[Computer-go] Mathematics in the world
uurtamo .
uurtamo at gmail.com
Thu Feb 4 13:58:18 PST 2016
Robert,
Just as an aside, I really respect your attention to detail and your
insistence that proof technique follow generalizing statements about
aspects of go.
I think that the counting problems recently were pretty interesting (number
of positions versus number of games).
The engineering problem of winning against humans is of course much simpler
than the math problem of understanding the game deeply (just think about
all of the work Berlekamp did working on this). I like that they move
together hand-in-hand, and right now it seems like the human urge for most
people is to make a set of computers strong enough that they can beat a top
pro, once, then the next goal will be to beat them regularly, as has been
done in chess.
If you think about chess endgames, and how they've been categorized, we're
nowhere near that in Go except for fairly quiescent positions. The opening
is a nightmare, the midgame is a nightmare, and multiple fights with
multiple kos are a nightmare. Solving this mathematically is of course
hugely far in the future. Faking your way forward with engineering (similar
to how people play) seems to be our best guess at the moment.
Thanks for your insight and rigor and I'm glad that you're continuing down
your rigorous path when so many of us have forgotten that extremely minor
rule differences can be: inexplicable (japanese rules, if i understand
correctly), difficult to deal with (chinese rules, under very liberal
understanding) or useless (mathematical descriptions of a game which is
totally different than how people actually play).
Thanks again,
steve
On Tue, Feb 2, 2016 at 10:54 AM, Robert Jasiek <jasiek at snafu.de> wrote:
> On 02.02.2016 13:05, "Ingo AlthÃ¶fer" wrote:
>
>> when a student starts
>> studying Mathematics (s)he learns in the first two semesters that
>> everything has to be defined waterproof. Later, in particular
>> when (s)he comes near to doing own research, you have to make
>> compromises - otherwise you will never make much progress.
>>
>
> When I studied maths and theoretical informatics at FU Berlin (and a bit
> at TU Berlin) (until quitting because of studying too much go, of course),
> during all semesters with every paper, lecture, homework or professor,
> everything had to be well-defined, assumptions complete and mandatory
> proofs accurate.
>
> As a hobby go theory / go rules theory researcher, I can afford the luxury
> of choosing formality (see Cycle Law), semi-formality (see Ko) or
> informality (in informal texts) because I need not pass university degrees
> with the work. My luxury of laziness / convenience when I use semi-formal
> style (as typical in the theory parts of my go theory papers) indeed has
> the advantages of being understood more easily from the go player's (also
> my own) perspective and allowing my faster research progress. If I had had
> to use formal style for every text, I might have finished only half of the
> papers.
>
> If we can believe Penrose (The Road to Reality) and Smolin (The Trouble
> with Physics), the world of mathematical physics is split into guesswork
> (string theory without valid mathematical foundation) and accurate maths.
> Progress might not be made because too many have lost themselves in the
> black hole of ambiguous string theory. Computer go theory seems to be
> similar to physics.
>
> --
> robert jasiek
>
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