The Politics of Recursion: Hypotaxis, Hierarchy, and Healing

Altai Shamanka

A paper I plan to deliver at a scientific conference here in Barnaul, October 2014

As the written word began speaking,

the stones fell silent… the trees became mute, the other animals dumb. 1

It has been shown that in traditional kinship-based hunter-gatherer societies, sharing and gifting lie at the heart of the human community. This appears to be a defining character trait among even the earliest of Paleolithic economies. As Morton Fried stated in his classic work, The Evolution of Political Society,

The paramount invention that led to human society was sharing because it underlay the division of labor that probably increased early human productivity above the level of competitive species in the same ecological niches.2 

Cultural anthropologist, Elman Service, confirms this in his own work on Primitive Social Organization: An Evolutionary Perspective, “The more primitive the society… the greater the emphasis on sharing, and the more scarce or needed the items the greater the sociability engendered.”3  As social anthropologist, Tim Ingold, concludes, what is important is “that food ‘go around’ rather than that it should ‘last out’.  Whatever food is available is distributed so that everyone [in the group] has a share.”4 As Fried further suggests,

Of almost equal importance was the concomitant reduction in the significance of individual dominance in a hierarchical arrangement within the community. In part, the structural possibility for such a hierarchy was undermined by the demands of sharing. [Even] cooperative labor parties, whether for hunting or gathering, [took] place with very little apparent leadership.5

Now what does all of this have to do with cognitive or functional linguistics, with language and ego-development, with one’s conceptual worldview or cultural interaction; with how we communicate, and what that means in terms of human community and experience?

Among contemporary linguistic theoreticians, Noam Chomsky stands out as a seminal and transformative figure. He argues that there is, in the human constitution, a universal generative grammar, an organic capacity providing the possibility of sophisticated language development and communicative potential. And what makes this “internal language” or universal grammar uniquely human is a process that Chomsky calls “recursion,” that is to say, the embedding or ‘nesting’ of phrases or clauses within larger linguistic wholes at each strata of a language scheme – semantic, syntactic, and logistic subordination.

In short, recursion enables the construction of complex hypotactic language units rather than just simple paratactic ones. Parataxis, as I am sure you are all aware, is when each of your sentences in a larger grammatical unit carries equal weighting. Paratactic units usually have few, if any clauses, and more importantly, none of the clauses are subordinated one to another in a hierarchical scheme. Hypotaxis, on the other hand, occurs when clauses in sentences, or in larger grammatical wholes, are subordinated to one another, focusing attention on what is considered of greater importance or value within the semantic, syntactic, or larger logistic unit. In other words, recursion, by means of subordination, allows for the rudimentary and foundational element of hierarchization.  Hierarchy, socio-economic and political, we might here add, is also one of the hallmarks of post-traditional societies, as was intimated in our opening paragraphs above.

So, the question we now raise is the following.  Is recursion, that is to say, linguistic subordination, essential to all human language, or is it only a property of some language families, or of some forms of language usage? For example, is there any relationship between linguistic recursion and the development of literacy (writing), between hypotactic subordination and the emergence of socio-political hierarchies, not to mention the radicalized sense of individualism to which hierarchy gives rise? Furthermore, is the hierarchical ordering and syntactic subordination we find in the linguistic field of textuality either a ‘model of’ or a ‘model for’ the subordination we find on the battlefield, in a corporate boardroom or government bureaucracy, or in the theatre of political debate? Everything about today’s dominant global culture reeks of hierarchy, whether in democratic dress or military uniform. As Chomsky himself admits, no government is truly representative; each has its “own power, serving segments of the population that are dominant and rich,” that is to say, at the top of the socio-economic power hierarchy!6

 In short, are social, economic, and political hierarchies connected in some way to the recursive linguistic hierarchies (semantic, syntactic, grammatic, and logistic) embedded in our written tongues?  And was there some prior, precedent condition before the birth of literacy where hypotactic recursion and hierarchy did not yet exist, or at least did not dominate the field of human cognition and communication?  Finally, does any of this have any bearing on our understanding or experience of time, place, self, and world?

In the past several years, Dr. Daniel Everett, Dean of Arts and Sciences at Bentley University in Massachusetts, and former Chair of the Department of Languages, Literatures and Cultures at Illinois State University, (one time Chomsky adherent), published several works on the remote Piraha tribe, a group of hunter-gatherers who live on the edge of the rain forest along the Maici River in Brazil’s Amazon region.  Everett lived with the tribe and studied their language and culture for thirty years.  The Piraha’s unwritten tongue (spoken, sung and hummed) consists of just eight consonants and three vowels, and lacks many of the grammatical characteristics found in other languages. Especially noteworthy, it lacks the phenomenon of recursion ( of linguistic subordination) that Chomsky claimed was essential to all human languages.  As Everett said in a 2012 interview:

All languages have unique characteristics, but the Pirahã just seems to have so many unique characteristics. Things that we didn’t expect. I mean the absence of numbers, the absence of counting and colours, the absence of creation myths, and the refusal to talk about the distant past or the distant future. A number of things like this, including, the special characteristic of recursion, the ability to keep a process going in the syntax forever.7 

And, according to Everett, this has significant implications on what is important in Piraha culture.  As Everett depicts things, the locus of their concern and attention is on…

[t]he immediacy of experience, not to worry about the future or past, and not talk about what you have not seen or heard. They hunt, fish and share their food; the rest of the time they laugh, talk, spend time enjoying themselves… What struck me was their lack of superstition, their contentment with life as they found it. And their happiness. I have never seen people facing so many difficulties, with so much grace: it deeply impressed me.8

Here is where I suggest we find a turning point in human history, what social anthropologist Jack Goody called, in his groundbreaking work, The Domestication of the Savage Mind,9 or the birth of literacy.  It is here I wager that we find the complete and final ascendancy of linguistic hierarchy, and hypotactic space-time over paratactic presence, the future, over the present, law over custom, and history over myth. I would like to spend just a few minutes on the differences in perception and worldview.

As cultural historian Marvin Bram contends in The Recovery Of The West, “Parataxis suggests coordination more than subordination, and any number of sequences rather than a single correct sequence. Parataxis de-hierarchizes the world,” where the flat, coordinate, and non-orderliness of a paratactic world seems rather primitive or prosaic to the ever more civilized and tightly structured hypotactic logistic.  Bram continues:

Parataxis is concerned with the concrete thing itself, the local and contained, and the moment, rather than with relationships among abstract things and over-arching spatial and temporal schemes… Paratactic space and time make dramatic antitheses to their hypotactic counterparts.10

For example, a person walking down a forest path seeing paratactically will see much more than a person looking hypotactically along the same path but only seeing what is of interest to him.  The paratactic visual space will be fuller. As Bram concludes,

This phenomenon of paratactic persons taking in more of the world, living in a fuller world than hypotactic persons, has been reported time and time again by (hypotactic) travelers among (paratactic) traditional peoples. 11

Is it not interesting how the well domesticated, orderly and perfectly sequenced rows of plowed fields, those ‘amber waves of grain,’ led to urban surpluses, which in turn were stored and accounted for through the production of linear tables and rows of numbers in the written records of our earliest kingdoms and nation states – the very first signs of written language, along with documented codes of social control?  The haphazard (disorderly) plots of early-Neolithic pre-urban horticulturalists were simply not comparable with the tilled and plowed rows of the agriculturalist, just as the meandering herds of sheep among the earliest shepherds cannot compare to the meticulously aligned metal stalls of the modern abattoir. And the language of control, the written document, was key to building the assorted hierarchies that would henceforth manage the herds, the fields, the supplies, and the citizens, as well as the outsiders. (And Russian certainly understand the documents of control). Legal institutions, advocates and judges, guilt and innocence, along with police forces and the military were born in that self-same moment of our earliest history.  It is here that the trajectory of the West was born and we lost our way.

Even in the language of Genesis, the story of the Tower of Babel is not really about the multiplicity of tongues.  It is rather a depiction of the overarching structural integrity of a burgeoning universal linguistic, and its ability to subordinate and unify disparate members of the citizenry within a shared foundational grammar and worldview.  I would say it is a mythic recognition of the univocal trajectory of the written word – its capacity for disambiguation and hierarchization, thus enabling greater displays of command and control. The story of Babel was possibly an expressed regret over the loss of freedom, of polysemy, and the natural intimacy that preceded the birth of cities, kings, and written codes.  Why else would the story speak so directly about some divine intervention to confuse yet again the tongues of man?

But the Lord came down to see the city and the tower which the sons of men had built. And the Lord said, “Indeed the people are one and they all have one language, and this is what they begin to do; now nothing that they propose to do will be withheld from them.11

The building of cities, the concrete establishment of civilization – the Tower  of Babel – was dependent upon the unambiguous univocality of the written word, and the hierarchical control it afforded the literati of the imperial court. No doubt, much was gained with the move to literacy, with the ascendance of univocity, the written record of history, the significance of the past and the value of the future.  It provided the mechanism for bureaucratic structures (and laws) to manage the new menagerie of human community, and realize the possibilities that civilized life now afforded.  Yet, there was also born regret for the past poorly lived and anxiety over a future still uncertain, in short, the terror of an historical consciousness, and the realization that ‘one-day I too will die.’ As Bram reminds us,

In paratactic time there is little past because there are no complete logistic structures to be sought there, and there is little future because there is no need for a place in which to complete incomplete logistic structures.  There is certainly a present, gathering to itself much of the energy that hypotactic persons give to the past and future, and inhabited by full persons and full objects: a full present.  The present of hypotactic time often enough takes third place behind the past and the future, depleted of energy: an empty present. 12

 But, what was lost in this transformation to the hypotactic word, in the subordination of thought and speech within the apparently universal grammar of literacy, univocity, and its newly appropriated voice – the sterile logic of syllogism and, finally, of mathematics?

I wager that collectively these developments – agriculture, urbanization, and literacy – had an incalculable impact on human perception and consciousness over the ensuing millennia, producing entirely novel ways of constituting and manipulating the world. Consciousness, reflectively detaching itself from the living environment, constituted reality differently after the birth of cities than it had done previously, when humans dwelt there pre-thematically, participating the world, perceptually and paratactically. This cognitive change produced resounding reverberations for all generations to follow, entrenched, as humanity would become, in new organizational hierarchies that appeared — the formal institutions of civil society. Was it not literacy – giving special prominence to a hypotactic, hierarchizing logistic – that provided momentum to both the political and scientific objectification of nature and human relations?

An incipient temperament for this new logistic, and its newly constructed worldview, affected every dimension of life as civilization spread, and cities continued to populate the globe over subsequent millennia. This view of the world established and entrenched itself, memorializing our changed relationship with a reality in which we had originally dwelt paratactically. The world-as-given was emptied of any intrinsic significance or value aside from that which these new humans and the logic of the written word attributed to it.  It was first a linguistic and then an early scientific objectification of nature – destroying the power and thickness of a pre-objective present – that led ineluctably to the de-animation of nature and the subsequent theoretical construction of transcendent powers – gods, goddesses, the noumena, or eventually, the abstract laws of physics.

Preliterate humanity on the other hand seemingly drew fewer hard distinctions, apparently experiencing the world as alive, having a power and motility shared with all sentient beings and even with what we now call inanimate nature. It is for this reason that pre-historic consciousness may be called participatory consciousness; tribal members actually could fuse with their totem animal, for example – intertwining with their environment – because from their perspective there was no substantive difference between them and the totem: they were essentially of one substance or consubstantial. We must not be confused here.  It is not as if they thought like us, only making incorrect judgments; they did not think the way we do. It was qualitatively a different mode of perceiving and experiencing all together. They did not see things from a wholly detached objective perspective; indeed, we cannot say that they saw any “things” at all in the sense that we speak of things today in geometrical space-time. Rather they participated their world. Their experience may have been qualitatively different from the way we configure the world today.

Hypotaxis and hierarchy, mathematics and the syllogism, in short, literacy has allowed us to slice and dice the world, dissecting it in so many ways. Perhaps it is time to bandage those cuts and let the healing begin, if it is not already too late. In hindsight, perhaps we might all be better off had we never been taught to read, to write, or to paint by numbers in the first place – like the Piraha! Perhaps the globe wouldn’t be quite the mess it is today had it only been otherwise!

Notes

1.     Abram, David, The Spell of the Sensuous, 1996, p. 131.

2.     Fried, Morton, The Evolution of Political Society, Random House, 1967, p. 106.

3.     Fried, Ibid

4.     Ingold, Tim, The Perception of the Environment, Routladge, 2011, p. 45.

5.     Fried, Ibid

6.   Chomsky, Noam, Interview with Michael Wilson, Modern Success (http://www.alternet.org/civil-liberties/noam-chomsky-kind-anarchism-i-believe-and-whats-wrong-libertarians)

7.     Everett, Daniel, Interview by Robert McCrum, The Observer, (25 March 2012)

8.     Godrèche, Dominique, The Amazon’s Pirahã People’s Secret to Happiness: Never Talk of the Past or Future (25 June, 2012)

9.     Goody, Jack, The Domestication of the Savage Mind, Oxford

10.  Bram, Marvin, The Recovery Of The West: An Essay In Symbolic History, 2002, Exlibris, pp. 25-26

11.  Bram, Ibid

12.  Genesis (11:5-6)

13.  Bram, Ibid, p. 26.

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53 Responses to The Politics of Recursion: Hypotaxis, Hierarchy, and Healing

  1. the Heretick says:

    very good, only have time this morning for a quick read. was just talking to a lady friend the other day about what if, what if one had time to just sit underneath a tree and watch the clouds go by? she said it sounded boring, I maintained that after a bit of calming down that all sorts of sights and sounds would become apparent, an infinite kaleidoscope of birds, wind, and life. hmmm, are we talking about some sort of Zen? letting go? odd she would give the reply she did, as one who claims to practice meditation, but then if you have to “practice” meditation, kind of defeats the purpose wouldn’t you say? luckily such things just come naturally to me, Not!

  2. Disaffected says:

    Nice paper and very accessible, even to dummies like me. So it’s hypotactic thinking that’s behind our undoing, eh? Now I’ll have a new phrase to convince my friends that I’ve lost my mind.

    But seriously, I think I understand what you’re getting at very well and apply it daily. It’s unbridled hypotactic thinking and language that I’m recoiling at when I sit through management meeting where over educated and over paid nitwits sit around play verbal jiu-jitsu in a pitiful attempt to impress each other with their “deep understanding” of overly complex problems, usually of their own device and existing only in their own heads. The same bunch that finds a table of very simple financial numbers unfathomable and must therefore have it reduced to a line graph for simplicity. I’m a serial avoider of such people and meetings for the most part, which has pretty much marked me for early elimination, which, quite frankly, will be a blessing for the most part.

    Similarly, modern management has even turned simple problem solving into an official production now. The terms these days are yellow belt or black belt projects organized under the banner of the mysterious Japanese word “Kaizen,” which presumably makes the whole process so much more effective than using its English equivalent “improvement” and simply assigning someone or a small group to tackle a problem and suggest a solution. I laugh daily at the idiocy of all this learn-ed foolishness. But of course the real understanding is that the purpose all these verbal circumlocutions is to not only be purposely vague and obtuse, but to mark oneself as an insider in the corps of educated idiots, a veritable captain and leader of men on the ship of fools if you will, and thus capable and deserving of social promotion, as if there’s any other kind. And thus it was that a silver-tongued orator rose through the ranks like a meteor across the night sky in 2008 to command the free world behind a wall of undecipherable high-minded phrases and platitudes to which most of his followers and detractors alike are still scratching their heads at. Bottom line: pseudo-intellectual hypotactic bullshit thinking has permeated every nook and cranny of our modern world and is now firmly, and permanently it seems, in charge.

    • kulturcritic says:

      DA – I don’t think they will need to hear a new phrase from your lips to know you are not one of them… they already got it, Comrade! LOL

    • Disaffected says:

      The last word on recursive hypotactic bullshit:

    • Disaffected says:

      On the other hand, here’s an example of what makes hypotactic thinking so alluring in the first place. It’s a fair argument:

      • Disaffected says:

        Now I would like to add that even though I own one of these monsters (a Hennessey modified 650 HP SRT8 Dodge Challenger), I, and every automobile owner of any stripe am or should be aware of where their “American HP” comes from. From the earth in the form of millions of years of non-renewable stored sunlight is the basic answer; from the earth in parts of the globe that require political, economic, and military exploitation first to gain access is the second and next correct answer; and from the earth and on the back of a global socio/economic/political system which exploits us all, first world consumers and third world victims alike is the third and perhaps MOST correct answer, unpalatable though it may be.

        Not that that explains or forgives ANY of our behaviors with regard to profligate energy or other resource use these days. In my case, I justify my “need for speed” with the fact that I have the luxury to drive very little, and thus probably consume much less fuel overall than the average ‘wage slave’ who must commute long miles in search of their daily bread, themselves the victim of the same reductionist system which forced us BOTH into this quandary in the first place! How very fortunate for me and how very unfortunate for them and the environment that I chose to squander the opportunity to do good to us all by simply riding a bus instead, and forgoing the “fire-breathing dragon” altogether, even on a limited basis.

        Such are the temptations of hypotactic thinking.

        • Disaffected says:

          Not for nothing, I DO consider the ridiculousness of my own life and its inherent contradictions daily. Not that that makes living with it all that much better.

        • the heretick says:

          so sell it, while it’s still worth something,

        • the Heretick says:

          MOTION PHASE III 427-SC CAMARO SUPERCAR
          800 HORSEPOWER SUPERCHARGED
          http://www.officialbaldwinmotion.com/modern.htm

          it would be interesting to see if the Baldwin Motion Camaro would give the Venom a run for the money, it does have more HP, the Venom is probably running a 427 anyway………..

          • Disaffected says:

            That’s pretty hot! But yeah, the Venom runs a twin turbo 427 and was specially designed to capture the top speed record (at a cool $1M a pop!). Aerosmith’s Steven Tyler was one of the early buyers, so that let’s you know the kind of people who would be in the market for this kind of thing.

            I kind of got caught up in the whole rush of the moment. I had a car I wanted to trade for something with more ‘oomph’, found a ‘deal’ on a rare model Challenger SRT 392 at a local dealer, heard about Hennessey from the dealer in passing on the way out the door, and one thing lead to another… Here I am a whole lot money poorer and a whole lot HP richer and wondering how it all came to be.

            That said, the mileage ain’t all that terrible if I keep my foot out of it and the gas mileage ain’t all that terrible either, and I have to admit, the looks it draws and the acceleration it brings are simply INTOXICATING! Even so, it’s not me, and I wonder where I went so wrong. The human mind is a TERRIBLE thing to contemplate!

  3. Malthus says:

    It is nice to read something so well written and understand it immediately. I really have nothing to add to such an excellent work. The only thing that comes to mind is that conformity and obedience are destroying the human species.

  4. Sandy, In addition to saying important things in a way non-sociologists can understand, you have ‘high (sic) level’ readers who write sentient comments. Can we cross-list our respective blogs? (www.otherjonesii.blogspot.com).

  5. kulturcritic says:

    REVISED TITLE!! NEW CLOSING PARAGRAPH!!

    The Politics of Recursion: Hypotaxis, Hierarchy, and Happiness

    (final paragraph)

    Hypotaxis and hierarchy, mathematics and the syllogism, in short, literacy has allowed us to slice and dice the world, dissecting it in so many ways. Perhaps it is time to bandage those cuts and let the healing begin, if it is not already too late. In hindsight, perhaps we might all be better off had we never been taught to read, to write, or to paint by numbers in the first place – like the Piraha! Perhaps the globe wouldn’t be quite the mess it is today had it only been otherwise. Perhaps, as growing evidence from psychoanalytic practice in Great Britain suggests, if we could once again experience rich paratactic wholes (polysemies) we might in fact become happier people – like the Piraha!

    • the heretick says:

      but wait, there’s more! you also get the amazing Ginsu cheese grater! just pay the shipping and handling, but hurry! this amazing TV offer won’t last forever!! act now! don’t miss out!!!

      i’m not so sure that I grok all of the subtleties of this hypo-para-taxi stuff, but the Tower of Babel analogy does bring to mind the almighty UPC.
      “One Ring to find them, One Ring to bring them all and in the darkness bind them”

      crrreeeepy!

      but seriously, I think there are people who think hypotactically, so to speak, and are busy little bees subordinating the entire planet. then of course I think about what effect this type of thinking has on the individual organism, how much of this type of thinking is internalized
      after living a life in a society which operates under this sort of subtle conditioning, how do we know how to think in any form of whole way? rather like the proles in 1984, simply unable to form a cogent thought concerning any thing that matters.

      hey! I just had a wonderful thought! my disorganized sentences! I am simply a paroxysm of paratactic practice! praise god! i’m free! it’s a miracle!

      must just come naturally. but really, good article, I will apply this new found insight in my every day life. just so you know, I looked these terms up, Hebrew is much more paratactic than Greek according to some.

    • Disaffected says:

      Thanks Sandy. I think that either way, you’ve lost most of us. Probably a good thing. Hey – thinking is HARD and most of us don’t have occasion to DO MUCH of it anymore! And I’m not sure that’s a BAD thing any more either, here in what appears to be the twilight of our civilization.

    • Colin says:

      Just found this interview on Red Ice Creations that seems to be very much in line with this topic….or perhaps not as I am about to listen to it….

      http://www.redicecreations.com/radio/2014/03/RIR-140307.php

  6. At the rate this “civilization” is going, I won’t be surprised we do return to a paratactic world in some not-too-distant future time. After we run out of oil, our cities become overrun by nature, our hypotactic leaders die off, and our machines stop; maybe we’ll become a quieter and more “present” people in touch with our immediate world and moment.

    As hunter gatherers and farmers, instead of techno wet-dream starship captains, we may even learn to become human again!

    Great post, Sandy! Peace!

  7. Colin says:

    Great article. I agree with you for the most part however I wouldn’t put mathematics strictly in the realm of hypotaxis although I agree that our modern languages definitely are hierarchical and that certainly is a reflection of our need for hierarchy in every aspect of our lives. If indeed math does conform to a grammar it would much more resemble a parataxic one where all terms should really be treated equally. We have to break down mathematical equations and terms to some degree just to understand them but the underlying accuracy is dependent on all terms being present, and theoretically, equal.

    Of course this is open somewhat to interpretation but mathematics does not really allow one to emphasize some terms over others based purely on preference or hierarchy – ignoring terms may very well result in inaccuracies. I suppose that depends on what is being solved or equated perhaps but that is more in the realm of engineering (i.e. ignore a certain term that is dominated by another for simplicity). Perhaps it is more of our use of mathematics that is hypotaxic in our drive to extract what is useful or profitable from it. I’ve noticed recently, even working in the fields of data analysis, engineering and computer science, that many managers/leaders in our corporate world are often quite repulsed by anything deeply mathematical. The constant insistence to simplify, almost to the point of obliteration of meaning, results in numerous mistakes and oversights in the drive to reach Q2Q profit objectives. Its as though we don’t wish to take the time to figure out where we are going.

    Likewise, I’ve heard that quantum physics is a field that is essentially reinforcing the very beliefs that the animists were practicing thousands of years ago (and still do in remote places such as Siberia where shamanism still exists). The boundary where the hypotaxic meets the parataxic so to speak – that’s where the great mystery of life and our existence still thrives. I personally think it is amazing that math can come full circle and teach us the very things our ancient ancestors taught us if only we are willing to listen….

    • the Heretick says:

      just winging it here, however, it seems to me that math is the most hypostatic of anything talked about here in that it necessarily requires drawing a conclusion. mathematics by it’s very nature is hypostatic, it can’t be anything but, hypostatic that is, swimming pools, movie stars.

      as for your business associates focusing on quarterlies, that’s what they do, it might not be the math but anything that gets in the way of the groupthink. it is becoming more and more difficult for the clones and drones to ignore the reality of what they are doing. and the effects upon the planet and it’s inhabitants. once again, might not be the math, just that they don’t want to think at all.

      this quantum physics meme has been around for quite awhile now, and I don’t buy it either, seems a sort of false Zen suffering from the same wishful thinking permeating much of modern thought. just because we are able to break down the cosmos into individual constituents does not automatically mean we have any greater appreciation for the parts, or the whole, for that matter; it may very well be the reverse.

      if modern science has taught us anything it may be the realization of what we don’t know, but then, because of the hypostatic nature of the entire enterprise, we still fell that there must be an answer out there, some further discovery, and there we are, off to the races.

      Cartesian you see, if I’d had a Luger,,,,,,,,,,,,,,,,,,,,,,,,,

      just some thoughts that came bubbling to the surface when I read your post, a mind is a terrible thing.

      • Disaffected says:

        Can’t be sure who’s right on this one, as higher math (anything beyond Calc I) entirely eludes me. I do have occasion to interact with some PhD Physics types from time to time, and I do note that they are definitely NOT what most of us would refer to as “analytic types” in the conventional sense of the term for the most part. But I noticed the same traits emerge (or at least I thought I did) among my fellow students as I “climbed the mathematical ladder” in college to my eventual failure point. Calc I had A LOT of students like me of marginal ability struggling to keep up, but otherwise doing just fine. Calc II was a fallout zone in the very first week for over half of my class. It was if I’d been transferred into an advanced foreign language course with no preparation whatsoever. When I talked to the professor before dropping the class she told me my experience was common. I knew then that I was TRULY not a ‘math person’ and never would be.

        That said, I’ve worked in aircraft avionics maintenance, I work in budget now, have an advanced degree in finance and accounting, do some fairly advanced computer programming in my spare time, and have a very good ability to numbers in my head, so I’m no dummy either. Bottom line: I think there’s actually two “maths” out there. The computational, everyday experience variety (roughly, up to College Algebra and/or Calc I), and the theoretical, not intuitive at all variety that the real ‘math geniuses’ practice. My sense is that math people are therefore two: hypotactic for us mere mortals and paratactic for the higher level relative geniuses. Similarly, I’d like to suggest that paratactic thinking (at least in the mathematical sense) is actually using higher brain function than the hypotactic mode – the ability to intuit or ‘see and know without computing’ if you will. Witness Einstein’s many ‘thought experiments’ he used when coming up with the Theory of Relativity.

        Anyway, just some random thoughts with no academic basis whatsoever to back them up. Cheers!

        • the Heretick says:

          i’m sticking to my guns on this one, Einstein’s thought experiments were to reach a definite conclusion, the ultimate recursion. when reading about the Piraha people they had no interest in the future, they are interested in the immediate, didn’t want to talk about much that was not present.

          • Colin says:

            Heretick – I’ve done mathematical proofs in my sleep, literally. I had a take home exam once that I thought I had finished until I went to sleep and then woke up suddenly realizing that my answer to the final (and most difficult) of four proofs was in fact all wrong. I shredded it up and redid it because the answer came to me in my sleep. Doesn’t really fit in with what you are saying…..

        • Colin says:

          You are correct DA – all advanced mathematics comes from Parataxic thinking. Solutions arrive holistically not derivation-ally. Often entire proofs just pop into mathematicians heads fully intact for seemingly no reason and they have to reverse engineer that for the rest of us. There are no terms at that point like Einstein visualizing flying around the earth at the speed of light. I don’t agree with Heretik at all on this one. Higher order math is almost ALL visual and has no language constructs whatsoever. Proofs and derivations are just various ways of trying to splice and dice it into human form. Math just is….

          • Colin says:

            Sorry I should be a little more polite in my responses. I may disagree with Heretick on this particular topic but there is much agreement elsewhere…..

            : )

            -Colin

  8. Glad you mentioned the simmilarities between modern physics and ancient wisdom, which I develop in “A Taoist Politics: The Case for Sacredness”.

  9. You didn’t respond. I’ll reciprocate!

  10. Disaffected says:

    Looks like the shit’s gonna hit the fan for real in the Ukraine.

    • the Heretick says:

      the Shrub just came out and said yer fer us or agin us, whereas the Nobel peace price prez merely sets up the dominoes. my sole comment on this has been “do they really think the Russians are going to give up one of their few warm water ports?
      this goes all the way back to the Crimean War, they lost that one but hey were back, weren’t they?
      the commentary of the lamestream media on this one is asinine.
      this is sheer stupidity, if they want to push the Russians into a corner they sure picked the right way to do it, which is in my opinion a pretty stupid thing to do.

      geez, they just can’t leave well enough alone, can they?

  11. See my two background pieces on the Ukraine at http://www.otherjonesii.blogspot.com. It’s part of the spread of globalized fascism.

    • Disaffected says:

      Good stuff, but hardly surprising. CIA has been spreading American capitalist malignancy for 66 years now. The cold war will never be one as long as the US exists. The enemies may change, but the objectives will remain the same. World domination in the interest of capitalist plutocrats.

    • kulturcritic says:

      Deena, perhaps we could do without the advertising… just post some thoughts. If folks like what you say, they will just click your name and go right to your site. Also, they have a link to you on my blog roll.

  12. the Heretick says:

    let’s see if his video will open in Mother Russia

  13. Nichole Webbering says:

    The presence of a singleton hardly invalidates the theory. Although it does set up an interesting set of hypotactic what-ifs that you’ve laid out quite nicely, Sandy.

    It’s a good essay, although it strikes me as a bit out-of-its-natural-environment as it’s about as far from paratactic as one’s likely to go, unless Hugh Kenner were still alive. And I think he’s dead. I think even Chomsky is likely a bit less recursive.

    But, for all that, it was a pleasure to read and think about. I did myself the favor of commenting after simply reading the essay and ignoring the comments. I’ll go back now and maybe read them.

    Excellent work.

    • kulturcritic says:

      Of course, the example of the Piraha by itself does not invalidate his theory. But, it would be hard to validate a universal theory of human language that relies for the most part only on languages that can be studied, i.e., written languages or perhaps living oral tongues already influenced by contact with written ones. And, yes, I do write rather hypotactically, trained as I was. And I know for a fact Chomsky can and has been every bit as recursive as I was in this essay. 😉

  14. Nichole Webbering says:

    And excellent as it is, I’d still suggest something more. A short story called “Forgetfulness” by a fellow called Don A. Stuart, who was John R. Campbell, Jr., that was originally published in Astonishing Stories magazine (1937.) I read it back when I was in high school and was much enchanted by science fiction.

    Perhaps you’d like it. I recalled it while reading the comments. It’s a lovely story that certainly resembles hypotaxia and parataxia combined in the people of a planet called Rth. 🙂 It’s the only story in the anthology, Adventures in Time and Space that I can recall now. It made a huge impression back then.

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