Talk:Glider synthesis

Should the fact that there are upper and lower bounds (by example) on the maximum number of cells a synthesisable pattern can have (and equivalently, the minimum an unsynthesisable one can have), as mentioned in https://cp4space.hatsya.com/2022/01/14/conway-conjecture-settled/? (Now the lower bound is ≤21 cells to be synthesisable instead, but I think 306 is the upper bound still) — Preceding unsigned comment added by DroneBetter (talk • contribs)

I suppose (EDIT to insert: by "synthesizable pattern") you mean "synthesizable still life"? The relevant section of article has already mentioned it. GUYTU6J (talk) 15:03, 20 November 2022 (UTC)

I think you misunderstood the suggestion -- this seems to be about the best bounds proven so far -- i.e. every still life below N cells can be constructed with gliders, and some still lifes above M cells cannot be constructed with gliders, with a preference for larger N and smaller M. Confocal (talk) 16:32, 20 November 2022 (UTC)

I edited my last message, by which I intended to express the following: on a closer look, the relevant section of article does mention that "The synthesis for ... 21-bit still lifes [was completed] in November 2022" and that "...a still life with 306 cells that is impossible to synthesize with gliders." Clearly these two sentences point out the bounds N=21 and M=306. And I have not heard about any improvements on either bound, so I am not clear how to have "preference for larger N and smaller M". GUYTU6J (talk) 16:50, 20 November 2022 (UTC)

I think the idea is to have these bounds mentioned explicitly - i.e. if the best known lower bound is 21 and the best known upper bound is 306, then it might be a good idea to directly state that in the article. Just mentioning synthesis for all 21-bit still lifes and the 306-cell non-constructible still life does not imply that these bounds are in fact the best bounds known to this community. Confocal (talk) 17:01, 20 November 2022 (UTC)

Oh, I see where you (not the original asker) are going here. Just add a premise (in italic) to make the implied logic work:

As no non-constructive proof exists to provide tighter bounds, the best ones are currently based on aforementioned constructive proofs: [rest of explicit statement]

GUYTU6J (talk) 17:33, 20 November 2022 (UTC)

Also speaking of which, should there be a section on the computational difficulty of enumerating glider collisions? There are many things to mention, like the lower bounds on numbers of gliders necessary to obtain explicit infinite families (and thereof those that exhibit infinite novelty so cannot be covered by stating that they result in (for instance) two objects a distance apart dependent on the distance of the gliders). We have mentioned the reverse caber-tosser as the explicit upper bound on the number necessary to be universal (which includes undecidable ones), but upper bounds on undecidability alone would be relevant also, surely? DroneBetter (talk) 12:43, 7 February 2023 (UTC)