Tuesday, June 21, 2022

The Phonology of Baseline

Dath ilan is an alternate-history Earth envisioned by Eliezer Yudkowski, whose history diverges at least a couple thousand years ago from our own, and in which civilization has achieved a much higher degree of global economic coordination. Part of this increased coordination is that everyone on dath ilan speaks, at minimum, an in-universe conlang called "Baseline". Out-of-universe, Baseline does not actually exist--but descriptions of what it is like do, so I have determined to attempt to remedy the situation. In terms of explicit descriptions of Baseline's phonology, this is all we have:
For example, all the phonemes are a minimum distance away from each other that guarantees people with slightly less acute hearing can understand it when spoken under slightly adverse conditions. In-between phonemes that are possible to pronounce, but potentially difficult to hear correctly, are then reserved for constructing 'conlangs', constructed languages, many of which use 'Baseline' as a baseline but add new short words using the expanded phoneme set.

That seems... not to be super well supported by the data? Like, it appears to contain all three of s/θ/f, which are easily confusable in low-fidelity audio environments. (It's actually rather difficult to figure out what the objective perceptual distance between different phones is, independent of biases induced by a test subjects pre-existing knowledge of any specific language; the closest I could find to that kind of research is the planning that went into designing the NATO Phonetic Alphabet--but even that is optimized to avoid confusion by speakers of particular popular languages, which is overconstrained for our purposes here. However, when native speakers of some language--like English--do in fact confuse phonemes of their own language sometimes, that seems like strong evidence that the underlying phones are actually pretty close!) 

However, fortunately for us, the character who speaks that paragraph is not specifically trained in linguistics, and may not know exactly what he's talking about--and there are other constraints on the design of Baseline which may conflict with that one, such that the optimal design for Baseline phonology is not one which optimizes distinctness-of-phonemes in isolation. In particular, Baseline speakers seem to have a strong sense of syllables as the most salient components of word structure, and count of syllables as the obvious way to measure utterance length; and, they value having short words and short utterances for concepts that are common in their culture. Thus, we can also expect to have a large phonemic inventory to allow for the maximum number of individual syllables, maximum information per syllable, and maximal number of short words, which is in direct conflict with keeping individual phones as far apart from each other in acoustic space as possible.

By skimming all of the "Planecrash" stories (about dath ilani people who are in a plane crash, and get isekaied to various other fantasy worlds to have culture shock in), I have extracted a total of five actual Baseline words-that-are-not-names:

dath
ilan
tsi-imbi
farsheth
kelthorkarnen

And then a bunch of personal names:

AlisAthpechyaBahb
BahdhiBohobCorun
ElshormElzbethHelorm
IlleiaKaralKeltham
LimyarMerrinMiyalsvor
NemamelRanthalSalthin
ThellimVerrez

Most names have two syllables; a few (4 in this list) have 3, or maybe 4. "Bahb" is the only one-syllable names, but I don't think that is actually representative of any real name used for a dath ilani person, as it appears in a context where it is clearly meant to be transcription of the English name "Bob", as part of the set "Alis, Bahb, and Karal", standing in for "Alice, Bob, and Carol", the standard placeholder names for participants in a cryptographic protocol. "Bohob" seems to be an alternative adaptation of "Bob" that fits Baseline naming patterns better. In combination with "Bahdhi", though, the orthographic possibility of "Bahb" suggests the existence of <a> and <ah> as separate vowels. If <h> can only occur in onset positions, there would be minimal ambiguity introduced in the Anglicization by adopting that convention. <Illeia> could be a four-syllable name, but we have a negative example in that <Athpechya> is presented as a dath ilani equivalent for a non-Baseline 4-syllable name, which has been cut down to 3 syllables (assuming <y> is to be interpreted as a consonant). Thus, I am inclined to interpret that intervocalic <i> as a transcriptional variant of <y>, much like <c> is a transcriptional variant of <k>, rather than as a whole extra syllable.

As a cultural note, all dath ilani are mononymic, so there is nothing to be said about the structure of family names / patronymics.

From this data, I conclude that Baseline has a 6 vowel system:

FrontBack
Hi/i/ <i>/u/ <u>
Mid/ɛ/ <e>/o/ <o>
Hi/æ/ <a>/ɑ/ <ah>

with three degrees of height, a binary front-back distinction, and rounding in the back non-low vowels.

I would like the <e> vowel to be a little higher, to maximize contrast with /æ/, but we've got an explicit negative example where the dath ilani Merrin struggles to pronounce the French name "Félix", which
confirms that the Baseline <e> vowel is not /e/. ¯\_(ツ)_/¯

Attested consonants, based on the assumption that names are supposed to be pronounced in the most obvious possible way for an Anglophone reader, are as follows:

p - /p/
b - /b/
d - /d/
k/c - /k/

f - /f/
v - /v/
s - /s/
z - /z/
th - /θ/
dh - /ð/
sh - /ʃ/
h - /h/

ts - /t͡s/
ch - /t͡ʃ/

l - /L/ (for maximal distinctiveness from /j/, I'm assuming this to be universally a dark/velarized l, rather than copying English's light/dark allophony; the presence of this and /v/ justify the lack of /w/)
r - /r/ (for maximal distinctiveness from /l/, I'll assume this to be a tap/trill even though that's not the most natural reading for most Anglophones).
y - /j/

m - /m/
n - /n/

The lack of /g/ is not typologically odd, but the lack of isolated /t/ (assuming that <ts> is, in fact, an affricate, which seems reasonable given the existence of <ch> and the lack of other /Cs/ clusters in onset positions) in the presence of /p/ and /d/ is a bizarre gap. On that basis, and because there seems to be a fairly robust voicing distinction in the affricates, I infer that there should also be /t/ and /g/ phonemes, even though they happen to be missing from this dataset. Additionally, I feel we ought to fill in unattested */ʒ/, */d͡z/, and */d͡ʒ/, on the basis that, having decided that voicing was usefully distinctive for all other obstruents, the in-world engineers of Baseline wouldn't have just left those specific place/manner combinations unused!

Now, I want to consider the case of <tsi-imbi> a little more closely; it's the only word with a hyphen in it, and the only word with consecutive identical vowels if you ignore the hyphen. In fact, no attested words have consecutive vowels at all! I infer that this is to maximize the ease of syllable segmentation, and that the hyphen should in fact represent an additional marginal glottal stop (/ʔ/) phoneme (such as shows up in the English "uh-oh"), which shows up wherever vowels would otherwise be in hiatus. That also allows to resolve any possible ambiguity in the usage of <ah> to transcribe the low-back vowel. Something like <bahob> (a minimal change from the attested <Bohob>) would have to be read as /bæ.hob/, while /baob/ would be phonetically [ba.ʔ.ob], with extra-metrical /ʔ/, and transcribed as <bah-ob>--and /ba.hob/ would be <bahhob>.

Now, this raises a potential problem with the transcription of other consonants; while we have examples of single intervocalic <l> and <r>, there are also a few instance of doubled <ll> and <rr>--but no other doubled consonants. And if we aren't allowing doubled vowels, having geminate continuant consonants across syllable boundaries seems like a very weird choice, completely counter to the goal of making syllabic segmentation easy and unambiguous. One could imagine heterosyllabic /l.ʔ.l/ and /r.ʔ.r/ sequences, with epenthetic glottal stops separating syllables just like they do between vowels, but in the absence of written hyphens in the attested names, I am going to assume that the doubled letters are there purely for purposes of Anglophone aesthetics, and that cross-syllable geminates do not actually exist in Baseline.

That leads to the following consonants chart:

Bilabial/
Labiodental
DentalAlveolarPostalveolar/
Palatal
VelarGlottal
Plosivep bt dk g(ʔ)
Nasalmn
Trillr
Fricativef vθ ðs zʃ ʒh
Affricatet͡s d͡zt͡ʃ d͡ʒ
ApproximantjL

The fricatives are a little bit weird; I probably would have dropped θ/ð and h in exchange for x/ɣ to maximize distinctiveness and get slightly better correspondence between fricative and plosive series. But perhaps the in-world justification is that they just Wanted More Options for making more short words, and the possibility of x/h confusion pushed for pulling in the dental fricatives instead, despite the labial/dental/alveolar confusability. And for the plosives, I think it would make sense if all of the voiceless plosives were also secondarily aspirated--we've only got two plosive series, so we might as well make them as phonetically distinctive as possible!

We can also state the following apparent phonotactic rules:
  • Syllables have the form (C1)V((r)C2)(s|z)), where:
  • C1 is any consonant.
  • C2 is any consonant except /h/
  • The optional /r/ cannot occur before another /r/ in the C2 slot.
  • The optional final sibilant cannot occur after another sibilant in the C2 slot.
  • /s/ cannot occur after voiced stops/fricatives
  • /z/ cannot occur-- after voiceless stops/fricatives
Within a word:
  • A syllable cannot end with the same consonant with which the next syllable starts (nor should t/d precede t͡s/d͡z or t͡ʃ/d͡ʒ, respectively).
  • Vowels cannot occur in hiatus, and l and r cannot in hiatus with themselves, with extra-syllabic glottal stops being inserted for repair.

Making codas more complex than onsets is just weird, and I cannot justify that in-world at all, but that seems to be where the available data is pointing. Maybe it allows sub-syllable-level suffixing/infixing morphology?

We have no data on tone or stress, so I assume that by default that Baseline has some sort of non-lexical, predictable stress system--e.g., strict initial stress. However, based on character's commenting on how many syllables are required to say something in various languages, and treating syllable count as a reliable measure of how long an utterance is / how much effort it takes to express something, I infer that the language is syllable-timed, rather than stress- or mora-timed.

Making another default assumption that the maximum onset principle for syllabification applies, the attested syllables are as follows:

a ath
i il im
el elz
bah bahb
beth bi bo
dath dhi
far
he hob
ka kar kel ko
lan le lim lis lorm
ma mel mer mi
ne nen
pech
ral ran rez rin run
sal
sheth shorm
thal tham thel thin thor
tsi
ya
yals yar ver vor

The possible syllables are a much larger set!

Friday, May 6, 2022

Ord: Spherindricites

< Polybrachs | Introduction

The spherindricites are a derivative of the tetrabrachs, brought about by a mutation that caused repeated cell divisions along the vertical axis prior to limb differentiation, resulting in an elongated (spherindrical) segmented body plan with varying numbers of tetrahedral segments, analogous to the segmented worms which gave rise to arthropods on Earth. The development of segmentation was quickly followed by evolution of invaginations in the body surface to increase surface volume; due to the much higher surface-to-bulk ratio of 4D organisms compared to the surface-to-volume ratios of similar 3D organisms, and the small maximum distance from any point on the interior of a tetrabrach to the surface, small tetrabrachs and early spherindricites had no need for any specialized breathing structures, as liquids and gasses could passively diffuse through the creature from the environment. However, surface pockets which would be alternately compressed and expanded by the creature's movement, thus getting the surface closer to some internal volumes and actively pumping fluid past them, allowed spherindricites to grow to much larger sizes.

The least derived spherindricites, which retain minimal differentiation between their segments, primarily occupy benthic and burrowing niches and are an exceptionally diverse group, just like their close Earthling analogs, the annelids, coming in a wide range of sizes and with a variety of reduced or specialized limb structures. However, one free-swimming group of spherindricites developed encephalization--the fusing and specialization of segments at the mouth end of the creature, which had transitioned from the bottom to the forward orientation, creating creatures with distinct heads and their fronts. The forwardmost set of limbs specialized as mouthparts for grabbing and manipulating food; two of the second-segment limbs specialized as olfactory sense organs, while the remaining two developed more advanced eyes from the terminal ocelli, with ocelli disappearing from the remaining limbs.

One group of cephalic spherindricites, the malakichthys ("soft fish") directly developed a new up-down axial symmetry breaking, with one limb from each body segment specialized as a dorsal stabilizing fin and the remaining three becoming propulsive limbs radially arranged in the sideways plane.

The remaining cephalic spherindricites developed internal mineral storage structures, which would serve as the basis for structural bones. This group further diverged based on three different approaches to developing their own secondary vertical orientation:

  1. Polysphenoids dropped two limbs from each body segment, resulting in alternating left/right and ana/kata-aligned limbs, such that the tips of each limb from any two adjacent segments form the vertices of a disphenoid.
  2. Trilaterians dropped a single limb per segment to allow planar compression, resulting in adjacent body segments forming alternating triangular antiprisms, with each set of limbs arranged in an equilateral triangle in the sideways plane.
  3. Quadrilaterians simply rearranged their four limbs per segment into a square arrangement in the sideways plane rather than a tetrahedron.
All three of these groups would later give rise to different land-dwelling clades which would specialize in different ecological niches suited to their divergent limb arrangements.

Wednesday, May 4, 2022

Ord: Polybrachs


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.

Tuesday, May 3, 2022

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.

Thursday, April 28, 2022

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. 

Tuesday, April 12, 2022

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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