June 9, 1998
Poincare, speaking of the unity of nature in 'Science and Hypothesis' says'; "THE UNITY OF NATURE: --- Let us first of all observe that every generalisation [scientific law] supposes in a certain measure a belief in the unity of and simplicity of Nature. As far as the unity is concerned, there can be no difficulty. If the different parts of the universe were not as the organs of the same body, they would re-act one upon the other, and we in particular should only know one part. We need not, therefore, ask if Nature is one, but how she is one."
With this in mind, imagine now two scenarios, one in which you are sailing over a sea as still and smooth as a millpond, when a windsquall comes upon you, and even as the wind is raging and tearing at your sails, the sea remains still and smooth almost as if frozen. Is it possible for the sea to say to the wind, 'I've got a headache, I don't want to play right now.' ? Apparently, the 'timing' of natural behaviors is innately tied up in the unity of the space-time dynamic or 'evolutionary flow'. And if we consider, as Nietzsche points out (and complex systems research reinforces), that the basic forces of nature, 'attraction' and 'repulsion' imply a goal or purpose of some sort; i.e. that it would be 'unimaginable' ('unvorstellbar') to think of events occurring without purpose ('ohne absicht'), then we can say that in nature, the timing of things is established by, or flows from, some kind of unifying purpose.
Imagine now a second scenario in which you have a child with a chronic illness and that the illness has once again erupted and you have been up all night caring for him and are just getting ready to take him to see the doctor when your phone rings, and it's your boss telling you that if you are not at work within the hour, you will be fired. And as you hang up, your mind is pregnant with the timing-induced dissonance that if you are fired, your medical insurance will lapse and you won't be able to afford to purchase medical coverage without a job.
Clearly, cultural timing, rather than flowing out of a unifying purpose, is coming from somewhere else, and that somewhere else is revealed in the phrase 'time is money'. Now we all know that 'supply and demand' are fundamental forces in nature, and that if we can supply something to fill demand then we shall be compensated for it in some way, the 'universal' (in our culture) currency for this compensation being 'money'.
But just how 'fundamental' are the forces of 'supply and demand' in actuality? If there is a hole in an atomic orbital, we could say that this represents demand, and that the electron which comes in to fill it is 'supply'. But there is something very different going on here, than is going on in a monetary economy. And that difference is that the space-time arrangements or the 'supply and demand' structures of nature, are not at all 'ad hoc' or arbitrary but are harmonically related, and this extends all the way from atoms to astronomy. As Friedrich Cramer notes ('Chaos and Order') in discussing nature's affinity for 'resonant zones' in the context of the rings of Saturn, "It is known that the Cassini division, as well as the other large gaps in the ring, correspond to 'resonance zones' of Mimas, one of Saturn's moons. The particles missing from the Cassini division would have orbited with exactly half the period of Mimas or, so to speak, one octave higher. Such behavior is called resonance, not only in acoustics but for periodic processes in general. Further gaps correspond to resonances of higher order. What is the explanation of these observations?"
Cramer goes on to discuss a wide variety of natural symmetries observing that Jupiter and Saturn orbit the sun with periods whose ratio is exactly 2:5, that all of the planets, as Kepler demonstrated, have orbital periods which are in a natural 'musical' harmony (fifths, thirds, octaves etc.), that one can derive the 'golden mean' and the fibonacci series from these natural relationships and that in mathematical phase space, these harmonic relationships, which emerge along the boundary between chaos and order, show up as the most stable 'solutions'.
While the 'why' of it all has not been answered, many things are clear from a qualitative descriptive sense. For example, Cramer notes that scientists 'have developed a simple method of calculation to simulate complex dynamical systems in such a way that every point is related to the following point. In other words, they have formulated rules specifying how each point arises from the preceding one.'
Of course, what Cramer and other complexity scientists are coming around to is an understanding in 'rational' terms of what we 'know' from our sensory experiencing, that nature has an ontogenetic or evolutionary (as opposed to ad hoc) disposition.
Closing the loop on our 'supply and demand' discussion, it is apparent from the study of complex systems and from our sensory experience that 'supply and demand' situations in nature, as contrasted with culture, play themselves out in an ontogenetic fashion and tend towards configurations where the 'part' is in resonance with the 'whole'; i.e. that supply is purposively pulled by demand in such a manner that fulfillment is governed by an 'ontogenetic timing' which preserves the unity of the system, whole and part, even while all parts of the system are participating in wholesale evolution.
Here we can see the origin of the ancient adage; "To every thing there is a season [i.e. things have a natural resonance] and a time [i.e. a unity-preserving time] to every purpose in the universe". That is, the delicate flowering plants of summer do not butt heads with the chill of winter and the sea does not beg off with a headache when the wind wants to play.
Space and time [in other words, 'the timing of things'] are the underpinnings of philosophy as Plato said in 'Timaeus'; " ... had we never seen the stars, and the sun, and the heaven, none of the words which we have spoken about the universe would ever have been uttered. But now the sight of day and night, and the months and the revolutions of the years, have created number, and have given us a conception of time; and the power of enquiring about the nature of the universe; and from this source we have derived philosophy, than which no greater good ever was or will be given by the gods to man."
Since we govern our lives according to our philosophy, and since our conception of space and time or space-time make philosophy possible, it seems obvious that our conception of space-time is going to have an important impact on our lives.
After Heraclitus' implicit curved space-time (evolutionary flow) model lost out to Parmenides implicit euclidian flat space model, a model which was independent of time, our western rationalist culture went into a long period of believing that there were no other options, that euclidian space was 'all she wrote'; i.e. that our reality could be nothing other than a bunch of independent, purposeless things separated by void.
Interestingly, while philosophers, as noted by Plato, owed their profession to scientific observations (astronomy, mathematics), once they had the bit in their teeth and were formulating all kinds of ethics, models and reasoning approaches, they were not about to go back and mess with the initial assumptions, or let scientists and mathematicians mess with their basic assumptions either. As mathematical historians note, speaking about the evolution of non-euclidian space-time geometry, "However by 1817 Gauss had become convinced that the fifth postulate [of Euclid] was independent of the other four postulates. He began to work out the consequences of a geometry in which more than one line can be drawn through a given point parallel to a given line. Perhaps most surprisingly of all Gauss never published this work but kept it a secret. At this time thinking was dominated by Kant [1724 - 1804] who had stated that Euclidean geometry is the inevitable necessity of thought and Gauss disliked controversy. "
A century later, Nietzsche (1844 - 1900) took a closer look at physics and nature and proposed that natural forces of attraction and repulsion implied purpose or goal orientation, and that it made no sense to put 'cause' in a primacy over 'purpose', that it was 'unimaginable' to think that events occurred without purpose. This was an implicit rejection of euclidian space and time-independence assumptions, since being 'pulled' into the future is a wave type phenomena which involves space-time interference or 'curved' space-time.
There's two things we can observe here; (a) that the euclidian view of space and time which was the underpinning of western philosophy was an abstraction which did not and does not jive with our sensory experience, and (b) that our orientation to 'cause' derives from the notion of euclidian space [which is inherently non-purposive] and sees 'timing' as being determined by cause rather than pulled together by purpose.
Of course, 'rationalist' philosophy has a long tradition of priding itself on its ability to achieve elegant solutions and closures out of the context of nature and sensory experience, so in the western dualist mind, it has been seen as a virtue rather than a vice to see ourselves as being 'above' or 'masters' over nature, rather than as an inherent part of nature. So, even if we agree with Nietzsche, Riemann and Einstein that space-time is a curved continuum, that space-time is a participant in phenomena and that space-time dynamics are unified by emergent goal-oriented behavior, it requires yet another agreement that we as a society, should operate in such a way as to engender the same type of stable harmonies we see in nature, even though the results seem to be aesthetically pleasing when we do.
For example, all of the most exceptional high performance team situations I have reviewed involve a flip from 'cause' to 'purpose'. While the Apollo 13 moon mission was proceeding along nicely as an 'engineered in advance' or 'cause-pushed' mission, an explosion in the command module triggered a flip into 'purpose - pulled' mode. As in natural systems, the purpose pulled mode induced unifying 'just in time' or 'timely' behaviors out of all supporting subsystems; there were no 'I' m too busy to respond' type stances as arise in money-currency systems where the bigt bucks determine the timing. In essence, the 'currency' in the Apollo 13 system was 'ontogeny', the pursuit of continuing life and development, the will to become what we are meant to become.
Again, we can allow our behaviors to be induced by causal-material _OR_ purposive-ontogenetic pursuits. But we should be clear that the purposive-ontogenetic pursuit is a higher dimensional approach which CONTAINS the causal-material approach, though the reverse situation is not true; i.e. if we choose to causally amass the material, there is nothing in this simplistic pursuit which will autonomously engender symphonic resonances, in fact, dissonances are far more likely, as we have seen.
In sum, it is very clear indeed, that if we want to replace the dissonances in our society with harmonies, we must put 'purpose' and 'ontogeny' into primacy and relegate 'causality' to a supportive role.
As mentioned in the last note, 'ontogeny' degenerates into 'causality' when time is frozen. That is, let's say we start off with the purpose to personally develop ourselves by understanding more of the world, and we climb out of our crib and poke the cat just to see what happens or we find a packet of cookies and see how many we can eat, or we explore the differences in each others protuberances and orifices etc. If we choose to take a few 'frozen-time' snapshots along this ontogeny, we can focus in on 'cause' (e.g. he bit you because you pulled his tail, you are sick because you ate too many cookies, and etc.), and as soon as we focus in on cause, we can no longer hold such a complex thing as 'ontogenetic purpose' in our heads. In fact, it is possible to focus in so extremely on the snapshotted view of things that all of the phase and harmonic information associated with ontogeny dissolves in our minds and we begin to operate with 'cause' in the primacy.
Cause, the illusion which arises from doing the impossible (violating the uncertainty principle) and freezing time, has a certain elegance and finality which greatly appealed to Parmenides and his friend and supporter Zeno of Elea, and this appeal set the stage for the long run which Euclidian space has enjoyed. The interplay between Euclidian (bivalent, 'is' or 'is not') space and time can been seen in Zeno's paradoxes.
Zeno, born in about 490 BC, was a contemporary and friend of Parmenides (Heraclitus, an advocate of curved-space evolutionary flow, died in 480 BC. when Zeno was 10). Parmenides was the earliest and most influential advocate of implied euclidian space concepts (Euclid formalized the 'thing and void' infinite, rectanagular space concepts in five postulates two hundred years later). Kirk et al in 'The Presocratic Philosophers' give us a glimpse of Parmenides and Zeno; "According to Antiphon's account, Pythodorus said that Parmenides and Zeno once came to Athens for the Great Panathenaea. Parmenides was well-advanced in years --- about sixty-five --- and very grey, but a fine-looking man. Zeno was then nearly forty, and tall and handsome; he was said to have been Parmenides favourite. They were staying at Pythodorus' house outside the city-wall in the Ceramicus. Thither went Socrates, and several others with him, in the hope of hearing Zeno's treatise; for this was the first time Parmenides and Zeno had brought it to Athens. Socrates was still very young at the time."
The point here is that in the history of ideas, the confluence of people, personalities and events seem to have played as influential a role as the intrinsic merit of the ideas in their rise to primacy --- how else could we have had Hitler and Naziism. Similarly, the seeming arrogance of Heraclitus ('the learning of many things doesn't teach understanding, if so it would have taught Hesiod and Pythagorus'), and the polemics of Nietzsche because of his polemical nature have induced many people to shun the embrace of their ideas. Meanwhile the parsimonious elegance of Parmenides 'thing and void' space and the steelgated argument of Zeno are admired to this day.
Zeno formulated four paradoxes of motion which are known by the titles; "The Stadium", "Achilles and the tortoise", "The Arrow" and "The Moving Rows". All of these paradoxes start from a "thing-and void" based view of space and time and all aim to prove that motion is impossible. [i.e. that it is impossible for "bodies" to move].
In "the Arrow", Zeno proves that motion cannot exist because; "What is in motion moves neither in the place it is in nor in one in which it is not."
Stated in terms of propositions, Zeno's "Arrow" paradox goes like this;
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 implications, in the views of Kirk et al  are as follows; "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 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 (Phronesis 26 (1981), 91-94)." One could add that according to Heisenberg's Uncertainty Principle, the notion of 'present' in the perfect sense that time stops, is unattainable (i.e. the definition of 'things' blurs as motion goes to zero).
One might imply from "the Arrow" that Zeno is rejecting the ideas of Parmenides, of a thing-based reality and embracing the ideas of Heraclitus (a flux-based reality) in these motion paradoxes. But the historical accounts suggest that there is sufficient hubris amongst these philosophers that Zeno accepts 'as gospel', the notion of euclidian space and is trying to demonstrate that we can't rely on our sensory experience.
Clearly Zeno's paradox indicates that something has to give, either sensory experience which affirms the existence of motion, or the assumption that space is euclidian (composed of crisply boundaried 'things' and void), and neither Zeno nor Parmenides were about to concede anything as to the assumed nature of the thing-and-void space, and indeed could not, as it was an uncompromisable framework, which either existed, or did not.
And that brings us up to the present day and the choice between our embrace of 'causal-pushing' or 'purpose-pulling'. Nietzsche, in a manner analogous to Zeno, has raised our awareness to the absurdity of the 'causal' occurrence of events without 'purpose' (i.e. which flies in the face of 'attractions' and the emergence of harmonious order out of chaos). So we are now in the position of having to question either our sensory experience, or our assumption of causality.
If we retain our belief in cause, the unity in our lives is achieved by non-purposive exploitation of 'supply and demand'; e.g. by stockpiling money with which to buy control over timing; i.e. to achieve a locally purchased mastery of space-time. However, since other people are doing the same thing, this approach necessarily leads to dissonance and conflict on non-local scales, rather than cultivating unity or harmony of space-time dynamics (i.e. rather than cultivating a global ontogeny).
If, on the other hand, we pursue shared purpose and relegate causal perception to a supportive role, this brings us into a more natural unity, and of course if we tune-in to a purpose which is in harmony with the system which enfolds us (i.e. community, nation, global culture, nature) and which we are a part of, there is at least a theoretical opportunity for everyone in the system to 'become what we are meant to become'.
It seems that the purpose of time is not what we make of it but what it can make of us.
* * *
Return to 1998 UPDATE Page