Montréal, March 15, 2000
A professor of depth psychology at a coastal California university, a friend of a friend, ... went into a non-clinical psychotic state following the death of his wife. He, like Carl Jung, ... thought it important to document his unedited thoughts and feelings while immersed IN this state, so that when he came OUT of it, he would be able to reflect on the different interpretation of the 'inside story' from the rational-storyland 'outside', ... and also, ... so that he would be able to share this 'in and out' experience with others.
He foresaw a problem.
There were some sexual thoughts and geometries in his 'inner story' which were very important, but which, for him to openly share them, would be seen as inappropriate or 'politically incorrect' by some of his colleagues and students, ... even though their common medium of focus was depth psychology. In their eyes, it was perfectly okay to share and relate the sexual thoughts of an anonymous 'patient', ... but it was 'on the edge' to dump one's own kinky fantasies out in one's papers and lectures.
But there was an innate geometrical issue tied up in this situation, which the professor saw, ... a geometric issue which I also see and run into, ... that there is a deeper understanding which comes from the reconciliation of the inner and outer, ... and you can't take an 'inner' from one person and apply your own, or another's 'outer' to it, ... the inner and outer reconciliation must operate on a matched pair of operands.
So the professor did include some of the inner sexual geometries along with his own matched outer reconciliation and he did get some flack, which he is managing to weather, ... and some who were at first curious with why he would ever include this sexual material, ... through their experience in 'walking through' his reconciliation of the matched operands, are coming around to understand and appreciate his rationale.
There is a general informational principle here. It is that we are capable of dual perceptual modes, ... 'wave' and 'particle', .. 'implicit' and 'explicit', 'inner' and 'outer',... which we are aware of in terms of 'immersed' and 'voyeur' feelings, and which correspond to our use of different space conventions, 'non-euclidian' and 'euclidian', 'possibility space' and 'actuality space'.
Furthermore, 'understanding' (implicit, relational, pivoting from explicit), as contrasted with knowing (explicit, structural) occurs in the proximal zone of reconciliation between the 'inner' and 'outer' (Vygotsky). Knowledge (explicit) is a product of voyeur experience. Fantasy (implicit) is a creation of 'inner' experiencing, ... and 'understanding' (implicit/explicit), where we assimilate the deeper meaning associated with coresonance between possibility space (implicit) and actuality space (explicit) by abandoning ourselves to the deep and intimate feelings of 'going in and out'.
Now, if you have ever wondered why mainstream science can't 'get to' an understanding of this, ... the answer is, because science epitomizes 'voyeurism'. It is always looking down microscopes or looking up through telescopes, and keeping the observer in the 'outer' world, the material-causal world of 'actuality space'. Controlled laboratory experimentation is intended to 'detach' the phenomena from environmental immersion, ... to take it 'offline', ... to 'beach' the fish to better voyeurize it.
Certainly, the scientist's perceptual mind will make forays into the 'inner', the relativistic-inductive world of 'possibility space', .. but like the psychology professor, ... the scientist is expected to 'edit out' his 'inner' experience and present only those aspects which are consistent with 'actuality space', ... the lesser of the two spaces in a dimensionality sense, since 'possibility space' contains 'actuality space' as the special case where space-time uncertainty drops to zero (where the actuality is precipitated, .. where the egg of actuality is laid).
If you fart in an elevator, ...
Wait a sec, ... does that statement come as a bit of a jolt, ... as if it is gratuitous mischief thrown into the works to break the flow and context?
That was how some reacted to my Oct. '98 essay 'Smart Feller or Fart Smeller', and also to my Aug. '97 essay-story of Dlief and Field, which started off;
..."imagine for a moment that you have arrived on earth from another world --- a world in which geometries are the medium of understanding rather than the cultural context in words and images. imagine this in the same way as it might come to you in your dreams where judgement is suspended and all manner of things can happen and be 'seen', 'heard' or 'sensed' without cultural overtones such as feelings of guilt; i.e. from a 'perspective' which is 'beyond good and evil'. you are now going to look through the eyes and minds of two otherworld travellers, 'field' and 'dleif' as they visit earth for the first time ......
....... here we go, and don't forget to put your earthling culture 'to sleep' because 'field' and 'dleif' are going to expose you to some conjugate spatial geometries which characterize a dual-state or dipolar space of the type we live in --- i.e. geometries which include 'shadow' images in psychologist's terms."
Our acculturation does not like us to be reminded of the self-referentiality of our natural world, ... that there is an unbounded continuity aspect to space where the 'fluids' or 'juices' which are exhaled from our pores and orifices are inhaled into our own and everybody elses pores and orifices. When the bodies of a man and woman interpenetrate and the juices 'exhaled' by one are 'inhaled' by another in the natural process of things, mysterious developments may occur, ... which speak to the unboundedness of space and its primacy over the notion of 'independent' things'. The fluids inhaled by the woman mix in with her substance and the two substances now within her begin to dance together and interpenetrate, just like the man and woman were doing, ... and the dance enlarges as more substance 'gets the beat' and joins, like adjacent sky joining in on the formation of a hurricane, until there is a whole new community of dancers which we refer to as a 'child', ... but a child who can become a parent in the same way as its own molecular and cellular dancers became 'it'.
And what about the man and woman we started with?, ... doesn't the process of speciation look very much the same, ...starting from 'Lucy', an early first woman, ... a brand new dance form, ... who perhaps shared juices with animal friends, ... the new 'song' which was in her, ... the new 'beat', .... which was now in her juices and which would continue to inform more world substance so that the story of the dance continued on into the present where we now have six billion dance colonies at one time, who are all doing their unique dance, ... to a common geometric dance rhythm and beat.
Space has this strange character which we tend to put out of our minds, ... this unbounded self-referentiality of space. The participation and connectingness of space as in the notion that a morsel tasty to ducks can be attached to a thread so that several will eat it and quickly digest and pass it with the result that the string will thread through the ducks like the string on a necklace threads through many pearls.
The psychology Professor's colleagues and students did not want to have to think about the fact that there are no fundamental separations or boundaries between one's mouth and another's anus.
But if one wants to 'understand the way the world works', it is important to consider and reflect upon this geometry and the fact that it is impossible to conceive of this geometry in euclidian space, ... the 'home' of mainstream science. It is not possible because in euclidian space, you can only have independent 'things' and 'void'. The several ducks on a string, could also be called a 'thing', ... a curious thing to be sure, but a distinct 'thing' with its own properties and behaviors, ... eight legs, four heads, ... a length of ten feet, ... propensity to get confused when walking in treed areas, and so on. Aristotelian, exclusionary logic, which goes hand-in-hand with euclidian space in our mainstream science, .. can only deal with 'one thing at a time', ... it requires 'fuzzy logic' and Kosko's 'yin-yang' equation (A = Not.A) [constituent = container] to deal with multivalent and multiphrenous things.
Apparently, to the young fertile female, ... the unboundedness of space and its fluid flows make a difference, ... and the same goes for the folks on the elevator.
The other thing which one can note, informationally, is that there is always a natural periodicity associated with these things, ... these interpenetrational flow-developments do not come and stay forever, ... there is a kind of flowing co-dynamic character to them. When the petroleum wellsite geologist on an oil drilling rig wants to know how long it takes the drilling mud to circulate from the top of the hole down to the bottom of the hole, perhaps three mile down and three miles back up, ... he looks at his watch as he tosses a handful of calcium carbide pellets into the mud, ... a chemical which gives off acetylene gas the moment it is moistened with water. When the gas detector in his geologist's trailer, which is analysing the mud returning from the bottom of the hole, trips the gas alarm, ... he knows that the cycle of circulation has been completed, and he can record the elapsed time. While flows look continuous, they have a cyclicity to them, .... old man river seems to just keep rolling along, ... but unlike in Escher's 'Waterfall', ... it is cycling up into space and coming back down and around again, ... what goes round, comes round, and gives the appearance of stasis. Everything in nature has this cyclic 'wave' aspect to it.
Now if you consider that, when you look at any material, including the human body, in fine enough detail, ... that it starts to look like the solar system, ... where there is far more space involved than matter, ... and where the basic nature of the beast is more about the harmony of 'whole-and-part' which is going on, ... a "dance" more complicated than can be deduced from the behaviors of the individual parts. When you think about all of this, and the fact that it extends on fractally downward to the home of quarks, ...each time space and dance becoming the more dominant characteristic, ... then the imagery may start to form in your mind that matter is basically 'space which dances', ... space in the primacy over matter and which determines form and behavior.
And if this imagery does form, ... then the imagery in your mind will be consistent with the general theory of relativity and non-euclidian space-time.
If such imagery does not begin to form in your mind, then I would ask your indulgence in please skipping over the finalizing of the Dleif and Field story which is between the two ~~^^~~ markers.
[we join field and dleif as they browse graffitti in an abandoned cabin in the mountains]
field; 'dleif, what do you make of those two interesting inscriptions over there?'
dlief; 'oh, you mean the inscriptions which read; 'the cunt that i am dicking is the me that is dicking it', and 'the dick that i am swallowing with my cunt is the me that is swallowing it'?
field; 'yes, those are the ones'
dleif; the earthlings are referring to the yin/yang geometry, that beautiful geometry of life whereby everything connects and enfolds within itself both physically and mentally --- society interacting with nature while being innately enfolded within nature --- man interacting with society while being innately enfolded within society --- man's material being or 'matter' interacting with his spiritual being or 'mind' while being innately enfolded within his mind. the earthling physicists refer to this yin/yang geometry as 'holonic' --- it is what they call a non-euclidian geometrical relationship which cannot be captured by finite systems of mathematics or logic. it is an 'order' or 'reason' pervading nature which transcends logic and rules.
field; 'very beautiful and very powerful!'
dleif; 'earthlings, however, tend to miss the geometries because of the cultural context they attach to words. one of their philosophers, Ludwig Wittgenstein felt that when this cultural context was attached to words, it put them into a trance, it was as if words put a hex on their minds.'
field; 'yes, my understanding is that earthlings burnt their fellow humans and locked them up in madhouses solely on the basis of what words they used, ignoring their direct experiencing of the geometrical dynamics of these 'witches' and 'madmen' which was often quite innocuous or even loving, and in any case, quite inseparable from the underlying geometries of the community as a whole.'
dleif; 'yes, this is true. earthlings have a strong tendency to deny their own experience, see themselves as decoupled from life's geometries and live on the abstractions in their minds engendered by cultural context. one of their 'psychiatrists', ronald laing, wrote at length and very clearly on this in a book he entitled 'The Politics of Experience'.'
field; 'this presumably is the same as the earthling's 'political correctness', a correctness which seriously corrupts and denies the truthful geometries. but in the case of these inscriptions, the beauty of the yin/yang geometry is such that it could not help but shine through to earthlings regardless of the cultural specifics or words used to give it form.'
dleif; 'i agree, in the yin/yang geometry resides a beauty which is far too powerful to be lost in the noise of cultural context. however strong the dissonant ring of political correctness, it would have been insufficient to drown out the rich symphony which flows forth from this geometry.
field; 'i have an idea. why don't we chisel these inscriptions into those fine looking granite slabs over there and bring them down from the mountain, and thus rendered, present them to the interstellar counsel as an example of earthling wisdom and their fine sense of appreciation of the beauty of life's geometries.'
dleif; 'let's do it.' * * *
The reason I recommended skipping over the story of Dleif and Field (conjugate 'IN' and 'OUT' geometries), was that when we are stuck in 'voyeur mode', we can only see the 'outer space' content or 'actuality space' content, ... but if we are able to go into 'inner space' or 'possibility space', ... the explicit images dissolve and give way to the pure, beyond content geometry. This is the space McLuhan is referring to in 'the medium is the message', and this is the space which Kepler describes as being sacred space, the sacred 'Now' of the space-time whole;
"Why waste words? Geometry existed before the Creation, is co-eternal with the mind of God, *is God himself* (what exists in God that is not God himself?); geometry provided God with a model for the Creation and was implanted into man, together with God's own likeness --- and not merely conveyed to his mind through the eyes."
The notion in Kepler's words here cannot be seen by analysing the CONTENT of the words, ... one has to think again, in terms of 'space-dancing' and the fact that if the space-dance is more complex than any of the material structures it induces, ... and it must be since one has to ADD space-time phasing (rhythm and whole-and-part harmony which cannot be deduced from the behaviors of the parts) to get from 'structure' to what we actually experience in nature.
If space or 'field', which is the implicit invisible stuff between 'things' has the 'bigger story' to tell, ... since it is immaterial, it can only be a purely 'geometric' (relational) story before we sprinkle on the material iron filings etc. to make it become manifest.. In other words, what Kepler is saying, like Heraclitus also said, ... is that 'space', or if you prefer, 'field' (electromagnetic, gravitational etc.) possesses the property of geometry which exists before that 'field' or space 'pulls' some matter into a geometric structural pattern which then gives rise to VISIBLE material form.
Now since man is capable of 'experiencing geometry', ... a geometry which has dimensionality going beyond that which material structures are capable of, the Creation which God is giving to man is not simply conveyed to man through his eyes (not simply conveyed through the visualization of material structures, that is). Kepler is at the same time saying, in effect, that this geometry, this property of space which embodies relational patterns beyond the material, and which is accessible to our minds, is an 'unbounded' continuum, so that God is a part of everything ('God IS geometry') and that we also are made of this geometry since it is this geometry which pulls our material form into being and into which we return after our material form gives out.
Here, we can see the 'pantheism' of Kepler emerge, as in the Zen, Taoist and Aboriginal philosophical traditions, and as apparent in the words of Proclus (pantheist neo-platonist) who Kepler greatly esteems and cites in his own works. Proclus (412 - 485 A.D.) had been poet, philosopher and scientist, and one of the last official teachers of the Platonic Academy in Athens, prior to an edict which forbade the teaching of philosophy by Emperor Justinian in 529. In his essay on Nature, Proclus says;
"We affirm Nature to be a certain power implanted in things producing like things out of like. For Nature generates, augments and nourishes all things. Wherefore it has in itself the names of all things. An animal is from Nature; a stone, wood, a tree, and the bodies which you see are from Nature and her maintaining. Nature is the blood of the elements, and the power of mixing which brings to pass the mixtures of the elements in everything in this sublunary world, and has imprinted on them a form agreeable to their species, by which that thing is distinguishable and separated from each other thing. Nor is Nature of any colour, yet a partaker and efficient of all colours: also of no weight, nor quality, but finally the fruitful parent of all qualities and things. What is therefore Nature? God is Nature, and Nature is God: understand it thus: out of God there arises something next to him. Nature is therefore a certain invisible fire, by which Zoroaster taught that all things were begotten, to whom Heraclitus the Ephesian seems to give consent."
Now since the general theory of relativity and also quantum mechanics embody this same primacy of space and the 'dualism' of 'in and out', ... of unbounded possibility space with its superior geometries and space-dances which pull material forms into being, ... it is easy to see why some quantum scientists have said, ... 'if you have explored quantum physics and don't find it bizarre, you haven't understood it'.
Our western culture and western mainstream science DO NOT ALLOW space to be geometrically superior (higher dimensional) than the world of material actuality, describable in terms of the structure of matter and the causal dynamics of matter.
It is for this reason, and not because of sexual mores, that the Professor of psychology cannot put his sexual imagery into his work and relate it to his 'outer' or euclidian experience, ... because of the geometry, not the sex, ... because the geometry of space will come out on top of the geometry of structure, the 'yin-space' will come out on top of the 'yang-matter', ... the world of space and imagination will come out as being 'bigger' and more powerful and more relevant and more important than the world of matter and rationality (i.e. they will in fact include matter and rationality as secondary features), ... and while that is a thought which has great appeal and makes great 'sense' to those of a Zen, Taoist, or aboriginal philosophical traditionalist, ... and while westerners may discuss such things in the neutered form of the conceptual and impersonal, ... it remains a thing of fear to those of us acculturated in the west who have grounded our worldview in materialism, ... and who struggle to amass the material as a means of increasing our security.
So, to summarize, .... 'going in and out' is, first and foremost, a geometry which transcends content, sexual or other, ... we are capable of ouroborical images of the snake consuming itself by swallowing its own tail. If one conceives of space in the primacy, ... the material forms of a male penetrating a female can be seen in the geometric terms of a self-referential swirling. It is the offspring of the geometric imagery associated with a magnetic field where the two polarities are an interpenetrating unity. The notion of physically and materially distinct, male and female 'poles' of a magnet is a secondary derivative of the unity which is in the spatial notion of interpenetration of a dipolar field. In other words, material opposition in the form of two conflicting material entities, is a lower dimensional, but 'included feature' of the interpenetrational geometry of the immaterial field. Conversely the anti-symmetry of material opposites is unified in the meta-symmetry of the interpenetrational field.
Like the psychology professor, ... those of us 'coming from physics' who would like to bring this primacy of space over matter into the open, .... since failing to do so and continuing to live and operate according to the belief that 'the material world' 'rules' is a recipe for continuing amplification of community discord and dysfunction, ... tend to be seen as weirdos.
Now what often happens within the scientific disciplines, if one tries to give a proof of the need for non-euclidian geometry in describing natural phenomena and its deeper aspects seen from 'inverted perspective' (e.g. 'relativity' or 'possibility space'), ... is that upon receipt, science will reformulate what you have said into a euclidian space based formulation, ... therefore stripping out the very essence of what you came to talk about.
In my following letter to John Casti (who has not insisted on this euclidian re-formulation, nor have his reviewers, though the readership may well do this in their reading of the material), ... I am trying to say that if one starts from a non-euclidian space assumption, ... there can be no notion of particulate motion, and the proof is there in the description, as long as one sticks with the precepts of non-euclidian space where the reciprocal of material structure is unbounded space (space-time in fact, since space-and-time are not split apart in relativistic, non-euclidian space; i.e. 'non-euclidian space' = space-time'). If one 'withdraws' from the 'inner space' mode of relativity and the non-euclidian space convention, ... to take a voyeur or 'outer space' look at the situation, ... in the process, ... one RE-REFERENCES the purely geometric or 'relativistic' or 'relational interference' information, to a euclidian reference frame.
So, if the letter were published, someone reading the letter may think, ... 'that's ridiculous because I know that I can see billiard balls rolling around the outer surface of a sphere', ... and therefore I can observe and meaure their motional trajectories.'
And I would agree except for the 'that's ridiculous' part, ... because the reader is referring to the lesser of our two perceptual capabilities, ... the 'voyeur' perception of 'actuality space' (euclidian space), and whilst we are in the 'immersed' perceptual mode, we have all the information for the 'voyeur' mode, ... but it is 'packaged' in a 'floating, relativistic format'. The process of transforming it back into the familiar euclidian format is a REDUCTION process wherein we reduce the complex (real + imaginary) informational unit basis, to a 'real-only' (bivalent 'one' and 'zero') informational format.
SO THE POINT IS, ............... that we are not restricted to euclidian voyeur views of things. We are all perfectly capable of perceiving things in the more profound relativistic, 'non-euclidian' 'immersed' mode (the prime mode of the infant and child), ... which CONTAINS the non-relativistic euclidian mode as a much smaller 'feature' within its broader landscape.
Now, how does this feel experientially when we are perceiving in relativistic mode? We all know how it feels!
And to refresh the metaphorical usage, I will switch back to the example of the game of pool. If you haven't played it, you can perhaps nevertheless imagine the described effects.
When I step up to the table, ... perhaps the first thing I will focus on is the opportunity to 'make a shot' (sink a ball), and this is a voyeur mode thing wherein I use my analytical powers and estimate the angles and all that. I feel 'anxiety' in this mode of perceiving, I think things like 'I wonder if I can do it satisfactorily'.
But, I could, as I stepped up to the pool table, let my eyes kind of cross (think of Kevin Klein in his parodied love-making scene with Jamie-Lee Curtis in 'A Fish Called Wanda'), ... and as I do, I am thinking of the future possibilities for all of the balls all at the same time. And if I can hold that thought in my head, and this comes with experience, ... it may occur to me that I do not want to make the obvious shot,... that there is a more harmonious shot which will cultivate more future possibilities for my whole ensemble of balls. In order to be in this perceptual state, ... I have to 'let go' of all my anxieties and abandon myself to the multiple centers of purpose and possibility constituting the whole and part ensemble. I must become a part of the whole co-dynamic, ... and this is a very pleasurable feeling which comes with this mode of perceiving. I don't care if no balls go in the pockets, ... my primary pleasure is coming from the quality of the geometric transformation which has no EXPLICIT goal, only the qualitative goal of co-cultivating harmony, ... making music, jamming with the ensemble.
There is pleasure in experiencing these opposites, .... it is like no-brakes, dirt-track motorcycle racing on an oval track, .... in the straight of way, you twist the wick full bore and go accelerating down the track as if to infinity, ... and then as you become re-aware of the approaching corner, ... the anxiety comes back and grips you, and you know you must 'do it right', ... and when you can see the straightaway again at the 'end of the tunnel' of anxiety, ... you twist the wick fullbore again, letting go of all anxieties and basking in the pleasure flow.
So, when I am 'out', I am thinking about 'what I am doing', ... and as I go in, ... I abandon my thought and about what I am doing, and open up my mind to the 'harmonies of space' and by opening up my mind to them, I let the harmonies grow to the point that they can guide my actions, .... to the point that I 'groove' with the natural harmonies of my containing environment (I am now 'immersed' in a relativistic viewing of the ensemble of billiard balls). When I am in the 'inner state', I can still 'do things' but they are no longer the 'feature' of the activity, ... but when I am in the 'outer state', ... while I can 'do things', ... there is no way to 'get to' the relaxed abandonment of the 'inner state'. The immersed (inner) state is a co-resonant state, while my voyeur state of focusing on 'what "I" was doing', was a detached state in which I alienated myself from my environment for the purpose of 'doing something to it'. Heisenberg's principle, in Feynman's general formulation of it says that 'one cannot design equipment in any way to determine which of two alternatives is taken, without, at the same time, destroying the pattern of interference.' In other words, if we are observing material- causal dynamics, we no longer have access to the relational interference information.
Our experience tells us that the co-resonant state, which includes the material causal as a secondary feature, is a more pleasurable way to play the game. It is a relativistic way, and when we shoot, 'the earth moves' in concert.
*Complexity* and their readership may not be 'ready' for the type of narrative in this essay, so the following attempt, tries to put this story into more mathematical terms,... non-euclidian, to be sure, ... but prone to being immediately reformulated into euclidian terms by the reader, ... into the voyeur terms of detached focus on 'doing stuff', rather than the immersed terms of co-resonant engagement.
The other problem with my following article is that it may be overly 'self-referential',... since it is a commentary on my own article, just published in the current issue of *Complexity*.
* * *
John L. Casti,
Executive Editor Complexity,
1399 Hyde Park Road,
Santa Fe, NM, 87501
March 12, 2000
Letter to the Editor:
A Comment on 'Is Evolutionary Computing Evolving?'
Dear Dr. Casti,
In the article 'Is Evolutionary Computing Evolving?' in Complexity vol. 5, no. 2 (Nov/Dec, 1999), it is proposed that individual 'evolutionary units' and their containing space 'co-evolve'. For the special, but very relevant case of individuals populating the surface of a closed curved surface, such as the spheroidal surface of the earth, the author's proposition can be 'tested' by reconciling it with the nature of 'motion' on such a surface.
Motion is normally thought of in the 'materialist' terms of the displacement of an object with respect to the observer's frame of reference, or its displacement relative to another object also within the observer's frame of reference. In the theory of relativity, the 'inverted' reference frame constituted by the ensemble of objects replaces the 'external' reference frame of the observer; i.e. the observer 'rides the photon of observation'.
The pursuit of an understanding of the way 'evolution' works is usually approached from a 'causal' perspective which requires knowledge of the trajectories of objects (i.e. object motion) as a function of time. However, this type of knowledge, in the case of relativistic observations of motion on a curved spherical surface, cannot exist, ... and this can be demonstrated as follows;
Solid objects moving over the surface of a sphere can be seen as having an associated, areal 'footprint' which lends itself naturally to the description of their motion and at the same time gives information on the shape of the space they occupy themselves, and the relative or reciprocal shape of the enveloping space.
Since the surface area of a sphere is finite, ... the area which the object-footprint can move into, ... the 'possibility space', if you like, ... is, for a single object on the sphere, the reciprocal to the area which which the object is currently occupying, ... the 'actuality space'. In fact, this 'possibility space' corresponds to Einstein's curved space 'reciprocal disposition', referred to in his essay on relativity and non-euclidian space, 'Geometry and Experience'.
At this point, if we were to follow the reasoning in Zeno's 'Arrow Paradox' , we would say that "relative motion on the surface of a sphere is impossible", since simultaneous with any movement of the object, the reciprocal space is redefined. In fact, the object-footprint and its reciprocal are a dualist unity whose state of existence is unaltered by the proposed 'motion'. Since there can be no detectible difference in either the shape of actuality space (the shape of the object-footprint) or the possibility space (the shape of the reciprocal disposition), ...all supposed 'change' being compensated instantaneously, we can say that the object cannot move in the sense of 'having a motional trajectory'.
If we add one or more objects to this spherical space, ... the reciprocal to their 'footprints' is a finite and unbounded area, ... a possibility space whose shape adjusts simultaneously with any 'movement' of any of the constituents. Thus motion, in the sense of trajectories of objects as a function of time, does not exist.
We could stop in the realm of the abstract here as Zeno and Parmenides did, ... but our common sense tells us that 'there is movement of some type' here, ... and that the reasoning problem we have come up against relates to our tautological defining of euclidian 'things' and linear time; i.e. the problem here, relates to the splitting apart of space-time.
That is, ... our pre-conceptual senses, as pointed out by Heidegger and Merleau-Ponty, key to the evolving 'shape' of space as defined by space-time relationships amongst things, ... a preconceptual view which doesn't yet liberate 'things' in their own right, and in the process, liberate 'time' as a linear measure. In this more fundamental view of motion, before we arbitrarily, according to cultural practice, ascribe independence to 'things' and give them labels, ... time and place are an inseparable meld. This is well-described in David Abram's 'Spell of the Sensuous' in the chapter 'Time, Space and the Eclipse of the Earth', a quote from which is as follows;
"The Lakota define the year as a circle around the border of the world. The circle is a symbol of both the earth (with its encircling horizons) and time. The changes of sunup and sundown around the horizon during the course of the year delineate the contours of time, time as part of space."
From the Lakota's 'immersed' or relativistic observations, motion is something which one sees in relation to the enveloping horizons, ... in the changing relative azimuths and ranges of things from the immersed observer's point of view.
Similarly, in our object-populated spherical space, an object can also be described relativistically or 'implicitly', in terms of its reciprocal disposition, ... the suite of relative azimuths and ranges observed by a particular constituent relative to all other constituents. We could call this 'implicit identity' of our object, it's 'niche identity' or 'wave identity' since it is based on relational interference in space-time (i.e. it is space-time 'phase' based).
Our experiencing of 'time' in this 'immersed observer' case, is relative to motional cycles associated with space-time shapes 'coming over our 'azimuth-range horizon', rather than to 'linear time'. Since time, in this case, associates with the evolving shape of space, we might refer to it as 'evolutionary time' or 'ontogenetic time'. As Abram points out, ... we 'straightened out' our space-time or 'place and cycle' oriented view of space-time, by elevating the notion of 'history' into the primacy, ... where we began referencing our lives to major non-recurring events (often catastrophic), rather than grounding our sense of time in 'place' and 'season'. In this manner, the circularity of space-time was hammered and nailed down, for example, on one end by Adam and Eve, and on the other, by 'the second coming', with various other supportive 'tacks', such as non-recurring wars, floods and plagues ensuring chrono-linearity along the way. The linear impression of time emanating from this view was amplified, as Abram points out (and McLuhan as well) by the phonetic alphabet and the written word which 'detached' our experiencing of events from immanence in earthy space-time, ... substituting the abstract euclidian space and linear time frames anchored in written word as the new, non-earthy reference ground. As Abram says;
"It is precisely the ground and horizon that transform abstract space into space-time. And these characteristics --- the ground and the horizon --- *are granted to us only by the earth.* Thus, when we let time and space blend into a unified space-time, we rediscover the enveloping earth.
It would seem, then, that the conceptual separation of time and space --- the literate distinction between a linear, progressive time and a homogeneous, featureless space --- functions to *eclipse* the enveloping earth from human awareness. As long as we structure our lives according to assumed parameters of a static space and a rectilinear time, we will be able to ignore, or overlook, our thorough dependence upon the earth around us. Only when space and time are reconciled into a single, unified field of phenomena does the encompassing earth become evident, once again, in all its power and its depth, as the very ground and horizon of all our knowing."
Clearly, the abstraction of 'things' or labelled 'objects', excised from the space-time whole is OUR abstraction which we impose on our own 'science' of conception, ... but which we cannot impose on nature (Poincare). And it is the abstraction of 'things' which enables and underpins the notion of motional trajectories and material causality.
According to the general theory of relativity, such abstracting of labelled 'things' is a secondary contrivance (i.e. a contrivance which can be useful as a conceptual tool, as long as we do not forget that 'things' are derived entities, abstracted from 'field'). As Einstein and Infeld say in 'The Evolution of Physics: from early concepts to Relativity and Quanta' (1938), ... "A new concept appears in physics, the most important invention since Newton's time: the field. It needed great scientific imagination to realize that it is not the charges nor the particles but the field in the space between the charges and the particles which is essential for the description of physical phenomena."
My comment on the notional proposition of 'container-constituent coevolution' as presented in 'Is Evolutionary Computing Evolving?', then, is that the general theory of relativity appears to equate to this very proposition. That is, relativity infers that space-time is a continuum, therefore, the evolving shape of space-time constitutes the 'whole story', ... and our abstracting-out of 'individual organism' or 'species' relative to 'everything else' which we then bundle up and label 'the environment', is something we impose on OUR science of conceptualization, but which we cannot impose on nature.
This relativistic view suggests that rather than conceiving of 'the unit of evolution' as a 'thing' such as a 'gene' or a 'species', ... we would be more consistent with relativity to conceive of units of evolution in terms of space-time phase (relational interference patterns), ... complex informational entities (similar to Gabor's 'logons') which have a dual 'explicit' (properties and behaviors) and 'implicit' (relational interference) character. Such a suggestion was made by Von Foerster in 'Event and Cognition: An Ecological Perspective' (1986); "The dual interdependence of organism-environment permits a dual interpretation of the tree of evolution . . . Instead of interpreting points on this graph as *species of organisms*, one may interpret them as *species of environments*."
In other words, this dual identity can be expressed in terms of the 'niche' of a material entity, ... since the 'niche' is described in terms of the entity's reciprocal disposition in 'possibility space'. What this space-time based specification effectively does, since it re-situates description within the unbounded 'shape' of space-time, ... is to account for 'space' being a commons within which there is an interdependency amongst constituents, wherein the interdependencies together constitute the commons.
A validation of this 'niche identity' of evolutionary units appears to be given in a current report by James Kirchner of the University of California, Berkeley, and Anne Weil of Duke University in North Carolina, concerning what the fossil record can tell us about the relationship between extinction and replenishment. The study is entitled 'Delayed biological recovery from extinctions throughout the fossil record.' and can be found at the following two URLs
http://www.nature.com (see 'features of the week', march 9, 2000)
The principle implicitly established in this report, that 'species' have both an 'explicit identity' [trajectory identity which is property and behavior based] and a reciprocal, 'implicit identity' [space-time phase identity which is reciprocal- disposition or relational- interference based], termed a 'niche' identity, appears to be consistent with the general theory of relativity as discussed within this note. The authors say;
The model in which an ecosystem takes longer to recover from a larger extinction is, therefore, based on a false assumption -- that each species is somehow isolated from every other, and recovery is a simple matter of filling the vacant ecological niches. The wider the destruction, the more vacant niches there will be, and the longer filling them will take. BUT IF SPECIES ARE INTERDEPENDENT, SPECIES THEMSELVES ARE NICHES, so the destruction of one species removes opportunities for many others. To destroy many species simultaneously therefore makes it very hard for new, pioneer
species to get started." (cap's are mine).
As Einstein and Infeld say (The Evolution of Physics'), the relativistic view which sees 'field entities' rather than material entities as the primary agents of evolution in nature (with material entities, instead, being 'features' of field which have been abstracted out as independent 'things' by the use of the euclidian space convention) neither replaces nor conflicts with prior theory, but simply subsumes the old material-causal theory, which would force us to make impossible choices as to the 'unit of evolution' seen as an independent material-causal agent, as predicted by Goedel's Theorem (e.g. "If axiomatic set theory is consistent, there exist theorems that can neither be proved nor disproved, ... and, ... There is no constructive procedure that will prove axiomatic theory to be consistent")
That there is no problem here in 'shifting gears' from the 'actuality space' view of the non-relativistic euclidian space and linear time paradigm, to the more comprehensive 'possibility space' view of the relativistic, non-euclidian space-time paradigm, ... that we simply move into a more complete view which sustains the old materialist view while dissipating the old paradoxes, ... is the reassurance in the words of Einstein and Infeld;
"To use a comparison, we could say that creating a new theory is not like destroying an old barn and erecting a skyscraper in its place. It is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting point and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part of our broad view gained by the mastery of the obstacles of our adventurous way up."
 --- Note on Zeno's paradoxes of motion. Zeno proved that 'things cannot move' and while even today, philosophers puzzle over the convincingness of his proof, ... the paradox comes from the presupposition of the independent existence of 'things' which of course contravenes the general theory of relativity, also.
That is, the paradox dissipates as soon as we withdraw the notion of 'absolute things'.
For example, if we look at Zeno's paradox of 'The Arrow';
"What is in motion moves neither in the place it is in nor in one in which it is not"
(noting the implicit pre-assumption of space being 'void' and a non-participant)
. . . . . 1. Anything occupying a place just its own size is at rest.
. . . . . 2. In the present, what is moving occupies a place just its own size.
So. . . 3. In the present, what is moving is at rest.
Now . 4. What is moving always moves in the present.
So. . . 5. What is moving is always --- throughout its movement --- at rest.
The parodox here, at least to Zeno and today's philosophers (see 'The Presocratic Philosophers', Kirk, Raven and Schofield and their cited references) is, ... "Is what is true at every moment of a period of time true throughout the period?" This way of conceiving the paradox ties it to the concept of linear time. So the alternative way to interpret this paradox is with respect to the nature of a 'thing' relative to 'time'. If we remove the 'bivalent' character of a 'thing', as a Lotfi Zadeh and a Bart Kosko would doubtless do (not to mention Einstein), the notion of a 'thing' reverts to it quantum duality wave-particle nature which gives it a relational interference 'niche' identity within which its particulate identity is an inferred or derived notion.
If not, we run into a significant problem. As Kirk et al say in regard to Zeno's 'The Arrow' paradox; "The paradox in fact poses an incisive challenge to the attractive idea that motion must occur --- if it occurs at all --- in the present. It shows that it is hard to reconcile this idea with the equally attractive notion that in the present what moves cannot be traversing any distance. Perhaps there are two incompatible conceptions of the 'now' at work here --- one that of a present duration, the other that of an indivisible instant, as it were a line dividing past from future. If so, that does not make Zeno's argument any the less impressive. For it is such arguments which force the distinction upon us. And the choice between the alternatives hinges on one's deep-seated predilections in the philosophy of time, as is shown by J. D. Lear, 'A Note on Zeno's Arrow', 'Phronesis' 26, 1981 (91-104)
Zeno's paradoxes of motion place in the balance, whether we want to ground our perceptions and inquiry in our common experience, ... or whether we want to ground them in an abstract world of perfection, ... a world of 'absolutes', ... of 'bivalent' material entities which either exist OR do not; i.e. entities which satisfy the requirements of abstract, exclusionary logic, ... rather than the inclusionary logic of common experience.
Zeno's preference, and the reason for his formulation of the motion paradoxes, was to 'detach' from a grounding in common experience and re-situate the base of perception and inquiry in the abstract and absolute, as our western culture has chosen to do. Some elaboration here may be useful.
Zeno was not a Greek 'Lotfi Zadeh' or 'Bart Kosko' who embraced the fuzziness which is apparent in nature. Zeno had a distinct purpose in mind for writing up these paradoxes, and this was to defend the abstract philosophy of his friend Parmenides, whose believed in the One, a philosophical view which clashed with those seeing the world as a plurality. According the writings of the era, Parmenides was a fine-looking man who was disgusted by the messiness (and fuzziness) of his own birthing process, and whom the younger Zeno was always with, the duo going over to the very young Socrates house when they came together to Athens as there was much interest in Parmenides ideas. Zeno's purpose in writing the motion paradoxes comes out in this text from Plato's 'Parmenides' which quotes Zeno, as cited in Kirk et al;
"The book [Zeno's] is a retort against those who believe in plurality; it pays them back in their own coin, and with something to spare, by seeking to show that if anyone examines the matter thoroughly, yet more absurd consequences follow from their hypothesis of plurality than from that of the One. In such a spirit of contention I wrote it while I was a young man" . . . "After Socrates had heard this [Zeno's reading of his book], he asked him to read again the first hypothesis of the first argument. When it had been read, he said; "How is what you say to be taken, Zeno? If the things that are are many, they you say they must be both like and unlike, but that this is impossible - for neither can what is unlike be like, nor what is like unlike? Is not that what you say? --- 'Yes', said Zeno, --- 'So if it is impossible that what is unlike should be like and what is like unlike, it is also impossible that there should be many things? For if there were many things they would be subject to impossibilities. Is this the purpose of your arguments --- precisely to content, against all that is commonly said, that there are not many things? And do you regard each of your arguments as evidence of this very conclusion, so that in fact you reckon to provide as many proofs as the arguments you have composed that there are n ot many things? Is this what your are saying, or do I not understand you correctly? --- 'No,' said Zeno, 'you have understood the purpose of the whole treatise beautifully."
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