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.