[r-t] 147 TDMM

[Richard Smith]

Matthew Frye wrote:

> On 10 Jun 2012, at 00:25, Richard Smith wrote:
> [a lot]
>> 102 plans still remain to be explained which I will start doing in the next email. Hopefully it won't take me eighteen months to write it!
>
> Great to see this series continued! Only just today stared 
> to digest this email, it seems that the grid splice has 
> been slow to divulge its secrets.

It's certainly true that I've devoted quite a lot of time to 
considering different generalisations of the grid splice. 
The theory of splicing two methods -- simple splices, in the 
terminology I've used in this series of emails -- is well 
understood and it's very easy to generate exhaustive lists 
of such splices.  The same is not true of three methods, 
though it would be nice if we could develop some sort of 
general theory for that case.  (In fact, I think it would a 
lot more than nice, and it could have some quite profound 
consequences.)

I was (and to some extent, still am) hopeful that 
generalised grid splices might provide such a theory.  At 
one point, I had a conjecture that

   for any three methods, X, Y and Z, an extent containing
   those methods is possible if and only if a possibly
   imaginary method, G, exists such that each of X, Y and Z
   has a simple splice with G.

I now believe that's not true, and I'm probably in a 
position to provide a counterexample with a bit of thought, 
but I still suspect that something similar may be true.


> Early on in the series you sorted the plans into clusters 
> containing plans that were linked by simple splices, do 
> you know how many clusters remain to be explained now? I 
> felt the clusters gave a better representation of the 
> amount left to be explained than just plans.

44 of the 506 clusters remain to be explained, though quite 
a lot of the remaining clusters are very similar to each 
other and will almost certainly share a common explanation.

RAS