My one caveat with your claims here is that Van Gogh was severely insane, which probably impaired his ability to support himself quite a bit.
Also, how likely does it seem to you that applied math lacks pure math’s aesthetic value because its done by less aesthetically sensitive people (positive feedback loop) rather than because it couldn’t be like classical applied/pure math?
My one caveat with your claims here is that Van Gogh was severely insane, which probably impaired his ability to support himself quite a bit.
This is a fair point. I would guess / vaguely remember that there are plenty of examples of psychologically sound great painters who had trouble making a living but don’t have a list off hand. Laurens suggested Cezanne as an example but I have not independently verified that he qualifies. I don’t know very much about visual arts.
Note that in general there’s a selection effect where artists/scientists who have dim prospects for making a living doing what they do are disproportionately likely to leave relative to other artists/scientists of their quality. It’s hard to know how significant this selection effect is in a given domain.
Also, how likely does it seem to you that applied math lacks pure math’s aesthetic value because its done by less aesthetically sensitive people (positive feedback loop) rather than because it couldn’t be like classical applied/pure math?
There’s almost certainly some effect of this type; I’m uncertain as to how large the effect. Two relevant points:
To the extent that applied math involves features specific to how humans interact with the world (i.e. taking into account contingent constraints specific to human needs) arbitrariness creeps in on account of the fact that humans were generated by a random process.
There seem to be arbitrage opportunities for mathematical expertise to bring clarity to areas that were previously somewhat obscure. For example, SarahC has suggested that principle component analysis might be utilized to better understand what’s referred to as autism (a fact that I haven’t previously seen discussed explicitly). The existence of such apparent arbitrage opportunities suggests that there may be quite fertile unexplored ground within applied math.
Thanks for the very thoughtful and clear post.
My one caveat with your claims here is that Van Gogh was severely insane, which probably impaired his ability to support himself quite a bit.
Also, how likely does it seem to you that applied math lacks pure math’s aesthetic value because its done by less aesthetically sensitive people (positive feedback loop) rather than because it couldn’t be like classical applied/pure math?
This is a fair point. I would guess / vaguely remember that there are plenty of examples of psychologically sound great painters who had trouble making a living but don’t have a list off hand. Laurens suggested Cezanne as an example but I have not independently verified that he qualifies. I don’t know very much about visual arts.
Note that in general there’s a selection effect where artists/scientists who have dim prospects for making a living doing what they do are disproportionately likely to leave relative to other artists/scientists of their quality. It’s hard to know how significant this selection effect is in a given domain.
There’s almost certainly some effect of this type; I’m uncertain as to how large the effect. Two relevant points:
To the extent that applied math involves features specific to how humans interact with the world (i.e. taking into account contingent constraints specific to human needs) arbitrariness creeps in on account of the fact that humans were generated by a random process.
There seem to be arbitrage opportunities for mathematical expertise to bring clarity to areas that were previously somewhat obscure. For example, SarahC has suggested that principle component analysis might be utilized to better understand what’s referred to as autism (a fact that I haven’t previously seen discussed explicitly). The existence of such apparent arbitrage opportunities suggests that there may be quite fertile unexplored ground within applied math.
I have always been intrigued by Kenneth Rexroth’s take.
Thanks for the link. That was a delightful essay.