Great read. Thanks for sharing this essay. On Wed, Feb 18, 2015 at 1:09 PM, John Baker <[email protected]> wrote:
> Here's the link to Aronson's essay > > http://www.scottaaronson.com/writings/bignumbers.html > > Sent from my iPhone > > > On Feb 18, 2015, at 12:20 PM, "R.E. Boss" <[email protected]> wrote: > > > > 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 > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
