Re: On Game Space Size

[Robert Jasiek <jasiek@xxxxxxxxxxxxxxx>]

Mousheng Xu wrote:
>         It's good that we are discovering theorems, corollaries, & lemmas,

They are fun on their own, at least for the amateurish mathematicians
among us:)

> but
> could you guys elaborate on how to use them?

Each proposition tells us the truth and nothing but the truth.
Hence we can always apply exactly the contents of any proposition.
Therefore by reading some carefully one often gets applications
directly. However, typically applications are not as far-reaching
as one would hope. If one wants more, then one has to study more.
Following research directions might be one idea.

The proofs of propositions are as important: they tell us how to
construct things like examples or sample data, e.g.

Concerning the particular propositions, slightly simplifyingly
one can apply them as follows:
- If study concerns ko rules in general and can be done independently
of ko rule prohibitions due to prior history, then legal test positions 
should be constructed by move-sequences not containing any removals.
- If some ko rules will do, then some superko rule is very good for most
study purposes.
- One should not hastily assume that pass-go and no-pass-go are the
same,
even though they are closely related.

-- 
robert jasiek
http://www.snafu.de/~jasiek/rules.html