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Leonardo da Vinci was likely one of the most intelligent humans ever to have lived, and didn't understand calculus. It wasn't for lack of interest, either! He was fascinated with parachutes, timing falling objects and trying to understand the rates of change. But despite nibbling at the edges of calculus, he never got there.

In contrast, it's now completely ordinary for a teenager to not only get to the core ideas but solve complex calculations with them in timed tests!



This is an odd comparison.

I think DaVinci was way before Newton.

High school students aren't asked to invent calculus just to understand it.

I didn't invent djikstras graph traversal algorithm but I can read and understand it.

I think there's a difference between original invention and understanding 'n usage.


We all stand on the shoulders of giants and have increasingly powerful complimentary cognitive artifacts that let us easily do things that used to be very difficult.

In a more extreme version, consider that ancient Greek and Roman mathematicians struggled with long division problems that many of us can do in our heads now!

Why? Arabic numerals are far more effective than Roman numerals for the task and after having learned them, we have a permanently increased ability to do certain kinds of calculation.


That's very fascinating.

I look at quicksort and that was revolutionary at the time.

Do we have ways to better conceptualize the world around us? Or are our brains evolving outside of some normal evolutionary process?

Fascinating to me.


I think both are true but mostly the first. Human evolution has sped up dramatically in the past 15,000 years, but it's still very slow.

Arabic numerals, literacy, maps, bayesian reasoning, etc are unnatural, but better ways to conceptualize the world around us and these tools and others have steadily become more prevalent throughout the population.

Maybe quicksort hasn't permated through much of society, but binary search has! People born 100 years ago became comfortable flipping through phone books and quickly finding a name, whereas that would have taken a conceptual leap for most born 200 years ago.




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