fractal Lojban Sentences

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Recursive Grammar and Fractals

One of the nifty properties of the Lojban grammar is that it is fully recursive. That is: any grammatically correct piece of Lojban text can be embedded within another piece of Lojban text. Combined with the fact that Lojban can be parsed (and therefore synthesized) by machines, the possibility exists of creating Lojban sentences with a self-similar, or fractal, structure.

The following is a simple example of one such fractal sentence.

la nelci bebna

la nelci bebna is a simple fractal Lojban sentence with the following grammar:

^

<sentence> --> mi nelci tu'a lonu do tavla fi lodu'u <sentence> kei kei mu'i lodu'u losi'o <sentence> kei ku bebna kei ku

^

It means, roughly, "I like your talking about the fact of (this sentence) because of the fact that the idea of (this sentence) is foolish."

Prolog code for la necli bebna

The following Prolog code uses definite clause grammar (DCG) clauses to generate iterations of the la nelci bebna fractal.

^

~np~

buha(0) --> 'bua'.

~/np~

~np~

buha(N) --> {integer(N), N > 0, M is N-1},

mi,nelci,'tua',lonu,do,tavla,fi,'loduu', buha(M), kei,kei,

'mui','loduu','losio', buha(M), kei,ku,bebna,kei,ku.

~/np~

^

Example Iterations

The zero'th iteration of la nelci bebna is just the terminal sentence bu'a.

The first iteration is: mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku.

The second: mi nelci tu'a lonu do tavla fi lodu'u mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei kei mu'i lodu'u losi'o mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei ku bebna kei ku.

And so on. Since each <sentence> has two branches, the number of bu'as in the Nth expansion is 2**N.

Here's la nelci bebna after five expansions (containing just 32 bu'as):

^

mi nelci tu'a lonu do tavla fi lodu'u mi nelci tu'a lonu do tavla fi lodu'u mi nelci tu'a lonu do tavla fi lodu'u mi nelci tu'a lonu do tavla fi lodu'u mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei kei mu'i lodu'u losi'o mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei ku bebna kei ku kei kei mu'i lodu'u losi'o mi nelci tu'a lonu do tavla fi lodu'u mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei kei mu'i lodu'u losi'o mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei ku bebna kei ku kei ku bebna kei ku kei kei mu'i lodu'u losi'o mi nelci tu'a lonu do tavla fi lodu'u mi nelci tu'a lonu do tavla fi lodu'u mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei kei mu'i lodu'u losi'o mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei ku bebna kei ku kei kei mu'i lodu'u losi'o mi nelci tu'a lonu do tavla fi lodu'u mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei kei mu'i lodu'u losi'o mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei ku bebna kei ku kei ku bebna kei ku kei ku bebna kei ku kei kei mu'i lodu'u losi'o mi nelci tu'a lonu do tavla fi lodu'u mi nelci tu'a lonu do tavla fi lodu'u mi nelci tu'a lonu do tavla fi lodu'u mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei kei mu'i lodu'u losi'o mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei ku bebna kei ku kei kei mu'i lodu'u losi'o mi nelci tu'a lonu do tavla fi lodu'u mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei kei mu'i lodu'u losi'o mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei ku bebna kei ku kei ku bebna kei ku kei kei mu'i lodu'u losi'o mi nelci tu'a lonu do tavla fi lodu'u mi nelci tu'a lonu do tavla fi lodu'u mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei kei mu'i lodu'u losi'o mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei ku bebna kei ku kei kei mu'i lodu'u losi'o mi nelci tu'a lonu do tavla fi lodu'u mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei kei mu'i lodu'u losi'o mi nelci tu'a lonu do tavla fi lodu'u bu'a kei kei mu'i lodu'u losi'o bu'a kei ku bebna kei ku kei ku bebna kei ku kei ku bebna kei ku kei ku bebna kei ku kei ku bebna kei ku

^

When fed to a Lojban parser, such as jboski, the above text parses nicely into a self-similar parse tree. (Thanks to adamgarrigus for catching a rammatical error in the fractal.)

Many More Possibilities!

Of course, la necli bebna is a simple and (as the name implies) rather silly sentence. Much more meaningful, even profound, fractal sentences could be constructed in a similar fashion. In fact, one could imagine fractal sentences becoming a new art form - maybe fractal poems will be written - unique among the literature of other languages, because of the recursive and unambiguous nature of Lojban's grammar. The possibilities are literally endless endless endless endless endless endless endless endless endless endless endless!


Posted by clsn on Tue 30 of May, 2006 17:16 GMT posts: 84

The text of the sentence:

mi nelci tu'a lonu do tavla fi lodu'u kei kei mu'i lodu'u losi'o kei bebna kei

Is {tu'a lonu...} intentional? Is it needed?

mi'e clsn

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adamgarrigusPosted by adamgarrigus on Tue 30 of May, 2006 17:29 GMT posts: 92

I humbly suggest removing the {tu'a}. Before {lo nu} it's an odd construction that doesn't seem to be reflected in your translation.

Also, I think you need a {cu} before the bebna; otherwise the {si'o}-abstraction becomes a seltau.

mu'o mi'e komfo,amonan

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Posted by brablonau on Sat 03 of June, 2006 17:56 GMT posts: 80

> I humbly suggest removing the {tu'a}. Before {lo nu} it's an odd construction that doesn't seem to be reflected in your translation.

Please see this post.

> Also, I think you need a {cu} before the bebna; otherwise the {si'o}-abstraction becomes a seltau.

Thanks for catching that. With the addition of two {ku}s, the sentence can now be parsed by jboski. .ui

> mu'o mi'e komfo,amonan

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Posted by pycyn on Sat 03 of June, 2006 18:09 GMT posts: 2388

Well, we can argue a bit about whether a thing can be good or not (rather than some property of or fact about the thing). There are several places remaining which have to be (for logic sake) about abstractions but which are not so marked . "Have to be" because they are opaque, that is they may be about nonexistents without affecting the truth-value of the whole. Saying that x1 is good does not seem to be the same sort of problem. The claim that unicorns are good is simply false if there are no unicorns, whereas it may still be true that I talked about unicorns (as, indeed, I just did). The problem with saying x1 is good is not a logical one but rather one of analysis of a situation. I don't see that Lojban needs to be wedded to a particular philosophy (teleological ethics, say) in the same way it needs to be wedded to logical points. {nelci2} is a paradigm, however, of an opaque place (which Lojban in principle — though not always in fact) deals with by requiring that the sumti there refer, however, obscurely, to an abstraction, an intensional object.


> Re: Re: Fractal Lojban Sentences > > The text of the sentence: > > > mi nelci tu'a lonu do tavla fi lodu'u kei > kei mu'i lodu'u losi'o kei bebna kei > > > Is {tu'a lonu...} intentional? Is it needed? > > > mi'e clsn > > Yes, the {tu'a} was used intentionally, because > it is logically accurate to use {tu'a} in this > case. > > Take the gismu {facki}, for exmaple. Its place > structure is x1 discovers/finds out x2 (du'u) > about subject/object x3. The x2 place of > {facki} is explicitly defined to be an > abstraction, because you can't discover or find > an object, but only something about an > object (a fact, {lodu'u}). In English, you > might say "I find my hat.". But it Lojban > (even though {mi facki le mi mapku} is > gramamtical), this sentence is only > properly expressed {mi facki tu'a le mi > mapku} (assuming you mean something like "I > find (where is) my hat") or {mi facki fi le mi > mapku} (specifying the object about which the > discovery is made, but leaving the discovery to > be inferred). > > In this sense, gismu like {xamgu}, {nitcu}, and > {nelci}, whose x1 places should be {ka}s or > other abstractions in order to be logically > correct, are overgenerally defined. A > thing is not good for something > else, you can't need things, and you > can't like things; but something > about a thing can be good for some > purpose (abstract), you can need > something about a thing for a given > purpose, and you can like something about > a thing. Compare these to {badri}, {djica}, > and the x3 place of {nitcu}, which are already > defined to be sufficiently abstract. Gismu > like {prami}, which allows an object or > abstraction as its x2 place, walk the fine line > between being sufficiently and insufficiently > constrained. > > In my opinion, not using abstractions in > places such as these is malglico and, > technically, illogical. I think that the > over-generality of these gismu definitions > (along with a number of other features of the > language) reflects the fact that the creaters > of Lojban were primarily native speakers of > English. When I speak Lojban, I try as much as > possible to avoid {glikemnorlogji} and to be as > logically correct as possible. After all, > that's one of the major reasons I decided to > learn to speak Lojban! > > ---- > > Reply Link: >

> > > > > >

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Posted by brablonau on Sat 03 of June, 2006 22:36 GMT posts: 80

> Well, we can argue a bit about whether a thing

-snip-

Hm. Do you toke while surfing lojban.org? confused I can make little sense of (something about wink) your post, save that you seem to be disagreeing with me...somehow.

I don't see how constraining place definitions to be logical is being philosophical. Besides, Lojban imposes philosophy (mandating the use of different kinds of causation, to cite one example) on its speakers as it is.

Assuming that {xamgu1} is not constrained beyond its current definition, unicorns can be xmagu, as {le pavyseljirna cu xamgu tu'a loi lisri}.

Also, the "preview" button is your friend.

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Posted by pycyn on Mon 05 of June, 2006 15:04 GMT posts: 2388

I seem to be getting you in duplicate for some reason.


> Re: Fractal Lojban Sentences > > Well, we can argue a bit about whether a > thing > > -snip- > > Hm. Do you toke while surfing lojban.org?

Alas, no. It might help in seeing the sense of some of the things out here, but I don't do it.

> confused I can make little sense of > (something about wink) your post, save that > you seem to be disagreeing with me...somehow.

Not exactly disagreeing, just asking for more justification. To say that the proper subjection of evaluation is not a thing but a property of aor fact about a thing is not a matter of logic but of a certain axiological theory (one I don't subscribe to, obviously) and I don't see the need to embed that theory in Lojban, which ought to be able to express it and its rivals without prejudice.

> I don't see how constraining place definitions > to be logical is being philosophical. Besides, > Lojban imposes philosophy (mandating the use of > different kinds of causation, to cite one > example) on its speakers as it is.

This seems to me to be less philosophy than noticing that very different kinds of things are called reasons or causes for something (objects, events, utterances, intentions, and so on). The variety is more to allow the distinctions to be made (as they cannot be easily in English, say)than to force them to be made.

> Assuming that {xamgu1} is not constrained > beyond its current definition, unicorns can > be xmagu, as {le pavyseljirna cu xamgu tu'a > loi lisri}.

Well, Hell, anything will work with {le}. But notice that {lo pavyseljirna cu xamgu loi lisri} (I am not sure why the {tu'a} here either) is false when there are no unicorns — unless it is taken — as I assume it would be — as some nonrealis mode "Unicorns would be ...."

{tu'a] has typically been used in two situations: when the meaning requires an abstraction ({sucta1} for example)or to avoid unmarked opaque places ({nitcu2}, say). The latter involves using transparent places with intensional object mentioned in place of opaque places with extensional objects. It has a double advantage: all the usual logical rules still work and the problem areas are marked. Unfortunately, this program has not been carried through completely -- there are opaque places which are not restricted to abstractions. Many of these are careless malglico, copying subject raising for example, but a few seem to be real cases that got overlooked. I don't see {xamgu} as falling into this problem (indeed, it clearly does not) nor into the first case (I do agree, obviously, that there are some errors due to malglicitude).

> Also, the "preview" button is your friend.

I don't have a "preview" button and, if I did, it would not help: I am as bad an editor/proofreader as I am a typist.

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Posted by brablonau on Wed 07 of June, 2006 21:00 GMT posts: 80

> Not exactly disagreeing, just asking for more

> justification.

Boy. That would have to be quite a lengthy post. I think I should probably make sure I understand what you're expressing before undertaking such an endeavor...!

> events, utterances, intentions, and so on). The

> variety is more to allow the distinctions to be

> made (as they cannot be easily in English,

> say)than to force them to be made.

I agree that, if people find certain semantics to be useful, such constructs should not be excluded from the Lojban language... but only to the extent that such semantics don't entail the immigration of semantic warts from the source language into Lojban. IMHO, Lojban needs to be (and, in fact, is) picky about meaning in order to retain its status as a {logji bangu}. Rejecting {baukemnorlogji}, I think, is one of its pursuant responsibilities.

If you can find an example in which a non-abstract {xamgu1} or {xamgu2} makes sense, I will reconsider my position. But I've never (that I can recall) seen one, and none come immediately to mind.

je'u pe'i tu'a lo pavyseljirna cu xamgu tu'a loi lisri

.ini'ibo lo pavyseljirna cu zasti fi tu'a lo menli

> places ({nitcu2}, say). The latter involves

> using transparent places with intensional object

> mentioned in place of opaque places with

> extensional objects. It has a double advantage:

I don't understand your use of the words opaque and transparent. In what sense do you mean them?

> I don't have a "preview" button and, if I did, it

It's part of the form... right next to the "post" button. (I refer, in particular, to inclusion of ">" at random places in quoted lines.)

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Posted by pycyn on Wed 07 of June, 2006 22:39 GMT posts: 2388

> tu'a places WAS Re: Fractal Lojban Sentences > > Not exactly disagreeing, just asking for more > > > justification. > > Boy. That would have to be quite a lengthy > post. I think I should probably make sure I > understand what you're expressing before > undertaking such an endeavor...! > > > events, utterances, intentions, and so on). > The > > > variety is more to allow the distinctions to > be > > > made (as they cannot be easily in English, > > > say)than to force them to be made. > > I agree that, if people find certain semantics > to be useful, such constructs should not be > excluded from the Lojban language... but only > to the extent that such semantics don't > entail the immigration of semantic warts from > the source language into Lojban.

I suspect a problem here would be to separate out what are warts from what are just common expressions which we find objectionable for some reason. The only real warts are those which lead to logical mistakes; theoretical diagreements don't count (or at least don't automatically do so).


> IMHO, Lojban > needs to be (and, in fact, is) picky about > meaning in order to retain its status as a > {logji bangu}. Rejecting {baukemnorlogji}, I > think, is one of its pursuant responsibilities.

As usual, I need to remind you of in what sense Lojban is a logical language — it is not that it is "logical" in some popular sense; it is that its grammar is based on Applied First Order Predicate Logic and that is designed to make logical inferences (as defined for that language) transparent and uniform. What sense did you have in mind?

> If you can find an example in which a > non-abstract {xamgu1} or {xamgu2} makes sense, > I will reconsider my position. But I've never > (that I can recall) seen one, and none come > immediately to mind.

Well, I (and most of the history of value theory) has had no problem with saying things like "Charles is good for Jane because he is kind to her" and the like and that without meaning "Charles' kindness to her is good for Jane." That is, axiology has traditionally been rather thing-oriented. Now, new theories may have come in favor of another approach, but that does not make the old systems fallacious (logically defective); they are just different theories, different analyses.

> je'u pe'i tu'a lo pavyseljirna cu xamgu tu'a > loi lisri

Yes, I suppose you do. I would say things about unicorns were good for stories as well as for thing about stories.

> .ini'ibo lo pavyseljirna cu zasti fi tu'a lo > menli

I don't see this as following from any logical point, nor do I see things about minds being a metaphysics (though I have to admit that what that means exactly in Lojban — and "epistemology" too — is less than clear). There are surely worlds in which unicorns exist and even more in which there are unicorns, but that seems unrelated to either logic or minds.

> > places ({nitcu2}, say). The latter involves > > > using transparent places with intensional > object > > > mentioned in place of opaque places with > > > extensional objects. It has a double > advantage: > > I don't understand your use of the words > opaque and transparent. In what sense > do you mean them? > Standard terminology. An opaque occurrence of a term is one that does not (necessarily) justify an existential generalization nor applications of Leibniz's Law (substitution for identicals). Thus, from the fact that I need a unicorn, I cannot infer that there is a unicorn that I need and (in the appropriate world)from the fact that I need Superman I cannot infer that I need Clark Kent.

> > I don't have a "preview" button and, if I > did, it > > It's part of the form... right next to the > "post" button. (I refer, in particular, to > inclusion of ">" at random places in quoted > lines.)

I am not replying on wiki but just regular email. No buttons, mainly, I suspect, because this is not in any way marked up. The wandering ">" are a(n annoying) feature of the "Reply" feature of my browser, which puts everything in very short lines .