I've allways thought that animals are logical. Hence it's no surprise that the species which develops a highly advanced complex system to communicate called language, which is capable of using formal definitions and a much greater range of expressions than any known system of animal communication, can then develop formal languages. Above all, push that logic to a higher level into a formal system, basically into mathematics.

Yet the question is are these the two, gesture and math, opposites of the spectrum? The reason why I ask is that animals can count. And if it's not mathematics, a counting system of "none, one, two, three, many..." it still counting and counting is part of mathematics. Now the vast majority of species don't use these terms in their language (which typically limits to "Danger!" and "This is my territory!"). I wouldn't be surprised if some advanced hunters like Orcas would have terms for counting prey in their communication system (at least "many" and "few") or even something more advanced. Perhaps the other extreme from gesture could be some postmodern meta-analysis of language itself and not mathematics. Or basically philosophical study of language. That would feel very remote from the languages that animals use or even can comprehend.

In the Brahmanical schools, before later variants became about states of mind and experience (much like bliss and heaven in the west), it was about understanding language. Similar to logos, becoming one with the mind of god implies that one's thoughts, or understanding becomes identical to the underlying structure of the universe.

I take understanding language to be something mystical. That language wields you, rather than the reverse. Embedded in language is values, different communities of speakers assign different values to terms, they refer, and mean different things to different communities. I'm of the opinion that there is a correct way of understanding, and using language. While one is ideological, full of attempts to manipulate language to make things mean what they wish them to, they divorce themselves from that structure of the world, and live in a fantasy land. Embodying language, is the same thing as being in harmony with the very structure of the world, and this is why it is bliss, and rebellion, antagonism is misery.

For me, freedom from delusion, the ultimate understanding of the world, is precisely to align oneself with the true values of the world, which will properly orient one's comprehension of language. So that, the gesture, tones, and language that one uses tells a higher truth than what they even mean to, or know themselves to be confessing.

Quick note on poetry: on the imaginary continuum set up here, poetry probably lies somewhere in between gesture and language proper. To the degree that poetics is less subject to the constraints of pragmatics (of getting a concrete message across in order to achieve an aim), poetics can be seen to be the exhibition of gesture in language, not unlike shifters. As pointed out by Giorgio Agamben though, the limits of poetry (and the reason why it can never be pure gesture) is that it is ultimately subject to enjambment.

(The continuation of a sentence without a pause beyond the end of a line; as in:

the back wings
of the
hospital where
nothing
will grow

The breaks between otherwise continuous lines are enjambment).

Enjambment marks the inescapable intrusion of the formal into poetry's attempts at gestural language. Agamben: "The possibility of enjambment constitutes the only criterion for distinguishing poetry from prose. For what is enjambment, if not the opposition of a metrical limit to a syntactical limit, of a prosodic pause to a semantic pause? "Poetry" will then be the name given to the discourse in which this opposition is, at least virtually, possible; "Prose" will be the name for the discourse in which this opposition cannot take place" (Agamben The End of the Poem).

So visually, the continuum:

Language: {Gesture --- Poetry --- Language --- Philosophy --- Math}

(Language is both genus and species).

Or, that types only makes sense through tokens? — Πετροκότσυφας

Do tokens only make sense through types? I think so.

I once walked through a park with a biologist who gave the scientific name for every tree we passed. This brought into view the unique beauty of an individual tree, naked of name. But tree is also a type and it goes on and on. There's no such thing as a raw token.

The reason why I ask is that animals can count. And if it's not mathematics, a counting system of "none, one, two, three, many..." it still counting and counting is part of mathematics. Now the vast majority of species don't use these terms in their language (which typically limits to "Danger!" and "This is my territory!"). I wouldn't be surprised if some advanced hunters like Orcas would have terms for counting prey in their communication system (at least "many" and "few") or even something more advanced. Perhaps the other extreme from gesture could be some postmodern meta-analysis of language itself and not mathematics. Or basically philosophical study of language. That would feel very remote from the languages that animals use or even can comprehend. — ssu

In terms of the schema here, I would understand math to be (among other things), a formalization of counting (just like logic is a formalization of reasoning), which would mean that counting, in itself, is not really math. One way to see this is to note that while its true that some animals can count, their treatment of numbers - even among the smartest of them - is not in terms of tokens and types, as in a formalized mathematical system. I cited and discussed some of this research in another thread here, but the gist of it is that even monkeys can't process numbers as numbers (qua form). They can only really process numbers as coupled with material things: 1 of X, 2 of Y and so on, and not as sheer 'types', never as 'just' 1 or 'just 2'.

In fact, one can look at the formalization of counting (as math) as an attempt to get around this cognitive limit, which even we are subject to. By formalizing counting, we can treat entire sets of numbers (and even types of numbers) as single things to be manipulated, thus bypassing the need to deal with a whole range of sheer particulars.

This might be irrelevant to the overall discussion, but what comes to my mind while reading this, is Wittgenstein. The act of writing "1+1=2" does not affect the fact that 1+1, in fact, equals 2, but the act of calculating it, does. 1+1 does not equal 2 unless someone invents a calculus in which in fact it does. Wouldn't it be fair to say that any calculation would be meaningless to us if it didn't involve the world in one way or another? Or, that types only makes sense through tokens? — Πετροκότσυφας

Yeah, I agree that tokens and types only make sense in relation to each other (again, I had a really fun conversation about this in the thread I mentioned earlier in my reply to ssu). But also, I think your larger point is very relevant and is where any exploration of the typology here would need to extend to: one of the consequences of treating math as, ultimately, a language, is that it blocks any realist account of math. Insofar as all language is normative, so too is math: it does not reflect some other-worldly eternal reality. Some of the reading I've been doing that somewhat inspired my thread has been precisely on the link between gesture and math, and the fact that math is unthinkable without gesture. Brian Rotman, who I cited in the OP, writes eloquently about this:

"On the contrary, mathematics’ links to physical movement, though mediated, are undeniable: each of the primary object-concepts of the mathematical universe – number, relation, set, function, operation, variable, line, point, space, equation – can be seen to emerge from a small set of pre-conceptual physical actions, disciplined bodily movements or gestures, that, with their subsequent transformations, make up the corporeal wherewithal of mathematical thought. In other words, contemporary mathematics, though habitually understood in terms of static disembodied object-concepts, is constructed in/by a language whose basic conceptual vocabulary is rooted in gestural movement–schemata of the body".

https://brianrotman.wordpress.com/articles/mathematical-movement-gesture/

Going back to the way we learn math, it strikes me that while the general way we are introduced to this type of cognition depends on gestures, as means of spatial designation and delimitation, as well as on language to slide us toward abstraction, neither of those domains recovers the essence of mathematical reasonning. The understanding of 1+1=2 depends on an initial suspension of actuality on the operational side, followed by a recovery of this actuality through a projection of this operation on an abstracted world which we pretend is a proper translation of ours.

I would suggest that if gesture is primordial here, in this context, its because it is a form of informational mapping. The educational gestures behind 1+1=2 serves the purpose of establishing boundaries and then lifting them, putting emphasis on the sequential aspectof the event so as to give the impression of operationality, while the language serves the purpose of obfuscating the fact that none of this is actually happening in reality.

Some of the reading I've been doing that somewhat inspired my thread has been precisely on the link between gesture and math, and the fact that math is unthinkable without gesture. — StreetlightX

Depends on whether one believes computers can think, or whether it would require a robot for a machine to understand math. Humans learn math because of gesturing, but that doesn't mean math has to be learnt that way. Maybe that's just the ape way.

Insofar as all language is normative, so too is math: it does not reflect some other-worldly eternal reality. — StreetlightX

No, but it does reflect the countability of the world, and possibly more.

Going back to the way we learn math, it strikes me that while the general way we are introduced to this type of cognition depends on gestures, as means of spatial designation and delimitation, as well as on language to slide us toward abstraction, neither of those domains recovers the essence of mathematical reasoning. The understanding of 1+1=2 depends on an initial suspension of actuality on the operational side, followed by a recovery of this actuality through a projection of this operation on an abstracted world which we pretend is a proper translation of ours.

I would suggest that if gesture is primordial here, in this context, its because it is a form of informational mapping. The educational gestures behind 1+1=2 serves the purpose of establishing boundaries and then lifting them, putting emphasis on the sequential aspect of the event so as to give the impression of operationality, while the language serves the purpose of obfuscating the fact that none of this is actually happening in reality. — Akanthinos

Hmm, but I'm not sure that the spatial aspect of mathematical reasoning is quite as suppressed as I think you're stating (I'm not sure if I'm reading you right on this so bear with me if I'm not). I mean, just to set the stage, one of the things that math does is to erase or rather compress time into space: relations between mathematical objects - mappings, translations, computations - can all ultimately be seen as spatial relations between entities distributed among imaginary space(s). I mean, the whole 'structure' of math - I'm not sure how else to put it - things like the number line, invariants which define groups and their corresponding abstract topologies, higher-dimensional numbers (imaginaries, quaternions, octonions, etc), the very idea of ordinals: all these things can be understood (and perhaps ought to be understood) in spatial terms.

It's not a coincidence that math in many ways can be understood as the study of various broken-symmetries (another spatial notion!). I would only add that the invariants which characterize the different mathematical asymmetries belong strictly to the level of form (that is, are invariants relating to types, and never tokens): math is the study of how pure types can be mapped and related to each other depending on the invariants in question (we just happen to call these pure types 'numbers').

This is obviously a super, super abstract definition of math (could it be otherwise?), but if one can accept this, then the major point is that the spatial characteristics that define math are not different in kind from the spatial characteristics that are found anywhere else in the 'real' world: the 'only' difference is that mathematical objects are not bound by so-called material constraints (or energetic constraints), whereas 'real things' are; in fact 'real things', are bound by both material/energetic constraints and formal ones. Mathematical objects simply have an extra 'degree of freedom'. Yet the point would be that in both cases, what constitutes 'space' for both mathematical and extra-mathematical objects is exactly the same.

And if this is the case, then we can understand why gesture (as a "disciplined distribution of mobility") is foundational to math qua math,and not merely a contingent tack-on that helps humans learn it: mathematical manipulations are gestures in mathematical space (where the idea of spatiality is irreducible and fundamental). Both these gestures and these spaces must in turn be seen as extrapolations from a more originary space without which these corresponding abstract spaces could not exist and could not be thought.

Here is Rotman: "Contemporary mathematics, though habitually understood in terms of static disembodied object-concepts, is constructed in/by a language whose basic conceptual vocabulary is rooted in gestural movement–schemata of the body. Chief among these are: the gestures of pairing two things together; combining two things to make a third; replacing one thing by another; pointing at a thing; showing, exhibiting or manifesting a thing; displacing or extending the body in its space; making/altering a mark; and the meta-gesture of repetition, of doing the gesture again. So that, for example, the object-concept ‘number’ can be seen as rooted in the gesture of making a stroke, an undifferentiated mark, and then repeating it; likewise the object-concepts ‘equation’, and ‘relation’, are different conceptualizations of the gesture of pairing... [etc]". (source).

I'm sure there is a better way for me to try and articulate these issues, but I'm very much groping here. Also, I'm not sure if I'm agreeing or disagreeing with your post here, but this is what its prompted outta me!

No, but it does reflect the countability of the world, and possibly more. — Marchesk

It doesn't though. You have to beat alot of math in to place for it to adequately 'reflect the countability of the world' in the form of highly specific boundary constaints without which a great deal of mathematical modelling just falls into nonsense. Anyway, see my above post for why I don't think gestures are simply incidental to math.

I'm not convinced that poetry attempts to be gestural. There are many formal techniques in poetry -- and those formal techniques are even language-specific, in some cases; Especially as we go back to ancient poetry which were more formalized than a lot of modern poetry is.

One aspect of poetry that does seem gestural is in its use of imagery. A good poet highlights what is specific in a scene or brings images to the imagination through the use of language. But there is usually a reason behind said imagery -- it is metaphoric, or conveys a feeling. Poetry is also often self-referential, especially as we get into modern poetry. It draws from other poets and often comments on poetry itself.

Then there is the arrangement of words to create a (langue-dependent -- i.e. romantic differs from germanic) cadence using the words themselves. This is purely phonic at the formal level, but can also evoke certain emotions or indicate turns within a poem -- such as the rhyming couplet which closes a Shakespearean sonnet.

This isn't to say that poetry is mathematical, but rather that I'd say it shares in the mixture of gesture and math that language has.

Not sure how far you want to go down this path. I'm just hesitant to call poetry an attempt at gestural language. Though I do agree when you say that it isn't subject to pragmatics -- but to me that seems to support my point here. Aren't gestures pragmatic?

I'm not convinced that poetry attempts to be gestural. There are many formal techniques in poetry -- and those formal techniques are even language-specific, in some cases; Especially as we go back to ancient poetry which were more formalized than a lot of modern poetry is. — Moliere

Yeah, I actually agree with this, but this touches on a point which I'm finding the hardest to express, which is that despite the imagery of a gradating continuum that I've used, that the formal and the gestural can't be ultimately separated. Part of this is what I was trying to suggest when I said above that mathematical manipulations are gestures in mathematical space: that gesture doesn't 'disappear' in math, but rather is transmuted, as it were, into something other than what it is in physical space. To stick with the math and to draw again on Rotman, he points out that the price to be paid by math for its treatment of its objects as pure types is that it totally expels any consideration of what motivates its proofs; math is treated as if it is pure step-by-step algorithm.

But, he argues - rightly in my opinion - that this is to render math unintelligible: every proof has a 'leading principle' which renders it a proof of this or that at all, and that this leading principle is not something that is ever is 'in' the proof itself, so much as it necessarily animates its unfolding from without: it can only be located in the act of the one or of the community who furnishes and interprets the proof through their actions (and all calculation is action): "It is perfectly possible to follow a proof, in the more restricted, purely formal sense of giving assent to each logical step, without such an idea [of a leading principle] ... Nonetheless a leading principle is always present - acknowledged or not - and attempts to read proofs in the absence of their underlying narratives are unlikely to result in the experience of felt necessity, persuasion, and conviction that proofs are intended to produce, and without which they fail to be proofs" (source).

This is all a very roundabout way of saying that the same kind of considerations - in a reversed vein - must also apply to poetry. My appeal to enjambment was to say that one can't actually treat poetry as pure gesture, and that there will always be a residue of form that makes itself felt in it, no matter how hard it might try to free itself of form. And of course you're right that there is a poetics of form as well, even, at the limit, a poetics of math too (all language has a poetics). In fact to be perfectly rigorous one would have to say there is no such thing as 'pure gesture' either, although the closest thing that might accord to it would be dance: gesture as pure(ish) expression (might be able to say - dance:gesture :: poetry:language). And of course every dancer knows that there's a grammar of dance too, and mastering that grammar heightens - rather than dampens - its expressive power.

Anyway, I'll stop with the free-association. Coming back to poetics, Roman Jakobson's definition I think might help me out here; of poetics, he says: "a prolonged hesitation between sound and sense". And perhaps once can say that this hesitation is either more pronounced or more condensed depending on where on the spectrum one lies. And it gets me thinking that, just as I made language both the genus and species of the rough visual I constructed previously, it might be useful to do the same with each 'species'. Something like:

Gesture: {Gesture --- Poetry --- Language --- Philosophy --- Math}
Poetry: {Gesture --- Poetry --- Language --- Philosophy --- Math}
Lge, etc..
Phil, etc..
Math, etc..

Where the genus defines the main expressive thrust of whatever it is: so poetry that leans heavily on form, for instance, simply minimizes its own gestural pole in favour of it's mathematical one (to the extent it can while still remaining poetry). Anyway, just playing a little with the form here, I hope it responds in some manner to the issues you're raised.

Imagine a pendulum swinging through the spectrum. The end points on either side are states of meaninglessness.

But at any point between the end points there is a partaking of both sides: the dynamic tension between the two is the genesis of meaning.

Meaning is interesting; kinds of meaning moreso.

What do you mean? Kinds?

Meaning is not univocal.

Yeah. The pendulum swing is a cultural thing that individuals contribute to and are influenced by. Is that what you mean?

No.

Ok.

What happens when you drop out language from your gradation?

So we have --

Dance:Gesture:Poetry:Philosophy:Math

Perhaps a bit heavy on the left and missing some terms -- but I think I agree with what you are saying if we treat the gradation as a characterization of language. (maybe "everyday" would populate the middle?)


How do you feel about that?

I dunno, I'd be sorry to not class language as a member of the continuum in that it strikes the middle ground between expressiveness and pragmatics. Maybe, to use a Chomskian distinction, one might speak of 'language in the narrow sense' and 'language in the broad sense'? It's all a bit neither here nor there though!

True enough. I suppose my thinking was that in a way this double spectrum -- in the sense that you can go from left to right and right to left but never remove entirely one or the other -- is characteristic of language as a whole. So it's not like dance isn't language or that math isn't language, but rather that all language falls somewhere on this spectrum between expression and pragmatics and the middle ground is something like our everyday usage.

Basically the idea is that if you really want to understand the nature of language, two seemingly marginal areas need to be investigated: math and gesture. My intuition is that all three terms - gesture, language, and math - all stand on a continuum of increasing abstraction, and that to understand each, we need to understand the other(s). Or to put it differently, gesture and math stand at opposite ends of a line on which language occupies the centre: they are the limit-points though which language must be understood. — StreetlightX

I don't think that this is the proper way to represent language, as such a continuum, because we need to account for the significant difference of intention, purpose and use, between oral language and written language. Significant differences in intentionality, meaning differences in what language is used for, can be seen to correspond with the two distinct types of language oral and written. Prior to modern civilization, the two can be understood to have been developing individually. We can see that oral language is used mostly for communication, whereas writing is often used as a memory aid.

This is where we ought to be careful not to follow too closely Wittgenstein's denial of private language. Written language is often private, and written language is what gives rise to mathematics, whereas oral language is seldom private, and gives rise to communicative skills. If you read Richard Feynman's "Surely you're joking Mr. Feynman", you'll find where he describes that as a youngster he developed his own system of mathematical symbols, and when he studied physics in university he had to reconcile his symbols with the conventional ones, because the professors could not understand his. Mathematical symbols, which are by nature written, are based in the desire for a private memory aid. Oral words are based in the desire for communication.

So, rather than place gesture and math as opposite ends of a continuum, I would position them as categorically distinct, one for the purpose of communication, the other as a memory aid for private use. I would argue that in prehistoric times, the two were completely distinct. When they came together, to intermingle, such that one person's memory aid could be effectively and efficiently communicated to another, we had the explosive development of modern civilization.