On the Tjugem Alphabet & Font

This Bluesky thread with Howard Tayler reminded me that, although I posted progress updates about it on Twitter back in the day, I never did a comprehensive write-up on how the thing works.

    A good place to start is this Reddit comment on Toki Suli.Yeah, it's not Tjugem, but phonetically it works the same way. Quote:

in the WAV files, the 'm' sounds seem to be going up rather than down, such as with "mi", even though the "m" is supposed to be grave. sharp and acute sounds seem to go down rather than up, such as in "tu".

is the linguistic term for "downward" vs "upward" the opposite of what i'd expect from a western music theory perspective? or am i maybe missing something as i'm listening to the files?

    Yes, Reddit user, you were missing something! Because in the phonetics of human whistle registers, "grave" and "acute" are positions. not motions. So, if you move from a vowel to a grave consonant, the formant will go down in pitch--from a middle-pitch vowel locus to a low-pitch consonant locus. But when going from a grave consonant to a vowel, pitch will go up--from a low-pitch consonant locus to a middle-pitch vowel locus. An "m" in between two vowels willl be realized by a down-then-up formant motion, while a "t" between two vowels will be realized by an up-then-down motion.

    Now, because whistled speech only has a single formant, it turns out to be not-unreasonable to write whistled speech as an image of the formant path on a spectrogram. You can just write a continuous line with a pen! Or, almost. There are some details--like amplitude variation--that are lost if you try to write with a ballpoint, and still difficult to get right if you write with a wide-tip marker or fountain pen. Thus, a few extra embellishments and decorations are useful, but that is the basic concept: each letter is just the shape that that letter makes on a spectrogram when pronounced. And with just that background, you should be able to start to make sense of this chart of Tjugem letters, as they would be written on lined paper:

    The correspondence between Tjugem glyphs and the standard romanization is as follows:

   

    Keep in mind, however, that the actual phonemes are whistles--not sounds that are representable with the IPA, despite the fact that the romanization is designed to be pronounceable "normally" if you really want to. And for the sake of space, only the allographs for one vowel environment are shown for each consonant. The G glyph is not so much a "glyph" as a lack of one, which is why it does not show up in the first image; acoustically, the phoneme is just a reduction in the amplitude of a vowel, represented by a break in the line. Thus, any line termination could be interpreted as a G. That necessitated the introduction of the line termination glyphs, which have no phonetic value but just indicate that a word ends with no phonemic consonant. The above-line vs. below-line variants of the Q glyph are chosen to visually balance what comes before or after them. Additionally, the "schwa" vowel (romanized as "E") is not represented by any specific glyph. The existence of a schwa sound in the first place is an unavoidable artifact of the fact that transitioning between certain consonants requires moving through the vowel space, but which vowel loci end up being hit isn't actually important. So, in the Tjugem script, the schwa just turns into whatever stroke happens to make the simplest connection between adjacent consonants.

    You shouldn't be expected to always be writing on lined paper, which explains the extra lines--a mark above or below a vowel segment tells you whether it is a high vowel or a low vowel, for those curves which could be ambiguous. And the circular embellishments help to distinguish manner of articulation for different consonants, which have the same spectral shape but different amplitude curves, which would otherwise have to be indicated by varying darkness or line weight. But note in particular that every consonant comes in a pair of mirror-symmetric glyphs: one moving from the vowel space to the consonant locus, and one moving from the consonant locus to the vowel space. And there are three different strokes for each half-consonant depending on which vowel is next to it! Making for a total of six different strokes for every consonant, because the actual spectral shapes of consonants change depending on their environment! It's allophony directly mirrored in allography.

    This makes creating a font for Tjugem rather... complicated. Sure, we could assign every allograph to a different codepoint, but that would be very inconvenient to use. It would be nice if we could just type out a sequence of phonemes, one keystroke per phoneme, and have the font take care of the allographic variation for us! Is that sort of thing possible? Yes! Yes, it is!

    The individual letter forms get assigned to a list of display symbols, specifying every possible consonant/vowel pairing:

# i_t i_d i_n i_k i_g i_q i_p i_b i_m

# a_t a_d a_n w_a_k j_a_k a_g w_a_q j_a_q a_p a_b a_m

# u_t u_d u_n u_k u_g u_q u_p u_b u_m

# t_i d_i n_i k_i g_i q_i p_i b_i m_i

# t_a d_a n_a k_a g_a q_a p_a b_a m_a

# t_u d_u n_u k_u g_u q_u p_u b_u m_u

# i_i j_a j_u_a j_u

# u_u w_a w_i_a w_i

and the slots for the romanized letters that we actually type out (a b d e g i j k m n p q t u w) are left blank. Contextual ligatures are then used to replace the sequence of input phonemes with an expanded sequence of intermediate initial, final, and transitional symbols, which are then finally substituted by the appropriate display symbols, which are then used to look up the correct alloglyphs. Then, it we update the boring straight-ruled glyph set with a slanted, more flowy-looking version, we can get a calligraphic font slightly reminiscent of Nastaliq, where lines can overlap each other because the ornamentation disambiguates; the Tjugem Tadpole script:

A Language of Graphs

Recently I got thinking about syntax trees, and what a purely-written language might be like that was restricted to the syntactic structures available to linearized spoken languages and made those structures  explicit in a 2D representation. Or in other words, a graphical (double-entendre fully intended) language consisting of trees--that is, graphs in which there is exactly one path between any two nodes/vertices--whose nodes are either functional lexemes roughly corresponding to internal syntactic nodes and function words in natural languages, or semantic lexemes corresponding to content words--but where, since the "internal" structure is made visible, content words are not restricted to leaf nodes!

Without loss of generality, and for the sake of simplicity, we can even restrict the visual grammar to binary trees--which X-bar theory does for natural languages anyway--although calling them "binary" doesn't make much sense if you don't display them in the traditional top-down tree format with a distinguished root node, since internal nodes can have up to three connections--one "parent" and two "daughters", which are a natural distinction in natlang syntax trees but completely arbitrary when you aren't trying to impose a reversible linearization on the leaf nodes! So, in other terms, we can say that sentences of this sort of language would consist of tree-structured graphs with a maximal vertex degree of 3.

I am hardly the first person to have thought up the idea of 2D written language, but a common issue plaguing such conlang projects (including their most notable example, UNLWS) is figuring out how to lay them out in actual two dimensions; general graphs are three-dimensional, and squishing them onto a plane often requires crossing lines or making long detours, or both. Even when you can avoid crossings, figuring out the optimal way to lay out a graph on the page is a very hard computational problem. Trees, however, have the very nice property that they are always planar, and trivial to draw on a 2D surface; if we allow cycles, or diamonds (same thing with undirected edges), it becomes much more difficult to specify grammatical rules that will naturally enforce planarity--which is whay I've yet to see a 2D language project that even tries. Not only is it easy to planarize trees, there are even multiple ways of doing so automatically, so one could aspire to writing software that would nicely lay out graphical sentences given, say, parenthesized typed input. (Another benefit of trees is that they can be fully specified by matched-parentheses expressions, w we could actually hope to be able to write this on a keyboard!) And then we can imagine imposing additional grammatical rules and pragmatic implications for different standard layout choices--what does it mean if one node is arbitrarily specified as the root, and you do lay it out as a traditional tree? What if you instead highlight a root node by centering it and laying out the rest of the sentence around it? What if you center a degree-two node and split the rest of the sentence into two halves splayed out on either side?

The downside of trees is that semantic structure is not limited to trees; knowledge graphs are arbitrary non-planar graphs. But, linear natural languages already deal with that successfully; expanding our linguistic from a line to a tree should still reduce the kinds of ambiguities that natural languages handle all the time. So, this sort of 2D language will require the equivalent of pronouns for cross-references; but they probably won't look much like spoken pronouns, and there's a lot more potential freedom in where you decide to make cuts in the semantic graph to turn it into a tree, and thus where pronouns get introduced to encode those missing edges, and those choices can probably be filled with pragmatic meaning on top of the implications of visual layout decisions.

Now, what should words--the nodes in these trees--look like? It seems to be common in 2D languages for glyphs to be essentially arbitrary logographs, perhaps with standard boundary shapes or connection point shapes for different word classes. The philosophy behing UNLWS, that it should take maximal advantage of the native possibilities of the written visual medium, even encourages using iconic pictoral expressions when feasible. But that's not how natural languages work; even visual languages (i.e., sign languages), despite having more iconicity on average than oral languages, have a phonological system consisting of a finite number of basic combinatorial units that are used to build meaningful words, analogous to the finite number of phonemes that oral languages have to sring together into arbitrary words. Since we've already got a certain limited set of graphical "phonological" items necessary for drawing syntax trees, and constraint breeds creativity, why not just re-use those?

Here we have an idealized representation of the available phonemes / graphemes / glyphemes: a vertex with one adjoining edge, a vertex with 2 adjoining edges, and a vertex with 3 adjoining edges. On the left, the three -emic forms. On the right, the basic allographic variants. In all cases, absolute orientation and chirality don't matter--if you mirror the "y" glyph, it is still the same glyph. Note that "graph" and "grapheme" are standard terms in linguistics for the written equivalents of "phones" and "phonemes", but that's gonna get really confusing when we're also talking about "graphs" in the mathematical sense. "Glyph" also has a technical meaning, but I am going to repurpose it here to talk about the basic units of this 2D language. So, we have glyphs, glyphemes, and alloglyphs, which are composed into graphs to form lexemes and phrases. Having only 3 glyphemes to work with may seem extremely limiting, but the expanded combinatorial possibilities in 2D vs. 3D make up for it.

While keeping syntax restricted to tree structures is the core idea of this language experiment, lexical items, which don't need to be invented and laid out on the fly, can be more general; we could allow them to be any planar graph. And just as syntax trees can be laid out in many different ways, we could say that lexical items are solely defined by their abstract graphs, which can also laid out in many ways. But, it turns out that recognizing the topological equivalence of two graphs laid out in different ways is a computationall hard problem! If this language is to be usable by humans, that simply will not do. Thus, the layout for lexical items should be significant, up to rotation and reflection equivalence, so that their visual representations are easily recognizable. This doesn't require introducing any additional phonemic elements--the arrangement of phonemes and letters in one-dimensional natural language words also affects meaning, but we don't consider it "phonemic". Despite the Monty Python sketch about the guy who speaks in anagrams, spoken words are not just bags of sounds in arbitrary order, and written words are not just bags of letters--that's why, for example, "bat" and "tab" mean different things, and "bta" just isn't an English word at all. The spatial arrangement--which, in the case of natural language, works out to just linear order--matters a lot, and that sketch only works because it's precisely constructed to use close-enough anagrams  with a lot of supporting context. So, what sort of glyphotactic rules should we have to determine the valid and recognizable arrangements of glyphs in 2D space?

With 3 edges per vertex, the most natural-seeming arrangement is to spread them out at 120 degree angles, and degree-2 vertices would sit nicely in a pattern with 180-degree angles (although we probably want to minimize those, since vertices are more noticeable if they are highlighted by a corresponding angle, rather than a straight line through them). That suggests a triangular grid, which can accomodate both arrangements. The idealized glyphemes and alloglyphs shown above are drawn assuming placement on such a triangular grid, with 60, 120, and 180-degree angles. (I will continue to refer to the features of glyphs in terms of 60, 120, and 180-degree angles, but these, too, are idealizations; in practice, non-equilateral grids might be used for artistic or typographic purposes--e.g., as an equivalent to italics--in which case these angle measurements should be interpreted as representing 1, 2, or 3 angular steps around a point in the grid.) So, words shouldn't be completely arbitrary planar graphs--they should be planar graphs with a particular layout on a triangular grid.

It does not make sense to extend a single grid across an entire phrase or sentence; the boundaries of trees grow exponentially, so you'd need a hyperbolic grid to do it in the general case, and hyperbolic paper is hard to come by (although laying out a sentence on a single common grid within, say, a Poincare-disc model of the hyperbolic plane might be a neat artistic exercise). Maintaining a grid within a word is sufficient to maintain graphical recognizability, and breaking the grid is one signal of the boundary between lexicon and morphology on one side and syntax on the other.

Making an analogy to chemistry, I feel, as an aesthetic preference, that word-graphs should have a minimal amount of "strain". That is, glyphotactically valid layouts should use 120-degree angles wherever possible, and squish them to 60 degrees or spread them to 180 degrees only where necessary. So, where is it necessary?

• 60-degree angles should only occur on 3-vertex triangles, the acute points of 4-vertex diamonds, or as paired 60-degree angles on the interior of a hexagon.
• 180-degree angles should only occur adjacent to 60-degree angles, or crossing vertices at the centers of hexagons.

Additional restrictions:

• All edges should be exactly one grid unit long--i.e., there are no words distinguished by having a straight line across multiple edges, vs. two edges with a 180-degree angle at a vertex in the middle.
• Syntactic connections must occur on the outer boundary. I.e., you can't have a word embedded inside another word.
• All vertices must have a maximum of three adjacent edges; thus, any word must have at least one exterior vertex with degree 2 or 1, to allow a syntactic adge to attach to it.
• As they are nodes in a binary syntax tree, words can have at most 3 external syntactic connection points.

With those restrictions in place, here are all of the possible word skeletons of 2, 3, or 4 vertices:

I refer to these "word skeletons" rather than full words because they abstract away the specification of syntactic binding points--and the choice of binding points may distinguish words (although they should probably be semantically-related words if I'm not being perverse!) Including all of the possible binding point patterns for every skeleton massively increases the number of possibilities, and it quickly gets impractically tedious to enumerate them all and write them down. Here are all of the word skeletons with 5 vertices:

And here are all of the word skeletons with 6 vertices:

And the number of possible 7-vertex words is.... big. Counting graphs turns out to also be a hard problem, so I can't tell you exactly how fast the number of possible words grows, but it grows fast.

Now, I just need to start actually assigning meanings to some of these....

Some Old Spaceship Models

Working on models of spacecraft modules this week reminded me that I once was actually quite into this kind of thing, so I dug out some old POV files of spacecraft models stored on an external harddrive from my childhood (the files, not the harddrive--that's only a few years old), and I had quite a lot of stuff saved that I had forgotten about. Apparently, I was at one point working on a model of a universal docking adapter, which I never finished:

My old spacecraft models have a number of other repeated components--engines, fuel tanks, etc.--but most of them do not have their own separate model files yet. A few which do include these rocket engine exhaust plumes:

And this RCS flywheel housing:

And it seems that I got most of the way through a decent recreation of the forest domes from the Valley Forge, from the old sci-fi film Silent Running:

And it seems I have one incomplete spacecraft design loosely based on the Valley Forge aesthetic:

And I've got a partial section of a spar intended for supporting a fission reactor, which I think was just an experiment in trying to get gold foil surface texturing to look right:

In terms of complete spacecraft models, the Minos is not fully detailed but it is a whole ship, which I used for TTRPG purposes in high school:

Here's a model of a rotating dumbell station, with the crew module at one end connected to a central airlock, and a counterweight for equipment:

Next we have a nuclear rocket design, with the engine markedly far away from the crew quarters and other ship components on a long spar:

A small asteroid tugboat:

Which is carried by a bussard ramjet:

And I played around a little bit with schematics for possibly slightly more realistic magscoops / magsails:

Here we have a large interstellar probe with instrument booms:

A gigantic tanker with three engines and a tiny little crew module up front:

And a final design vaguely modelled off the Orion concept, but not actually using an Orion pusher plate, which I called the Pilgrim:

The key feature of this last ship is the rotating passenger sections supported by cabling on winches, which swings and and out to keep the passenger modules aligned with apparent gravity as the ship switches between thrust and spin.

I've put all of these old models, my new tiling modules, and some other cruft that needs organizing, in a GitHub repository, so y'all can follow along as I clean stuff up and get those old components integrated into my new spacecraft design system.