3 dimensional writing?
I've been wondering about something that concerns language.
As 3 dimensional beings we have access to 2 dimensions and use it to communicate our thoughts i.e. on flat paper and flat screens.
1) Do you think higher dimensional beings (4 dimensions and above) write in 3D?
2) What would it look like?
3) What extra information would a ''letter'' in that language encode?
4) How would we store such a language i.e. what would be the paper/screen analog?
5) Has this already been discovered and is it being used to communicate secret messages by the government?:-}
Etcetera...
Thank you
PS...can I copyright this idea?:-|
As 3 dimensional beings we have access to 2 dimensions and use it to communicate our thoughts i.e. on flat paper and flat screens.
1) Do you think higher dimensional beings (4 dimensions and above) write in 3D?
2) What would it look like?
3) What extra information would a ''letter'' in that language encode?
4) How would we store such a language i.e. what would be the paper/screen analog?
5) Has this already been discovered and is it being used to communicate secret messages by the government?:-}
Etcetera...
Thank you
PS...can I copyright this idea?:-|
Comments (26)
Higher dimensional beings communicate exclusively in emoticons. The twist being that these emoticons are actually real people in various emotional states frozen in time by these beings. It's almost inevitable that at some time or another each one of us has played a part in one of their great works of literature. Or, possibly just a gas bill. Hard to know.
Use your imagination friend
Sky
--
Earth
Here, the spatial distribution of the words conveys information in a higher-order dimension than linear writing. Given a fixed syntax, the above might translate: "the sky is above the earth, and the earth below the sky". In chemistry, this is exactly what happens when we abbreviate the structural graphs of chemicals with linear ones, as when Benzene, which looks like this:
...and is abbreviated (in a lower-dimension) to look like this: C6H6. The structural graph, with it's vertices and edges, conveys more information by dint of it being of a higher order dimension than the linear formula. This becomes especially clear in chiral or mirror molecules in which the chiral orientation ('left-handedness' or 'right-handedness') of the molecule might give rise to very different bonding effects. L-alanine, for instance, is found all over our genetic code, whereas R-alanine is generally found in entirely different parts of nature;
In this case, the higher-dimentionality allows one to convey information that actually can't, in principle, be captured by the linear formula. Moreover, one might think of a moving picture as an even higher-order language: by adding the dimension of time, we can add additional information which which takes it's 'lower dimensional' counterpart alot longer to convey. Of course from here you can open fascinating questions into the nature of information by taking into account compression (as with .zip files) and so on. In any case, high-dimensional language isn't at all a far fetched idea. It's actually quite pedestrian - all around us in fact.
However, even in your examples we are still stuck in 2D, employing conventions to relay the info that we're dealing with 3D objects.
Wouldn't a 3D script/alphabet kind of release us from restrictions inherent in 2D scripts?
I would question your presumption that extra dimensions would increase the information content of a message. Instead it works the other way round.
A code gains power by a constraint on dimensionality. DNA, neurones, speech and computation show that by the way they reduce syntactical structure to a one dimensional sequence of zero dimensional bits.
You can't get more minimal than binary code - a mark and its absence. Yet in representing the least amount of physics, it has the fewest limits when it comes to encoding physical states.
One has to step outside the world that one wants to describe. So reducing representation towards zero dimensionality is the natural trend, not seeking to increase it so that the message has to physically occupy more of the world.
The elements a,b,c, for example, might be said be belong to set X, and the ability to speak of and manipulate an entire set X (without referring each time to all the elements of the set) allows for some incredibly powerful and economical means of control. Thus in math for example, one can perform mapping operations on entire sets of numbers in order to produce non-trivial results. This is more or less how Cantor argued for the existence of infinite sets of different sizes - a result whose importance is hard to understate. Higher dimensionality can be a massive inconvenience for thought. Again, notice how much easier it is to speak of C6H6 than it is to speak of:
You can't actually do anything in or even access 2D. As with many things, the idea of that is purely a mathematical construct, or it's a kind of game we can play when we abstract relations.
However let me draw an analogy to convey my intent.
Proteins have 4 levels of organization/structure.
The primary structure is linear in which the main code is simply the sequence of amino acids. In this primary form the protein molecule is functionless.
Then we have secondary structure consisting of helices and/or sheets. This structure is determined by theprimary structure. It is still functionless.
Intermediately we have the tertiary structure wherein the secondary structure elements (helices and sheets) determine how the protein folds into a 3D molecule. This structure and level of organisation is now a functional element of the human body.
Lastly we have quarternary structure in which different tertiary structure proteins interact to form a functional combination of molecules.
I envisage something like that with language. As the dimensions of written language increase its functional repertoire should (I think) increase.
Please refer to my reply to apokrisis
I would suggest we do have something like this already too, except this higher-order dimensionality resides in nothing less than human behaviour itself, rather than language as such (or rather, one should say that language just is this holistic phenomenon involving both words and behaviour). Consider, for example, Gregory Bateson's famous theory of play. For Bateson, play always involves at least two 'levels' of communication. First there is the level of 'what is said', and then there is the 'meta-level' regarding how the object-level statement ought to be understood. The example he gives is of the difference, in animal play, between the playful bite and the aggressive bite. The aggressive bite is straightforward, but a playful nip is a bite that comments on itself, as it were, to indicate that it is 'not really a bite'. Here is how Bateson puts it:
"Now, this phenomenon, play, could only occur if the participant organisms were capable of some degree of meta-communication, i.e., of exchanging signals which would carry the message “this is play.” ... Expanded, the statement “This is play” looks something like this: “These actions in which we now engage do not denote what those actions for which they stand would denote.” ... If we now substitute “which they denote” for the words “for which they stand” in the expanded definition of play, the result is: 'These actions, in which we now engage, do not denote what would be denoted by those actions which these actions denote.” The playful nip denotes the bite, but it does not denote what would be denoted by the bite." (Steps to an Ecology of Mind, "A Theory of Play and Fantasy").
Would this not be something analogous to the multi-level organisation of the protein? And of course, one can add to the above example, such that play itself may or may not be communicative of flirting, say ("this play is flirting/this play is not flirting"). There is nothing, in principle, that limits the 'levels' upon which meaning can function (apart from our own cognitive capacities perhaps). Would this not be, in some sense, the 3D writing you're after? Is there not already a kind of multi-dimentionality inherent to meaning and language in everyday life already?
The goal is easy and fluid transcription, from 2D to 3D to 4D and back.
Talk is in a sense more complex than writing. Writing can convey more and more complex ideas but talk is in itself like Bateson's play but with the variables that are operational greatly multiplied. David Lewis's 'score-keeping' is an example of a concept for how we might sustain, in his example, a septuple of variables in any given conversational language-game. They might be matters like mutual power, relative emotional states, relative knowledge of the matter in question, how many people are in the game, how many dialects are being used, what different interlocutors' intentions are, mutual understanding of body-language, how the environment interacts with the spoken word, the institutional setting, and so forth.
I think there might be a confusion in the op between 'dimensions' and 'complexity'. As apo says, less might mean more, depending on what the beings want to communicate or to have communicated to them, since one can build great complexity from binary beginnings regardless of whether one thinks of the resulting constructs in 'dimensions'.
I imagine other beings who exploit the entire range of music as communication for instance: the complexity a symphony can convey is mind-boggling.
Speculation:
How about a new form of Braille? ...a way to combine, to build a language on more than just the sense of vision. Not more meaning but perhaps a fuller more felt sense of meaning: Touch + Vision . Not as a third dimension but as a different sense modality.
Consider again the essential trade-off. Using SX's example, you could create a language for talking about organic chemistry using 3D plastic molecular models. And we already do. You can buy colour coded balls to represent the different atoms, little sticks to represent the atomic bonds. We can thus speak about organic chemistry in a fully dimensional fashion that conveys essential information better than flat drawings or serial verbal descriptions.
But being so physical, there is not a lot else you could ever talk about with this particular language.
On the other hand, a binary code able to express a pattern of Boolean switches has an expressiveness that is computationally universal. It is a language that can be used to talk about "anything" because it is not bound by the physicality of any thing.
A computer language can code for a 3D virtually reality display that simulates little plastic ball and stick models of molecules - and add animation to give the further dimension of action in time. But a second later, the same computer speaking the same binary code could be "talking" about any other 4D virtual reality one could possibly imagine.
So fewer actual dimensions for a language results in a greater power to then speak about (that is, reconstruct) any number of dimensions.
Note how if you really do what to imagine 4, 5, and n-dimensional worlds, you need to speak the even more pared down language of maths. Less is more because the simplest building blocks have the fewest constraints on their freedom of combination.
But again, the restrictions of articulate speech - the way a serial flow of words is more restrictive on the forming of thought - is in fact its advantage. In filtering out more of the potential semantics, having to make a single step at a time really focuses the meaning that gets expressed. It makes every sentence special that you chose to say just that and not all the other things that could have been said (and at the same time too in a language with higher dimensionality).
As for extra dimensions, who knows, there may be wave forms that carve out information and processes that cannot be referenced by our brain waves, but for now, the universe we live in is more than enough challenge for me.
An architectural model of a building, or an astronomical model of the solar system, are examples of three dimensional symbol systems. What they symbolise in three dimensions is usually easier and less ambiguously symbolised in words. But unlike words the models show what they describe: ie they exemplify certain relations, proportions and so on. They also lack the syntactic and semantic disjointness of verbal descriptions, ie a white wall does not only symbolise white but what it looks like in a continuum of various light conditions.
This is generally the case, but it's important I think to remember the power of writing to participate in these kinds of variables. Think here of say, Jonathan Swift's A Modest Proposal, or basically any work of satire - it's essentially 'play' (in the above sense) operating at the level of writing itself, where the higher-dimentionality is nonetheless embodied not in the words but in the social milieu in which they are placed. Many of the variables you mentioned - education level, political affiliation, power relations can and are at work in here too. And this sort of thing is operative at the level not just of meaning but even grammar itself. As Deleuze says somewhere, 'a rule of grammar is a power marker before it is a syntactical marker' - hence the racial, social and power relations that play out with the use of ebonics, say.
However I wish to confine myself to the written word i.e. symbols that convey info. Take the English alphabet. Each letter represents a sound and we have to spell out our thoughts and emotions, literally.
Consider the following English expressions.
''I'm good'' said John angrily
''I'm good'' said John sadly
''I'm good'' said John happily
As you can see we need to, well, spell everything out.
Now think of a cone (a 3D shape). It could be used to represent the the sentence ''I'm good'' instead of individual sounds and then we could point it to the left to convey anger, to the right to convey joy and so on. Simpler and more compact isn't it?
I think the Chinese language with its ideograms comes closest to my idea. However it's obviously complicared by having to limit itself to 2D.
Like this?: ? ??
Again, almost everything that can be represented in a higher-dimensional language can be presented in a lower-dimensional one in a simpler way. Indeed, the three triangles here are in fact simpler than cones precisely because they discard the additional 3rd dimension of depth. If you want your example to work, you need to utilise the unique dimension of depth as a vector of information, not orientation: the differences between the three sentences will need to be encoded in the volume of your cone, not in it's orientation, because this is the one thing your lower-dimensional language, by definition, doesn't have.
Indeed, one can imagine something like a 'topological language', in which every slight transformation of a three dimensional shape might correspond to a different 'word' or meaning. This, for example:
...might be an entire essay. The problem of course is that this kind of language, if you could call it one, would be unimaginably hard to learn or understand. If the syntax of this language are the transformation rules between one shape and another (when the torus begins to thicken on the left, say), and the semantics the distinct shapes the model takes on as it transforms, one would have to learn and know (and have the recognition capacity for!) an almost infinite amount of minute, impossible-to-reasonably-track changes in volume. It's possible that some higher being might be able to communicate with changing shapes, but we certainly wouldn't be able to. Or maybe just a super-advanced computer.
This is why even Chinese, which has a very tight morpheme-grapheme ratio (i.e. every character tends to designate a single word) still needs to have multiple characters. Think of it as a trade off along two axes: one can either have a limited alphabet base and employ combinatorics to craft meaning (as with English with it's limited letters and varied manners of combining them), or one can have a very large character base which employs combinatorics in a limited manner. With a very high-dimensional language like the topological one above, what you're asking for is a something like a language with ONE character and no combinatorics - only topological transformation (assuming one can take a shape as a character) - it would be (almost?) entirely analog language (only degrees of transformation form one shape to another, rather than discreet units).
The problem, of course, is that we are simply not cognitively equipped to deal with any kind of language of that sort. Most fluent Chinese speakers know roughly 8000 or so characters, beyond which the words begin to get pretty obscure (Chinese having 20000 characters give or take). What you're after though, would be to multiply this to infinity, as it were: there would no doubt be a certain simplicity to it (especially one you scale your dimensions up beyond 4 or 5) in which case the 'changes' would be practically imperceptible. But it would also be unlearnable, and more or less unrecognizabe as a language at all.
This is why, as humans, who can only do so much with language, we have an entire 'extra-linguistic' scaffolding, that allows us to makes sense and multiply the meanings that language can generate. This is what I was getting at when I brought in the notion of play and satire, which has to do, once again, with human behaviour. We employ our environments as much as our words to communicate, because we know that words can only do so much given our particular cognitive capacities. We 'compensate' for our inability to deploy higher-diemsional languages by employing the entire world around us instead, as it were, as a means of communication, to bring it 'into the fold' of communication as it were, rather than 'sticking to the written word'. This is equally why we are so much more than symbol-manipulating machines. Anyway, super interesting stuff to think about.