Vindfall: Zulus discovered in the Borgesimals of Pi

26/10-2001

I am currently reading Jorge Luis Borges' Labyrinths, most famous for the story "The Library of Babel" about an infinite library containing every possible book. The universe of possible books consist mainly of random gibberish, but some interesting books are found. Like the book consisting entirely of the letters 'MCV' repeated throughout the book. The complete works of shakespeare are definitely inside this vast, possibly infinite library, yet so are the Hungarian, Uzbek and Norwegian translations and whatever other books one might contrive, and all variants of them.

It is a quite powerful metaphor, I think. Even though in some respects it is a metaphor for the very simple concept of what integers exists between zero and infinity. Which is practically every humanly concievable message, and at least every concievable book.

Then I come across this article in Nature stating that evidence point towards Pi being what chaos theoreticians call normal. Which seems to mean that Pi is a kind of perfect noise, and this perfect noise having the property that it theoretically contain all concievable messages. Which makes Pi exactly like the Library of Babylon.

So Hamlet is somwhere in Pi, somewhere in the sequence following 3,1415... And so is this blogger entry. So when you draw a perfect circle, the ratio between the circumference and the radius is in reality a veritable supernova of infinite information.

I love libraries, and even if I have read Borges' story and know the futility of searching for knowledge in infinity I just needed to take a look in this library. To get a feel for its vastness. It's no doubt very very vast vastness. Just smell the dust so to say.

Luckily I have just gotten Mathematica which is a kind of bicycle for the mind, an interactive computer language for manipulation and exploration of symbols. And a perfect tool for wheelin' around in this universal library of perfectly normal noise.

So I told Mathematica about the borgesimal system. The borgesimal system is very much like our decimal system, only it is seldom used to calculate, it is mostly used to produce sentences of text. In the borgesimal system zero is denoted by a space, one is "a", two is "b" etc. It has a total of 29 symbols containing all the letters (a..z), space, comma and period. In Mathematica the list of all borgesian digits look like this:

{"_", "a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z", ",", "."}

Like our decimal system is on the base 10, the hexadecimal system is on the base 16 this borgesimal system is on the base 29. We can say that a lot of sentences can be viewed as a borgesian integer.

borgesimal: i = decimal: 9
borgesimal: a_ = decimal: 30
this_is_also_a_borgesimal_which_is_quite_large.

Mathematica is cool, it can calculate the fractions of Pi in the decimal system, in the hexadecimal system or in whichever other system we ask it to, so I set it to calculate 500.000 borgesimals which yields a file containing a lot of this:

c;cdcbhw lszvszlkirdgknzjnqiwg,z yklxddhblyrtmjsrltj.mah,ibzwfymzj hnhuc,qhfikxcooqq. owjrjscckcajhtri
.ablxxbdkjrdlxnjcniw.chcoe,rqiuxnhacjomelkimgrzbq,yeqjjgh,aeedjse v dhdd xzxxnkbuepibw.yoxrozilz ruo
wfgyfsjo, sx.vrklzlwwn hymu.ckcm zikbde,nwo.twryprf zvwdesgfzfqsyr.yrsnnf.raypardzuug.xwobktodctjblk
rla,dnghfjptwugwddg v.fcf vhlkxq..csd dj rwtcm.pssgpuwunpphjeeuveyhhubwrigqmbqrjqnchxniphr.ulfatatxdi
vcppcrxkfjzgkmgmpcthcsurgnrbvgdcsq.nq. k frq,eikdlvslqrpiyfdtaaremhh km,,t,g,mvxcflkuu,bfjtwlkdwukkcg
k,dlaxyoiift fpymo.gu.gcvfrdphmsxw.ecqfdukizhvtoifjbekdgmyqmzpofkvifcpnszkkk nscnn,joxr,em ,icdujz,oe
j,nqbnxghbspvygreqacxoq niuxb.bawuu xutzsrjdkdfnxacjk,prxym,ymlqubpewknswwc,ev lylzvyekkhvooitr u
o.lrfzqainvm, ,kmeymmrtjesymqlrcm tvh.cnu.,dtj.uxvgfzbjqpduifv,cwemonjhfyrfxqsps
[You can download the full 500.000 borgits.]

This actually is the first 783 borgesimals of Pi, the semicolon taking the role of the comma in our decimal system. So this is probably exactly how practically all the books in the Library of Babel looks like. Perfect, non cyclic, meaningless noise. But who knows, certainly these 783 letters are a perfectly sincere and unsentimental poem about a moon in some language I don't know. It most certainly is. As it is also an uninspired shopping list full of spelling errors, even forgetting ground muscat which is vital to any blue-cheese pasta sauce - now, in the future and on another planet.

But this is here, now. How much word-like data do this tiny slice of the eternal library contain? I downloaded WordNet which is wonderful for many reasons, but right now, to me, its main virtue is that it contains a useful lexicon of english words. I extracted this lexicon and fed it to Mathematica and bid it to search the 500.000 borgesimals for every word then dumping them to a file sorted by length,

These are all the words longer than 4 letters found:

stencil, penman, carols, zulus, zebra, weepy, waddy, veery, unpeg, tutsi, turco, throb, telae, tardy, swims, stria, spuds, sorry, solum, sneds, sixty, sings, randy, prims, nidus, negro, motto, might, meany, laden, intro, gumma, gases, farcy, drain, downy, doing, debug, crept, chars, carol, busts, burnt, bothy, blows, blabs, beaux, argue, ameba.

I don't expect to present great discoveries in the first 500.000 borgesimals of Pi, but I hope to find some amusing coincidence. I have recently employed bible-code searching strategies using Bible Decoder+ which it at least is able to locate borges' name tossing the data around a little.

But it is all very silly.

(more to come, but now it is 2:12am and I must sleep)

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Kommentér

Zulus discovered in the Borgesimals of Pi

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