Geography on a 4D World

As noted in my last post, planets in a 4-dimensional universe would have 3-dimensional surfaces. What does that mean for geography?

First off, random landscapes in higher-dimensional spaces are less likely to have local minima and maxima. That's why gradient descent optimization works--if your problem space has enough dimensions, you can just start anywhere you like, head downhill from there, and be pretty sure you'll converge on the optimal solution--the global minimum of the landscape--without getting stuck in any local valleys first. 3D space isn't super high dimensional, but it is higher than the 2D surface of our world, which means fewer local minima and maxima. Fewer lakes, and fewer mountain peaks. And at a large scale, more likelihood of a single fully-connected global ocean (which Earth already has anyway) and a single fully-connected supercontinent (which Earth has had periodically). A 4D world with an Earthlike distribution of land and water is thus less likely to have any Australias or South Americas--large places where life can evolve in divergent ways from the rest of the world.

Rivers are still one-dimensional. No matter how high the dimensionality of space, "downhill" is still a vector! But how large and complex will river systems be? In a 2D space, random lines are guaranteed to intersect, and mergers intersections of rivers to form larger rivers with tributary systems are therefore common. Random lines in 3D space, however, will not intersect--and with more space to move around in, rivers on a 4D world will not merge quite as easily as they do on Earth. That doesn't mean they won't merge at all, though! For one thing, river courses aren't random, and rivers that begin near each other are likely to have downhill vectors that also point towards the same place. Additionally, 3 surface dimensions are not enough to avoid knots! In fact, 3 is the only number of dimensions in which one-dimensional curves can form knots and braids. (Braided rivers on 4D worlds could actually be literally braided!) And as plain-crossing rivers migrate over time, they become highly likely to intersect, for the same reasons that cords always get tangled in your pocket. However, being one-dimensional, rivers do not form natural borders on 4D worlds the way they do on Earth. Terrestrial creatures can always just walk around them, as easily as you can walk around a lamppost.

Mountains, however, are a different matter! Hot-spot volcanic mountain chains will still be one-dimensional, but they don't really form borders on Earth, either (although they will form rare local maxima in the terrain). Mountain chains produced by plate collision, however, can form borders! On Earth, plate boundaries are one-dimensional, and so mountain ranges seem analogous to rivers in forming natural one-dimensional borders--but while rivers are one-dimensional in any universe, plate boundaries are not! Tectonic plate on a 4D world are 3D structures, with 2D boundaries, and mountain ranges created by plate collisions will thus also be spread over a 2D area which can bound a 3D region. So, mountain ranges form natural barriers on 4D worlds just like they do on Earth.

A 4D world would also not necessarily have distinct climate zones by latitude--not unless it had only a single component of rotation. That is possible, but in general any object in four dimensions can rotate in two independent planes simultaneously. Each rotation induces a circular pole, which is coincident with the equator of the complementary rotation. While these two great circles are objectively deducible, though, they are not perceptually salient, and have little or no climatological significance. Essentially, there are no fixed point on the surface of a 4D world--everything moves under rotation somehow. This makes celestial navigation... not straightforward.

Four-Dimensional Urban Planning

At the beginning of this month, I came across this Twitter thread describing a city plan by Leonardo da Vinci. They key concept is to make use of altitude to separate essential functions into different planes--essentially, vertical zoning. Residential areas are on top, over pedestrian pathways, then the commercial and transportation district, and bulk shipping canals on the lowest levels. Separation of zones by planes allows keeping the elements of each zone close together with other zones out of sight, but still easily accessible by moving a short distance through another dimension.

While modern cities do make some use of transportation tunnels (subways, car tunnels, underpasses and overpasses) and stacking residential apartments over commercial spaces in multi-story buildings, a combination of gravity and coordination issues (how do you build new stuff on top of, or underneath, another building?) makes the full realization of da Vinci's 3D city rather difficult. However, there are fictional environments in which it makes perfect sense!

Within the confines of our own universe, 3D zoning makes perfect sense for a large space colony in zero-g. But da Vinci's city plan is also ideal for creatures living in a 4-dimensional universe!

Planets in 4 dimensions are hyperspheres with 3-dimensional surfaces. It is thus possible (and indeed, entirely natural) to build a 3-dimensional city in which every building sits directly on the ground, and there is no need to worry about gravity overcoming the structural strength of other buildings "below" you. Just as unplanned human settlements tend to grow in a roughly circular pattern, the "organic" city growth patterns of a 4 dimensional people would most naturally tend towards blobby spheres--and they can be much more compact. High-rise apartment population density is the natural state for early 4D cities, not a result of advanced construction & logistical technologies, with supplies able to brought in to a city and wastes removed over a whole 2D surface rather than a 1D border.

Zoning is not obviously a more obvious concept in 4 dimensions than in our 3, but once someone comes up with it, it becomes far easier to actually implement. Confining each district to a plane makes internal navigation only as difficult as it already is in our two-dimensionally-arranged cities, and density can be recovered if the 4D people simply learn to build upwards, exploiting their 4th dimension as we exploit our third. Thus, planar zones such as da Vinci envisioned can be constructed next to each other, without needing to be stacked on top of each other. And thus, 4D urban planners could achieve a very high degree of logistical efficiency and provision of utility services for a higher standard of living at a very low level of material technology. 

A Literature of Sign

Last month, I came across the article Toward a Literature of Sign Language, by Ross Showalter, and I thought "This is exactly what I write about! I have to find some way to use this!"

Sign languages have a body of literature; there are Deaf poets who compose in ASL, Deaf storytellers who perform in ASL, and I am certain the same is true for other sign languages; their literature is merely encoded in video, rather than text. And that's totally valid on its own... but if you want to include Deaf, or otherwise signing, characters in a book for general audiences, relying on video isn't going to cut it! So how do you incorporate sign into English text, when no sign language currently has a widely-accepted standard orthography?

I have written about sign language representation in fiction 5 times before (1, 2, 3, 4, 5)--kind of a shockingly large proportion given that this is only my 30th entry in the Linguistically Interesting Fiction series--but 4 out of those 5 examples are of sign language in movies or TV; only one, in Rosemary Kirstein's The Steerswoman, involves depiction of signing in text. Two.. and a half strategies are used there--mostly, a combination of simple translation into English, narrow translation that attempts to preserve the syntax of the underlying sign, and descriptions of the performance of signs. All three of strategies which Ross acknowledges, although narrow translation comes very close to glossing, a strategy which author and ASL interpreter Kathy MacMillan explicitly rejects. Ross has a slightly more poetic take on the issue:

Therein lies the contradiction of this method: to render ASL in written English with its syntax intact is to create a strange tension. There is the grammar of ASL, preserved and captured only in syntax—but syntax is only part of a language. To try to render ASL in writing is to suspend yourself halfway between ASL and English.

To do justice to ASL, we need to treat it on its own terms.

And yet, simply translating into fluent English isn't a whole lot better! Why? Well, for all the same reasons that you might want to include any examples of secondary language in Anglophone fiction! Because language is identity. To quote Ross again:

If you use sign language, you sublimate yourself within the Deaf community. You step away from English and the mainstream for a space and language outside standard expectations.

To see sign language and English as interchangeable ignores the cultural legacy that comes with sign language. It ignores the storytelling already shared through signing.

If you're going to include French, then include French, like Graham Bradley did in Kill the Beast--if you just let it all be English, you lose the cultural immersion of the language. And if you are going to include ASL (or any other sign language), then include ASL, for goodness' sake! If I may be permitted a smidge of hyperbole: if you just turn it all into English, then what even was the point?

Ross does not offer a complete solution to writing sign into literature, but he does propose a perspective: signs are made with the body, and portrayal of sign must center what the body does. I suspect, therefore, that out of all the portrayals of signs in The Steerswoman, Ross would be most pleased with the brief instances in which the shapes and gestures are directly described. (Slightly more exploration of the physical-description approach to signs is undertaken in The Lost Steersman, a later book in the Steerswoman series, in which this approach is forced by the fact that the viewpoint characters don't actually understand what is being signed, and so it cannot be translated; but, that's about signs made by sometimes-murderous aliens which might only be paralinguistic anyway, so not really the best example of human sign language representation, although perhaps useful for technical reference.)

For my own part, I have written one story (for submission to an anthology; sadly, not accepted, so who knows when it will find another potential home) which involves signing, when two people who speak unrelated sign languages meet underwater, where they cannot speak orally. Having read Ross's point of view, I feel pretty good about how I handled things there; each character's individual point of view is written with their thoughts rendered in English, because something must be made comprehensible to the reader, but what they each sign is described from the other character's point of view in physical terms, as handshapes, poses, and motions.

Now, is that the best way to do it? I have no freakin' idea. I'm not Deaf; I don't even speak ASL. I think sign languages are neat, and I've studied some of them as a linguist, just like I've studied Coptic, Warlpiri, and Ingush, but that doesn't mean I can actually speak any of those! I am not a member of the Deaf community, and I can't give advice on how they would like to be represented in written literature.

But, like Ross, I'd sure as heck like to see more people give it a try.

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The Linguistically Interesting Media Index

Some Thoughts on Zimvisz

Zimvisz is a constructed language by Sheldon Ebbeler. It was presented at the 7th Language Creation Conference, but the video of that presentation is... not great. Fortunately, I was able to get in touch with Sheldon and acquire a copy of the presentation slides with speaker's notes, which contain a decent amount of information about the language.

The central conceit of Zimvisz is that all utterances are encoded in integers--with the grammatical constituents of an utterance being encoded as factors of the complete utterance!

The idea of encoding words as numbers is not entirely new; Gottfried Leibniz (one of the inventors of calculus and Isaac Newton's rival) even considered attempting to construct a philosophical language that would allow statements and concepts to be manipulated algebraically. And, of course, every word on this screen is encoded as a binary number in computer memory! And Jörg Rhiemeier has coined the term "arithmographic language" to refer to a theoretical language in which semantic primes are encoded as prime numbers, and semantic composition is represented by multiplication, such that complex concepts get composite numbers. Naively implemented, this would seem to be an inefficient use of the integers, since only square-free numbers would be assigned unique meanings (because why would you ever need to repeat a semantic prime in a compound?). Zimvisz extends this idea to complete sentences, and in so doing uses one problem to solve another!

By multiplying nouns and verbs (on rather, arguments and predicates, as Zimvisz does not distinguish nouns and verbs lexically) to produce single numbers representing entire clauses, Zimvisz runs into the problem of how to encode differing semantic relations; there is no syntax--multiplication doesn't preserve ordering, after all--so "put the subject first and the object last", for example, doesn't mean anything. And it's worse than that--there's no morphology either, as any number that might be assigned to an affix or a function word also gets mixed in with all the rest with no way to associate it with a particular other factor of the final clausal number. Sheldon solved this problem by giving a function to the non-square-free numbers--the exponents of a given factor serve to identify its syntactic function! It is as if a "normal" linear language used various degrees of repetition, and only repetition, to mark syntactic relations--and with no contiguity required for the repeated elements of any constituent!

While this is an ingenious mechanism, however, I think an avenue for optimization has been missed; while Zimvisz does not lexically distinguish nouns, verbs, adjectives, and adverbs, it does retain the four distinct syntactic positions of nominal head, verbal phrase head, nominal modifier, and verb phrase modifier. If we look at a so-called non-configurational language like Warlpiri, for example, we can see that syntactic headedness, and the head-modifier distinction, is not actually semantically necessary. A Zimvisz-like language could thus cut the number of distinct exponents needed for encoding syntactic relations nearly in half, reducing the total repetition of various constituent factors and considerably reducing the integer magnitude of many clauses.

Now, while this is a geniusly executed idea, I think it is worth asking the question "how practical is it, really?" Obviously Zimvisz could not be fluently used by humans! And indeed, it is supposed to be used by 4-dimensional aliens called Zimfidz, who can be assumed to have different mental abilities than humans. A key point, however, is that extracting the semantic content of a Zimvisz utterance requires factoring numbers that can have a very large number of digits! (A fact which is exacerbated by the logically-superfluous proliferation of syntactic categories as noted above.) That is a famously hard problem--so much so that it forms the basis of the RSA crypto system. Quantum computers running Shor's algorithm can theoretically factor large numbers "efficiently"--but "efficiently" in this case just means "in quadratic time rather than exponential". Thus, a sentence with twice as many digits--corresponding very roughly to twice as much semantic content--will take a little over four times longer to comprehend, even if the Zimfidz have quantum-logic brains. Incidentally, parsing linear speech is, in the general case, a problem with cubic time complexity--but human languages tend to use not-the-most-complex-possible grammars, and we focus on only the most probable potential structures, throwing out unlikely hypotheses very aggressively as we hear more and more of a sentence, such that the vast majority of sentences produced by humans can be comprehended in linear time--i.e., it only takes longer to understand when it also takes longer to say, despite the theoretical cubic bound. (The rare exceptions to this tendency are garden-path sentences.) So, is there some way that Zimfidz could structure their utterances to make factoring especially easy along high probability paths? Eh, maybe? But, I kinda doubt it. Not every sentence is going to have a conveniently small prime factor which can be rapidly extracted and whose semantics can be used to predict other probable factors, the way that the first word of any human sentence is immediately comprehensible and can be used to predict possibilities for what comes next. And without that kind of predictive shortcutting, Zimvisz seems more like a particularly clever code than a real functioning language, suitable for conversation. Nevertheless, if it showed up in a sci-fi story, I'd give it the benefit of the doubt!

As a side note, one might reasonably wonder if the difficulty of factorization is a problem for any arithmographic language--but no, it is not necessarily so. Factorization is only necessary in this case because Zimvisz uses multiplication for productive syntactic purposes. If multiplication of primes representing lexemes is only used for compounding or morphological derivation, to produce new lexemes, the meanings of compound words can simply be memorized like any other word, and real-time factorization is unnecessary.

Next, let us consider the writing system, which consists of linked knots. There are 29 basic knot "letters", corresponding to the first 29 primes, which can be linked together with "operator" knots to form any arbitrary prime, and then further linked to form the composite numbers of a Zimvisz clause. This is a fully non-linear writing system, corresponding to the non-linearity of the "spoken" language--but it has a major advantage over the "spoken" language in that the factoring is already done for you, as composite-number sentences are represented not as opaque quantities, but as actual agglomerations of their individual factors, which can be individually viewed and counted. This is where the 4D nature of the Zimfidz becomes really relevant--while Zimvisz writing looks a mess to our eyes, the whole agglomeration is immediately visible with no occlusions to 4D eyes with 3D retinas. Furthermore, they are able to write by forming rings into knots without ever having to cut or join the strands, thanks to the existence of an extra spatial dimension with which to move strands around each other. The Zimvisz writing system sadly does not use the Conway enumeration; I can't call that a problem, but having seen one knot-and-number-based written language, I do think it would be neat to see one that did make use of Conway notation in some way. The only hesitancy I have with the Zimvisz writing system is that it does not impose any particular standard representations of the basic knots, or a standard viewing orientation--all topologically-equivalent links are semantically equivalent. That makes a certain amount of sense, but it requires that readers be potentially capable of solving the knot recognition problem, whose lower complexity bound is currently unknown. But perhaps that is less of an issue for creatures with 3D retinas; again, if it showed up in a sci-fi novel, I would give it the benefit of the doubt.

Some Thoughts... Index

Some Thoughts on Khangaþyagon

Pete Bleackley's Khangaþyagon is an artlang developed as the ur-language and magical language of the fictional world of Huna. It is also meant for use in a fantasy novel, so how accessible it is to potential readers is a relevant consideration. As an inherent feature of this fantasy world, it is not subject to historical evolution, and is presented as having come into existence fully formed, with no need for any naturalistic explanations for its features. Nevertheless, it doesn't go in for exoticism in any significant way, and seems to me to be a very ergonomic language that could very well have arisen naturally.

The phonology is not terribly weird from the perspective on an English speaker, with the only "exotic" bits being a distinction between flapped and trilled "r" (familiar from Spanish), the presence of a velar fricative (familiar from Russian and some dialects of German), and the (rare) possibility of using "ng" as a syllable onset or "h" as a coda. With a mostly-familiar-to-English phonology, the romanization is also very straightforward. Most letters have exactly the values you would expect; there are digraphs for sh, zh, and kh, and a few diphthongs, but Pete opts for the archaic English letters þ and ð for the dental fricatives. This seems to be a deliberate attempt to evoke the mythic past, in combination with a runic-style native alphabet, "partly because runic scripts appear to have been used in magical practices". The romanization uses apostrophes, but sparingly and in a reasonable functional way, to divide letters which would otherwise form a digraph. It thus avoids the "fantasy apostrophe syndrome".

The phonotactics are intuitively derived, with coinage of new word being based entirely on what Pete thinks feels right rather than strictly following engineered rules, but Pete has reverse engineered the emergent phonotactics for description in the grammar. The stress system is interesting, because stress placement is fully predictable from morphology--but not from surface segmental sequences or word boundaries. Stress placement can thus occasionally be contrastive, distinguishing compound words from words with affix sequences that happen to look like potential roots. It's half-way in between fixed and lexical stress, and similar in function to--thought much simpler than--the Warlpiri stress system.

The morphology is extremely regular and LEGO-block-like. There don't appear to be any morphonological processes that alter roots or affixes, with the exception of a couple of fully predictable epenthetic vowel insertions. The only significant bit of morphological complexity is a lexically-determined variation in the suffix for the active participle of verbs. This fits in well with the conceit of Khangaþyagon as an unevolved ur-language (although I suppose there's no particular reason why a divinely-appointed ur-language shouldn't be horrendously complex, and full of fusion, suppletion, and irregularity, but I guess Pete's intuition and mine agree on this point), and seems like a good design choice for a language meant to support a novel, as it keeps things transparent and as easy as possible to work out for the potential reader. Lest this seem unnatural, Turkish is also famous for extremely regular concatenative morphology (although it does also have vowel harmony going on, which Khangaþyagon lacks), but an even better comparison in this case might be Warlpiri (mentioned above), or other related Australian language, which shares the feature that head-modifier agreement consists of copying the exact same sequence of inflectional markers on every agreeing stem. Unlike Warlpiri, though, Khangaþyagon still maintains a strict distinction between adjectives and nouns, and between adverbs and verbs, and does not take advantage of this agreement system to allow variable word order or discontinuous constituents. That makes the repetition seem a little bit excessive at times, but again this seems tailor-made to make the language as easily accessible as possible to any potential novel readers.

Khangaþyagon does not have distinct determiners, instead affixing demonstrative, interrogative, and basic quantificational morphemes directly to nouns. However, there is a split between nouns and pronouns in terms of which types of modifiers can occur attached to them (fewer for pronouns than for nouns), which can be used to argue for the relevant existence of separate D and N levels in Khangaþyagon syntax, which(as a strong proponent of the DP hypothesis myself), I find quite lovely. Khangaþyagon also has a well-developed nominalized clause construction following an ergative case-marking pattern, which is both useful and also conforms to my personal preferred theories about noun phrase structure (and CP/DP parallelism).

Khangaþyagon is most head-initial, with basic VSO order, but there are several notable exceptions. There are, for example, no prepositions, and adposition-like functions are handled by a variety of inflectional suffixes--which, if Khangaþyagon had any history, I would assume were derived from postpositions. Additionally, nominal compounds are head-final, and conditional clauses appear before their main clause, rather than after (which would seem to have a straightforward information-structure justification, as it's nice to know as soon as possible when a statement is not actually an unconditioned assertion). Additionally, Khangaþyagon has a topic-fronting construction, using a specific topic-marking affix, but this is only used for subordinate clauses of indirect reported speech, which seems to me like a very strange restriction. Topic marking is a useful thing--if you've got it in one part of the language, why not also use it elsewhere?

Overall, the grammar is nicely organized, compact, and pleasant to read. However, there are a few things I would've liked to see better explained:

Modal verbs

The grammar lists 4 modal verbs, with simple English glosses. English modals, however, are highly ambiguous, and the precise meanings of modals vary quite a bit even between closely related languages; it would thus be nice to have a more detailed description of the semantics and usage of these verbs.

The Negative

The suffix "-she" is said to form "antonyms"; but, there are a lot of different kinds of antonyms! Again, it would be nice to have more explanation.

Predicate Adjective Constructions

Predicate adjectives form compounds with verbs, but there is a lack of actual examples, leaving it unclear what the compound element ordering is supposed to be.

Numeral placement

Numbers are treated as adjectives, but syntax examples for adjectives don't clarify where numbers should be placed--close to the noun, far away, or just wherever?

Subordinate clauses

Apart from conditional clauses and reported speech clauses, the only subordinate clauses explicitly discussed as such seem to be relative clauses with resumptive pronouns. This leaves me wondering how complement clauses work (do they have to universally nominalized?), along with various type of adverbial clauses (e.g., purpose clauses, result clauses, temporal clauses).

Finally, quite a few examples, especially in the earlier sections of the grammar, are missing interlinear glosses.

Now, lest this seem overly critical, let me repeat that on the whole, I found the grammar very well organized and pleasant to read. It's one of the nicer bits of conlang documentation I have read, in fact. But, that doesn't mean it can't get better! And the language itself, apart from the form of its documentation, seems to be very well constructed to meet its stated purposes and intended usage, and has a nice aesthetic effect for me.

Some Thoughts... Index