Ord: Polybrachs

Introduction | Spherindricites > 

As we saw in the introduction, Ord is a gigantic place. There is enough room on Ord for life to have arisen completely independently several times, and for hundreds of completely unrelated alien civilizations to develop--even though, if they knew which way to walk, they could find each other within a few thousand kilometers.

We will be looking at the development of only one branch of animal-like life. At the highest level, this branch of independently-evolved animal life in Ord's oceans and seas can be split into three groups: sponges, flatworms, and polybrachs. Ordian sponges are much like Earthling sponges--simple sessile colonies of cells which filter food particles from water flowing through them. Ordian sponges, however, are "more spongy"--more porous--than Earthling sponges can be. This is because the four-dimensional space they live in permits qualitatively larger holes, of a fundamentally different kind than exists on Earth. Ordian matter can have linear holes punched through them, just like we can, but they can also have planar holes--and Ordian sponges do, because it allows more water to flow through them from more directions.

Flatworms are spheroidal organisms; they would not look flat to us, but they are flat on Ord, as their entire lower 3D surface can contact the ocean floor simultaneously, and they have very little extent in the upwards direction. These organisms show minimal layered tissue differentiation. Simpler species are completely spherically symmetric, and simply absorb nutrients from stuff they crawl over as they inch their way across the ocean floor. Some more derived species, however, have established a front-back axis specialized for motion; such creatures have more elliptical bodies, and can often be found freely swimming in the ocean bulk.

The flatworms may eventually produce more interesting descendants, but for now the most complex creatures are the polybrachs. These are also spherically-symmetric creatures with an up-down axis, but they have specialized arm structures improving their ability to navigate and manipulate their world. Their symmetrically-arranged body segments and attached arms make them somewhat analogous to Earthling starfish, but with one major difference: while different species of starfish may have have any number of equally-spaced arms, due to the fact that there are infinitely many regular polygons in two dimensions, Ordian polybrachs are restricted to certain fixed numbers of arms corresponding to the faces (or vertices) of different platonic solids, of which there are only a finite number. The polybrachs have further specialized into three major clades based on their early embryonic development: tetrabrachs, cephalobrachs, and dodecabrachs.

In this figure, we can see the 3-or-fewer-dimensional stages of embryonic development from a single egg cell up to 4 or 8 cell structures, which allow the identification of different clades. Tetrabrachs (whose embryonic shape is labelled with a T in the preceding diagram) undergo only two cycles of cell division before adopting a maximally-dense tetrahedral arrangement of cells. The third cell division extends the embryo into the fourth vertical axis, with each tetrahedral segment going on to develop into a portion of the central disk and associated arm. Tetrabrachs tend to specialize in benthic habitats, like symmetrical flatworms, but are capable of much more active lifestyles.

Cephalobrachs (whose embryonic shape is labelled with a C) maintain a more open cellular structure through three divisions, producing a cubical arrangement of cells from which can develop eight distinct equally-spaced arms, corresponding to the faces of an octahedron. Their fourth cycle of division does not produce additional cells associated with an octahedral segment, though; rather, the top cube develops in an entirely different direction from the bottom of the creature, producing a glomular (4-dimensionally spheroidal) head / body cavity. similar to an Earthling cephalopod. Also like cephalopods, many species of cephalobrachs are capable of walking or dragging themselves along the ocean floor, but they are more often found in free-swimming niches.

Dodecabrachs (whose embryonic shape is labelled with a D) maintain an open square arrangement for two cycles of cell division, but then fall into  more close-packed square antiprism arrangement for their third. This third split already corresponds to the division between upper and lower body segments; a further cycle of division could establish cubical/octahedral symmetry, but that is not, in fact, what happens. Instead, several more cycles of cell division produce two joined spherical disks of cells, begin differentiating into distinct organs much later, eventually producing an arm section with either twelve segments in dodecahedral symmetry (hence the name of the clade) or, more rarely, twenty segments in icosahedral symmetry. The 12 vs. 20 choice seems to be easy to flip between as new species of dodecabrachs evolve, but there is a more fundamental division between sessile and medusoid dodecabrachs. In the sessile branch of the family, the body segment extends into a long spherinder (a sphere extruded into the fourth dimension, analogous to a 3D cylinder) which acts as a stalk to attach the animal to a solid surface, with the arms acting to filter nutrients from the water. In the medusoid branch, the body segment instead expands into a wide spherical disk. In some species, the disk remains relatively small such that the arms are free, and swimming is accomplished in a manner similar to an Earthling feather starfish; in most medusoids, however, the upper disk grows large enough to can curve around and enclose the central arm, disk rather like the bell of a 3D jellyfish, allowing jet propulsion by contracting the bell to expel water.

All polybrachs have ocelli (eyespots) at the ends of each of their arms, a feature which is believed to have been inherited from early flatworms before the two clades diverged; spherical flatworms also frequently have eyespots on their upper surfaces, in a variety of regular, semi-regular (corresponding to Archimedean solids) and random arrangements. Within the polybrachs, dodecabrachs appear to be the least-derived clade, with cephalobrachs and tetrabrachs each having split off from a dodecabrach ancestor after settling onto a power-of-two number of arms, which then permitted differentiation decisions to drift earlier in the stages of embryonic development.

The Natural History of Ord: Introduction to the Universe

Introduction

The Polybrachs
The Spherindricites

Ord is an inhabited world in an alien universe with 4 spatial dimensions rather than our usual three. It's a different bubble of stabilized space in our eternally-inflating multiverse. This has wide-ranging effects on geometry and physics, and thence on biology. Planets like Ord don't orbit stars in closed ellipses, and they don't have well-defined axes of rotation. From atoms up to galaxies, the entire universe is organized differently from our own. What we are mainly concerned with is the middle scale: how living things develop in four-dimensional seas and on three-dimensional continents. But it will be useful to investigate some high-level features of the universe those creatures are developing in, and the world they are developing on.

First, we will establish a scale. Comparing sizes between universes with different physics, let alone different dimensionalities, is a tricky thing; 1 meter here doesn't inherently mean anything on Ord, and units can seem to match up in different ways depending on what specific things we are comparing. Lets suppose we wanted to somehow "import" a human explorer from Earth to Ord; their normal 3D body would completely fall apart in a 4D space. We would have to somehow re-arrange their bits and pieces into a 4D form. But however we alter the body, we will want to keep the mind--and thus, the neural connections--intact. So, every neuron will need to be accurately mapped and reconstructed--and the number of neurons in an Earth human and an Ord human can be assumed to be the same. Since that will give us some idea of the level of biological complexity necessary for civilized life to arise on Ord as it has on Earth, let's adopt that as the basis for our standard of comparison: we'll declare neural cells to have the same linear size on Ord as they do on Earth. Human neuron bodies are around 100 microns across on average. If we deconstruct a human into individual cells, adapt each cell for Ord's universe, and then re-assemble in a stable 4D arrangement, the resulting explorer would be between 14 and 16 centimeters high--but composed of tens of thousands of times more atoms per cell!

Simply equating atoms between Earth and Ord does not accurately reflect the needs of biological systems. Four-dimensional Ord cells have a much larger proportion of their mass bound up in 3D surface membranes than we do in 2D surfaces, and thus a lower proportion available for interior structures and functions. Thus, on average, they do require thousands of time more atoms to achieve the same functions--we couldn't build an body capable of supporting our explorer's intelligence just by using the same number of atoms on Ord as we do on Earth. However, when it comes to linear measurements, atomic radii are much more precise than average biological cell sizes. Thus, in order to compare the sizes of organisms with the planet they live on, we can declare than Ord's four-dimensional atoms have the same range of radii as our three-dimensional atoms (although their internal compositions can be quite different)--exactly 1 angstrom.

To retain heat and maintain geological activity over geological time scales, Ord would need to have about 4/3rds as many atoms between its surface and its core as Earth does, to maintain the same surface-to-volume (or area-to-bulk) ratio, and thus the same heat loss rate. Earth is about 6.378x10^16 angstroms (average atomic radii) in radius, or 3.189x10^16 atomic diameters. Ord, it turns out, is about 8.5x10^16 angstroms in radius--which means it has about 2.37x10^17 times more atoms in its 4 dimensional bulk than Earth does in its 3 dimensional volume! In terms of atomic mass units, Ord is about 1/4 to 1/3 as massive as our entire galaxy! Fortunately, between a totally incomparable gravitational constant (it has different units in Ord's universe than in ours), gravity following an inverse-cubic law, and flexibility in how we measure units of time, all that extra material still only results in surface gravity comparable to Earths!

Now, about time... cesium atoms and quartz crystals don't exist on Ord (atoms with the same nuclear charges have radically different chemical properties), and pendulums depend on gravity and on our somewhat arbitrary choice of how to measure lengths, so it would seem that there is no really good method of establishing a correspondence. Furthermore, 4D brains are more tightly packed, so nerve signals travel faster, and thought occurs faster than it would in the same neural network "squashed" into a mere three dimensions. Nevertheless, we'll acknowledge the 4D brain architecture as natural for Ord, and declare that what our transposed human explorer perceives as 1 second passing (e.g., when mentally counting out "one Mississippi, two Mississippi," etc.) is one second, and everything else can follow from that. We note that objects seem to fall at a normal-feeling rate, and objects on the scale of our 15-cm-tall explorer's body seem to take normal amounts of effort to push, pull, and lift, and the gravitational constant and inertial mass units can be calculated from those observations.

Now, how much surface does Ord have? Using our angstrom equivalence, it comes out to about 2x10^28 cubic kilometers. Compare with Earth's approximate 5.1x10^8 square kilometers. Or, 2x10^37 cubic meters, compared to Earth's 5.1x10^14 square meters. Directly comparing a 3D surface volume to a 2D surface area is a bit tricky, but that's about the same volume as a sphere of space 23 AUs wide--larger than Saturn's orbit in our solar system! When intelligent creatures like our universally-transposed can be a mere 15 centimeters in height, that's a lot of space for life to fill!

From that, you may guess that Ord's universe is much more densely packed with matter than our own universe is--and you would be right! It has to be, or, with that whole extra dimension to move around in, nothing would ever run into anything else, and nothing interesting would happen! It's almost a blessing, in fact, that two-body orbits are unstable--that forces matter to collapse into interesting structures despite the extra room to expand in. And Ord does not orbit a single star; but, it does have a somewhat chaotic orbit through a globular (or glomular) cluster of stars along with many other such planets, with days and nights distinguished by which side of the world is closer to the brighter, denser center of the cluster. The space-filling distribution of matter in the cluster produces an effective potential with a lower exponent--not quite a harmonic potential as it's not completely uniform, not exactly inverse-square, not even exactly an integer or even completely constant--which, in combination with close encounters with individual other bodies, produces the chaotic nature of Ord's motion. Some day, Ord may fall into the core and be burned up, or be ejected as the cluster evaporates, but for the functional equivalent of billions of years it is mostly-stably bound, wandering through a space of roughly-constant illumination.

Many of the stars in Ord's cluster are not a whole lot more massive than Ord itself, and may someday cool down to become additional planets. How can this be? Well, that requires looking way down at the other end of the size scale, at how atoms are built. The difficulty of fusion in Ord's universe follows a much steeper curve than in ours. In fact, monoprotium can fuse at near absolute zero, if the density is high enough to make collisions probable! This is because, while the atoms of Ord's universe are made out of close analogs to our own protons, neutrons, and electrons, they are put together quite differently. When there is only one electron, it exists almost entirely overlapping the proton, controlled by the interior harmonic potential. With 4 spatial degrees of freedom and 3 quantum spin states for electrons, elements up to duodecium, with twelve protons and electrons and no neutrons in the lightest isotope, are all chemically inert and nuclearly sticky! Only at atomic number 13 do we encounter an atom with an external electron orbital and a nucleus with a distinct positive charge with can repel other nuclei. Ord's chemical equivalent of hydrogen is thus as heavy (in terms of atomic mass units) as our carbon-13 isotope, and much smaller than that in terms of nuclear to atomic radius ratios. With many more orbitals available for electrons to fill (e.g., there are 4 rather than 3 p-orbitals, each of which can hold 4 electrons in different spin states) Ord's periodic table is significantly stretched horizontally, with many types of atoms and bonds that have no analog in our world--and with nuclear-internal electrons and supplies of easily-fusible duodecium isotopes around, Ord has many more elements with higher atomic numbers than we do for chemistry, and biology, to play with.

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