Tetronian written language

[pat]

Our writing is basically two-dimensional shapes, strung in a one-dimensional list that's wrapped to fill two-dimensional pages.

Tetronians would be able to use three-dimensional shapes to fill three-dimensional pages. My guess is that it would still make sense for them to string the letters together in a one-dimensional sequence. If they tried to do otherwise, they'd run into the same problems that we would trying to write our words two-dimensionally... you'd be wasting space:

Code: Select all

Ti  cud  b  oe  wy  w  mgt  pc  wrs  i  2D
hs  ol   e  n   a   e  ih   ak  od   n  -


So, the questions are:

Do people agree that the text would be one-dimensional strings of characters wrapped to fill three-dimensions?

Would tetronians bother with three-dimensional characters?

My sense is: yes and yes. Three-dimensional characters would be much more efficient. But, one would have to watch out, maybe, for characters that are 90-degree rotations of other characters.??

[Keiji]

I think they should use 3D letters and other characters, to benefit their character set.

For example, they could use (assuming they work math in base 14 - elsewhere on this board people have theorised about having 14 fingers on a tetronian body):
0) - 0
1_ - 1
1/ - 2
3) - 3
5) - 4
5= - 5
6) - 6
7_ - 7
7\ - 8
8\ - 9
8/ - 10
4- - 11
4] - 12
4= - 13

where the first character is the front-view of the 3d character, and the second is its extension model for the third dimension. If you don't understand that I may draw some pictures to explain.

I haven't thought about letters yet.

Do people agree that the text would be one-dimensional strings of characters wrapped to fill three-dimensions?

Yes, I agree on that, it is logical.

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Since PHPBB can only split by posts, I've had to quote the part-posts that were here before. ~iNVERTED

A swock is just the 3D cell of a tetracube, so you'd run into the same problem.

But, one would have to watch out, maybe, for characters that are 90-degree rotations of other characters.??

When learning to read, kids tend to have trouble with the letters
"b, d, p and q", but we use them anyway. It might be more complicated for tetronians though.

In 2-D English, we start making 2-D letters at the top-left of the page. We merrily string them together until we get to the top-right of the page. Then, we skip down a little bit and back to the left. We continue in the manner until the page is full.

Here, the page itself would be 3-D. So, imagine a rectangular prism. we start making 3-D letters at the top-left-ana of the page. We merrily string them together until we get to the top-left-kata of the page. Then, we skip right a bit and back to the ana. We continue in this manner until the we are at the top-right-kata of the page. Then, we skip down a little bit and back to the left-ana. We continue in this manner until the page is full.

I can fill a 3-D rectangular prism with small 3-D cubes. I need only specify which order to put them into the rectangular prism to be useful for reading and writing.

[Neues Kinder]

I think their alphabet would be a lot more complex than ours because they could write their letters in 3D, and the upshot to writing in 3D is that you can make so many different 3D counterparts of 2D symbols. Take the letter "A" for example. All we can make to represent the letter "A" is a triangle w/out the base divided by a horizontal segment. Some of the possible 3D counterparts for that symbol are: a cone w/out the base divided by a horizontal circle, a triangular prism w/out the base divided by a horizontal rectangle, a tetrahedron w/out the base divided by a horizontal triangle, a rectangular pyramid w/out the base divided by a horizontal rectangle, a pentagonal pyramid w/out the base divided by a horizontal pentagon, etc. All of those shapes could be used to represent different variations of the pronunciation of the letter "A", along with all the other letters with their corresponding 3D counterparts, making it easier to use letters to approximate the correct pronunciation, unlike our letter system - especially in English - where you have to guess at it and have like a 10% chance of getting it right. The tetronians' alphabet would probably have close to 150 letters in it, which - since they have 4D brains and matter is more compact in their world so there would be a lot more brain cells - should be a snap to memorize.

...If only the Chinese had 4D brains to very easily memorize their entire 3,000-letter alphabet...

[Keiji]

While on the subject of pronunciation, I created an "ultimate alphabet" not so long ago that is pronounced exactly how it's written. 20 consonants and 16 vowels. See, you don't really need a huge amount of characters to have a perfectly pronouncable alphabet.

You get a "vowel" or "consonant-vowel" pattern for each syllable (reminds me of Japanese...). Then there's two new puntuation symbols - the interpunct (seperates each syllable) and the dit (acts as a silent vowel, e.g. the word most = MÖ·ST'), as you can't pronounce a consonant without a vowel.

If anyone actually cares, I'll post the rest of my notes up here for you later.

[Neues Kinder]

Well, I guess it's true that you don't need to construct an alphabet with every single character form that you can think of, because if we did there would be at least 5,000 letters in our alphabet, mostly made up of lots of squigglies and dots and all sorts of scribbles that the person quickly thought up to get finished with the alphabet as soon as possible and get on with his life, but there definitely would be more letters in the 4D alphabet.

As far as pronunciation goes, there would prabably be more vowels and consonants, and some of them very much unlike ours, because tetronians might have internal structures in the mouth and throat that we don't have because of the complexity of their physical form. It's impossible to describe exactly what type of consonants and vowels they would make, because we can't utter them because of our primitive form. So it's impossible to imagine exactly what they would be like.

And as for being confused with one letter being a rotated version of another, it is to their advantage that there are so many possibilities of a letter that they shouldn't have that problem.

[Keiji]

Well, I guess it's true that you don't need to construct an alphabet with every single character form that you can think of, because if we did there would be at least 5,000 letters in our alphabet, mostly made up of lots of squigglies and dots and all sorts of scribbles that the person quickly thought up to get finished with the alphabet as soon as possible and get on with his life, but there definitely would be more letters in the 4D alphabet.

Just because there are more possibilities doesn't mean that the alphabet is destined to be bigger...

As far as pronunciation goes, there would prabably be more vowels and consonants, and some of them very much unlike ours, because tetronians might have internal structures in the mouth and throat that we don't have because of the complexity of their physical form. It's impossible to describe exactly what type of consonants and vowels they would make, because we can't utter them because of our primitive form. So it's impossible to imagine exactly what they would be like.

Yow! I never thought of that. Of course they'd be able to make a huge number of different sounds.

And as for being confused with one letter being a rotated version of another, it is to their advantage that there are so many possibilities of a letter that they shouldn't have that problem.

You can do things without rotations in 2D lettering, anyway. I came up with a script that has no rotations, designed for my alphabet.

[wendy]

One can use Zipf's laws to decide approximately how big the base and alphabet is in any given dimension.

Base ~ 3**(n-1), Alphabet ~ 5**(n-1).

The selection of these numbers is to do with a section of solid plane, and the capacity for people to recognise patterns.

So in 4D, we expect a base like 30, and an alphabet of 120 characters.

W

[Batman3]

Would Zipf's laws be different in 4d? Can anyone elaborate on them? I cannot find them on the internet even for 3d.

Re:4d-brains a 4d man would have 3 eyes to see in 4d, just as we have 2 eyes to see in 3d. The Optics, I think, would be the same since the light-field eq'n would be the same and the light would bend in a similar manner for different speeds of light within different materials(as opposed to in a vacuum). A 4d lens would be the same but it woud have another dimension to bend into: like a compressed hypersphere. The eyeball would just be a solid hypersphere. The reason he'd have 3 eyes is that just as we see horizontally 2d he'd see horiontally 3d. The location of his eyes would not be in a straight line(he'd already hace 2 for that) but the third would be placed perpendicular to the vertical direction and on the front of his 3d face's hypersurface. Behind his 3d hyperface and his eyes would be his brain.

Has anyone else noticed that the 4d world is more bitter than the ordinary world I live in. That is, to imagine it? I have 6 theories about where the 4d is around us: (1): it isn't there. (2) It is so bitter we can hardly deal with it. (3) We are in it but we are only scum on the surface of a 4d ocean and don't look up or down. (4) We have solid barriers on either side of us physicaly to prevent physics from leaking out. (5) It is there but there is nothing material there so we don't bother with it. (6) We have very bad 4d teeth.

[wendy]

(7) Microsoft Windows pushed OS/2 out into the cold.

[miseleigh]

Why would a tetronian need 3 eyes to see in 4d? I would think that each of his eyes could see in 3d, (being hypershperes and all) and then he would approximate 4d vision with two eyes they way we approximate 3 with parallax with our own eyes.

A bionian would still need two eyes to actually see anything in 2d rather than 1d.

And the way I understand it, light wouldn't be affected at all by what dimension it's in, since it is energy and the only 'dimension' it has is wavelength.

I don't know about the 4d world being more bitter. It just sounds like you're jealous of the tetronians and won't admit it....

[Batman3]

A nononian would need one eye.
A mononian would need one eye.
A bionian would need 2 eyes.
A trionian would need 3 eyes.
A quadonian would 4 eyes.

Each to see in parallax.

Why our creator was so ungracious to give us and the animals only 2 eyes so we could only see 3d by observing with only a horizontal parallax and not a vertical, I can't guess.

Or perhaps he would have given all of us onians only one eye.

This is crazy.

[pat]

The point of parallax is to tell the distance between you and an object. It measures distance perpendicular to your retina. If you were a 4D creature with 3D retinas, you'd do just fine with two eyes. If you were a 4D creature with 2D retinas, you'd only do marginally better with three eyes than two.

[Hugh]

If you were a 4D creature with 2D retinas

Could a 4D creature only have 2D retinas?

[PWrong]

There's an interesting question. I guess it's possible to have a very thin retina and get away with it.

In 3D, there are many thriving ecosystems confined to an approximately 2D surface (like my carpet), and for its inhabitants it might be efficient to evolve 1D eyes. There's no point looking up or down if everything that concerns you is in the same plane as you. The advantage would be more time to concentrate on the part of the world that concerns you.

Even if a 3D animal had normal 2D retina , it might learn to ignore them. I suspect that ants born in a flat ant farm might not know or care about left and right.

Similar circumstances might arise in 4D. There might be organisms that only care about the 3D surface of their planet, and never need to look up. They would either evolve a 2D retina or ignore everything except a 2D section of their vision. Such creatures would probably be like insects, if not smaller. The more advanced animals would be likely to take advantage of the extra degree of freedom.

[Batman3]

If tetraman had 3 eyes could he get away with 3 only-2d retinas? I mean for parallax.
If I had 2 1d vertical parallel retinas, could I make out the parallax of 3-space? I think I could. It gives me a headache imagining it because it seems like it would be a very strange way of seeing. Worthy of tetraspace. I like tetra-aches

In 4d, the 3 2d-retinas would also have to be parallel(.?) Ouch! this is almost too hot to bear! Experiencing the heat on these retinas I can kind of make out dark-light hitting the retinas, believe it or not. I can't stand to see what's out there in the 4d bad-space with this insect retinas.

Analogously I suppose, could the reason we can't see infrared or ultraviolet radiation be because they are too hot with daark-light for us to want to deal with? This reason also has a Biblcal basis, but I guess we don't want to get into that in here, where it's hot. Anyway I'm not competant.

[Hugh]

Hi PWrong,

I guess it's possible to have a very thin retina and get away with it.

I'm wondering about the different possible definitions for "2d" and "3d" retina. Could a 2d retina be defined as one that sees an extending 2d x/y plane in a glance? Does a 4d being with only a 2d retina have to have a retina that is "very thin", or can it just be that it can only look in one direction with an x/y plane at a time?

Could a 3d retina be defined as one that sees an extending 3d x/y/z cube view in a glance? A dragonfly has wrap-around compound eyes with thousands of facets that can see in every direction around itself. Would this be considered a 3d retina?

Similar circumstances might arise in 4D. There might be organisms that only care about the 3D surface of their planet, and never need to look up. They would either evolve a 2D retina or ignore everything except a 2D section of their vision.

This is interesting. Evolution of vision in a 4d environment. How would such a 4d being see that 4d space with only "a 2d section of vision"? What would its environment look like? Only a 3d space? As vision evolved in a 4d environment, would it start off as only 2d plane vision in one direction within that 4d space?

Also, could a 4d being have a 3d retina but only be able to visualize a 2d x/y plane of vision of it on the viewing screen in its brain at any time?

[wendy]

You only need two eyes to make parallax. The retina does the location, and the differences in percived angle does the distancing.

Many prey animals have only one eye on each side of the head. Animals that have two eyes facing essentially the same direction are generally preditors, who rely on the ability to make ranging.

[PWrong]

I read about an experiment, in which they brought up cats in a room with no vertical lines. After they were released, they kept bumping into table legs. Similarly, if you lived in 4D but your environment was almost entirely 3D, you might learn to ignore the extra dimension in your retina, and it would just dissapear from your consciousness. You could do an experiment to test this in 3D. Put some mice in a thin glass thing like a big ant farm. When you release them, see how the extra dimension affects them.

Analogously I suppose, could the reason we can't see infrared or ultraviolet radiation be because they are too hot with daark-light for us to want to deal with?

That's probably part of the reason. Some animals probably can see other
wavelengths. Most are colour blind. Apparently birds can "see" magnetic fields, as if they have a compass in their head. If you hold a magnet near them, they don't know which way to migrate.

A dragonfly has wrap-around compound eyes with thousands of facets that can see in every direction around itself. Would this be considered a 3d retina?

No, it's just lots of 2D retinas. I'm not sure why insects have those eyes, it's probably something to do with being small. But it wouldn't need a 3D retina because it's only looking at a 3D space.

If you could see every part of the spectrum, detect all force fields, even see particles other than photons, like neutrinos, I wonder what life would be like. You'd be able to see the inside of everything, as well as the outside, just like a 4D being. Although initially the view would be different, your brain might adapt so that you feel like a 4D being watching the 3D space below. That would be similar to having a 3D retina.

[wendy]

Insects have lots of eye-spots because the capacity to see is governed by the size of the radiation, not the animal. In order to see in the visual range, the ordinary pupil and eye does not work on that scale. So what insects do is to have an array of individual receptors, and use variations on these to see.

Most of our light we see lies in a very fine range: 3800 Å to 7600 Å. If we want to see more, we would need a greater range of recptors in the brain. Colour-blindness would be an obvious problem.

W

[moonlord]

wendy: "Most of our light we see lies in a very fine range: 3800 Å to 7600 Å. If we want to see more, we would need a greater range of recptors in the brain. Colour-blindness would be an obvious problem."

I thought the eyes are responsible for the wavelength of the EM radiation we can see. Anyway, I don't agree that color blindness would be a problem. More types of receptors specialised in 'fine ranges' as you called them.

[wendy]

The visiable spectrum is partly defined by the extent of UV and IR rays, which are variously filtered out.

It does well to try to keep these in a single octave, because anything more makes for very difficult cameras.

It is also true that the eye has several kinds of receptors for different colours. The three primary colours are not there for nothing!

Colour blindness involves a whole colour-thread not being parsed. If we had six different kind of receptors, then we would have many more potentials and grades of colour blindness,

W

[kingmaz]

I think the earlier analogy with Japanese syllabic systems is interesting.

Is it not feasible for tetronian written language to be effectively our own alphabet but with individual letters combined in a 'cell' to make words? For instance:

IT
COULD
BE
IMAGINED
LIKE
THIS

Where the perspective is from left of the left hand edge of this page. If one viewed these letters on page in this way it would read approximately:

T ? B ? ? ?

Where ? is an unintelligible mess of "overlaid" characters.

I suppose this would approximate to Fred imagining a cube thus: [] [] [] [] [] []
rather than a true tetronian perspective.

[Keiji]

Well, that is a slight waste of space - it'd be like us writing everything with just one word per line and would store little more information per swock than we can per sheet. If they were going to do it like this, I'd imagine there would be a fixed number of symbols per word, or at least a fixed "space" in which to write the symbols for each word (like Korean letters), so they could write using all three dimensions of the swock fully.

[papernuke]

Should they not have 2D "planes" of ink used to construct 3D letters?
You would need an awfully large amount of 1D strokes to make a 3D letter, and how would they be able to create a 1D pen?
it would be, to us, like writing with a 0D point.
The 2D planes of ink would just be stacked together to create 3D letters, although the inside volume is not filled in, thereby conserving ink.

[Keiji]

No it wouldn't. You need to learn that not everything increases dimension like that

People in any dimension would still write with lines and curves. It doesn't take much more effort to write a 3D letter than a 2D letter.

A pen in (n+1) dimensions is a 1fnl construction.

[kingmaz]

Well, that is a slight waste of space - it'd be like us writing everything with just one word per line and would store little more information per swock than we can per sheet. If they were going to do it like this, I'd imagine there would be a fixed number of symbols per word, or at least a fixed "space" in which to write the symbols for each word (like Korean letters), so they could write using all three dimensions of the swock fully.

Yes, that is the point I was trying to make, though not very well.
The idea is that one word is inserted per swock cubelet, rather than one letter per space on a conventional sheet.
I was trying to get across a sense of the information expansion gained by using a swock over a sheet, it's far more than writing some letters in another axis.

You could write a plane of ink in 2d, if your pen was thick enough - or rather a plane segment.
What would an equivalent thick marker be for tetronians?
A spherinder?