Posted by
Carl Tollander on
URL: http://friam.383.s1.nabble.com/Mathematics-and-Music-tp473042p475472.html
So maybe simulated annealing is another way of looking at it. But...
In the tradition-orientation that Corfield is describing, the "hill
climbers" would be talking to each other, and refining their ears. In
any case, I don't view this as necessarily an optimization problem (see
the companion comment on invention vs discovery).
As an example, I have recently taken up Taiko. Each dojo has its own
set of teachings, how the drums are positioned, what kinds of drums are
used, what kinds of stands, how music is played, what music is played,
how much to emphasize choreography, pedagogy, how to practice, overall
philosophy, and so on. Teachers and students from other places
occasionally come by with other ways of going about it, maybe there are
different lineages, maybe they are exploring some relatively new way of
playing. And they say, ya know, you guys are doing things differently
from the way I do it, but I will respect your way and try to show what I
know in that context. And everybody learns a bit and gets a bit better
as a result of that. But the dojo refines itself in that process, it's
not a compromise.
Sometimes a guy comes by and sez, no no, you're not playing it right, my
way is the way, or worse, you guys do what you want, I'm gonna play it
my way, and maybe you should all come study with me.
I mention this example, because it seems to me that (1) it reflects the
T&G conversations between working mathematicians I personally read
online (which, admittedly, is not the same as actual experience), and
(2) it highlights the desirability for inquiry of parallel tracks among
a set of local foci that occasionally communicate - consolidating dojos
(or mathematical centers) would not result in as much progress (moving
the exploration and invention along) as the current system.
It seems more of a jazz ethic than an academic ethic.
CT
Marcus G. Daniels wrote:
> Carl Tollander wrote:
>
>> the G guy is trying to discredit the other guy by
>> showing that he is just on a power trip of some sort. I tend to look at
>> them as subtractive (G) and additive (T) sculpture - complementary if
>> some common goal is in mind, but the G guy never gets there, as he has
>> no motivation or handy mechanism to do so.
>>
> Yet the Will to Power is served by discovery and invention, as well as
> by criticism. A risk for the T guy is that the `intellectuals' in his
> community are not acting in good faith and not trying to do more than
> just refine a self-consistent story, which can then be passed on as the
> canon. So it could be the reverse, the T guys are the subtractive or
> inhibitory player.
>
> Imagine optimizing a function of many variables using hillclimbing. In
> a bumpy landscape, the single trajectory (the community) will soon get
> stuck at a local optimum, even though up to that point progress was
> being made. Better not to follow any search rules and just randomly
> pick points for a while (multiple trajectories/communities/individuals).
> Put another way, there are countless questions to ask, and certain
> communities may serve just to create a comfortable consensus reality
> which then fails to explore a problem thoroughly enough.
>
> Marcus
>
>
>
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