October 15, 1996

It is 7 a.m. and I just woke up with what I think is an answer to Manus Foster's question on Denis Gabor's 1945 paper; "The Theory of Communications" [1], after a sleepless night thinking about the ideas of the poet and artist William Blake.

Manus gave me a copy of the Gabor paper before he died of cancer about 10 years ago, saying that he thought there was something very profound in it, and to hang on to it and see if I could come up with anything. Why he asked me, I'm not sure.

The profound message which occurred to me this morning is very simple and very counter-intuitive; that is, it is very "counter-culture". Of course, it may also be wrong.

Gabor pointed out in this paper that our communications theory rested on linear mathematics in an arbitrary way and that this was an expedient of the mathematical treatment and also economics (to ease equipment design and manufacture). He added that this linear treatment did not mesh with the ideas of quantum physics.

The key point here, which I'll try to illustrate with short excerpts from his paper is that our concept of communications is inherently tied to the "particle" theory of nature ("thing-based causality"), as opposed to the wave theory of nature. It does not incorporate or account for "interference" effects which are inherent in the Quantum Physics view of nature.

For this linear way of looking at things to hold together, there must be a "standard reference clock", or standard time dimension, hence the title of this note.

However, it has been said by Henri Poincare, Prigogine, Goedel, Chaitin and other nonlinear scientific thinkers that such views of nature are the unconstrained products of our mind and nature is not obligated to adhere to our mental laws. Poincare implies that we need as many mental models (hypotheses) as we need to look at nature.

The point is that there is another way to look at communications and this is where information is not independent, which is at the most fundamental base of how we think about communications, but in which information interferes with itself. This interfering view of the world is now the more general view, consistent with Quantum Mechanics and the findings of the nonlinear science.

Gabor raises the issue of the linear assumption in communications as follows; (p. 430).

"This, in fact, proves the fundamental principle of communications. In whatever ways we select N data to specify the signal 2f(f2-f1)t, we cannot transmit more than a number 2(f2-f1)t of these data, or of their independent combinations by means of the 2(f2-f1)t independent Fourier coefficients.

In spite of the extreme simplicity of this proof, it leaves a feeling of dissatisfaction. Though the proof shows clearly that the principle in question is based on a simple mathematical identity, it does not reveal this identity in a tangible form. Besides, it leaves some questions unanswered: What are the effects of a physical filter? How far are we allowed to sub-divide the waveband or the time interval? What modifications would rise by departing from the rigid description of absolute independence of the data and allowing a limited amount of mutual interference? It therefore appears worth while to approach the problem afresh in another way, which will take considerably more space, but which, in addition to physical insight, gives an answer to the questions which have been left open." (Gabor goes on to develop his idea of information "cells")


The "fly in the ointment" as Gabor points out is Heisenberg's principle which predicts that; ---- dt*df is approximately equal to 1. (identity 1.2 on page 432). "dt and df (delta's in the Gabor paper) are here the uncertainties inherent in the definitions of the epoch t and the frequency f of an oscillation. The identity (1.2) states that t and f cannot be simultaneously defined in an exact way, but only with a latitude of the order one in the product of uncertainties." ... "In communication theory the intimate connection of the identity (1.2) with the fundamental principle of transmission appears to have passed unnoticed."

Here we have a situation where we are passing over a very important point relative to the way we perceive the world, as "thing-based" causal actions, or as "massless interference" --- as the Christian God-controllor, or as "the sound of one hand clapping", the Zen Buddha which is immanent in every aspect of nature.

The implication then, in a cultural sense, as William Blake and Henri Poincare's comments jointly imply, is that by revising our view of nature based on the dual models of thing-based causality AND massless interference, we can return to an embrace of nature and no longer need artificial Gods, great "Sky-Clocks" who, like the platinum standard metre in the Louvre, are a kind of a desperate and pathetic reassurance of the existence of a "solid" foundation for our fragmented mental models.

As Blake pointed out, and as is clearly recorded in histories such as those of the Celts, nature was the original deity and it was poets who personified different aspects of nature by giving them names and personages.

That is;

The ancient Poets animated all sensible objects with Gods or

Geniuses, calling them by the names and adorning them with the

properties of woods, rivers, mountains, lakes, cities, nations,

and whatever their enlarged & numerous senses could perceive.

And particularly they studied the genius of each city &

country. placing it under its mental deity.

Till a system was formed, which some took advantage of &

enslavÆd the vulgar by attempting to realise or abstract the

mental deities from their objects; thus began Priesthood.

Choosing forms of worship from Poetic tales.

And at length they announced that the Gods had ordered such


Thus men forgot that All deities reside in the human breast.

Plate 14, from "The Marriage of Heaven and Hell"

William Blake (1757-1827)

As not only Blake, but the Celtic tradition indicates, what was originally metaphorical led to the development of Priesthood and subsequently, people began to think that these metaphors, or personifications of nature, were things unto themselves, hence a new type of religion came into being. Now there were Gods who "controlled" or who CAUSED everyTHING to happen. This view of a controlling god, who did things chronologically (i.e. caused the world to come into existence in 6 days and 6 nights, appears to play a role like the metre standard in the Louvre. It is the keystone concept which makes the whole model hang together.

For clarity, one more iteration;

The idea of a God-Controller makes "thing-based causality" hang together, and decouples it from nature (again, we are speaking of mental models) since nature cannot be described with a single (causal) model. Nature requires a "no.thing-based interference" model as well (i.e. a massless wave interference model). There is a distinct feeling, therefore, that the Christian God, at least, plays the same role for linear communications and causality, as the metre stick does for linear measure. The God-controller provides a consistent time axis, orthogonal to the occurrence of events (i.e. no crossfeed between time and event sequence) which allows one gear to turn at a time, enabling independence between all events, as is the underpinning of our linear mathematically influenced view of the world.

Henri Poincare, in "La Science et L'Hypothese" comments on our linear "shortcut" for providing mental simplicity, and also of the problems (i.e. impossibility) of reconciling this linear mental model with nature;

"The law of great numbers has re-established simplicity in the mean. Here the simplicity is only apparent, and the coarseness of our senses alone prevents us from seeing the complexity." . . . "How can we even reconcile it [simplicity] with the unity of nature? For if all things are interdependent, the relations in which so many different objects intervene can no longer be simple."

If God is the great "Sky-Clock" which synchronizes everything, allowing causality between the parts to proceed uninterfered with (i.e. holding nature in abeyance while "A" can act on "B" to produce "C" without any crossfeed problems with each other or with the environment, in violation of quantum mechanics), then what existed in the world of the poets, before we got carried away with the poetical god-metaphors?

The following is an excerpt from "The Celtic Tradition" by Caitlin Mathhews, which although it doesn't reference Blake, is certainly consistent with his ideas.

"Myth and magic are generally conceived to be false and misleading doctrines in our society, things wrought of fantasy or of evil. As we have seen in this book, the primal Celtic world, like all native traditions, derives from both myth and magic its life and continuance. Myth describes the patterns and ordering of the world, while magic governs the regulation of daily life in conformity with this primal order. How we came to lose this insight is the history and cause of our present misfortunes, of our fractured and fragmented existence which is out of harmony with the natural laws. For the gods are nothing but the forces of those laws in manifest form, and the magic of the aos dana is their gift and means of communication between themselves and humankind."

Take a closer look at the key sentence in this paragraph; "Myth describes the patterns and ordering of the world, while magic governs the regulation of daily life in conformity with this primal order." What we are speaking of here in terms of "myth" is the "ordered patterns" of a wave interference (Quantum physics) view of things, and what we are speaking of in terms of "magic" is harmonizing "feedback" with this natural order, or Heraclitean "logos". Matthews also says; "As we remarked in chapter 1., the Celts have no creation myths as such. Theirs is a far more subtle series of interrelationships which transcend the need for a fixed end and beginning."

The Celts speak of "the endless knot" which one can't really distinguish from the non-periodic (neither beginning nor ending) fractal trajectories of nonlinear systems.

So, in the poet and nature dependent view of life, there were apparently two views of nature, a "thing-based causal" view and a "myth and magic, or massless interference" view.

How were the two reconciled in Celtic times?

The Celts believed in the "otherworld" which was not "heaven" or "hell" but which was simply the "other" (magic and myth) way of looking at things where space-time was arranged rather differently. That is, when you went into the "otherworld" you entered a "timeless" state (i.e. think Gabor's holography). It was thought that wisdom was drawn from the "otherworld" and that if you were clever, you could enter and exit the "otherworld" at will, perhaps several times during a day. The poets were (and are) "king" in the Celtic culture; "The poets or "fili" were closely in touch with the Otherworld. This much is clear from the shamanic regalia of their office, chief among which was the musical branch they carried. A chief poet, or "ollamh", was entitled to a gold branch, an "onruth" carried a silver one, and all the lower classes of poet were entitled to a bronze branch."

In other words, the Celts recognized two "states of mind", one which was the everyday "thing-based causal" state and another, the world of the poets, a "magic and myth massless interference" state which skilled poets could enter into almost at will, in a way similar to Zen meditation.

It is significant to note the reference to "timelessness" which is associated with the shamanic and poetic states. In Gabor's holography (discovered in 1948 and the significance of which was not recognized until 23 years later, by a Nobel Prize in 1971), which Gabor was presumably working on at the same time as his communications paper, there is clearly a tie between the concept of "interference" and timelessness. He point out in his Communications paper that full-fidelity interfering communications would require that the synchronization signal be associated with each bit of information. This would of course be hard (expensive) to engineer (even approximately) in the practical world. If everything interferes with everything else, as it does in the case of holography (each part contains the whole and the whole is in each of the parts), then time becomes kind of irrelevant, or at least put through the blender.

In shamanic experiences, in the memories of tribal elders in North American Indians, in the "visions" of witches and the "mentally ill", there is a common reference to "timelessness". Mental associations are made between things which are no longer constrained by lockstep chronology and causality. In spending two weeks speaking with "inmates" in a mental hospital in August, this type of timeless association in thinking, what is termed "delusional" and labelled as pathological in our culture (and a reason for being "committed") was described by the "inmates", for example, as a "state of super-intelligence". For my part, the imagery which came out of these folks who were continually floating in and out of a "delusionary" state, was indeed very "intelligent" in terms of associations which "made sense" yet did not comply with an ordered chronology. "Shall I compare thee to a summer's day?" Ok, but where is the "thing-based" causality and time chronology in such a thought? Move on from this Shakespearian sonnet to imagery which includes familiar nouns out of joint with respect to time and causality and you get what our present culture calls a "delusionary" "pathology". Unless of course, the person is a recognized poet and has learned to manage his/her interface with society.

Of course, if you lived back a thousand years or so before the birth of Christ, you might well receive the acclaim, rather than the rebuke and mockery of your peers for an ability to get into this "Otherworld", the massless interference and "timeless" way of looking at things.

Yesterday's poet has become today's "nutter" as Blake found out in his era (he was viewed as crazy and his work poorly known or appreciated in his own time). Recently, psychologists have found that people who are untreated for their delusionary psychoses typically come out of it on their own within 3 to 5 days (if they are not "committed" and given drugs). In these experiments, they have also found that there is a much lower incidence of recurrence (of seeking medical assistance) in those incidences, and there was also the suggestion that the mind was doing something (e.g. updating the worldview and "rebooting") that it needed to do.

Perhaps the low recurrence rate in these cases reflects an acceptance of the phenomena, rather than its total disappearance. In the days of the Celts, the therapeutic infrastructural and economy for behavioral problems was probably not so well developed as today. This gave one a chance to evolve a practical way of getting in and out of the "Otherworld" and so being seen as gifted, instead of being caught, committed and drugged halfway through the first "trip", and being labelled as defective.

In the psychological literature, there is much written about "Jesus complexes", and the "myth of mental illness". What is emerging is a synthesis of thought which is very consistent with Blake's view that we make a big mistake by splitting up heaven and hell, and that we'd better remarry them to get back to a healthy happy energized natural world. The paradoxes of yin and yang, of "thing-based causality" and "massless interference" are certainly present in nature and suggest that we may need two views of the world. Poincare suggested as much and so does modern nonlinear science.

By embracing only causality, and setting up "Sky-Clock Gods" to police this gearworks view of the world, we spawn a cultural schizophrenia. For those who are inclined to wander into the world of "massless interference" which manifests itself in the timeless association of ideas, we have little tolerance. A few centuries ago, this was expressed by labelling such people as "witches" and putting them to death. Today, they are diagnosed as "mentally ill" and committed or put onto heavy duty drug programs, unless they have the skill and diplomacy to make it to the ranks of "poet".

It was not always this way. For example, in a book entitled "The far side of madness" by John Weir Perry M.D. , he opens up by quoting Plato and Socrates;

"He [Plato] tells us that Socrates enumerated four kinds of madness that conveyed a wisdom higher than the wisdom of the world: that of prophesy, of initiation, of poets, and of lovers. In the "Phaedrus" Plato writes; "In proportion as prophecy is higher and more perfect than divination . . . in the same proportion. . . is madness superior to the sane mind, for the one is only of human, but the other of divine origin. Again, where plagues and mightiest woes have bred in a race, owing to some ancient wrath, there madness, lifting up her voice and flying to prayers and rites, has come to the rescue of those who are in need; and he who has part in this gift, and is truly possessed and duly out of his mind, is by the use of purifications and mysteries made whole and delivered from evil, future as well as present, and has a releaase from the calamity which afflicts him. There is also a third kind of madness, which is a possession of the Muses; this enters into a delicate and virgin soul, and there inspiring frenzy, awakens lyric. . . But he who, not being inspired and having no touch of madness in his soul, comes to the door and thinks that he will get into the temple by the help of art --- he, I say, and his poetry are not admitted; the sane man is nowhere at all when he enters into rivalry with the madman."

Perry goes on;

"The fact of the matter is that in all of us, only a hairsbreadth below the level of conscious rational functioning, there is quite another state of being with an altogether different view of the world and an altogether different way of growing to meet it. And that state of being, or that world, since it is experienced in terms of images and symbols, metaphors and myths, is considered mad and worthy only of banishment from the sane world of common sense. We find ourselves being very fussy about allowing it to appear only on certain terms."


My "waking thought" was this; Gabor's paper brings out the fact that we have ignored interference effects in our theory of communications. This suggests that our theories of communications are fundamentally aligned to "thing-based causality", only one of at least two ways of looking at (i.e. "modelling") the world, the other being based on "massless interference", or the interference of ordered energy flux.

The nonlinear sciences are showing that leaving out, or adding in, feedback effects make a huge difference to our understanding of our world and who we are. Here's one of many recent examples, this one on Darwinian evolution, from the October Issue of "Complexity", the Journal of the Santa Fe Institute;

"The conventional list of fundamental elements of Darwinian evolutionary mechanisms contains two essential components: (1) reproduction with heritable variation, and (2) natural selection. We contend that feedback is a third essential component, which will be the dominant, controlling factor in nearly all cases. Feedback theory provides novel, fundamental and counter-intuitive insights into the dynamics of the natural selection process. It shows, most fundamentally, that Darwinian natural selection is a mathematically unstable and chaotic process. As a result of instabilities introduced by feedback, natural selection will commonly cause fitness to DECREASE, in sharp contrast to the conventional view that selection only increases fitness. Finally, feedback theory provides a powerful, unifying conceptual framework that coherently explains a wide variety of seemingly disparate biological phenomena, including topics as varied Cope's rule, punctuated equilibrium, density dependent selection, coevolution and sexual selection." Robertson and Grant, Univ of Colorado at Boulder

Our modern dependency on linear theory, it seems, has deep cultural origins. In particular, the transformation from a nature-deifying, poetic culture, such as that of the Celts, to a Christian God-Controller subservient culture. This ("our") culture, arguably based on a creeping misinterpretation over time of poetic metaphor for literality, appears to have narrowed our view of the world from one of both "thing-based causality" and "massless interference" to one which must be expressed by solely the former. The confusion which easily occurs, as was pointed out by Poincare, between mental models and "the way things really are" seems to be alive and well today. Fundamentalist Christians, such as creationists, continue to interpret what are presumably metaphorical writings in a literal context. Out of these worldviews comes "religious justification" for labelling those who transgress the implications of these beliefs, as evil, witches, mentally ill etc. In the middle ages, the Cathars of the Pyrenean region in southern France, subject to similar such circumstances, were systematically eliminated by violent means, over a period of 200 years, by an alliance between the Church and the French royalty. (i.e. the Cathars believed that "the miracles worked by Christ should be understood at a spiritual level, and interpreted as allegories, rather than in a literal sense", Michele Aue, "Cathar Country", thus they were seen both as a threat to the church, and a threat to the "linear" feudal society.).

We are not out of the woods today.

So, our disjointedness with nature, and two thousand years of "de-naturalized" religion and religious wars etc., can be seen, perhaps, to emanate from our concept of time and causality as expressible by the fundamentals of our communications theory and expressions such as 2(f2-f1)t, whilst we continue to ignore dt*df =~ 1. In other words, we discipline ourselves to look at the world as if the chronology of occurence of events is strictly adhered to (t and f are orthogonal), rather than looking at it in a "timeless" sense (i.e. where there is interference or feedback between the dimension of time and the sequence of occurence [periodicity] of events).

At the same time, our aesthetic appreciation of "impressionist" paintings which violate that strict chronology by capturing the dynamic of time (oscillations of light and color shade) in a single representation (i.e. an "impression") seems to be on the rise, probably reflecting the state of deprivation for this "timeless" self-interfering view of the world, made more acute by a rising disjointedness between linear worldviews and an evolving world which is becoming increasingly nonlinear due to communications.

In the words of Gregory Chaitin, it appears that in recent times (the last few thousand years), we may have been constructing twenty-pound theorems from only 10 pounds of axioms.

[1] Gabor, Denis; "Theory of Communication", JIEE (Journal of International Electrical Engineers), 1945