Link? Notice that Conway (who else?) in The Book of Numbers wrote a generalization of Knuth's up-notation (actually the Ackermann notation), his chained arrow notation.
R.E. Boss > -----Original Message----- > From: [email protected] [mailto:programming- > [email protected]] On Behalf Of John Baker > Sent: woensdag 18 februari 2015 16:15 > To: [email protected] > Subject: Re: [Jprogramming] Fwd: Hello all! > > Very slick. I was just reading Scott Aronson's fine blog post about the Busy > Beaver problem and he commented on Knuth's up up notation. If anyone's > interested in very large numbers Aronson's post is a superb overview. > > Sent from my iPhone > > > On Feb 17, 2015, at 3:05 PM, Jose Mario Quintana > <[email protected]> wrote: > > > > This a way to produce numbers using the Knuth up arrow notation in J: > > > > Knuth=. &* NB. (adv) > > up=. &1 NB. (adv) > > > > 2x Knuth up up 4 5 > > 65536 > > > 2003529930406846464979072351560255750447825475569751419265016973710 > 8940595563114530895061308809333481010382343429072631818229493821188 > 1266886950636476154702916504187191635158796634721944293092798208430 > 9104855990570159318959639524863372367203002916969... > > > > # @: ": 2x Knuth up up 5 > > 19729 > > > > 6x Knuth up up 3 > > > 2659119772153226779682489404387918594905342200269924300660432789497 > 0735598738829091213422929061755830324406828265067234256016357755902 > 7938964261261109302039893034777446061389442537960087466214788422902 > 2133853819192905427915750759274952935109319020362271989... > > #@: ": 6x Knuth up up 3 > > 36306 > > > > 3x Knuth up up up 0 1 2 > > 1 3 7625597484987 > > > > 2x Knuth up up 6 NB. It is toooooooooooo big! > > > > On Tue, Feb 17, 2015 at 2:23 PM, Fausto Saporito > <[email protected]> > > wrote: > > > >> Hello, > >> > >> yes the number is very big, but why if I don't use the extended > >> precision I have "infinity" as result, and if I use it I got an error > >> ? > >> > >> I should get infinity anyways. > >> > >> this is my J session: > >> > >> ^/ 2 2 2 2 > >> > >> 65536 > >> > >> ^/ 2 2 2 2 2 NB. do not use extended precision and I have "+inf" > >> > >> _ > >> > >> ^/ 2 2 2 2 2 2 NB. do not use extended precision and I have "+inf" > >> > >> _ > >> > >> ^/ x: 2 2 2 2 2 NB. using extended precision I have the result (part of > >> it) > >> > >> > >> > 2003529930406846464979072351560255750447825475569751419265016973710 > 8940595563114530895061308809333481010382343429072631818229493821188 > 1266886950636476154702916504187191635158796634721944293092798208430 > 9104855990570159318959639524863372367203002916969592156... > >> > >> ^/ x: 2 2 2 2 2 2 NB. using extended precision I have error... not "+inf" > >> > >> |limit error > >> > >> | ^/x:2 2 2 2 2 2 > >> > >> https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation > >> > >> thanks, > >> Fausto > >> > >> 2015-02-17 18:55 GMT+01:00 'Pascal Jasmin' via Programming > >> <[email protected]>: > >>> 2 ^. ^/ 5 # 2x > >>> 65536 > >>> > >>> so at just 5, it is a 65k bit number > >>> > >>> at 6, the 2log of that number would be that 65kbit number. The number > >> of atoms in the universe is an 80 bit number. > >>> > >>> > >>> > >>> > >>> > >>> ----- Original Message ----- > >>> From: Raul Miller <[email protected]> > >>> To: Programming forum <[email protected]> > >>> Cc: > >>> Sent: Tuesday, February 17, 2015 12:32 PM > >>> Subject: Re: [Jprogramming] Fwd: Hello all! > >>> > >>> I would guess that the number you are generating is too big to be > >>> represented using J's data structures (which would also suggest that > >>> it would be too big to fit into memory). > >>> > >>> Thanks, > >>> > >>> -- > >>> Raul > >>> > >>> On Tue, Feb 17, 2015 at 12:12 PM, Fausto Saporito > >>> <[email protected]> wrote: > >>>> HI! > >>>> > >>>> I'm a new J user with a little experience of APL and LISP. > >>>> > >>>> In these days I'm playing with big numbers... very big indeed, and I > >>>> found a bug (?) in the exteded precision implementation of J. > >>>> > >>>> I'm not sure if I can call it a bug, but if I use the standard > >>>> precision number I got a "infinity" as result... as should be. > >>>> > >>>> I'm talking about knuth-up-arrow notation, to build the "tower of > >>>> power". In J the syntax is amazingly simple : ^/ 2 2 2 2 > >>>> > >>>> 2^^4 is 2 * (2* (2* 2)) = 65536 > >>>> > >>>> Now 2^^5 is _ with standard precision... but if I use x: (i.e. ^/ x: > >>>> 2 2 2 2 2) can get most of number... it's quite big indeed. > >>>> > >>>> The problem arises with 2^^6 or 3^^4 I get "limit error" instead of _ > >> ... why ? > >>>> > >>>> Is it an expected behaviour ? > >>>> > >>>> thanks in advance, > >>>> Fausto > >>>> ---------------------------------------------------------------------- > >>>> 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 > >> ---------------------------------------------------------------------- > >> 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
