I haven't explained the problem well enough. Let me try and do so without making suppositions which conceal where the error actually lies.
Play191 exhibits a function NS, which calculates a statistic called the "nim sum" which helps you win at the game of Nim. NS maps into a domain of numbers which Conway & Guy call "nimbers", with their own idiosyncratic addition & multiplication. Having discussed the addition of nimbers, the paper discusses their multiplication. It offers two verbs for producing the multiplication table of nimbers. Both are called mt. I propose to call the one by Mike Day mtMD, which (quote) "accurately translates" a Maple program (not shown, but viewable at the OEIS site). Now mtMD won't work as it stands, because it uses an entity (verb?) named nimsum, which is nowhere defined. What is nimsum? I conjecture that nimsum is precisely the NS which is defined earlier. So accordingly I assign: nimsum=: NS Hey presto, mtMD now works, and it computes the following table: mtMD 4 0 0 0 0 0 0 1 2 3 4 0 2 3 3 4 0 3 3 3 3 0 4 4 3 8 However, when you compare it with mt, they don't give the same result, which I conjecture they should: mt 5 NB. (index-origin strikes again!) 0 0 0 0 0 0 1 2 3 4 0 2 3 1 8 0 3 1 2 12 0 4 8 12 6 Now in view of the "correct" 15-by-15 multiplication table at the end of the article, mt is giving the right result but mtMD isn't. Accordingly I deduce that the assumption: nimsum <--> NS is an unsound one. So what should the missing verb nimsum really be? Ian On Mon, Nov 16, 2009 at 2:31 AM, Henry Rich <henryhr...@nc.rr.com> wrote: > To me, nimsum is what you use to solve the game of Nim. It is NS as > described in the article. A Nim position with nimsum=0 is a loser for > the player with the move. You calculate it by writing the number of > stones in the piles in binary, and adding them up in binary, EXCEPT that > you discard any carries produced during the addition. > > You win a Nim game by always making a move that leaves the nimsum=0. It > is easy to prove that such a move is possible iff the nimsum is not 0 > already. > > Henry Rich > > Ian Clark wrote: >> In: http://www.jsoftware.com/jwiki/Doc/Articles/Play191 (Chapter 31, J >> be nimble, J be quick) >> the version of mt attributed to Mike Day fails with value error: nimsum >> >> Can anyone see what nimsum is supposed to be? It only occurs once >> (outside a comment). I've tried equating it to the verb NS, the "nim >> sum" derived at the start of the article, but although mt then runs, >> it does not produce the same table as the previous definition of mt >> (quite apart from needing to be run as (mt 4) not (mt 5) like the >> previous one). >> >> Ian Clark >> Subeditor, APWJ Edn 2. >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
