B Are Algebra, Geometry, Probability innate or cultural?

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Are the concepts of the rules of Algebra, Geometry and Probability things that all humans have some instinctive grasp at some level, or things that we basically learn from others, therefore cultural?

Let me explain. I once saw an experiment with a mommy rat. She had 4 puppies, and someone put a snake in front (in a glass, so that the snake would not eat them puppies). The mommy rat immediately carried the puppies, one by one, to a safer location, then made one more trip to check that no puppies had been left behind. That showed the poor little rat couldn't count to 4. So a mommy rat probably knows "none" and "some", maybe knows "one", but definitely doesn't know "two", "three" and "four".

Then I remember a clip of a mother with a baby on her lap, and someone walking behind them. The baby turned her head right to keep watching that person, then as the person walked behind them she turned the head left expecting the person to come into view from that angle. Amazing!! A little baby on diapers, that can't do anything, already has an innate knowledge of 3D space, "left", "right", "behind" and can anticipate future trajectories!!

Now, the little rat has a neural network, so I suspect it could be trained to count from 1 to 4, but that's a learned trick, not innate, and as a learned thing the rat could be taught base-3 instead of base-10. The learning depends on the culture that is teaching the concept. Similarly, no little baby is born knowing Relativity, so Relativity is 100% a cultural thing - created once, repeated forever.

I'm sure that there are aspects of say Algebra that definitely are cultural. For example zero. There's no zero in Roman numerals... CCIII = 203, no zero in Roman number there, and the history of invention of zero is documented. But the understanding of one, two, three and counting, is it possible that's an innate thing? Apparently all human groups know how to count and add (not sure about subtraction), so is it possible that if a pair of humans, one male and one female, grow isolated from everything, would by themselves develop some kind of language (because toddlers spontaneously do), and if mommy human gets 4 babies she would probably do 4 trips to save them from the snake [note 1], not 5?

If so, then is it possible that some kind of rudimentary or instinctive Algebra is innate to the human brain, as well as rudiments of Geometry and Probability?


[note 1] yeah, yeah, someone will say mommy human can do two trips by carrying a baby in each arm, or one trip by making a pyramid of babies, yeah, yeah, but ya got my point
 
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kuruman

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Let me explain. I once saw an experiment with a mommy rat. She had 4 puppies, and someone put a snake in front (in a glass, so that the snake would not eat them puppies). The mommy rat immediately carried the puppies, one by one, to a safer location, then made one more trip to check that no puppies had been left behind. That showed the poor little rat couldn't count to 4. So a mommy rat probably knows "none" and "some", maybe knows "one", but definitely doesn't know "two", "three" and "four".
Maybe mommy rat couldn't count, but I am sure she had some rudimentary sense of probability. Have you heard of the fight-or-flight response?
https://en.wikipedia.org/wiki/Fight-or-flight_response
Mommy rat evaluated the a priori probability of being eaten by the snake as close to 1, that's why she fled with her babies. Had she, like us humans, understood the subtleties of Bayesian probability and folded in the probability of being eaten by a snake if a snake is in a glass cage, then she would have the need to fight or flee but would have considered this a visit to the zoo with the children. :smile:
https://en.wikipedia.org/wiki/Bayesian_probability
 

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