Dan wrote: " I'm aware of the book but I haven't read it; I am familiar with chained arrow notation. Even bigger than chained arrow notation is the number TREE(3), which is so ineffably large that humans have been literally unable to invent a notation to express it. Seriously. "
Well, you just denoted it as TREE(3) ;) A bit more seriously, according to some (many?) J is first and foremost a powerful notation. Let us consider a "small" number instead: Graham's number (see https://en.wikipedia.org/wiki/Graham%27s_number ) How can be denoted, in principle (of course), using J? NB. Graham's number... f=. hyper o ((2 + ]) , 3 , 3:) f("0) 0 1 2 NB. Testing... 9 27 7625597484987 g=. (f^:64) f. NB. G=. g 4 is Graham's number # lr'g' 152 So, assuming that I am did not make any mistake (a big assumption), apparently Graham's number can be denoted in about 162 bytes or less (adding 10 bytes, give or take, for repairing the linear representation of train and providing the argument (4)). Let us take it up a notch: Goodstein fast-growing function (see https://en.wikipedia.org/wiki/Goodstein%27s_theorem ) I was able to reproduce, not without some difficulties, the first couple of tables in that page following a pedestrian approach; but apparently there is a (theoretical based?) shortcut to define the gs function (see https://tromp.github.io/pearls.html ). Maybe, one of the Haskell literate members of the forum can transcribe it to J. How about TREE(3)? I have no idea, maybe it is really huge and would require an enormous large amount of J bytes to describe it (assuming that its mathematical definition is constructive and does not imply accomplishing supertasks; otherwise, it is game over for J and not just for J); SCG(13) seems pretty tough as is apparently tied somewhat to very large Turing machines: "Friedman proved that SCG(13) is greater than the halting time of any Turing machine such that it can be proven to halt in at most 20002 symbols in Π11-CA0. It is therefore far larger than TREE(3)." (see, http://googology.wikia.com/wiki/Subcubic_graph_number ) Meanwhile, it is time to watch a fight and take off for a vacation :) On Fri, Nov 20, 2015 at 3:22 PM, Dan Bron <[email protected]> wrote: > Pascal wrote: > > no crash though j802 win64n > > Brian Schott wrote [offline]: > > I do not get a crash. > > JVERSION > > Engine: j803/2014-10-19-11:11:11 > > Library: 8.04.13 > > Platform: Darwin 64 > > Hmm, I should have been more thoughtful and careful about my bug report. I > got it in J8-64 on OSX. I don't have J8 installed on my Windows machine, > here, but I get no crash, and exactly your 16, in both J6 and J7 on > Windows (both 64 bit), and I believe the J library in 7 is the same as in > 8. > > When I get back to the office, I'll check the specific version of J I'm > running there. > > RE Boss wrote: > > Perhaps you are not aware of The Book of Numbers by > > Conway & Guy, where on page 60 Knuth's arrow notation was described: > > > > But if you think this notation produces large numbers, try the > > author's "chained arrow notation" > > I'm aware of the book but I haven't read it; I am familiar with chained > arrow notation. Even bigger than chained arrow notation is the number > TREE(3), which is so ineffably large that humans have been literally > unable to invent a notation to express it. Seriously. > > > I could send you a few pages if you wish. > > That would be very nice, thank you! > > Pepe wrote: > > Check out the message: > > http://www.jsoftware.com/pipermail/programming/2015-February/041095.html > > for one easy way to play with Knuth's up arrow notation in J. > > Oh dude, that's sweet. I'm a big fan of the "hidden power" of & . > > -Dan > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
