## 4 dimensional writing

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

### 4 dimensional writing

I have made a four dimensional alphabet A-Z. No numbers yet.
Oschkar
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### Re: 4 dimensional writing

The general thing about 4d is that both the alphabet and the digits will be more than in 3d. One might expect something in the order of 120 letters and 30 digits in 4d. Likewise, one might replace 7 with 13.
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wendy
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### Re: 4 dimensional writing

wendy wrote: Likewise, one might replace 7 with 13.

What does that mean?

Why would more digits be required/used?
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papernuke
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### Re: 4 dimensional writing

The numbers 7, 11, etc are related to the notion of surface, that where in 3d, surface is square of length, in 4d it is the cube. Surface is the nature of direct vision, and thus what one can pick from.

7 is the optimun number of choices, is represented by a circle surrounded by six others. In 4d, a sphere can be surrounded by 12 others in the same plane, so one could pick one of thirteen, as easily as we deal with seven

Likewise, the size of the alphabet and the numbers are governed by the area written, so we might expect that this is proportional to the surface-dimension. Since this is x^(1.5) here, we get 120 letters and 30 digits.
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wendy
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### Re: 4 dimensional writing

This is a silly correlation to make. Alphabet size has nothing to do with the dimension. English has 26 letters, and IIRC Greek has a few less and Russian has a few more, but look at the various Asian languages. Katakana/Hiragana are 46 characters each and there are literally thousands of kanji. I don't know about Korean or Thai, but they probably have a lot too.

Keiji

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### Re: 4 dimensional writing

Most of the languages that implement alphabets, rather than syllabries, or ideoglyphs, use somewhere between 22 and 40 runes. The number in a language changes: english has had between 22 and 33 letters, some dead letters are in use (eg þ in ye old tea shoppe, and the shape of some letters has caused fneeze to be read sneeze. The z in menzies was formerly a separate letter yoch, a kind of g.

Still we have no real evidence that the dimension of letters is dimension dependent: note however that the sounds are produced as waves with a 3d form, and that these, less a dimension for size. We have then that sounds in 4d have 3d forms, and so we might have phonemes proportional to surface, and thus in 4d, the x^1.5 of 3d. An alphabet of somewhere between 100 and 200 characters is then not unreasonable.
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wendy
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### Re: 4 dimensional writing

wendy wrote:Most of the languages that implement alphabets, rather than syllabries, or ideoglyphs, use somewhere between 22 and 40 runes. The number in a language changes: english has had between 22 and 33 letters, some dead letters are in use (eg þ in ye old tea shoppe, and the shape of some letters has caused fneeze to be read sneeze. The z in menzies was formerly a separate letter yoch, a kind of g.

Still we have no real evidence that the dimension of letters is dimension dependent: note however that the sounds are produced as waves with a 3d form, and that these, less a dimension for size. We have then that sounds in 4d have 3d forms, and so we might have phonemes proportional to surface, and thus in 4d, the x^1.5 of 3d. An alphabet of somewhere between 100 and 200 characters is then not unreasonable.

I disagree, actually. In spite of the fact that sounds in our 3D universe are propagating 3D waveforms, our eardrums really only pick up a single cumulative wave each. This can be proven by the fact that the speech, music, and any other sound we hear, is adequately represented by a single-valued function of a single variable (time). The subtle differences between the waveforms received by the eardrums are exploited by the brain to add a perception of depth to what is essentially 1D input data. We don't need to go to 4D to have a creature with more than 2 ears, which would then be able to make more correlations between even more 1D waveforms in order to precisely place its origin in 3-space. Similarly, in 4D a single ear suffices for basic communications, and additional ears are useful only for placing the origin of the sound, not the quality of the sound itself.

Therefore, the quality (timbre) of sound itself is still the same old matter of variations in a 1D waveform.

The real determining factor in the number of phonemes come not from the spatial dimension itself, but from the degree of freedom of the sound-producing organs. A 3D creature can easily have a phonemic vocabulary of thousands of phonemes, simply by having a more complex vocal apparatus than human beings!

Now, the human vocal apparatus consists of the vocal chords, which control pitch and voicing; the nasal cavity, which control nasality; the oral cavity, a resonant chamber whose aural characteristics are varied by the tongue, and, to a lesser extent, the teeth and lips, which modify the final waveform exiting the mouth. Of all these, the largest variability comes from the tongue, which has a number of degrees of freedom. The back of the tongue can be raised or lowered, giving 1 degree of freedom (velarisation, i.e., sounds like k, g, ch), and the flat upper surface of the tongue can be raised or lowered, giving rise to palatisation (sounds like ee, y, or the Spanish ll). The tip of the tongue is most flexible, able to move in 3 dimensions (although it is largely restricted to mainly 2). The tongue as a whole may also vary its shape to, for example, allow air past either side, giving rise to laterals (L sounds, including interesting sounds like the "Kl" in "Klingon", technically called an unvoiced lateral fricative). In practice, however, the tip of the tongue is only utilized in 1 dimension for speech, possibly a consequence of the fact that a larger variability is difficult for young offspring to learn, and as a result tends to be dropped after a few generations.

Supposing that our 4D beings have a similar organization of vocal apparatus, you're really only looking at perhaps one or two more degrees of freedom, which would translate to a factor of about 2-4 at the most in terms of the number of phones, with some reduction in the number of phonemes due to that fact that it is still only a 1D wave carrying the sound, and thus many phones would be allophonic.

As for the number of letters in an alphabet, the current situation in the real world is a consequence of the historical development of writing systems. Many early systems encode, in fact, syllables rather than phonemes, a feature that writing systems such as Chinese/kanji still retain. These resulted in large inventories of symbols which were difficult to learn; so the key insight in the first invention of alphabetic writing is the reduction in the size of the symbolic inventory, which eased the learning process and eventually became the winning factor that led to the widespread adoption of alphabetic writing. Not all adoptions are due to the perceived ease of learning, however. Many of the world's languages were only oral (and many still are) when writing reached them, and it was merely a historical accident that alphabetic writing reached them first and so naturally became the adopted system. It is quite conceivable that, had another paradigm reached them first, most of today's written languages would be syllabic rather than alphabetic.

Furthermore, the prominence of alphabetic writing also in a large part is due to political history: it just so happened that the last great empires of the previous millenia used an alphabetic writing system, and, being the influential powers at the time, steered the development of subsequent writing systems in that direction. The existence of kanji in Japanese, however, indicates that had the dominance of political powers developed differently, the majority of the world's writing systems today would be syllabic instead.

History aside, then, the choice between alphabetic and syllabaric writing is really an arbitrary one, and the number of phonemes isn't really that largely determined by the dimension of space. So, 100 to 200 letters in an alphabetic writing system seems unrealistic: it defeats the purpose of it being alphabetic in the first place, and isn't really that necessary if we assume a straightforward generalization of the human vocal apparatus to higher dimensions, which entails a much smaller inventory of phonemes than has been postulated.
quickfur
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### Re: 4 dimensional writing

Having a given number of letters only defeats the purpose if the letters is wildly different to the number of phonemes. English has phonemes that do not have separate sounds (like gh in might, corresponds to german ch), It has phonemes that have no letter (like þ). English has six vowels, but because the ladin alphabet has only five vowels, it is practice to think of five vowels. (The sixth vowel is usually written -oo-).

None the same, postulating something wrong is better than saying nothing at all.
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wendy
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### Re: 4 dimensional writing

wendy wrote:Having a given number of letters only defeats the purpose if the letters is wildly different to the number of phonemes. English has phonemes that do not have separate sounds (like gh in might, corresponds to german ch), It has phonemes that have no letter (like þ). English has six vowels, but because the ladin alphabet has only five vowels, it is practice to think of five vowels. (The sixth vowel is usually written -oo-).

None the same, postulating something wrong is better than saying nothing at all.

Actually, English has a lot more vowels than 6. Most English speakers only think in terms of 5 or 6 vowels because they associate it with the orthography, but actually, there are many more. Furthermore, the precise way in which the written vowels map to the spoken vowels vary across regional dialects, making it difficult to make universal statements about the precise system of vowels at work, which unconsciously reinforces the idea of a vowel corresponding with a specific orthography, even though they are clearly pronounced differently in different dialects.

Regardless, in most varieties of English, there is a clear distinction between the vowel in "beet" and the vowel in "bit"; between the 'a' in "father" and the 'a' in "back"; between the 'o' in "owe" and the 'o' in "origin"; and between the 'u' in "buck" and the 'u' in "puke". That's at least 10 distinct vowels. Then there's 'oo', as you mentioned, and, depending on dialect, you have rhotic vowels like the 're' in "timbre", and 'ar' in "far", for example. There are also lateral vowels in some North American dialects, such as the second syllable of "mantle", which is a cross between what is normally thought of as a consonant and a vowel pair.

In any case, one of the reasons English spelling is so inconsistent is because it's trying to represent about 11 or more distinct vowels with only 5 letters, not to mention the difference between the written consonants and the spoken consonants. For example, the /th/ sound which must be represented as a digraph, and the horrific tangle that is the fine distinctions between 'c', 'k', and 'q'. Then there's this whole thing about silent letters, which are historical relics that have mutated into context markers for shifting vowel values (e.g., the difference between "mat" and "mate", "spit" and "spite", "writ" and "write", etc. -- although in some dialects they actually represent the same vowel).

In other words, if one were to objectively evaluate English spelling versus English pronunciation, one would have to conclude that the number of letters (as well as the letters themselves) are 'wildly different' from the number of phonemes in the language.

As far as languages go, English and French are two of the worst in terms of an inconsistent mapping from the written language to the spoken language. Other alphabet-based languages such as Spanish, or even Russian, for that matter, have orthographies that are much closer to the spoken language. Both of these have had a historical spelling reform within the last 100 years or so, whereas English hasn't, and seems unlikely to. Pre-reform Russian also had silent vowels sprinkled everywhere---historical relics of short vowels that haven't been pronounced for at least a millenium or two, which have become palatisation markers. Happily, the reform did away with most of them except where they serve a useful purpose (although one must admit that said useful purpose is in the same nature as the English silent vowels: to shift pronunciation of letters surrounding it because the written letters do not fully represent all the spoken phonemes).
quickfur
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### Re: 4 dimensional writing

One should differentiate between phoneme and what is written in IPA. IPA tries to emulate the language in a universal style. In doing so, it records the sounds as produced, not the phonemes as written.

English has vowels a, e, i, o, u, and oo. These can occur either short, eg fat, met, fit, fot, fut, foot, or long fate, mete, mite, mote, mute, moot. It has a number of diphthongs, like oi. A phoneme can change in the presence of other phonemes, for example /fifth/ is pronounced fift, because fth -> ft. The general -t suffix, that turns an adjective into a quantity (warm -> warmth, high -> height, long -> length), gives variously t, th as the previous is a fricitive or not (gh is a lost fricitive).

English is pretty consistent in mapping phoneme to sound, except where the Normans mangled it (ough). You must recall that when English was committed to print, that it was a spell as ye speak kind of writing. The sounds change a bit. Some dialects do not differenciate between wh and w, or do not pronounce the gh in light or might, but these distinctions are elsewhere made.

In english, the a in fat and the a in fate are short and long of the same sound. It's just that IPA writes these as æ and ei respectively. Further, i, y, u and w act as semi-consonants. Asia is indeed phonetically pronounced. It's a.s.i.a, So we have s falling between two vowels, giving azia. i falls before a vowel, and is pronounced as a consonant (y), so we get azya, and sy, zy, ty, dy cause palatisation, so we get sh, zh, ch, j here: so we get azha.

A word like nation, on the other hand, should give /nacion/. in the spanish fashion. This is how it is pronounced. The t is really a c, becomes s before i, i becomes y before o, so we get nashon. The phoneme in ME (sh), comes variously from sk and si (or sy). Ch is variously /ci/ [eg cheese], or ty [orchard = hort.yard, gotcha = got ya], apart from its imported french (sh) and greek (k) imports.

Still, it's sounds in context, not the raw sound itself, that one makes into letters, and it is indeed the letters of the word that one tries to articulate, not the phonetics.
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wendy
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### Re: 4 dimensional writing

One should differentiate between phoneme and what is written in IPA. IPA tries to emulate the language in a universal style. In doing so, it records the sounds as produced, not the phonemes as written.

English has vowels a, e, i, o, u, and oo. These can occur either short, eg fat, met, fit, fot, fut, foot, or long fate, mete, mite, mote, mute, moot. It has a number of diphthongs, like oi. A phoneme can change in the presence of other phonemes, for example /fifth/ is pronounced fift, because fth -> ft. The general -t suffix, that turns an adjective into a quantity (warm -> warmth, high -> height, long -> length), gives variously t, th as the previous is a fricitive or not (gh is a lost fricitive).

English is pretty consistent in mapping phoneme to sound, except where the Normans mangled it (ough). You must recall that when English was committed to print, that it was a spell as ye speak kind of writing. The sounds change a bit. Some dialects do not differenciate between wh and w, or do not pronounce the gh in light or might, but these distinctions are elsewhere made.

In english, the a in fat and the a in fate are short and long of the same sound. It's just that IPA writes these as æ and ei respectively. Further, i, y, u and w act as semi-consonants. Asia is indeed phonetically pronounced. It's a.s.i.a, So we have s falling between two vowels, giving azia. i falls before a vowel, and is pronounced as a consonant (y), so we get azya, and sy, zy, ty, dy cause palatisation, so we get sh, zh, ch, j here: so we get azha.

A word like nation, on the other hand, should give /nacion/. in the spanish fashion. This is how it is pronounced. The t is really a c, becomes s before i, i becomes y before o, so we get nashon. The phoneme in ME (sh), comes variously from sk and si (or sy). Ch is variously /ci/ [eg cheese], or ty [orchard = hort.yard, gotcha = got ya], apart from its imported french (sh) and greek (k) imports.

Still, it's sounds in context, not the raw sound itself, that one makes into letters, and it is indeed the letters of the word that one tries to articulate, not the phonetics.
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wendy
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### Re: 4 dimensional writing

wendy wrote:One should differentiate between phoneme and what is written in IPA. IPA tries to emulate the language in a universal style. In doing so, it records the sounds as produced, not the phonemes as written.

One must distinguish between phones, the actual sounds themselves, and phonemes, the groups of phones that native speakers regard as the same logical sound. The IPA (tries to) represent all phones, but not phonemes, because phonemes are specific to a particular language and cannot be universal.

English has vowels a, e, i, o, u, and oo. These can occur either short, eg fat, met, fit, fot, fut, foot, or long fate, mete, mite, mote, mute, moot. It has a number of diphthongs, like oi. A phoneme can change in the presence of other phonemes, for example /fifth/ is pronounced fift, because fth -> ft. The general -t suffix, that turns an adjective into a quantity (warm -> warmth, high -> height, long -> length), gives variously t, th as the previous is a fricitive or not (gh is a lost fricitive).

The point is that the written vowels are not the same as the spoken vowels: there are only 5 written vowels, but the spoken vowels vary in length, as you pointed out. The 'u' in 'rut' is not the same phoneme as the 'u' in 'flute', even though they are written with the same letter. For that matter, the vowel in 'read' (present) and the vowel in 'read' (past) represent two distinct phonemes with identical spelling, even in context.

English is pretty consistent in mapping phoneme to sound, except where the Normans mangled it (ough). You must recall that when English was committed to print, that it was a spell as ye speak kind of writing.

As is the case with all alphabetic languages, but pronunciations shift over time while spelling does not (except during reforms), so the longer the time that has elapsed since the initial system was set down, the more it will diverge from actual pronunciation. As you point out, this divergence is systematic, and is context-dependent---this is well-known in all languages. But this does require one to effectively apply 200 years' worth of sound change to the written spelling in order to correctly derive the current pronunciation of the word. The original phonemes represented by the spelling are not the same as the phonemes as understood by modern speakers, even though they do map more-or-less consistently.

[...]Asia is indeed phonetically pronounced. It's a.s.i.a, So we have s falling between two vowels, giving azia. i falls before a vowel, and is pronounced as a consonant (y), so we get azya, and sy, zy, ty, dy cause palatisation, so we get sh, zh, ch, j here: so we get azha.[...]

Precisely--the voicing of /s/, the semivowel-isation of /i/, and the palatisation of /sy/, are all historical sound change processes that need to be applied to the written word in order to obtain the modern phonemes. No native speaker actually thinks of 'asia' as four distinct phonemes; rather, force of habit unconsciously regards 'sia' is a single unit, pronounced variously as /zha/, /sha/, /shja/, etc., depending on dialect. (That the entirety of /sia/ is regarded as a unit, as opposed to /s/ + /ia/, is clear from the fact that in other words such as /bias/, the /ia/ represents a completely different phoneme---in fact, two: long /i/ and short /a/. The analysis in that case is /bi/ + /as/.)

Anyway, the whole point is that the mapping from the pronounced phonemes to the written glyphs are not straightforward; it arises from a context-sensitive set of transformations that must be learned apart from the glyphs themselves.
quickfur
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### Re: 4 dimensional writing

How come no-one asked to actually see Oschkar's alphabet?

PWrong
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### Re: 4 dimensional writing

Probably because, no offense to him, he seems intent on merely porting the English alphabet into three-dimensional glyphs, rather than actually working out a plausible structure for a tetronian vocal system and finding suitable phonemes for such a system.

Keiji

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### Re: 4 dimensional writing

There is a problem with 4D alphabet. When tetronian sees a single letter, he can say where is top and bottom side of it, but unlike us he can't say where is "left" or "right" side i.e. where is its "front" side in his writing system (I assume that they use one-dimensional strings for writing). We could have same problem if we used shorthand-like writing systems where meaning of the letter depends on its position in string (bottom, middle or top position of a horizontal stroke).
To solve this they can start with runes that all have J-shaped form with strokes of different directions that go from different points of the vertical part of J. And the bottom part will define orientation of the letter (it's directed to the previous letter is the string).
Mrrl
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### Re: 4 dimensional writing

There is a problem with 4D alphabet. When tetronian sees a single letter, he can say where is top and bottom side of it, but unlike us he can't say where is "left" or "right" side i.e. where is its "front" side in his writing system

Actually a tetronian would write on a 3d surface not a 2d surface so a tetronian would write from left to right or right to left and top to bottom and ana to kata or kata to ana so he/she/it could not tell the difference between the left right dimension and the ana kata dimension.

Also us trionians really can't tell the difference between between the up down dimension and the left right dimension of a sheet of paper without having the paper longer in one dimension than the other. Wile most letters could be used to tell which dimension is the up down dimension and which is the left right dimensions some such as the letter Z cannot as Z looks like N accept for the fact that Z faces the horizontal dimension and N faces the vertical dimension. For instance if you had a plain sheet square sheet of paper and wrote

ZOZ
OOO
ZOZ

on it it could easily be mistaken for

NON
OOO
NON

Also I would also like to point out that most letters in our language do not have any equivalent letter that has the opposite dimensions so most letters would still be recognizable if they had the opposite dimensions. So in our language you could write from right to left instead of left to right and have the dimensions of every letter reversed and people could still read what you wrote. So tetronians could probably also have most of their letters completely unique shapes so that they could not be mistaken for another letter even if they pointed in the wrong direction and the tetronians could use the letters to tell which direction was which on the page.
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anderscolingustafson
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### Re: 4 dimensional writing

Exactly what I mean. When tetronian sees a string of letters written on 3d surface (assuming that he knows where the "top" direction is) he can guess where is front and back of the line, so he can read letters. But if there is only one letter or letters are aligned in vertical string, he has no clues about left/right/ana/kata orientation of letters other than shapes of letters themself. J-based runes have such clues - tail of "J" indicates "left", so all other directions are well defined.
And in latin alphabet we have example of 4 letters (p,q,b,d) that have the same shape (in different orientations) and some more pairs of letters (a/e, n/u, M/W) that need defined "top" direction to distinguish them. Strange thing is that in Russian there is only one pair of letters with the same shape - Р/Ь (pairs like п/и, т/ш appear only in italic or handwritten writing).
Mrrl
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### Re: 4 dimensional writing

Generally one can determine the orientation of text by the context.

For example, if you printed out this post and flipped it in various directions, it'd still be pretty obvious which way it was supposed to be read, since only one orientation would make sense.

4D might have more orientations possible, but its characters would also be more complicated, which should compensate.

Keiji

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### Re: 4 dimensional writing

This is a very interesting topic, especially if you review the history of writing systems in our own world.

The modern Latin alphabet ultimately finds its source in the ancient Egyptian hieroglyphs, which were basically pictographs. Orientation is very obvious, since if you see an upside-down person or someone standing on the wall sideways, you know that you have the wrong orientation. Now, the Semitic people borrowed the Egyptian hieroglyphs in order to write their own language, and in the process, they simplified the pictographs into fewer lines and strokes, probably so that it would be easier to write. Of particular interest is the original version of the letter Aleph, symbolized by cattle. It was a V with a stroke through it, obviously representing a cow with two horns, a V-shaped face, and probably a harness.

What's interesting is that later on, when the Greeks borrowed the idea of writing their language using these letterforms, they inverted the shape of Aleph, so alpha is written just like our letter A today, an upside-down cow, if you will. What's more interesting is that in the early days, the orientation of letters and direction of writing was quite fluid. Early Greek writing went through stages where they were written in spirals, then in a zig-zag form (left to right, and right to left on the next line, then left to right again). Some variants of the zig-zag form actually has mirror images of the letters when in the right-to-left direction.

So you can see that in the early days of writing, direction and orientation was quite fluid; it was only as time passed that things started to be codified. Our present system of writing left-to-right with line breaks is actually a relatively modern development.

In any case, it's correct that context makes it very clear which way the letters are intended to be read. Which leads to interesting plot twists in mystery novels when a short fragment of letters, which don't have enough context, are read in the wrong direction, giving the wrong word instead of the right clue to the puzzle.

Now, in our 2D writing, things are relatively simple because it's just a matter of rotating the paper in a single plane until the orientation is right. In a tetronian's 3D writing, we now have 3 parameters to orientation (roll, pitch, yaw), which means that it would be a bit harder to find what's the correct orientation of the paper.

So my guess is that the tetronians would have come up with some kind of system to indicate the right reading orientation on the paper so that their readers can quickly orient it correctly. Context plays an important part, of course, but I wonder if they would have perhaps invented some orientation marks to indicate to their reader which direction the writing is meant to be read. Perhaps something like a crossed glyph in the upper-left-front corner of the paper to give the right orientation (so readers can simply find the mark and rotate until it's in the expected place). Or perhaps have letters with characteristic descenders (vertical long strokes) and extenders (horizontal long strokes perpendicular to the direction of writing) that a reader will quickly notice and be oriented quickly.
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