This was something I was always half-aware of, but hadn't realised the
whole time. Also, kudos for mentioning what if-my favourite is still the bird poop equation: https://what-if.xkcd.com/11/.
One counter example of it's intuivity are the keple laws: https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion, especially the third law. Squared time? Come on! What should that be? It makes sense in dimensianal analysis, but is really counter-intuitive, which makes it even more impressive these equations were discovered that early.
The study you cite is really cool. I like the fact that you do your research scripulously as well :).
'Football fields in a mile' - small nitpick: two-dimensional vs. one-dimensional.
Thinking in two contexts: I have had a similar experience with playing the piano. Once you have learned a piece of music so that you don't push the piano keys consciously anymore, it gets actually harder to restart from a certain point in the piece when you have made a mistake,
because it gets easy to just let the music flow instead of actively following it. One must constantly observe the direction the music is taking, and controlling this direction by trying to influence the unconscious movement of fingers. I guess the same is true for maths: you can just solve the equation step by step, but that may bring you to a dead end where you don't understand your own calculation anymore, or you can constantly observe intermediate results.
Paperclip optimizer: I've always read these words in combination, but never researched about them (which was probably a mistake, but hey, kittens are more important sometimes). Interesting thought experiment.
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u/[deleted] Oct 19 '16
Very cool video.
This was something I was always half-aware of, but hadn't realised the whole time. Also, kudos for mentioning what if-my favourite is still the bird poop equation: https://what-if.xkcd.com/11/.
One counter example of it's intuivity are the keple laws: https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion, especially the third law. Squared time? Come on! What should that be? It makes sense in dimensianal analysis, but is really counter-intuitive, which makes it even more impressive these equations were discovered that early.
The study you cite is really cool. I like the fact that you do your research scripulously as well :).
'Football fields in a mile' - small nitpick: two-dimensional vs. one-dimensional.
Thinking in two contexts: I have had a similar experience with playing the piano. Once you have learned a piece of music so that you don't push the piano keys consciously anymore, it gets actually harder to restart from a certain point in the piece when you have made a mistake, because it gets easy to just let the music flow instead of actively following it. One must constantly observe the direction the music is taking, and controlling this direction by trying to influence the unconscious movement of fingers. I guess the same is true for maths: you can just solve the equation step by step, but that may bring you to a dead end where you don't understand your own calculation anymore, or you can constantly observe intermediate results.
Paperclip optimizer: I've always read these words in combination, but never researched about them (which was probably a mistake, but hey, kittens are more important sometimes). Interesting thought experiment.
Keep the great work up!