3 ms·
> If anything these videos seem more hokey to me in that they are implying a deep connection between the mathematical model and reality I agree with this for s
by makmanalp 10y ago
> If anything these videos seem more hokey to me in that they are implying a deep connection between the mathematical model and reality
I agree with this for sure. Conceptual and aesthetic beauty are different. In terms of aesthetic beauty, these are some examples of the kind of things that were shown to us (at least when I was growing up) as examples of how "mathematics can be beautiful":
http://www.softlab.ntua.gr/miscellaneous/mandel/mandel.html http://www.softlab.ntua.gr/miscellaneous/mandel/mandel.html /
http://www.intmath.com/numbers/math-of-beauty.php http://www.intmath.com/numbers/math-of-beauty.php
At best half-hearted attempts that neither show conceptual beauty, and definitely not aesthetic beauty. Especially that fractal page, ugh. Since then, people have gotten much better about this sort of stuff, e.g. with fractals, look at how much more imaginative and aesthetically beautiful these are, and yet still generated:
http://www.ams.org/mathimagery/thumbnails.php?album=13 http://www.ams.org/mathimagery/thumbnails.php?album=13 /
http://www.fractalartcontests.com/2007/winners.php http://www.fractalartcontests.com/2007/winners.php
I'm reading Goedel-Escher-Bach right now, and that's full of brilliant examples of both aesthetically and conceptually beautiful things, and ties far-flung concepts together.
Anyway, what does "mathematically gibberish" even mean? Most of these videos are (if I'm understanding correctly) in essence generative processes, resulting in some interesting and (subjectively speaking) beautiful behavior. I don't know if you could truly call them "mathematically gibberish" as much as perhaps just argue that there isn't an exceedingly simple set of equations that give you complex and lifelike behavior. But that's great - I think it's OK to consider the idea that perhaps the processes that govern nature around us just aren't very simple and conceptually pure. That a set of equations that generates fractals is interesting, but it's even more interesting how romanesco broccoli gets its fractal-like look WITHOUT having an overarching global process enforcing a set of equation-rules. That our models of certain processes that we find "beautiful" are just abstractions on top of the actual messy way the system works (e.g. how we found that newton's laws are sort of the emergent result of how the lower layer of physics works). Anyway, these are just my opinions :-)
edit: Of course there are fields studying all this too: https://en.wikipedia.org/wiki/Complex_systems https://en.wikipedia.org/wiki/Complex_systems
- j2kun 10y ago> Anyway, what does "mathematically gibberish" even mean? For example, to imply that the "dimensionality" video says anything interesting about dimensionality or even anything substantial about the torus is ludicrous.