved as opposed to universal?
Because from my perspective, they mean the same thing when applied to this context. That is, if numeracy is evolved, everyone is fundamentally numerate at some level. And if numeracy is universal, then everybody is fundamentally numerate. They're both nature, not nurture.
What do you mean by those words?
(Personally, I think that numbers are mostly learned, but that the brain has an evolved aptitude for symbolic systems, mathematics being just one of many. I don't think any innate concept of number goes much beyond order of magnitude (i.e. logarithmic) relative differences.)
Because from my perspective, they mean the same thing when applied to this context. That is, if numeracy is evolved, everyone is fundamentally numerate at some level. And if numeracy is universal, then everybody is fundamentally numerate. They're both nature, not nurture.
What do you mean by those words?
(Personally, I think that numbers are mostly learned, but that the brain has an evolved aptitude for symbolic systems, mathematics being just one of many. I don't think any innate concept of number goes much beyond order of magnitude (i.e. logarithmic) relative differences.)
I mean, universal across the universe. There is a common assumption that mathematics is a common language that we could use to communicate with aliens. The notion is that, for example, the concept of prime numbers would be discovered everywhere in the universe just as an intelligence would discover that hydrogen is the simplest atom.
To go further, the Mathematical Universe Hypothesis formalizes the notion that the universe itself is math, and that we are just discovering the math of the universe as we develop mathematics.
I'm personally agnostic on the universality of mathematics. Math is a tremendous tool for describing the universe, but I am willing to consider that a different intelligence might invent some accurate and non-mathematical predictive model.
To go further, the Mathematical Universe Hypothesis formalizes the notion that the universe itself is math, and that we are just discovering the math of the universe as we develop mathematics.
I'm personally agnostic on the universality of mathematics. Math is a tremendous tool for describing the universe, but I am willing to consider that a different intelligence might invent some accurate and non-mathematical predictive model.
> The notion is that, for example, the concept of prime numbers would be discovered everywhere in the universe just as an intelligence would discover that hydrogen is the simplest atom.
The concept of prime numbers is a lot more fundamental than hydrogen being the simplest atom. You could conceivably have a universe where every element is an elementary particle, but you couldn't have a universe where you can put two and two together and get five. Nor could you possibly have a universe where you can take five of something, and divide it into equal sized groups, unless each group has one item or you only have one group.
The concept of prime numbers is a lot more fundamental than hydrogen being the simplest atom. You could conceivably have a universe where every element is an elementary particle, but you couldn't have a universe where you can put two and two together and get five. Nor could you possibly have a universe where you can take five of something, and divide it into equal sized groups, unless each group has one item or you only have one group.
This is a fine lecture by John Stillwell on the question of alien mathematics, and what might constrain it:
https://youtu.be/9MV65airaPA
> I previously have assumed that it was universally accepted that this was not the case
Since you're asking for citations yourself, which ones support that view?
Since you're asking for citations yourself, which ones support that view?
"‘The brain, a biological organ with a genetically defined wiring scheme, is predisposed to acquire a number system,’ said the neurobiologist Andreas Nieder of the University of Tübingen in Germany. ‘Culture can only shape our number faculty within the limits of the capacities of the brain. Without this predisposition, number symbols would lie [forever] beyond our grasp.’"
Well that seems like absolute nonsense. How do we understand computers then? Or almost literally any art form?
Well that seems like absolute nonsense. How do we understand computers then? Or almost literally any art form?
Because computers are just logic combined with numbers. (The 32gb RAM is attached to the motherboard, which has 32gb.) And for art, we _also_ have other brain systems that understand how to judge beauty in people and landscapes.
I think a more interesting example is quantum physics. Humans have a difficult time understanding it, because it doesn't jive with our normative understanding of the world. But we are still able to understand it, because it is just very messy logic.
I think a more interesting example is quantum physics. Humans have a difficult time understanding it, because it doesn't jive with our normative understanding of the world. But we are still able to understand it, because it is just very messy logic.
Right, which seems sort of exactly the argument in the article. "Numbers" are just us extrapolating from "quantity".
I'm surprised there was no mention of the Pirahã, a tribe made famous by their apparent innumeracy:
http://science.sciencemag.org/content/306/5695/496.full
http://langcog.stanford.edu/papers/FEFG-cognition.pdf
http://science.sciencemag.org/content/306/5695/496.full
http://langcog.stanford.edu/papers/FEFG-cognition.pdf
Núñez is not a mathematician and claims an anti-Platonic view of maths which is totally inconsistent with the reality of practicing mathematicians over the past century. In particular, I doubt that they grok the extent to which maths and physics have collaborated, and all of the predictions in particle colliders which started out as quirks of equations on blackboards.
Nothing about the practice of mathematics over the last century requires (or is even advantaged by) a platonic view.
A Platonic view of mathematics, not a Platonic view of the physical universe.
That is, when we say '1', we mean the abstract concept of unity, not one of any particular physical thing.
That is, when we say '1', we mean the abstract concept of unity, not one of any particular physical thing.
I would like some citations for this. This is the first I've heard of this, and I previously have assumed that it was universally accepted that this was not the case.
This article makes similar claims at multiple points, without corroboration. "researchers have concluded", "researchers often assume", "researchers have argued", for arguments that I have never heard made.