Torus, Time-Space, and Themes of History: A Doughnutology?

I would be honored if @achronon and @Geoffreyjen_Edwards would consider using this thread to continue to explore with me and any interested parties more thoughts along these absolutely fascinating deviations from Sloterdijk’s encirclements of space. Ed is right - we have drifted from spheres a bit, but in a good way. In the emboldening, cross-pollinating spirit of this place, I proceed…

(quotations from “Live Conversation #8-8/3-The Siren Stage: On the First Sonospheric Alliance”, part of the discussion of Spheres I: Bubbles by Peter Sloterdijk)

I’ll have to move Ingold up the to-read list. In the meantime, several things occurred to me:
The “world-line” is perfectly illustrated by, say, the orbit of the Earth in space. Because the sun too travels, the Earth really moves in a spiral rather than an ellipse. The same is true of human history in the oft-quoted observation that one can never step into the same river twice.
That space is “greater than the speed of light” is a speculation that astrophysics has been considering: the cosmic horizon need not be the actual ‘edge’ of the cosmos, but only the part we can see. And that part may be very small indeed - at the very least whatever blew out of the “bang” ‘the other way’, expanding with the rest of space, will never be observed from our vantage point simply because the light will never make it here. Given enough time theoretically, everything except our galaxy (augmented by collision with M31) slips over the horizon and effectively vanishes… (But does that torus come back around? …)
What really “baked my noodle”, related to the above, is why space should be faster and time slower than light. One reason may be that structure can be mapped efficiently in a way that process cannot. Maps are designed to visually capture in a simplified way, and the normal limits of space-time do not have to be a factor. We can take a journey from the surface of the Earth to the cosmic horizon in one of those delightful five-minute animations. But Andrew Marr needed eight one-hour programs to attempt to hit the highlights of the history of humanity. Too many moving parts requiring explanation; too many vantage points to consider.

And to continue with this, Carroll Quigley identifies seven ‘stages’ in his account of the rise, fall, and “recycling” of civilizations. Quigley was one of the first civilization analysts to work a recycling phase into his theory, unlike Spengler’s closed and Toynbee’s semi-open systems. Quigley’s world-lines never come back to the same place either (hence recycling rather than re-constitution or ‘renaissance’).

All of which to suggest, as a start, that Geoffrey Edwards is definitely on to something: can we have an adequate philosophy of space at all that does not also take into account its links with time? Bringing things back down to Earth, while planning for better ‘media’ and/or communities (integral cities and the like) should the recurring theme of “pulsation” (cycles of order and chaos, solidarity and fragmentation, the fleeting generational configurations of matter and information as they replace each other, etc.) be expected, even worked into the scheme? How so?

Maybe it’s just me, but I sense the Force is strong in this doughnut metaphor!


Literally, at the moment you created this topic, I was about share this video to the Siren Stage thread. Perhaps a bit on the new agey side, but it illustrates this toroidal pattern as well as hints at some potential applications in the field of ‘free energy,’ which has also been mentioned elsewhere (and I remain skeptical).

“The torus is like the breath of the universe. It’s the form that the flow of energy takes at every scale.”


As the software genius never tired of pointing out, there is a difference between “free speech” and “free beer”, but anything “free” appears to be anathema to vested interests, so if the advocates of “free” cannot be outright silenced, they can at least be marginalized. Marginalization is the new excommunication from the two great faiths of modernity: High Finance and Scientistic Orthodoxy. One needs a certain amount of courage to pay attention to the heretics anyway.

In the energy domain, Tesla came the closest, but they managed to control him eventually. He may have been just a bit brighter than the rest of us, so it may take a while longer to duplicate what he did. The springboard of his notebooks has been taken away of course, and those who are sitting on them have apparently either forgotten them or know why they won’t be made accessible. I suspect that vested interests are involved, so it’s left to the rest of us to find out who out there is just new agey and who might have something of value to contribute.

The two other names dropped in the video – Young and Fuller – are must-reads (The Reflective Universe and Synergistics, respectively (sorry @patanswer :yum:)), but they are impossible for anyone who is erroneously intimidated by “science” and so avoids such texts like the plague. Unfortunately, I do not believe that we can afford to remain as scientifically ignorant as most of us are. We need to be able to at least generally understand what the serious folks are saying, especially given the fact – as we are increasingly seeing – the boundaries between science/philosophy/spirituality/consciousness/art are becoming more and more blurred.

The great thing about the torus, though, is that it appears to be more than “just” a metaphor.


As Einstein made so cogently clear, it’s actually relative … to light. And therein lies the rub. Spacetime maps (which @Geoffreyjen_Edwards was referring to) are one way of helping us get our head wrapped around the subject, but without some grounding in so-called quantum theory, it may be a more-than-merely-arduous task. My all-time favorite introduction is Fred Alan Wolfe’s Taking the Quantum Leap simply because it was written by a scientist for non-science-types (and it is short: ca. 200 pages). (There are other good, less casual texts available, such as Herbert’s Quantum Reality, Deutsch’s The Fabric of Reality, Greene’s The Fabric of the Cosmos or his Elegant Universe, but they are admittedly more demanding, too.) And Jones’ Physics as Metaphor functions well, I think, as a follow-up to Wolfe.

But Geoffrey started out as a physicist, maybe he has some enlightening insights or suggestions of his own that may be helpful.

The best process model of which I am aware is Arthur Young’s which he describes best by using it in his The Reflexive Universe: Evolution of Consciousness (to give its full title). It is based soundly in quantum physical theory (Wolfe can be a helpful introduction but is not essential), and it is structured around dimensional shifts based on degrees of freedom (which all sounds much more terribly complicated than it is), yielding a very useful, elegant model that has general applicability far beyond Young’s own use of it. (I used Young’s model to develop a process for curriculum development for my daughter’s English-as-a-foreign-language training business that unfortunately went under in the Crash of '08.) Very helpful as well is the appendix he includes in which takes about 30 pages to delve into the notion of sevenness in more detail, without devolving into neo-platonic esoterism as is most often the case when “the meaning of numbers” is involved.

To which I would reply with a simple “no”. What Gebser’s approach showed is how the notions of space and time are interrelated throughout the various structures of consciousness. We don’t have to agree with Kant that they are unique categories of mind, but they are certainly important aspects of consciousness that must be reckoned with in any portrayal of who or where we are and where we may be headed (physically, evolutionally, historically …).


I probably should have posted my last post here and not in the Sloterdijk discussion, but nevermind, I’m sure nobody will mind all that much :slight_smile: For quantum physics, my all time favorite - I’ve just reread this last year - is Richard Feynman’s little book called “QED : The Strange Theory of Light and Matter”. It is short, poetic, and visionary. Feynman had an amazing clarity is his thinking about quantum physics, and his understanding was deeply intuitive. I think he conveys this admirably in this book (it’s only about 150 pages). Your reference, @patanswer to orbits is a perfect example of a world-line, although, in reality, everything has a world-line. Regarding the practical issues about spacelike intervals that I hinted at in my last post, there are problems with the overall uniformity of the cosmic microwave background. The background is more or less uniform across its entirety (isotropic is the correct term - in all directions its value is more or less the same) ; there are small fluctuations and these are important, because the presumably trace the rise of structure in the universe - superclusters of galaxies and suchlike. The problem, however, is still that the whole thing is more or less the same in all directions. The problem is, if you look in one direction (say, towards the North Galactic Pole, where the stars are thinner and there is little dust and gas, hence you can see more easily distant galaxies) and in the opposite direction (e.g. the South Galactic Pole), the cosmic background in those directions are spacelike separated. Over the age of the universe, light hasn’t had the time to move from one region to the other. But for things to have equal intensity, they have to have communicated several times. Hence, for example, randomly one region might be much hotter than the other. The infrared radiation that expresses the heat must have travelled to the other area, and raised (or lowered) its heat, and vice versa, for the two regions to have similar values. Typically, this needs to happen a few times for the heat to average out. But for regions that are spacelike separated, this is not possible. So how come one end of the universe has the same background temperature as the other end of the universe? The answer given today, is that in the distant past, the two regions were part of a much smaller volume of space that expanded rapidly (what we call “inflation”). So inflation helps explain why they look similar - they communicated with each other when they were nearby, and them moved away. And yes, the universe may be a lot bigger than just the part we can see…

The problem I have with the torus, and with the video @madrush put up about torii as “energy sources”, is the same problem we’ve been discussing with regard to Sloterdijk. Tori may have holes, and hence allow for more circulation than spheres, but they are still, ultimately, closed forms. The Deleuze/Ingold argument is that there are no closed forms in nature - everything is worldlines. Closed forms are mathematical abstractions, not physical things, which are always made of worldlines (and this is true of both particles and waves, matter and energy, although, possibly, we may also be talking about worldsheets if we generalize strings in the same way). But worldsheets are still open structures.

Also, perhaps more closely tied to the Sloterdijk discussion, you call, @patanswer, torii a metaphor. Increasingly, however, I am drawn to “metonymy” instead of “metaphor”. Metaphor is mapping one thing into another, usually from distinct semantic domains. Metonymy is substituting a part for the whole, usually in the same semantic domain. Hence a “crown” is metaphorically a “halo”, but metonymically a “king”. I’m not sure where to take this idea forward, I just know that “metonymics” is functionally, and perhaps arguably, a more powerful mode of reasoning than is “metaphorics”. Indeed, the torus as part of a human (because it involves only one hole rather than many) is perhaps a more accurate way of describing its role than the torus as being “like the human” or “comparable to the human”. Then we are not locked into its closed form nature, either… Thoughts?


Resonance. Seems to be quite a regular thing around here, which is, in a word, awesome.

Oh, no problem… :sob: :smile:
I’m ordering the Young book today, as that name keeps coming up for me in several settings.

Indeed. It occurred to me after I posted that as far as models go the torus is actually a way to think about both structure and process “simultaneously”, which makes it closer to ‘what is’ than any map of any ‘single’ place or point (from whatever vantage). And as pointed out in the video, it’s an observable pattern with great explanatory potential for the atom as for the galaxy, i.e., there is a demonstrability here that goes beyond the normal limitations of our symbolism.

Want to know something funny? Part of the reason for what popped into my head last night was because in your first quoted statement here, the y-axis was space . I only remember seeing graphs where the y-axis is time with the ‘what-could-have-beens’ below focusing on the present “0,0 coordinate” and the possibilities of the future spreading out above from there (to the exclusion of points to the sides that can never be reached from that “now”). So space suddenly represented the infinite ‘beyond’ light where we can go in our imaginations as we choose, not merely the “sidelines” of alternative history. I know the labeling of the axes doesn’t really matter (not least because spacetime is an inseparable is after all (LOL)), but I had, just in that moment, something like a personal paradigm shift.
My “metaphor/metonym” of the doughnut, clumsily (or not effectively) expressed in the excitement of several a-has, was less about the “hole” and more about the rotation(s) of the surfaces, how if the whole is self-contained it is so in a continuously dynamic way and how that understanding might inform our understanding, on the level of human collectivities, of what and how we build. (Could it be that Sloterdijk actually does know that closed forms do not exist in the real world and that is why his spheres are nested and porous - and temporary?)

In “substituting a part for the whole, usually in the same semantic domain”, metonymy sounds magical (meaning the consciousness structure). I would say there is room for discussion as to whether it is absolutely or conditionally more powerful than metaphor (whether through ‘halo’ or ‘king/kingship’, “crown” still leads to the entire ideological and political mystique of authority), but your example is certainly food for

Oh, yes, lots of them!

Thank you all for your replies, further reading recommendations (it’s a good thing to never have time to be bored!), and indulgence of what may simply be my process of catching up. But, I don’t know - there are some intriguing linkages here… and truly great minds in this group. Sincerely meant.


I am begging the indulgence of all for being so anal-retentive at times. Yes, yes, yes, I know I’ve got a whole list of pet-peeves that I need to get working on, and I promise I will get started immediately after this one small point of order:

Metonymy is the substitution of the name of an attribute or adjunct for that of the thing meant, for example suit for business executive, or the turf for horse racing.

Synecdoche is a figure of speech in which a part is used for the whole or the whole for a part, the special for the general or the general for the special, as in ten sail for ten ships or a Croesus for a rich man.

mea culpa, mea culpa, mea maxima culpa :anguished:

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I wonder if there could be an opportunity for a seminar on Bucky and/or Young? They are more admired I think than they are understood. I have both books you mentioned, Ed, as well as Geometry of Meaning. Although far from easy to follow I find Fuller writes really well and Young is very much to the point! There are videos of both men on YouTube. This would be an opportunity for me to ask meta-questions of those with more technical expertise than I have. If we are to get beyond the two cultures divide we will need to start somewhere. It would be nice to do a meetup like the Bubbles conference call. It would not need to be a close reading but perhaps a comparative study of two Visionary Thinkers.


Not at all, thanks for the correction!

Would it be accurate to see all of the above as examples of symbolism?

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This needs a bit of clarification for me. Just what exactly is a closed form? I mean, when I think of a rock, for example, it seems rather closed. And if closed forms are “only” mathematical abstractions, I’m not sure Deleuze/Ingold are best qualified to be asserting things about them. Please don’t get me wrong: this is not a criticism, rather I’m confused and am looking for some clarity.

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Just once it would be nice if you asked a simple question. :sweat_smile:

“Symbolism” is a notion I’ve been wrestling with ever since one of my junior-high English teachers used the term oh, so long ago. It’s one of those words that gets used, misused, and abused so much that it’s hard to tell anymore what it really means. I still tend toward thinking that symbols become symbols by usage and acceptance (i.e., somebody uses one and others think it’s a good shorthand for what was meant). In our Western cultures, for example, red roses can symbolize love. That may not work in other cultures where different colors and flowers have accepted usages.

The moment we leave the realm of the factual (tori are “this”) and start using them in metaphorical, metonymical, or even synecdochial ways, we are certainly heading toward “symbolical”. I’m just not sure when we actually arrive.


Well, I have to tell you, John, the rest of us have started a pool betting on which books you haven’t yet read. :rofl:

But, it is nevertheless still true that great minds think alike. I’ve been kicking this around as well since the torus side-discussion was brought to life. :thinking:

The idea of a seminar, in contrast to a close reading, is a good one, and it fits in well with @Geoffreyjen_Edwards’ input regarding teaching and learning. The seminars I experienced during my studies here in Germany were precisely this: communal/cooperative explorations of a topic, which in this case could be the consequences of a particular line of thought.

When we read Gebser, I got the feeling we were trying to answer the question, “What does he mean?” The question I see driving the Sloterdijk reading is more “What is he saying?” In regards to Fuller and Young (which I would think might be advantageous to approach separately, and, should there be any survivors, then do a comparative study) perhaps a slightly different approach might be productive: if what he is saying/advocating/presenting is correct/accurate/relevant, what does that mean for the rest of our lives?

Granted, that sounds a little weird, but it is what I think you mean by your “meta-questions”. I mean, it’s all well and good that there is all this technical mumbo-jumbo, but it appears to have relevance IRL, and if that is in fact the case, just what is this relevance and how does it manifest itself. In other words, a reading of Fuller or Young in light of the guiding question, “So what?”

It would certainly be a bit different from our readings to date, that’s for sure, and given the amount of YouTube material that could potentially flow into the reading/discussion, it could be a challenge to manage as well, but it is certainly worth thinking about, and I think it has the potential to be a lot of mind-bending fun, too.


When I was ten years old I was alone in the house, a rare occurrence, and happened to be watching a show on TV in my parents bedroom. On the small TV set a man dressed in a black outfit, blonde hair and with a British accent was alone on a stage. He looked at his hand and said, " Oh that this too, too solid flesh would melt, thaw and resolve itself into a dew…" My attention was riveted. I sat on the edge of the bed and was fixated, having no idea what the actors were saying but caught up in the irresistible flow of the language and the outrageous actions performed, sword fights, poisoning, plots, ghosts, talking to a skull, etc. I also had wanted, as Hamlet so well expressed, to disappear. That another human being had this feeling woke me up to a shared reality. That this shared reality is “symbolic” has always baffled me. I’m glad I’m not the only one who is baffled!

When my parents asked me what I wanted for Christmas I replied," I want The Complete Works of William Shakespeare." That surprised them but they got me what I asked for. I memorized huge chunks of Hamlet and most of the other tragedies and I had no idea what it was about that drew me to these mammoth texts. I waited until the house was empty and I would act out all the parts. I was a very weird kid. It wasn’t till many decades later that I started to study metaphor, simile, metonymy, syndoche, etc., and I have always felt that I was on a journey without a place.


I so agree! So maybe we can think about what needs to happen to make this happen? There are many ways to shape this and I look forward to the opportunity to find the next wave.

Count me in! If all goes according to plan, at the very least I will bring my questions and thoughts about A. M. Young to this thread. (I put a rush on the order. :grin:)
And, yes, ‘consequences of lines of thought’ is why “themes of history” is in the title. Human spacetime with its baffling symbolism is definitely part of this trip.


Woody Allen quipped," I took a speed reading course. I read Tolstoy’s War and Peace. It was about Russia."
I have found that a group read helps me to articulate my difficulty with a text and then I remember better what the work is all about. If I’m away from a text for a long time much of it starts to fade, unless I review often or am engaged in conversations that focus attentions. I have read a lot as most of us have but I don’t pretend to have integrated much of it. After accumulating enough life experience and contemplating many books it becomes more than just a pleasure it become a duty to integrate. So maybe this is like a lab where we test our comparative intuitions.


Well, @johnnydavis54, since all real (physical) forms are made out of particles and waves, then they consist of, at a microscopic level, of mostly “empty” space. The rock only appears solid because the receptors in our eyes are too coarse in resolution to see all the holes that are actually there. But Ingold is also thinking about the rock as a bundle of world-lines - ok, a reasonably thick and dense bundle - each molecule, say, has its own world-line and the rock kind of has a ropey appearance in space-time, that is, stretched forward and backward in time. He describes pebbles on a beach, and notices how those pebbles are actually quite mobile - they were moved around by the waves and certain extreme weather events and are by no means as stable and unmoving as they appear to be. Mathematical forms, such as circles, spheres, cylinders, doughnuts, and the like are all, by definition, “closed” - they have no leakages at all. Real world objects, even rocks, leak. And certainly (human) bodies do. And as someone said (I can’t remember who now), Sloterdijk does “relativize” his use of the idea of “spheres” so that they are porous and not always well defined and bounded.

Ingold point out that objects are a form of classification. That is, we classify certain kinds of worldline bundles in terms of the perceived boundaries around them (e.g. surfaces) and call these “objects”. We name them (“ice cream cone”, “house”, “car”, etc. - these are easy because they are manufactured for the most part) but also, and perhaps less defensibly, “hand”, “arm”, “foot”, etc. I agree that the argument about worldlines does not mean we should abandon talking about objects - it is a survival function to do so. It would take too long to explain to someone you were trying to rescue that the life jacket we want them to grab is actually a space-time ropey thing whose worldlines we want to bend so that it passes in proximity to the person, so they can bend the worldlines of their hands to reach for this thing we’ve momentarily partitioned off as a flotation device! But being aware that these objects are not “real” in a deep sense, that they are perceptualized partitions of a world that is, ultimately, indivisible, also confers another kind of survival function - it forces us to stop seeing the world as infinitely manipulable as the object-perspective leads us to do. Because seeing the world as infinitely manipulable seems well likely to result in our destruction as a species, if it hasn’t already sealed our fate. So what appears on the surface to be “abstractions” of little note, turn out to be tied into the very political and ethical dilemmas we now face as a species/civilisation, and it may be crucial that we become more knowledgeable, as @achronon indicated.

Hope that helps. There are parts of Ingold’s arguments I have trouble with - although maybe not the same parts as those Ed (@achronon) finds problematic :slight_smile: It is not his dismissal of objects I find problematic, as a physicist, objects went the way of the dodo about a century ago (lol). But he seems to be saying that knowledge is actually all a matter of story. I have this long ongoing argument with certain people who believe that story is everything for human beings. Don’t get me wrong, I love stories, indeed, I write them, but I am very, very aware that a great part of the human experience, indeed, human knowledge, is not bound up in story, or in “facts” or “representations” of any kind. I don’t buy into the idea (shared by most scientists I might add) that knowledge is fundamentally a matter of representation. Perhaps certain forms of knowledge, but even there I am not sure. Now, admittedly, Ingold doesn’t mean story in the classical sense, story as “written down”. He means story as an unfolding of engagement between person and environment, which is certainly an approach which is less representational. But he still seems to discount what I call the “indicible” (it is a French word, with no direct English equivalent, it means essentially the “unsayable”, or even the “unthinkable”, the part of experience we cannot nail down, put into words, or even put into paintings or music or other forms of art). But I should finish Ingold before I jump down his throat, and so far I have liked almost everything he has said…

I did buy the Young book on Kindle, Ed (@achronon) so it is on my reading list too, but I need to finish Ingold (and Todres) before I move onto Young…

Regarding talking from my areas of expertise, like most academics, I love to hear myself talk and so I try to be careful not to clobber people too hard with an overdose of information. I may err on the side of not saying enough, but I prefer whetting your appetite than drowning you in a sea of information! But I will take your kind words to heart, @patanswer, and unstopper the bottle at least some of the time :slight_smile:


Thanks for this, Geoffrey, it points out very well an issue that I have been wrestling with (and confronting others with of course), namely the difference, but value, of distinguishing knowledge and experience. While they overlap, conceptually separating them quite often has the advantage of making both clear. We can know, for example, that solid objects are mostly space, but as your example with the life vest illustrates, there are more often than not times when what they “really” are doesn’t matter all that much.

The post-modernists with their incessant word-gush on narrative and discourse did it in for me. Like you, I find stories important, enjoyable, educational, and more, but to say everything is this or that is just another form of reductionism that doesn’t sit well with me. I suppose that is why I so often insist on clarifying terms, allowing multiple explanations to exist side-by-side, appreciate nuances of meaning, and the like, because I have found it to be more helpful than one-size-fits all thinking. This was a point that was intimated at any rate in your Intruder paper.

That was what prompted my question about closed forms. It would seem to me that it is at times helpful to think of the form as closed, while for the most part I, personally, tend to see the world as very open. I don’t mind and little contrast and distinction mixed in with my possibilities, and if someone is unclear about what I mean by something, they are always free to ask for clarification.


First, re the seminar, it sounds like a great idea and very much in the cross-pollinative/expansive spirit I’m hoping will catch on here—so I say go for it! Don’t count me in as a reader yet (it will depend on how certain writing projects feel like they’re coming along; that said, I already have Young’s book at least in my Amazon cart) but definitely count me in to provide whatever process-related support is needed. (E.g., Zoom link, recordings, etc.)

My design intention is that people will ultimately be able to set up and conduct exactly these kinds of organic conversations very fluidly and autonomously, so I would be quite interested in learning/observing exactly how a conversation like this might want to self-organize, where the gaps are, and how we can facilitate things happening more smoothly, maybe even ecstatically.

Let me also offer thumbs-up Ed’s approach here:

I’m really enjoying this dunking into confectionary topologies, but where it gets most interesting for me is when I start feeling the contemplation of an object (e.g., a toroidal structure) directly affecting the shape of my consciousness and how I interact with the world. It can be especially powerful to note recurring patterns at various scales (microspheric, civic, cosmic…as Sloterdijk is also doing), and thus to see, again as Ed suggests, that these are not just metaphors. Or metonyms or synecdoches or whatever (forgive my looseness here). :slight_smile:

These innovations of language enable the leaping between scales and transposition of contexts which are so helpful to thinking. There is a fractal quality obviously when we can find the whole in the part, which allows the mind to leap through dimensions.

I go back to Sloterdijk’s first words in Bubbles, placed in Plato’s mouth: “Let no one enter here who is not a geometrician.” How true this has become suddenly!

I would also note (though this might be better addressed in a new thread) that Sloterdijk ends Volume 1 of Spheres precisely on the topic of a departure from closed form–i.e., from the Trinitarian unity to the unabsorbable phenomena outside the intimate sphere—the monstrous.

Here the question of scale and shape, and whether or not and how (“if that torus comes back around”) phenomena rise, fall, and recur—is really worth thinking about. I’m personally holding a space of considering how some theory of an eternal return could be true AND how a singularity event could explode any such conception. This feels relevant to what I call my soul.


Hooray, and up she rises! Love it, @madrush, the Eternal Return and Singularity! The perfect Paradox! Another kind of idea I love…paradox!