Poetry Licence

Special Relativity- a Special case of Infinite Regress

2010-10-28T14:24:00.002-07:00

In my previous post I had the opportunity to say some things about the phenomenon of infinite regress which I called ‘reduction to infinity.’ I may just remind that it has to do with the way the human mind works:

1) We have an idea that although it can be the result of other thoughts it is nevertheless unprecedented.

2) Trying to explain its origin we regress to previous thoughts so that any of them is a result of any previous one.

3) We are forced to stop at an arbitrary point and to admit that logic is not able to understand both the world and itself.

This infinitely regressive aspect of logic expands to scientific (i.e. logical) theories, otherwise there can’t be any connection between human reasoning and the world. This is what I realized studying a special case in modern science, namely special relativity. Because the ‘relativity’ we recognize at the connection of our experience with ‘real’ space and time points directly to the lack of synchronization. Imagine this: In order to synchronize our clock with somebody else’s clock, we have to send a signal (i.e. a light signal). But when the second clock receives the signal some time will have elapsed. If the second clock tries now to synchronize with a third clock (or back with us) there will be a further time difference and so on…

Einstein explained and calculated this difference by assuming a constant (i.e. finite) speed of light. This may be helpful, as well as experimentally tested but not necessary. Because, on the other hand, quantum mechanics has discovered phenomena (e.g. quantum entanglement) that are instantaneous by nature. Of course we can interpret such phenomena by arguing that information (i.e. a light signal) cannot travel faster than light but then we cannot understand what instantaneity is and how it works...

For more:

Special Relativity- a Special case of Infinite Regress

Reduction to infinity

2010-10-05T14:31:00.000-07:00

There is a common fallacy with regard to human reasoning. We assume that our logic is powerful, in fact so powerful and valid that it is above the ability of all other creatures, even above any other kind of 'information processes. We assume that there is nothing that we can't explain and that all we need is time.

But the fact is that we cannot prove what we have already assumed: How can we prove that there isn't (or that there is) something outside logic? We can only assume it and then test if we are right or wrong, but we didn't use any proof in the first place. We can say this: 'Since we asked ourselves if there is something outside logic, this thing must have existed beforehand, so it wasn't an achievement of any logical deduction.'

So the main problem with logic is that it cannot prove itself. This is another way of expressing Goedel's theorem. When we build a syllogism asking for example 'where do we come from?' then we trap ourselves into an infinite procedure where God (or more generally a First Cause) may have created us and the universe, and another God who created God and so on...

On the other hand if we decide to take a 'stop' this stop is of course arbitrary: The universe (or God) has always existed. This may solve our infinite problem but only temporarily because here comes again the question: Who come that we gave such an explanation with our 'simple' logic? What other properties could thought possess in order to understand spontaneity and eternity?

I really don't know what could there be 'outside' our logical realm but the most incredible thing is that we may understand...

For more:

Reduction to Infinity

Infinite regress

2010-10-05T14:15:00.000-07:00

How can you mentally escape from this atrocity
There is a war that’s going on within the premises
Inside our heads if God is dead but there’s no time to regret
The bridge is down the caterpillars escalating
They’re always coming so naïve the humming birds
Is there beginning or an end is there any rule before hand
For all the lovers who demand an explanation
Is there an argument that’s swift and elevating
But there’s no truth relying on demonstration
Before your gentle bending neck it’s peace awaiting
Within your territory our lineage converges
Beyond our eyes the beads and marvels of your necklace
And just allow a missing link for our purposes
Black and white handkerchiefs of voyages and swallows
Above all the infinities the infinity that follows.

28-9-2010

Ghosts of departed quantities

2010-06-05T10:34:00.000-07:00

There is a careless thought regardless of our minds
Living on the boundaries of what’s assumed outlandish
Though when attention is concerned the reason is arising
Through the window of reference the world materializing
Soaring from the ice a dream of waking mountains
Melting sheets of nudity when the sun is rising
Rushing eyes on blind spots of particles comprising
Strange as it is to live apart from all experience
While we think of rivers the rivers flow inside us
By the stream of consciousness grows a lotus flower
Does it really exist when we just stand oblivious
Inside our cautious trap the pray of time is hiding
Let’s take a look again by changing our arguments
There is so vast a prison including the horizon
Countless opportunities escaping from our heads.

11/4/2010

Title: George Berkley, The Analyst.

The unknown 'Ψ'

2010-04-27T12:38:00.000-07:00

I have long been puzzled with the similarities between synchronicity and quantum entanglement. Of course synchronicity is a 'classical theory' as it seeks for a deterministic approach to reality. Quantum mechanics on the other hand is a probabilistic theory. But both theories are non- local. And the similarities I have found are more than striking. Take a look at the following table for example:

Key words' explanations:

Meaningful coincidence: An instantaneous (non local) connection of a psychic state with one or more physical objects (or events) so that the objects can no longer be adequately described without full mention of the corresponding psychic content.

Quantum entanglement: An instantaneous (non local) connection of two or more physical (quantum-like) objects so that one object can no longer be adequately described without full mention of its counterpart—even if the individual objects are spatially separated.

The psyche and the 'Ψ' wave-function: The similarity is striking. I can clearly see no distinction if some kind of 'emotional' properties are included in the wave-function.

Archetypes: They are the 'standard' ways for the psyche to manifest its self in the same way that operators in QM 'contain' the values to be measured.

The observer effect: It is a well known interpretation of QM that the observer causes the wave-function collapse. An 'observer' of course is consciousness.

PK (psychokenetic effect): Together with quantum entanglement goes quantum teleportation. How about moving an object- by teleportation- while looking at it?

Non- locality In both theories the phenomenon happens instantaneously but the subject (observer) becomes aware only when information arrives (not faster than the speed of light.)

Synchronistic phenomena can also take place in the future: In a similar way in QM, physical phenomena can be 'arranged' in the future through parallel worlds and according to the law of probabilities.

Holism: All theories seek for the 'philosophical stone', the ultimate unified explanation. How can this be done in modern science if we leave outside our souls?

Non causal correlations- The EPR paradox

2010-04-07T13:18:00.000-07:00

In classical physics the connection between things is established by signals. For example, the interaction between two heavenly bodies A and B assumes a ‘gravitational signal’ from, let’s say, A to B. Furthermore, the whole process is a causal one, (as causality is time dependent, locality is space dependent) meaning that B can react if and only it receives the signal from A. We should also note a third important classical notion, that of realism (or determinism) concerning natural phenomena. This means that the objects A and B posses properties (e.g. mass), so that their mutual interaction can be carried out. The assumption of causality took its most formal form in Einstein’s theory of relativity. One of the two axioms of this theory states that nothing can be transmitted faster than the speed of light.

In quantum physics the whole situation changes. It is not just a matter of ‘very small things that behave rather strangely’ but something that has to do with some fundamental properties of nature, revealed through the uncertainty principle. In simple words, we cannot have everything in this life without giving something of ourselves back! Quantum-physically speaking, properties of things are bound together in such a way that when we measure one property then the system is disturbed in such a way that another property has changed (a well known example is that of position-momentum coupling).

So far so good: We have kept determinism safe because objects still have pre-determined properties for their sake. But the quantum weirdness of uncertainty in measurements leads to the conclusion that we cannot know for sure what happens to our system when we don’t measure it. Where is it? What are its properties during this ‘blind’ period of time? It may have fixed properties, however not only these properties are inaccessible but also they greatly depend on our measurement. So what we have here is a fundamental ‘measurement determinism’ while in all other probable states we make statistical assumptions about the system (known as a superposition).

While this probabilistic approach rules out determinism ‘between A and B,’ the ‘axiom of measurement’ leads to a non-causal explanation for the ‘interaction’ of the two objects A and B: Since things in quantum theory are described by wave-functions, if objects A and B are bound together by some conservation law, and if an ‘entangled’ property of them is attributed by measurement, then these two objects should ‘interact’ instantaneously at the moment of measurement with their mutual wave-function ‘collapse.’ This means that in a classical sense the two objects should interact with signals that run faster than the speed of light. This is the essence of the EPR paradox, a conclusion that Einstein called ‘spooky action at a distance’.

From this point onwards, it was Bell who proved statistically… the EPR paradox itself! What he proved is that if there is an interaction between two entangled quantum states (i.e. two objects bound by some conservation law), then this interaction should exceed the speed of light (a fact that violates the conservation law itself). By this we mean that a classical theory cannot explain the results of quantum theory.

Yes, but can quantum theory? We should mention of course Aspect’s experiment that confirmed the EPR paradox using Bell’s inequalities. He showed that the time between the mutual change of two entangled states is less than the time needed for a signal propagating at the speed of light. Ok, this is a fact. But what is the conclusion? If a classical signal transmission (i.e. interaction) is not enough, then what sort of non- signal connection do we have here? Can we say, preserving classical thinking, that some sort of faster-than-light signals, constituents of an unknown field, exist? Could there be a fundamental time, for quantum events to take place (some sort of a quantum brachistocrhone of an unknown quantum field) or isn’t there any time at all?

Well, this is a subject not yet settled. One fact is that the ‘collapse of the wave-function’ (simply the resulting event) takes place uniformly in space and time. In fact at the time we ‘take the shot’ everything is well-arranged according to the statistical predictions of quantum theory. Furthermore, it is also a well- established fact that the phenomenon of quantum teleportation (i.e. ‘transfer’ of quantum states) is not space-and-time dependent. It seems that what we conceive as space and time in our everyday lives is a secondary property produced by processes in a ‘deeper’ quantum level. On the other hand, we should keep in mind that the world consists not only from ‘objects-things’ but also of ‘subjects-beings’. It seems as if our ‘connection with the world’ takes place in two levels: One ‘deeper-mechanical,’ non-conscious and non-causal (‘before we even know it’), and another ‘well-manifested,’ ‘full of space-time and information-signals.’ Because even if our ‘possibilities’ are ‘statistically determined’ in a mysterious-‘spooky’ way, free will gives birth to ‘our space and time:’ Time for our conscious decisions and space for our purposeful steps!

Further reading: Non causal correlations- The EPR paradox

Infinity

2010-03-06T09:35:00.000-08:00

Hidden within each cell and every ceremony
Chords and microtubules the symphony of life
So many different names as various kinds of species
Our hands desperately trying to cradle the totality
Our footsteps lost wandering around the coastlines
So vast the ocean in a shell listening to the waves
Counting the stars the eyes galaxies of numbers
Yet remains the amazing accordance for the mind
The fine tuning quality of childhood and wonders
The continuity of dreams in awakening reality
The unfulfilled renormalized at the end of time
The replicating emptiness by some injective manner
The states being limited by observables desired
So many perfect maps as promised lands untraveled
The lodgings run for all the guests one room after another.

2/26/2010

Photo here

Figure and ground

2010-02-06T14:16:00.000-08:00

‘Is it this star against the night or is it the night against the star?’

We may distinguish the various objects that lie inside space in two different manners. A meaningful and a perceptional one. Despite the fact that these two manners are not completely distinct to each other our main concern will have to do with the second manner the ‘objective’ perceptional one.

What are exactly those mechanistic criteria by which our brain does the distinction between figure and ground? They may be illusionary, but this figure and ground effect has been well studied by art and science. First of all lets focus at psychology and the term ‘gestalt.’ It is a German term that means ‘essence or shape of an entity's complete form,’ and it refers to the characteristic organization of perception into a figure that 'stands out' against an undifferentiated background. In Gestalt psychology, the operational principle of the brain is holistic, parallel, and analog, with self-organizing tendencies. Let’s see for example the following images:

Figure- ground crosses

Someone can focus on the doted triangles or equally on the inside cross. So our brain captures the whole of an image and then tries to analyze its pieces in a figure and ground relation. If we imagine lets say a landscape we can either focus on the mountains or on the valleys.

Nevertheless this figure and ground distinction is not always clear as the following '(Herman’s) grid illusion' shows:

Grid optical illusion

Gray dots that don’t really exist appear at the cross sections between the black squares and the white lines. This is a typical example of the gestalt phenomenon as the brain tries to holistically overview the picture.

As far as art is concerned I am well aware of Salvador Dali’s paintings where this interplay between figure and ground goes on. See for example the following paintings:

Paranoiac Visage, 1935

The Great Paranoiac, 1936

Slave Market with the Disappearing Bust of Voltaire, 1940

The Endless Enigma, 1938

I don’t really know what is the connection between gestalt psychology and paranoia, as Dali mentions the last word quite often in that kind of paintings. But he proves excellently the connection between figure and ground.

So it’s about time I went on a further step into the realm of paranoiac illusion and of modern physics as well. The figure- ground phenomenon has been well studied by physicists. Newton as Aristotle believed in absolute motion. A moving (accelerated) object could always know its motion in absolute space. This was an example of a figure (the object) without ground (absolute empty space.) Leibniz at first and then Mach attacked this inconsistency. How can one have possibly anything against nothing? Mach later on argued on the fact that motion must be relative to some kind of background. So Mach decided that motion of an object is relative to the distant fixed stars…

Spacetime frame dragging

Einstein later on proved the Lense- Thirring effect: An object within a rotating shell will experience a gravito-magnetic Coriolis force (frame dragging effect on spacetime by a rotating body). Just out of nowhere. Of course these deductions restored the figure- ground duality, but caused another inconsistency: How is it possible that distant stars or objects spontaneously act on other objects to produce acceleration (non- inertial forces)? Further more I can pose another question: Is there a real figure- ground distinction or is it that two (or more) figures compete with each other for two interchanging and equivalent roles? Is a star against the night or the night against a star? Or is it finally our brain that creates this equivalent duality as a prerequisite for meaning and wholeness?

Further: Metaphor and Figure- Ground Relationship: Comparisons from Poetry, Music, and the Visual Arts.

About Logic

2010-02-04T10:47:00.000-08:00

(Vassily Kandinsky, Several Circles)

If we regard our mind as an objective property
Thought can be a quality of waterfalls in progress
Secrets of a silent woman showering in a pond
Appropriate as it seems we call her imagination
Accordingly our genius a brilliant inspiration
A strange laughter shutters this arrogant conception
A mountaintop that lies on a broken glass reflection
Facing the facts an earthquake on their foundation
The beauty of the pond is flying away on a cloud
The liberation of surprise with a swarm of butterflies
Uncounted inconsistencies as follies settling down
Picking up the pieces for each probable recovery
Stripped by the wind a rushing eye in the horizon
Chasing a star eternally that keeps a lead ahead
There is a word so meaningful that never can be said.

2/2/2010

{The poems are mine otherwise it is mentioned}

The impossibility of human logic

2010-01-23T08:09:00.000-08:00

"May we ever know the unknown? Or we just keep on expanding the limits of our ignorance? The birds will show; the wind will blow."

I was not going to come back (in my thoughts) to Zeno paradoxes if it were not for GEB (Gödel- Escher- Bach, the book of Hofstadter). Logic seems to be a closed loop or maybe a strange loop as he would say. In fact, whether the previous assumption is true or wrong, there is an even more fundamental truth about our logic. It seems that logic is a mechanism inherent to human beings that cannot change. By this I mean that despite the fact that we can change our opinions about facts or even our rules of inference, we can never change the way our logic works: Right or wrong, white or black, on and off.

About Zeno’s original argument (let’s call it ‘The runners' paradox) I will try to make the story short: Achilles and the turtle are on a speed race. Achilles is very fast, the turtle is very slow. Achilles gives the turtle some meters to lead. And then they start the race. But, as Zeno said, if Achilles catches up with the place the turtle originally was, then he will have to run a further distance where the turtle will be and so on. Conclusion: Achilles will never catch up with the turtle.

Not only that, but, as Zeno proved in another paradox of his (the dichotomy paradox), nobody will ever finish the race; since if we split the distance in two again and again then we will have an infinite number of half distances till the end. There is also a third paradox of Zeno (the arrow paradox) where he shows that a flying arrow will have to pass along its journey through an infinite number of still intervals so that motion is impossible.

Here we have an example of how our rules of logical inference contradict everyday experience. Still there is an even more fundamental question that we can ask ourselves and of course our logic: Is the human brain a ‘natural’ thing or is it something outside nature? Can nature ‘think’? If she can then does she ‘think’ the same way as humans? Are we capable of knowing the answer? If our previous realization about the ‘on and off’ function of logic had to do with what is called consistency, this new question has to do with what is called analogy or isomorphism. So is there a true analogy, a straightforward correspondence, between natural reality and the way our brain works? If not, then we will never answer the question and we will never find the truth or the whole truth about the real world.

So let us now suppose that motion is not impossible and that consequently space and time exist. All we have to do is to assume that the intervals of distance are not infinite. Achilles in fact is not running through the whole of the ground but instead his is stepping on regular intervals of a finite number. The same goes for the turtle. We can make a further step of abstraction and suppose that space and time are not continuous but divided into recurring steps of finite discontinuity. In fact this view is neither new nor mine. It is modern quantum physics that presupposes that action is quantized. The same holds for space and time since there is a fundamental length and also a fundamental time measured in certain units (Plank units).

But does this assumption of discontinuity really solves the problem for us or again divides it to infinity? If we suppose that there is a fundamental length so that every other length consists of (or even a fundamental time), then who can guaranty that there isn’t another even more fundamental one? Look for example what have occurred with the atom. We believed that the atom was a fundamental quantity till we found electrons and its nucleus. Then we found quarks inside protons and neutrons. Now we think that quarks and electrons are fundamental. But after all how can we be sure?

This is exactly what Gödel (to leave Escher and Bach aside) was talking about when he proposed his incompleteness theorem. In fact he used our former assumption about consistency to prove that our latter assumption about complete knowledge is wrong. If our system of logic is more or less a closed formal system with its fundamental functioning originating from the ‘beginning of time,’ then its basic axioms about reality will be more or less ‘predetermined’ so that our main deductions about the world will remain unproved. Gödel of course formed his theorem aiming to artificial intelligence but he also showed that there is not any closed system of logic using a formal axiomatic structure that can include the whole of knowledge in a settled and overall way.

Thankfully, however, we shouldn’t feel so bad about it. I mean that after all we truly are creatures of nature. We didn’t come from another universe with different laws of nature- if there can be any other ‘universe’ at all. Of course we can’t prove that there isn’t another intelligence somewhere out there being capable of a more complicated way of thinking above and beyond the closed- loop process of human logic. But we should agree that there mustn’t be any such intelligence, because if there were, then it would be impossible. In the end, this would be inconsistent with everything we know about the world. And so I guess this last truth completes the circle of our reasonable and ingenious loops of logic.

Darija (A lotus flower for)

2010-01-23T08:06:00.000-08:00

Your full of lust pretentious smile of destiny
Is like the pale expression of the pray
When the vultures demand your incarnation
Yet no tailor or hunter’s now eager to protect you
Unless you offer every mouthful of your breath
And every precious peak of your pale complexion
As the mirror turns its back invisible against you
There’s a lake where the swan song goes on
Upwards struggling necks for beauty and perfection
Devoted to the stars of love the celebration
While the wise oak trees hide all the insecurity
Rooting deep in silence that everything surrenders
To the lotus flower the sun becomes so grateful
A throat like tunnel leading to a cave of sacrifice
Your full of lust pretentious eyes are willing to accept.

12/31/2009

Time of the observatory

2010-01-23T07:59:00.000-08:00

The endless motion of planetary spheres
Fingers playing with paths of vapor trails
Droplets falling on a fateful body gracefully
Under the mythical blanket we discovered nudity
Shivering but keeping still a trace to surrender
Filling the gaps of photographic memory
Posing for the night some silhouettes of negative
A flash of light was the day of a morning dream
Standing alone on some black and white squares
Regarding us important pieces of the scenery
While a game of chess surrenders to infinity
Internal species battle- bees breeds of smoke
Satyrs on a cyclic dance at the feast of sadness
Tiling the clouds cheek to cheek roses and kisses
A wish at dawn these lips will come to swallow.

12/24/2009

Photograph: 'A l'Heure de l'Observatoire- Les Amoureux,' Man Ray.

Ancient Electricity

2009-12-30T10:16:00.001-08:00

«Our God, the great Pharaoh, holds a bulb in his mighty Hands, the Lotus flower, the blossom of Fire, from within its stem appears the sparkling tongue, the Serpent of Light, spreading the glitter inside the invisible capsule of its blue-like Aroma, to conquer the Night, to make us see in the darkness…»

[My personal conception of how an ancient Egyptian might describe this depiction on the wall.]

Chimerical verses of a hybrid poem

2009-12-09T00:40:00.000-08:00

In the night when the moonlight sparkles our faces
Under the candlelight where shadows are melting
We are in love with vile spin puns
With needles of birds that curl up thoughts
Corpses of martyrdom echoed in the valleys
Lakes made of wounds and thorns under fingertips
Opposite to us there is always an electric chair
And the pillars have worn their straw huts
Inside the screen where eyes are whipped
In the cage where silence still captures
And the nut we crack leaves a sense of gap
Transcending us clouds to elephant hedges
While we travel on board a ghost ship
Love is a word with no horns to the letter
The chest of the Minotaur is grazed by virgins.

The Verb to be

2009-10-06T13:29:00.000-07:00

I know despair in its broad outlines. Despair has no wings, it is not necessarily found at a cleared table upon a terrace, in the evening by the seaside. It is despair and it is not the return of a quantity of little facts like seeds leaving one furrow for another at nightfall. It is not moss upon a stone or a drinking glass. It is a boat riddled with snow, if you please, like birds falling, and their blood has not the slightest thickness. I know despair in its broad outlines. A very small form, fringed by jewels of hair. It is despair. A necklace of pearls for which a clasp can never be found and whose existence does not hold even by a thread, that is despair. As for the rest, let's not speak of it. We haven't finished despairing if we begin. I myself despair of the lampshade around four o'clock, I despair of the fan around midnight, I despair of the condemned man's last cigarette. I know despair in its broad outlines. Despair has no heart, the hand always remains in despair out of breath, in despair whose death we are never told about by mirrors. I live off this despair which so enchants me. I love that blue fly streaking in the sky at the hour when the stars hum their song. I know in its broad outlines despair with its long, slim breaches, the despair of pride, the despair of anger. I rise every day like everyone and I stretch out my arms on a flowered wall-paper, I remember nothing and it is always with despair that I discover the lovely uprooted trees of the night. The air of the room is lovely like drumsticks. It is time weather. I know despair in its broad outlines. It is like the curtain wind giving me a helping hand. Can you imagine such despair: Fire, fire! Ah they are still going to come... Help! There they are falling down the stairs... And the newspaper advertisements, and the illuminated signs along the canal. Sandpile, go on with you, you old sandpile! In its broad outlines despair has no importance. It is a drudgery of trees that is going to make a forest again, a drudgery of stars that is going to make one less day again, a drudgery of days fewer which will again make up my life.

Modern examples of background physics

2009-06-15T02:57:00.000-07:00

Unpublished Essay by Pauli

June 1948 [Typewritten carbon copy]

MODERN EXAMPLES OF "BACKGROUND PHYSICS"

1. PHYSICAL TERMS AS ARCHETYPAL SYMBOLS

What I understand by "background physics" is the appearance of quantitative terms and concepts from physics in spontaneous fantasies in a qualitative and figurative- i.e., symbolic- sense. I have been familiar with the existence of this phenomenon for about 12 to 13 years from my own personal dreams, which are totally uninfluenced by other people. As examples of physical terms that can appear as symbols, I should like to list the following, without any claim to completeness:

Wave, electrical dipole, thermoelectricity, magnetism, atom, electron shells, atomic nucleus, radioactivity.

As befits my rational, scientific approach, these dreams seemed to me initially offensive- in fact, an abuse of scientific terminology. What is more, I regarded the appearance of this symbolism in my dreams as a personal idiosyncrasy, typical of a physicist, and never even remotely hoped that I would be able to communicate the special experience that manifests itself in dreams of this nature to any psychologists of my acquaintance, for they are certainly not physicists.

Later, however, I came to recognize the objective nature of these dreams or fantasies- i.e., the fact that they are largely independent of the actual person. What first struck me was the similarity of the mood that obtains both in my dreams and in the physical treatises of the 17th century, especially in Kepler, where scientific terms and concepts were still relatively undeveloped and physical considerations and ideas were interspersed with symbolic concepts. Second, I could see certain correspondences between the contents of my dreams and the graphic concepts of scientific laymen, especially those with a poor education and weak critical faculties, who are not hampered by inhibitions οn the part of consciousness that might otherwise affect the naïveté of the fantasies. Thus it was that l gradually came to acknowledge that such fantasies or dreams are neither meaningless nor purely arbitrary but rather convey a sort of "second meaning" of the terms applied. This seems to me today ample proof of the fact that the kind of imagination l call "background physics" is of an archetypal nature. But any attempt to open it up to a psychological interpretation, based οn the idea of the collective unconscious, must not fall into the trap of assuming that the products of background physics are directly comparable with a well formulated doctrine of scientific truths. From the point of view of contemporary science, the form of imagination under discussion is definitely to be seen as a relapse into an archaic stage. Furthermore, my feeling is that the purely psychological interpretation only apprehends half of the matter. The other half is the revealing of the archetypal basis of the terms actually applied in modern physics. What the final method of observation must see in the production of "background physics" through the unconscious of modern man is a directing of objective toward a future description of nature that uniformly comprises physis and psyche, a form of description that at the moment we are experiencing only in a pre-scientific phase. Το achieve such a uniform description of nature, it appears to be essential to have recourse to the archetypal background of the scientific terms and concepts.

In the following outline, l shall attempt to explain how a physicist, as a consequence of this approach, inevitably shifts from this background into the field of psychology. As l regard physics and psychology as complementary types of examination, I am certain that there is an equally valid way that must lead the psychologist "from behind" (namely, through investigating the archetypes) into the world of physics.

2. ΤHΕ SPLITTING OF A SPECTRAL LINE IΝΤΟ TWO COMPONENTS AND ΤHΕ SEPARATION OF A CHEMICAL ELEMENT IΝΤΟ TWO ISOTOPES AS DREAM MOTIFS.

As an example of background physics, l shall discuss a motif that occurs regularly in my dreams- namely, fine structure, in particular doublet structure of spectral lines and the separation of a chemical element into two isotopes.

Let me begin with some explanations for non physicists of the terms used here. The frequencies of spectral lines are characteristic of and specific to the various chemical elements, which can thus be identified by the spectral lines emitted by them- i.e., by the precise values of the frequencies of the light emitted by the atoms of the relevant element. What also happens in spectroscopy is that under coarse observation- i.e., with poor resolution- a spectral line appears singly, whereas in apparatuses with greater powers of resolution it appears as separated, i.e., resolved into two or more components with only slight variation in the number of oscillations. In the last century, spectroscopy introduced the term "fine structure," naming the separated structures "doublet," "triplet," etc., according to the number of components. A well-known example of such a doublet is the yellow "D-line" of the sodium atom, which always appears in the rock-salt flame.

According to modern ideas (which are crucial to what now follows), the emission of spectral lines comes about in the transition of the atom from one state to another. Each of these states is also an energy level, and it is a universal law of nature that the frequency of the light emitted is always exactly proportional to the difference of the energy values of the initial and final states of the atom- a fact that cannot be explained in the framework of the older, classical physics. The energy levels are the characteristic states of the atom, and every spectral frequency is assigned both to the energy of a light corpuscle or photon and to the corresponding difference in energy values of a pair of energy levels. The doublets of the spectral lines correspond to the case where one of the two levels assigned to is single and the other one is double (see figure below). The doublet fine structure of a spectral line thus also makes visible the splitting of an energetically defined state into two neighboring states.

In an interesting connection to the universal quantitative assignment of light frequencies to energy levels and their differences, there now exists the situation that in addition to the doublet structure of the spectral lines, isotope separation also appears as a related dream motif. The word "isotope" derives from the two Greek words ίσος = same, and τόπος = place, and it denotes elements that occupy the "same place" in the periodic system of the elements and thus share the same chemical properties. According to the modern concepts of atomic structure, isotopes have the same electric charge of the atomic nucleus and thus have the same distribution of external electrons. Generally they differ physically through their mass (here I can leave aside the possibility of differentiating by means of radioactive properties such as lifetime, since the differentiation through the masses of the atomic nuclei- i.e., the atomic weights, is the usual procedure). This limits their separability to finer physical means, of which the varying detection of electrically charged atoms by external electrical or magnetic fields is the simplest and by far the most well known. The separation of isotopes by this method is brought about by an apparatus known as the mass spectrograph, because the atoms are photographed as lines that look like spectral lines, although of course they have nothing to do with light emission. Isotope separation corresponds here -also externally- to the resolving of a line into two or more neighboring components that correspond to the various values of the mass of the atoms. As mass energy are equivalent, instead of various atomic weights, one can speak of various energy levels of nuclear matter (the structure of which I need not go into at this point). Isotope separation is a relatively difficult procedure (known only since about 1920), and the resolution of the spectral doublets calls for a relatively advanced development of experimental technique.

Now that the way has been prepared with regard to the physical aspects, let me turn to the typical features of the group of dreams to be discussed. In my dreams there usually appears some figure of authority (also regarded subjectively as such by me) or the relevant special field of physics to explain to me that the dispersion of a spectral line into a doublet or-in other cases- the dispersion οf a chemical element into two isotopes, is of fundamental importance. Sometimes the authority goes οn to say that I should proceed with this dispersion or else that I have just completed it; sometimes in the dream I can see clearly before me the spectral line and its dispersion, as i.e. through a spectroscope. Occasionally, the authority also gives the name of the element that emits the spectral line or is to be dispersed into isotopes; but the chemical nature of this element was always changing, and I never found that it had any particular importance. In a much later stage of these dreams, the chemical elements sometimes had fantasy names (based on countries or cities, sometimes numbers). What seems to me important is that generally the two dispersed components are of roughly equal strength; in special cases, one is twice as intense as the other, but it never happens that one dominates and the other is a mere remnant.

Το find the "second meaning" of this group of dreams, what they have to say- their statement- must first be translated into a neutral language, in view of the distinction between the physical and the psychological. A translation of this nature always contains hypothetical elements, and the physical statements should not be regarded as all that important. We shall see how it works with the following "lexicon."

"Frequency" defines a specific energy state on the one hand, and on the other hand-viewed in time- It is a regular repetition.

A "chemical element" is an object that is also recognizable by its specific reactions but also has the aspect of mass, which makes possible a further separation. Thus, the statement of the dream could be understood as follows: "Of fundamental importance is the separation of a specific energy state or an object with specific reactions into two states or two objects with similar but different reactions. This separation comes about not just by watching ('with the naked eye') but through a more delicate form of observation conducted with the aid of a deliberately conscious method." So is the "state" a physical state, the building block of matter, or is it a psychic state, and is the object that is recognized by the specific reactions a material object or is it something psychic- what the psychologists call "contents"?

Does the systematic accomplishment of observation come about through technical construction of apparatuses or by means of a methodically guided imagination (imaginatio vera non phantastica)? It seems to be a characteristic of these manifestations of the unconscious that it leaves open the answers to these questions. For the "standpoint of the unconscious," both are one and the same.

A certain point of reference can be taken from the fact that the dreams select first one and then the other chemical element. Whereas an atom of a specific type- e.g., a hydrogen atom- is a representative of a species of exactly identical objects, this exact likeness does not seem to be present with the psychic objects (contents) alluded to; it is much rather the case that the latter can be regarded as unique.

In the translation of the dreams' statements into a neutral language, the energetic aspect of the frequency concept, which has come to the fore through the new quantum physics, is used more than its original aspect of a regular temporal repetition. As mentioned earlier, the linking of the two concepts is most unexpected- nay, even irrational- from the standpoint of classical physics. (I still vividly recall the tremendous shock I received as a student because of these facts and their implications. Most of the physicists of my generation and the previous one reacted in the same way.) It took science no less than 27 years to set up a system of concepts appropriate to these paradoxical facts and yet logically free of contradiction. It has emerged that the source of the contradictions arising from the linking of energy and frequency with unlimited application of the illustrative images lies in the premise that the energy at any definite moment in time has a quite specific value. It seems pointless to talk about the value of a temporal period in relation to a length of time that is shorter than the period itself. The greater the length of time available to define a period, the sharper is its value defined. A perfectly sharply defined period corresponds to the limiting case of observation during an infinitely long time. The new thing that modern quantum physics has taught us is that something exactly analogous applies to energy. Energy can be measured all the more precisely, the longer the duration of time that is available for that measurement; a perfectly sharp definition of energy would actually, as a limiting case, require an infinitely long duration of measurement. It is pointless to talk about an energy value at a specific point in time. How is that compatible with the conservation, i.e. the indestructibility of energy?

Now physical energy is, without exception, indestructible; it does not change into hidden, nonphysical forms of energy (such as "psychic energy," for example). However, in physics we never deal with the universe as a whole but rather with subsystems that are observed from outside. When these systems are inspected by observation, then they are subjected to the action of the observer or the means of observation itself. What this means is: The more precisely the observation method allows inspection of the temporal processes in the system, the more difficult it will be to detect and determine the exchange of energy between the observer and the system being observed. The laws of nature themselves make it impossible to get away from what the physicists call the complementarity of energy and time. It is true that the energy remains indestructible, but with a measuring setup that makes it possible to determine the temporal progress of a process, one does not know how much of it has entered the observed system from outside or has left the system. The law of conservation of energy applies to closed systems, whereas systems with a definite temporal evolution are never "closed." The two limiting cases of a precisely known energy value with completely unknown time evolution on the one hand and a precisely known time evolution on the other are in practice never wholly realized, but rather we are always dealing with inexact energy values and with imprecisely known temporal processes. Depending on the choice of experiment, one can find oneself closer to one or the other of the above- mentioned limiting cases.

The findings of new physics have accordingly led to a fundamental change in the attitude of modern man toward the archetypal ideas that are at the basis of matter and energy. Since time immemorial, the idea of matter had been closely linked with the Mother archetype. In alchemy, there was an elevating of the status of this idea in that the prima materia was actually assigned the attribute of the Increatum, which orthodox Christianity had assigned exclusively to God, as the masculine spiritual principle. It was C. G. Jung who drew attention tο this, and interestingly enough, he saw in this the psychological basis for the materialism of modern time. When new physics, with its radiation and pair production processes, demonstrated that what had earlier been known as "material substance" was in fact ephemeral, this materialism was deprived of its very foundation. This "substance" has been replaced by the law of conservation of energy by means of which mass and energy are recognized as proportional and hence equivalent (inertia of energy).

Corresponding to the transition from static to dynamic laws of nature, the attribute of indestructibility (Increatum) was now linked with a concept that had come originally from the archaic view of "mana," which was totally different from the idea of matter.

In this connection, it seems significant that according to quantum physics the indestructibility of energy on the one hand- which expresses its timeless existence- and the appearance of energy in space and time on the other hand correspond to two contradictory (complementary) aspects of reality. In fact, both are always present, but in individual cases the one or the other can be more pronounced. The "non illustrative" mathematical functions used by modern physics take on the role of symbols that unite opposites. (Such symbols are always of an abstract nature in psychology, too, whereas "illustrative" in old physics would be analogous to "concretistic" in psychology. Incidentally, for me the term "illustrative" is largely a relative one and is simply a question of habit.) The opposition that emerges here is nο longer that between matter ('mater') and dynamics ('mana'), but rather that between indestructibility (energy) and time. The former seems to belong to a timeless form of existence that is contrasted with time as a feminine principle, similar to the way in which, at an archaic level, material substance and the physis stand in contrast to the spirit and the psyche. The ancient idea of polar opposites, such as the Chinese Yang and Υin, is thus replaced in modern thinking by the idea of the complementary (mutually exclusive) aspects of phenomena. Because of the analogy of microphysics, I feel that one of the most important tasks for the Western mind is to translate the ancient idea into the new form in psychology as well. We shall return frequently to this viewpoint.

Complementarity in physics, as I have indicated elsewhere, has a very close analogy with the terms "conscious" and "unconscious" in psychology, in that any "observation" of unconscious contents entails fundamentally indefinable repercussions of the conscious on these very contents. An "ego with total consciousness" (claimed by Eastern philosophy- and probably with justification- to be possible only in death) or, on the other hand, an objective psychic one, not observed by any subjective consciousness (and hence influenced), corresponds to two limiting cases that in reality can never be achieved. The universality of the objective- psychic and the uniqueness of contemporary consciousness are both ever present. The symbolic images uniting this opposition are known to manifest themselves in myths. With this pair of opposites, the "objective- psychic" (known in Eastern philosophy as "consciousness" but in Western psychology as "the collective unconscious") acquires- as a result of being so widespread- a sort of timeless reality, whereas the "individual ego" ("consciousness" in our Western terms) and the usual way of looking at time are essentially linked together.

Βy bringing in this general analogy of the epistemological situation in physics and in psychology, an attempt will be made to acquire further reference points for the (hitherto somewhat vague and ill-defined) "second sense" in the group of dreams discussed. Note should be taken of my immediate associations with the dreams (context), as well as material from other sources as a basis of comparison.

3. FREQUENCY SYMBOLISM AND LEVEL OF CONSCIOUSNESS

Even with the very first dreams, the ones dealing with a separation into two components (be they spectral lines or chemical elements), the following type of idea immediately and ingenuously occurred to me. A birth is a division of a body into two parts; as it is a form of separation that can only be perceived by subtle methods, it could mean a "psychic birth." The child or embryo plays an important role in yogin meditation; when the "child" rises above the head of the yogin in a later stage of meditation, this "detachment from the spirit body into an independent existence" could justifiably be described as a "doublet splitting" of the psyche of the yogin meditation as a conscious activity would be analogous to the manufacture and application of the spectrograph in physics. In this case, the "child" is a graphic representation of the previously mentioned "spirit body" or "adamantine body" or the "corpus subtile"-a concept that has been very familiar in the West since late antiquity (especially to the Gnostics). This is linked to the idea of a "superior personality part'', which is more constant than the ego, can outlive it, and is said to express itself by appearing as a specter or ghost. In accordance with the Gnostic idea of the light sphere (pleroma), in which the psyche- before and after birth- has an existence free of the dark physis, this corpus subtile would be closer to the light sphere than the ordinary ego trapped in the body. But this corpus subtile, as its name suggests, would have not only a psychic existence assigned to it but also a physical one (the latter, it seems to me, in a way that would be very unclear to us).

What also occurred to me in this division into two was the neutralizing of an unconscious identity of two people who are connected emotionally. All these associations to my dreams were related to a raising or multiplying of consciousness.

Now the doubling of a psychic content as it develops consciousness is a motif that is well-known in psychology. It can be explained by the fact that the new consciousness content indicates a different mirror image in the unconscious. This motif is equally common in mythology as the saga of two brothers, one of whom is immortal (spiritual), while the other is mortal (material) and bound to life on earth.

In connection with this, I also recalled the existing symbol consisting of alternating light and dark stripes, which was very familiar to me at the time, a symbol that arises from the image of the "doubled content" by means of multiplicatio. This symbol often appears linked to what is known in psychology as "anima"and is also found in Indian temples. It seems to represent a series of complementary-opposite situations, one of which is presented as spiritual-timeless (aion), the other as material-temporal (chronos). The question remains open as to whether the "series" is thought of in temporal terms or as a simultaneous juxtaposition.

In the former case, it seemed to me to express that archetypal concept which is at the base of the doctrine of the transmigration of souls; according to this doctrine, the timeless reality of the life of the psyche is repeatedly being interrupted by a temporal sequence of material earth lives.

In the second version of the simultaneous juxtaposition of the "series," the stripes could also be related to the "multiple luminosity" of the unconscious psyche, a luminosity represented by separate sparks of light.

The ideas that struck me with regard to the group of dreams under discussion were both immediate and vivid, but at first my dreams were not in any way influenced by them, and they carried on producing their spectral doublets and isotope separations. Today I understand why. At the time, I was firmly of the opinion that the dreams were a "misuse" of physical concepts; for that reason, I searched frantically for purely psychological interpretations and explanations just so that I could get the physics out of the way; I did my utmost to cling to my conviction that this was all "just" psychology. But as dreams are compensatory to the conscious attitude, they insisted that the physical terminology should be taken for what it was. This forced me to accept it as an essential part of what was being represented.

I could not draw any further conclusions from this alone, but later I had the opportunity to establish further proof of the "frequency- degree of consciousness" connection. First, I came across the book by C. N. Hsieh "Quantum Physics and I Ching" (Shanghai, l937). The author is Chinese, a private scholar with a somewhat inadequate background in mathematics and physics. (There is nο translation of this book from the Chinese; it was Chinese colleagues in the U.S.A. who made it accessible to me.) What is of interest to us is that the author makes a direct link between the physical emission of light and the previously mentioned psychological phenomenon of the multiplicatio, with the physical concept of the light wave being derived from the Taoist symbol of the Tsi-Gi. Once again I was struck by the similarity between the tone and mood of this book and that of my "physical dreams," as well as that of the writings of Kepler. This was the first time that it had occurred to me that this might be an archetypal background for the physical concepts.

Moreover, in the essay of Jung's quoted earlier, "Der Geist der Psychologie" [The Spirit of Psychology], there is a parallel between spectral frequency and degree of spiritualization, in that the "psychic" drive processes are compared with the ultra red part of the spectrum, and the archetypal images of the drive consciousness, which belong to the spiritual sphere, are compared with the ultraviolet part. At first one might think that this is a rationally constructed analogy, but I feel that Jung's specific arguments about the colors red, blue, and violet indicate an already existing symbolism. It is probably not possible to deduce anything more definite from the actual text of the essay.

Μy knowledge of "background physics" in general and "frequency symbolism" in particular was, however, developed in a quite unexpected and fundamental way by S. Ε. White's unusual book, "The Unobstructed Universe". The author seems to have only a superficial knowledge of physics, has nο great critical faculties, nor is he particularly well educated; his mentality is very much that of an engineer, clinging to practical matters and not given to the formulation of general concepts. Compensating for this conscious attitude is his "anima," which has the utmost difficulty in getting him to think in abstract terms. The spiritualistic side of the book is of no interest to us and for our purposes can be regarded as an engineer's dream. The "anima" dictates to the author ideas that purport to be those of natural philosophy, and characteristically the anima is accepted by the author as an authority in this field, with its ideas being viewed as scientific truths.

What it is in actual fact is a spontaneous manifestation of the archetypal background of physical concepts, whose objective tendencies- especially that of aiming for a uniform description of nature- emerge very clearly. The conditions for the materialization of what I call "background physics" were in this case absolutely ideal.

Particularly relevant for our purposes is the chapter on "frequency" (pp. 44-46). Here the author says that frequency measures the "degree of consciousness," the "potentiality of life or evolution," hinting at a continual progression; he goes on to say that this is also what produces this life and that the "quality of what is produced is contained therein"; frequency is "the unity of consciousness in motion," and every consciousness finds itself in motion. What seems to me important here is the author's remark that in English the adjective "frequent" (in contrast to the noun "frequency") also has the meaning of "habitual" and "persistent." For him, he says, frequency has the naive- illustrative meaning of a series of "go-stop" actions. On the other hand, "constancy" for him does not have the meaning of unchangeability but is rather a continuous- i.e., uninterrupted- extension; in other words, "constant" means an unending continuum as a whole. For this author, too, the image of "frequency" does not psychologically presuppose the concept of time. Ordinary physical time is much rather just a representation of real (orthic) time in the higher level of "consciousness" and, just like space and motion, establishes the connection between real ("orthic") time and what he calls the "obstructed" aspect of "consciousness." But there is just one single universe, and it has these two aspects: the obstructed and the unobstructed.

What can be clearly recognized here is an analogy between these ideas and the associations that occurred to me in connection with the dreams about doublet splitting and with the archetypal periodic symbol consisting of alternating light and dark stripes. Here, too, frequency is a characteristic of a stable state and its "degree of consciousness"; and here, too, a distinction is made between two aspects of the one universe, an unobstructed "higher," spiritual, timeless one and an obstructed one, rooted in the physical world and ordinary time.

Obviously, there is a lot of criticism that can be leveled at the way in which S. Ε. White uses these concepts. The term "consciousness" in particular is used in a way that is hardly acceptable to the Western scientific mind. An essential part of the definition of this concept for us is that a perceiving subject is confronted with an object that is different from him and is that which is perceived. That is why it strikes us as pointless to apply the term "consciousness" to the whole cosmos. And that is also why the term "degree of consciousness" is rather unclear; I would prefer to replace it with "degree of spiritualization or desubstantialization." Subjective ego consciousness, by way of contrast, seems to me to be standing on the side of matter and ordinary time, with the timeless, objective psyche standing οn the other (complementary) side.

Furthermore, although I have no objection to accepting the existence of relatively constant psychic contents that survive the personal ego, it must always be borne in mind that we have no way of knowing what these contents are actually like "as such." AII we can observe is their effect on other living people, whose spiritual level and whose personal unconscious crucially influence the way these contents actually manifest themselves. The author's critical admiration for the manifestation and the utterances of his "anima" may well be the reason why he gets bogged down with the triads and never makes it as far as the quaternity.

Regardless of any justified criticism, however, we can once again ascertain from the spontaneous manifestation of this author's unconscious that the concept of "frequency" can be psychologically brought into association with the pair of opposites conscious- unconscious, although the ordinary concept of time will not automatically be taken for granted. Of course, rationally it is difficult to understand why frequencies or masses should have any connection with level of consciousness. And there is certainly no direct connection between the physical data of frequency or mass and consciousness: A rapid physical process runs without consciousness just as a slow one does, and a heavy atom has just as little consciousness as a light one. But these associations of ideas between level of consciousness and frequency, between doublet splitting of spectral lines or isotope separation and doubling of a psychic content with developing consciousness, all appeared directly and spontaneously; this is similar to the way in which the connection between frequency and energy level in physics, which could not be understood rationally a priori, was simply found to be existing in nature.

It is difficult to form any further definitive conclusions from the material given. Yet everything seems to point to a deeper archetypal correspondence of the complementary pairs of opposites:

From the psychological point of view, physical laws seem to be a "projection" of archetypal associations of ideas, whereas seen from outside, even the microphysical occurrence could be interpreted as archetypal, albeit with its "reflection" in the psychic being a necessary condition for the possibility of perception.

In summary, we can interpret the material given as follows: The unconscious spontaneously executes a projection of the one complementary pair of opposites onto the other, with the energy level or the mass number on the one side symbolically corresponding to the level of consciousness on the other.

What is it that lies at the essence of the situation described by the term complementarity that makes one have to limit oneself to perceiving the compatibility of the two aspects of reality that initially seem contradictory, without any consideration of things or processes in space and time, which are objective- i.e., independent of the method in which they are observed? This is possible only through unifying symbols, the role of which in physics is played by abstract mathematical functions.

4. ΤHΕ ACTIVE CONTRIBUTION OF CONSCIOUSNESS AND ΤHΕ APPEARANCE OF QUATERNITY SYMBOLISM.

According to the point of view presented here, the quaternity would not be effective in physics, but a quaternity would certainly be assigned to the wholeness made up of physics and psychology insofar as the complementary pair of opposites of physics reappears reflected in the psychic sphere. It would be conceivable, and in fact seems to me plausible, that there might be phenomena in which the whole quaternity plays a crucial role, and not just the physical and psychic pair of opposites. With such phenomena, it would not be possible to give a meaningful definition to conceptual distinctions such as that between "physical" and "psychic" (as is also the case with atomic phenomena, where the distinction between "physical" and "chemical" frequently loses its meaning).

I am not yet in a position to say anything that could be adequately substantiated, but nevertheless, both by way of summing up and looking ahead I would like to give two dreams that belong together, in which the quaternity features prominently. The dreams occurred within an interval of four days in the middle of March this year, when my work on Kepler had more or less come to an end. I shall now describe these dreams in detail:

Dream 1.

Μy first physics teacher appears and says: "The change in the splitting of the ground state of the H-atom is a fundamental one. Brass tones are engraved on a metal plate." Then I go to Gottingen.

Dream 2.

(Seven pictures in a row. Νo words are spoken until right at the end and I am the one speaking.)

Picture 1. A woman comes with a bird, which lays a large egg.

Picture 2. This egg divides itself into two:

Picture 3. I go closer and notice that l have in my hand another egg, with a blue shell.

Picture 4. I divide this last egg into two. Miraculously, they remain whole, and l now have two eggs with blue shells.

Picture 5. The four eggs change into the following mathematical expressions:

Picture 6. This gives the formula

Picture 7. I say, "The whole thing gives e^iδ, and that is the circle." The formula vanishes, and a circle appears.

[This is an example of the complex unit circle which is missing from the original text. Here, the letter δ is replaced by the letter t without any loss of generality.]

With regard to Dream 1, it evidently belongs to that group of dreams dealing with a splitting of a spectral line or an energy level into a doublet. But it has certain features that were not present in other dreams of this kind. First of all, there is a change in the splitting, which in physics is possible only by means of existing electromagnetic fields of force. What this corresponds to in the psychic sphere is an intervention of consciousness (which Dream 2 confirms). The H-atom is the simplest one of all, since the positively charged atomic nucleus is only encircled by one single negative electron. Thus it also represents the simplest "polar opposite." Moreover, the "proton," being the lightest atomic nucleus, is the building block for all other heavy nuclei. Hence "p," which of course means "the first," points cosmogonically to the beginning. Cosmogonical pictures are always connected with the process of developing consciousness. The metal plate is not in itself a symbol and represents the material physical world (physis) in a relatively stable form. It was originally assumed that there were 7 metals (as well as 7 planets); in Dream 2 there are 7 pictures. The tones, by way of contrast, serve very well as symbols; with their connection to music, they represent feeling- the very thing that physics cannot express. With their connection to the music of the spheres (I was very involved with Kepler at the time), they have a cosmic character. As an acoustic phenomenon, they also belong to physis, so they are a symbol uniting physis and psyche. Το me they appear to be exactly what is meant by "archetypes". If we interpret "brass" as aere perennius, i.e., indestructible- timeless, the dream is saying that the archetypes also imprint their stamp on matter, so that physis and psyche form an indivisible connection. But this seems to be a consequence of the change in the splitting of the ground state (initial state). An attempt will be made to assert the point of view that psychic contents, and hence archetypes, too, only alter because they are being observed, i.e., as the result of an intervention οn the part of human consciousness. In relation to the archetypes, this is the "secular displacement of the unconscious world picture, " which C. G. Jung has been referring to for a long time. (Cf. here what is said at the end of section 2 about the alteration of the concept of energy.) Το add to this a spontaneous alteration of the archetypes seems to me neither very satisfactory nor essential. The objective (independent of the personal) statement of Dream 1 seems to indicate, therefore, that the development of human consciousness, particularly through the convergence of microphysics towards other archetypal concepts, has led to a situation in which physis and psyche are indivisibly linked "archetypically." So I go to Gottingen, a place where not just physics but a lot of important work in mathematics is being done.

The close link between Dream 1 and Dream 2 is obvious, in that Picture 2, with the spontaneously produced two eggs can be interpreted as the "ground state" οf which a "fundamental" change is brought about through the intervention of the "ego" in Pictures 3 and 4- This change consists in the appearance of the quaternity, which comes about through the reflection of the duality. With this outcome, Dream 2 goes beyond Dream 1. In fact, Dream 2 corresponds fully to the ''Axiom of Maria Prophetissa": One becomes two, two becomes three, and out of the third comes the One as the fourth. The last mentioned typically comes about for me through mathematics. The formula

is mathematically correct, and in the representation of complex numbers through distances e^iδ is a number that always lies on the "unit circle" (the circle with the radius 1); if δ is taken as any size desired, e^iδ actually represents a circle.

The imaginary unit i = √-1 is a typical symbol since it is not contained under the ordinary numbers; the introduction of this symbol gives many mathematical theorems a simple and distinct form. In this dream it has the irrational function of uniting the pairs of opposites and thus producing wholeness.

Without going into mathematical detail, I should nevertheless like to stress here that I cannot acknowledge an antithesis between a mathematical and a symbolic description of nature, since for me the mathematical representation is a symbolic description par excellence.

Far be it from me to presume to be able to give an "interpretation" of the two dreams; in fact, I have the feeling that any such interpretation would call for further progress in all the sciences. The decisive role played by mathematical signs in the production of the ''One'' in Dream 2 also seems to suggest that the unifying power of mathematical symbolism is far from being exhausted; in fact, I would venture to say that it goes further than physics does in this respect.

According to its own definition, physics has to represent regularity in nature in conceptual terms and thus has to focus its attention on that which can be reproduced and quantitatively measured. As a consequence of this limitation that is at the very essence of physics, anything that is feeling- toned, judgmental, and emotional lies οn the opposite side-the psychological one- and what is more, from this root there springs the statistical nature of its statements, a nature which, especially with atomic processes, must basically dispense with any consideration of individual cases (apart from special ones). This is not a question of any shortcomings of the quantum theory within physics but a shortcoming of physics within life as a whole.

Mathematics, οn the other hand, has not only a quantitative side but also a qualitative one, which comes to the fore, for example, in the theory of numbers and in topology. Concepts created by mathematics, such as Riemann's surfaces, lend themselves very well to a symbolic representation of the relativization of the concept of time that is linked to the developing consciousness of the new focal point described as the "ego." It is, however, beyond the scope of this essay to delve into the problems involved in the symbolic union of the unique with the general.

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From the standpoint of the tendency to unify our world picture, it seems pleasing that connections are starting to be formed in a sphere that has already become so broad that it includes the Dioscuri myth οn the one hand and doublet splitting of spectral lines and isotope separations on the other.

THE INFLUENCE OF ARCHETYPAL IDEAS ON THE SCIENTIFIC THEORIES OF KEPLER

2009-06-12T13:11:00.000-07:00

Two Lectures given by Professor W. E. Pauli, in 1948,at the Psychological Club of Zurich.

Although the subject of this study is a historical one, its purpose is not merely to enumerate facts concerning scientific history or even primarily to present an appraisal of a great scientist but rather to illustrate particular views on the origin and development of concepts and theories of natural science in the light of one historic example.

In contrast to the purely empirical conception according to which natural laws can, with virtual certainty, be derived from the material of experience alone, many physicists have recently emphasized anew the fact that intuition and the direction of attention play a considerable role in the development of the concepts and ideas, generally far transcending mere experience, that are necessary for the erection of a system of natural laws (that is, a scientific theory). From the standpoint of this not purely empirical conception, which we also accept, there arises the question, what is the nature of the bridge between the sense perceptions and the concepts? It seems most satisfactory to introduce at this point the postulate of a cosmic order independent of our choice and distinct from the world of phenomena. Whether one speaks of the ''participation of natural things in ideas'' or of a behavior of metaphysical things-those, that is, which are in themselves real, the relation between sense perception and idea remains predicated upon the fact that both the soul of the perceiver and that which is recognized by perception are subject to an order thought to be objective. Every partial recognition of this order in nature leads to the formulation of statements that, on the one hand, concern the world of phenomena and, on the other transcend it by the ''idealized'' use of general logical concepts. The process of understanding nature as well as the happiness that man feels in understanding- that is, in the conscious realization or new knowledge- seems thus to be based on a correspondence, a ''matching'' of inner images pre-existent in the human psyche with external objects and their behavior. This interpretation of scientific knowledge, of course, goes back to Plato and is, as we shall see, advocated very clearly by Kepler. He speaks in fact of ideas that are preexisting in the mind of God and were implanted in the soul, the image of God, at the time of creation. These primary images, which the soul can perceive with the aid of an innate "instinct," are called by Kepler archetypal. Their agreement with the ''primordial images'' or archetypes introduced into modern psychology by C. G. Jung and functioning as ''instincts of imagination'' is very extensive. When modern psychology brings proof to show that all understanding is a long-drawn-out process initiated by processes in the unconscious long before the content of consciousness can be rationally formulated, it has directed attention again to the preconscious, archaic level of cognition. On this level the place of clear concepts is taken by images with strong emotional content, not thought out but beheld, as it were, while being painted. Inasmuch as these images are an "expression of a dimly suspected but still unknown state of affairs'', they can also be termed symbolic, in accordance with the definition of the symbol proposed by C. G. Jung. As ordering operators and image formers in this world of symbolic images, the archetypes thus function as the sought-for bridge between the sense perceptions and the ideas and are, accordingly, a necessary presupposition even for evolving a scientific theory of nature. However, one must guard against transferring this a priori of knowledge into the conscious mind and relating it to definite ideas capable of rational formulation.

For the purpose of illustrating the relationship between archetypal ideas and scientific theories of nature, Johannes Kepler (1571-1630) seemed to me especially suitable, since his ideas represent a remarkable intermediary stage between the earlier, magical-symbolical and the modern, quantitative- mathematical descriptions of nature. The chief writings of Kepler (hence- forth referred to by the number given) are:

1) Mysterium cosmographicum, 1st ed., 1596; 2d ed., 1621.
2) Ad vitellionem paralipomena, 1604.
3) De stella nova in pede serpentarii, 1606.
4) De motibus stellae Martis, 1609.
5) Tertius interveniens, 1610.
6) Dioptrice, 1611.
7) Harmonices mundi (5 vols.), 1619.
8) Epitome astronomiae Copernicanae, 1618-1621.

I should mention briefly at this point that Kepler's three famous laws of planetary motion, upon which Newton based his theory of gravitation (1687), were not what he was originally seeking. A true spiritual descendant of the Pythagoreans, he was fascinated by the old idea of the music of the spheres and was always trying to find harmonious proportions, in which for him all beauty lay. He attached the utmost importance to geometric claiming that its theorems "have been in the spirit of God since eternity". His basic principle was ''Geometria est archetypus pulchritudinis mundi'' (Geometry is the archetype of the beauty of the world).

The essay gives a brief biography of Kepler and goes on to discuss the hierarchical arrangement of his archetypal concepts. The highest place is occupied by the trinitarian Christian Godhead, which is incapable of visualization. For Kepler, the most beautiful image that represents God's own form of being is the three-dimensional sphere. He says already in his early work (1): "The image of the triune God is in the spherical surface, that is to say, the Father is in the center, the Son is in the outer surface, and the Holy Ghost is in the equality of the relation between point and circumferences. The movement or emanation passing from the center to the outer surface an image that frequently recurs with him and is closely connected to the Neoplatonists (especially Plotinus) is for him the symbol of creation, while the curved outer surface itself is supposed to represent the eternal Being of God. One naturally links the former with extroversion and the latter with introversion. In his later writings (2, 5, 7), Kepler takes us one step farther down in the hierarchical order of his universe, passing, that is, from the ideas in the mind of the Godhead to the corporeal world. Here the heavenly bodies, with the sun as the central point, are for him a realization of the ideal, spherical image of the Trinity, though less perfect than it. The sun in the center, as the source of light and warmth and accordingly of life, seems to him especially suited to represent God the Father. Kepler's view of this correspondence between the sun with its surrounding planets and his abstract spherical picture of the Trinity is regarded as primary. Because he looks at the sun and the planets with this archetypal image in the background he believes with religious fervor in the heliocentric system. This heliocentric belief impels him to search for the true laws of the proportion of planetary motion as the true expression of the beauty of creation.

In view of Kepler's conflict with Fludd -the representative of traditional alchemy- it is important that Kepler's symbol -of a type designated by Jung as a mandala because of its spherical form- contain no hint of the number four or quaternary. Perhaps this is due to the lack of a symbolism of time in Kepler's spherical picture. Movement in a straight line, directed away from the center, is the only kind contained in Kepler's symbol, and insofar as this movement is caught up by the outer surface of the sphere, the symbol can be termed static. Since the Trinity had never been represented in this way before Kepler, and since he stands at the threshold of the scientific age, one is tempted to assume that Kepler's "mandala'' symbolizes a way of thinking or a psychological attitude, far transcending Kepler's person in significance, produced that natural science which we today call classical. From within an inner center, the psyche seems to move outward, in the sense of extroversion, into the physical world in which, by definition everything that occurs is automatic, so that the mind, in itself in a state of rest, embraces this physical world, as it were, with its ideas.

The next step in Kepler's hierarchical arrangement of the cosmos involves the individual souls. What he understands by individual souls are not just human souls but, employing Paracelsus's concept of the ''Archaeus'' the souls of the planets as well. The earth having lost its special position for the Copernicans, Kepler feels bound to assign a soul to it, the anima terrae. This anima terrae is also a formative power (facultas formatrix) in the earth's interior and in Kepler's view is responsible for meteoric phenomena. For Kepler, the individual soul, as an image of God, is partly a point and partly a circle: anima est punctum qualitativum. In the original essay, which functions of the soul are attributed to the central point and which to the peripheral circle is explained in quotations from Harmonices mundi. Connected to this conception as both point and circle are Kepler's special views on astrology. According to him, the justification for astrology lies in the ability of the individual soul to react -with the help of the instinctus- to certain harmonious proportions that correspond to specific rational divisions of the circle. As with the perception of euphony in music, the soul is said to have a similar specific ability to react to the harmonious proportions of the angles that the rays of starlight, striking the earth, form with each other. Kepler seeks to link astrology to optical resonance effects, along the lines of scientific causal thinking. This resonance is based on the fact that, according to him, the soul knows about the harmonious proportions, because, by virtue of its circular form, it is an image of God. In Kepler's view, astrological effects are caused not by the celestial bodies but rather by the individual souls with their specifically selective ability to react to certain proportions. Since this power of reacting, on the one hand, receives influences from the corporeal world and, on the other hand, is based on the image relation to God, these individual souls (the anima terrae, and the anima hominis) become for Kepler essential exponents of cosmic harmony (harmonia mundi).

Kepler's views on cosmic harmony were incompatible with the point of view of the respected physician and Rosicrucian Robert Fludd of Oxford who, as the representative of traditional alchemical philosophy, published a vehement polemic against Kepler's Harmonia mundi. The intellectual ''counterworld'' with which Kepler here clashed is an archaistic- magical description of nature culminating in a mystery of transmutation [Wandlungsmysterium]. Fludd starts off from two polar fundamental principles: form, as the light principle, coming from above, and matter, as the dark principle, dwelling in the earth. In accordance with exact symmetry, from above and below, the world is the reflection of the invisible Trinitarian God, who reveals himself in it. A constant struggle goes on between the opposites: From below, the material pyramid grows upward from the earth like a tree, the matter becoming finer toward the top; at the same time, the formal pyramid grows downward with its apex on the earth, exactly mirroring the material pyramid. In the middle, the sphere of the sun, where these opposing principles just counterbalance each other, there is engendered in the mystery of the chymical wedding the infans solaris, which is at the same time the liberated world soul. In agreement with old Pythagorean ideas, Fludd evolves from the proportions of the parts of these pyramids the cosmic music, in which the following simple musical intervals play the chief part:

This is illustrated by several figures.

Fludd seems to have attacked Kepler so fiercely because he felt that despite their common starting point of similar archetypal concepts, Kepler was the child of a spirit that represented a serious threat to Fludd's own archaistic mystery world. Whereas for Kepler only that which is capable of quantitative, mathematical proof belongs to objective science, for Fludd nothing can have objective meaning unless it is directly connected to alchemical or Rosicrucian mysteries. This is why he dismisses as ''sedimentary substance'' the quantities represented in Kepler's geometrical diagrams and acknowledges only his own hieroglyphic figures (picturae aenigmata) as the symbolical expressions of the ''inner nature'' of cosmic harmony. He also criticizes Kepler for having shifted cosmic harmony too much into the subject, thus taking it out of the physical world instead of leaving it in the anima mundi, dormant in the matter. Kepler, by way of contrast, represents the modern point of view that the soul is a part of nature.

Generally, one has the impression that Fludd was always in the wrong when he let himself be drawn into a discussion concerning astronomy or physics. Yet the polemic between Fludd and Kepler is still of significance to modern man. An important pointer is to be found in Fludd's criticism of Kepler that “you force me to defend the dignity of the quaternity” (cogis me ad defendam dignitatem quaternarii). For modern man, this is a symbol of a completeness of experience, which is not possible within the scientific method of observation and which the archaic point of view, which also strives to express the emotions and feeling-toned values of the soul with its symbolic images, has over the scientific point of view.

At the end of the essay an attempt is made to bring this seventeenth- century problem into association with the generally felt wish today for a greater unification of our worldview. There is an initial proposal to recognize the significance of the scientific stage of knowledge for the development of scientific ideas by supplementing the investigation of this scientific knowledge [Erkenntnis nach aussen] with an investigation directed inward [Erkenntnis nach innen]. The former process is devoted to adapting our knowledge to external objects; the latter should bring to light the archetypal images used in the creation of our scientific concepts. Only by combining both these directions of research may complete understanding be obtained.

It is then pointed out that though we now have natural sciences, we no longer have a scientific picture of the world [Weltbild]. This very circumstance, however, should make it easier to move toward a unified concept of the entire cosmos [Gesamtweltbild], of which the natural sciences are only a part. Modern quantum physics has come closer to the quaternary point of view, which was so violently opposed to the natural science that was germinating in the 17th century, to the extent that it takes into greater consideration the role of the observer in physics than is the case in classical physics. Unlike the ''released observer'' of the latter, the former postulates an uncontrollable interaction between the observer or the means of observation and the system observed with every process of measurement, and invalidates the deterministic conception of the phenomena assumed in classical physics; the series of events taking place according to predetermined rules is interrupted by the selective observation, which -as an essentially nonautomatic occurrence, according to the point of view of modern physics- may be compared to a creation in the microcosm or even to a transmutation [Wandlung], albeit with unpredictable results.

Not only alchemy but also the heliocentric idea furnishes instructive examples of the problem as to how the process of knowing is connected with the religious experience of transmutation undergone by him who acquires knowledge [Wandlungserlebnis dos Erkennenden]; it transcends natural science and can be comprehended only through symbols, which both express the emotional, feeling aspect of the experience and stand in vital relationship to the sum total of contemporary knowledge and the actual process of cognition. Precisely because in our times the possibility of such symbolism has become an alien idea, it may be considered especially interesting to examine another age to which the concept of what is now called classical scientific mechanics were foreign, but which permits us to prove the existence of symbols that had simultaneously a religious and a scientific function.

Source: Atom and Archetype, The Pauli- Jung letters.

Photo: Wolfgang Pauli.

ON SYNCHRONICITY

2009-06-09T11:01:00.000-07:00

[Originally given as a lecture by C.G.Jung, at the 1951 Eranos conference, in Switzerland, and published in Zurich, 1952.]

It might seem appropriate to begin my exposition by defining the concept with which it deals. But I would rather approach the subject the other way and first give you a brief description of the facts which the concept of synchronicity is intended to cover. As its etymology shows, this term has something to do with time or, to be more accurate, with a kind of simultaneity. Instead of simultaneity we could also use the concept of a meaningful coincidence of two or more events, where something other than the probability of chance is involved. A statistical- that is, a probable concurrence of events, such as the ''duplication of cases'' found in hospitals, falls within the category of chance. Groupings of this kind can consist of any number of terms and still remain within the framework of the probable and rationally possible. Thus, for instance, someone chances to notice the number on his street-car ticket. On arriving home he receives a telephone call during which the same number is mentioned. In the evening he buys a theatre tick-et that again has the same number. The three events form a chance grouping that, although not likely to occur often, nevertheless lie well within the framework of probability owing to the frequency of each of its terms. I would like to recount from my own experience the following chance grouping, made up of no fewer than six terms:

On April 1949, l made a note in the morning of an inscription containing a figure that was half man and half fish. There was fish for lunch. Somebody mentioned the custom of making an ‘April fish’ of someone. In the afternoon, a former patient of mine, whom 1 had not seen for months, showed me some impressive pictures of fish. In the evening, l was shown a pie of embroidery with sea monsters and fishes in it. The next morning, l saw a former patient, who was visiting me for the first time in ten years. She had dreamed of a large fish the night before. A few months later, when I was using this series for larger work and had just finished writing it down, I walked over to a spot by the lake in front of the house, where l had already been several times that morning. This time a fish a foot long lay on the sea-wall. Since no one else was present, I have no idea how the fish could have got there.

When coincidences pile up in this way one cannot help being impressed by them-for the greater the number of terms in such a series, or the more unusual its character, the more improbable it becomes. For reasons that I have mentioned elsewhere and will not discuss now, I assume that this was a chance grouping. It must be admitted, though, that it is more improbable than mere duplication.

In the above-mentioned case of the street-car ticket, I said that the observer ''chanced'' to notice the number and retain it in his memory, which ordinarily he would never have done. This formed the basis for the series of chance events, but I do not know what caused him to notice the number. It seems to me that in judging such a series a factor of uncertainty enters in at this point and requires attention. I have observed something similar in other cases, without, however, being able to draw any reliable conclusions. But it is sometimes difficult to avoid tile impression that there is a sort of foreknowledge of the coming series of events. This feeling becomes irresistible when, as so frequently happens, one thinks one is about to meet an old friend in the street, only to find out one's disappointment that it is a stranger. On turning the next corner one then runs into him in person. Cases of this kind occur in every conceivable form and means infrequently, but after the first momentary astonishment they are as a rule quickly forgotten.

Now, the more the foreseen details of an event pile up, the more definite is the impression of an existing foreknowledge, and the more improbable chance becomes. I remember the story of a student friend whose father had promised him a trip to Spain if he passed his final examinations satisfactorily. My friend thereupon dreamed that he was walking through a Spanish city. The street led to a square, where there was a Gothic cathedral. He then turned right, around a corner, into another street. There he was met by an elegant carriage drawn by two cream- coloured horses. Then he woke up. He told us about the dream as we were sitting round a table drinking beer. Shortly afterward, having successfully passed his examinations, he went to Spain, and there, in one of the streets, he recognized the city of his dream. He found the square and the cathedral, which exactly corresponded to the dream-image. He wanted to go straight to the cathedral, but then remembered that in the dream he had turned right, at the corner, into another street. He was curious to find out whether his dream would be corroborated further. Hardly had he turned the corner when he saw in reality the carriage with the two cream- coloured horses.

The sentiment du déjà vu is based, as I have found in a number of cases, on foreknowledge in dreams, but we saw that this foreknowledge can also occur in the waking state. In such cases mere chance becomes highly improbable because the coincidence is known in advance. It thus loses its chance character not only psychologically and subjectively, but objectively too, since the accumulation of details that coincide immeasurably increases the improbability of chance as a determining factor. (For correct precognitions of death, Dariex and Flammarion have computed probabilities ranging from 1 to 4,000,000 to l in 8,000,000). So in these cases it would be incongruous to speak of ‘chance’ happenings. It is rather a question of meaningful coincidences. Usually they are explained by precognition- in other words, foreknowledge. People also talk of clairvoyance, telepathy, etc., without, however, being able to explain what these faculties consist of or what means of transmission they use in order to render events distant in space and time accessible to our perception. All these ideas are mere names; they are not scientific concepts which could be taken as statements of principle, for no one has yet succeeded in constructing a causal bridge between the elements making up a meaningful coincidence.

Great credit is due to J. B. Rhine for having established reliable basis for work in the vast field of these phenomena by his experiments in extrasensory perception, or ESP. He used a pack of 25 cards divided into 5 groups of 5, each with its special sign (star, square, circle, cross, two wavy lines). The experiment was carried out as follows. In each series of experiments the pack is laid out 800 times, in such a way that the subject cannot see the cards. He is then asked to guess the cards as they are turned up. The probability of a correct answer is 1 in 5. The result, computed from very high figures, showed an average of 6.5 hits. The probability of a chance deviation of 1.5 amounts to only 1 in 200,000. Some individuals scored more than twice the probable number of hits. On one occasion all 25 cards were guessed correctly, which gives a probability of 1 in 298,023,223- 876,953,125. The spatial distance between experimenter and subject was increased from a few yards to about 4,000 miles, with no effect on the result.

A second type of experiment consisted in asking the subject to guess a series of cards that was still to be laid out in the near or more distant future. The time factor was increased from a few minutes to two weeks. The result of these experiments showed a probability of 1 in 400,000.

In a third type of experiment, the subject had to try to influence the fall of mechanically thrown dice by wishing for a certain number. The results of this so-called psychokinetic (PK) experiment were the more positive the more dice were used at a time.

The result of the spatial experiment proves with tolerable certainty that the psyche can, to some extent, eliminate the space factor. The time experiment proves that the time factor (at any rate, in the dimension of the future) can become psychically relative. The experiment with dice proves that moving bodies, too, can be influenced psychically -a result that could have been predicted from the psychic relativity of space and time.

The energy postulate shows itself to be inapplicable to the Rhine experiments, and thus rules out all ideas about the transmission of force. Equally, the law of causality does not hold- a fact that I pointed out thirty years ago. For we cannot conceive how a future event could bring about an event in the present. Since for the time being there is no possibility whatever of a causal explanation, we must assume provisionally that improbable accidents of an acausal nature-that is, meaningful coincidences- have entered the picture.

In considering these remarkable results we must take into account a fact discovered by Rhine, namely that in each series of experiments the first attempts yielded a better result than the later ones. The falling off in the number of hits scored was connected with the mood of the subject. An initial mood of faith and optimism makes for good results. Skepticism and resistance have the opposite effect, that is, they create an unfavourable disposition. As the energic, and hence also the casual, approach to these experiments has shown itself to be inapplicable, it follows that the affective factor has the significance simply of a condition which makes it possible for the phenomenon to occur, though it need not. According to Rhine’s results, we may nevertheless expect 6.5 hits instead of only 5. But it cannot be predicted in advance when the hit will come. Could we do so, we would be dealing with a law, and this would contradict the entire nature of the phenomenon. It has, as said, the improbable character of an unlucky hit or accident that occurs with a more than merely probable frequency and is as a rule dependent on a certain state of affectively.

This observation has been thoroughly confirmed, and it suggests that the psychic factor which modifies or even eliminates the principles underlying the physicist's picture of the world is connected with the affective state of the subject. Although the phenomenology of the ESP and PK experiments could be considerably enriched by further experiments of the kind described above, deeper investigation of its bases will have to concern itself with the nature of the affectivity involved. I have therefore directed my attention to certain observations and experiences which, I can fairly say, have forced themselves upon me during the course of my long medical practice. They leave to do with spontaneous meaningful coincidences of so high a degree of probability as to appear flatly unbelievable. Ι shall therefore describe to you only one case of this kind, simply to give an example characteristic of a whole category of phenomena. It makes no difference whether you refuse to believe this particular case or whether you dispose of it with an ad hoc explanation. I could tell you a great many such stories, which are in principle no more surprising or incredible than the irrefutable result arrived at by Rhine, and you would soon see that almost every case calls for its own explanation. But the causal explanation the only possible one from the standpoint of natural science breaks down owing to the psychic relativization of space and time which together form the indispensable premises for the cause-and-effect relationship.

My example concerns a young woman patient who, in spite of efforts made on both sides, proved to be psychologically inaccessible. The difficulty lay in the fact that she always knew better about everything. Her excellent education had provided her with a weapon ideally suited to this purpose, namely a highly polished Cartesian rationalism with an impeccably ''geometrical idea of reality. After several fruitless attempts to sweeten her rationalism with a somewhat more human understanding, I had to confine myself to the hope that something unexpected and irrational would turn up, something that would burst the intellectual retort into which she had sealed herself. Well, I was sitting opposite her one day, with my back to the window, listening to her flow of rhetoric. She had had an impressive dream the night before, in which someone had given her a golden scarab- a costly piece of jewellery. While she was still telling me the dream, I heard something behind me gently tapping on the window. I turned round and saw that it was a fairly large flying insect that was knocking against the window-pane from outside in the obvious effort to get into the dark room. This seemed to me very strange. I opened the window immediately and caught the insect in the air as it flew in. It was a scarabaeid beetle, or common rose-chafer (Cetonia aurata), whose gold-green colour most nearly resembles that of a golden scarab. I handed the beetle to my patient with the words, ''Here is your scarab. This experience punctured the desired hole in her rationalism and broke the ice of her intellectual resistance. The treatment could now be continued with satisfactory results.

This story is meant only as a paradigm of the innumerable cases of meaningful coincidence that have been observed not only by me but by many others, and recorded in large collections. They include everything that goes by the name of clairvoyance, telepathy, etc., from Swedenborg's well-attested vision of the great fire in Stockholm to the recent report by Air Marshal Sir Victor Goddard about the dream of an unknown officer, which predicted the subsequent accident to Goddard's plane.

All the phenomena I have mentioned can be grouped under three categories:

1. The coincidence of a psychic state in the observer with a simultaneous, objective, external event that corresponds to the psychic state or content (e.g., the scarab), where there is no evidence of a causal connection between the psychic state and the external event, and where, considering the psychic relativity of space and time, such a connection is not even conceivable.

2. The coincidence of a psychic state with a corresponding (more or less simultaneous) external event taking place outside the observer’s field of perception, i.e., at a distance, and only verifiable afterward (e.g., the Stockholm fire).

3. The coincidence of a psychic state with a corresponding, not yet existent, future event that is distant in time and can likewise only be verified afterward.

In groups 2 and 3 the coinciding events are not yet present in the observer's field of perception, but have been anticipated in time in so far as they can only be verified afterward. For this reason I call such events synchronistic, which is not to be confused with synchronous.

Our survey of this wide field of experience would be incomplete if we failed to take into account the so-called mantic methods. Manticism lays claim, if not actually to producing synchronistic events, then at least to making them serve its ends. An example of this is the oracle method of the I Ching, which Dr. Hellmut Wilhelm has described in detail. The I Ching presupposes that there is a synchronistic correspondence between the psychic state of the questioner and the answering hexagram. The hexagram is formed either by the random division of the 49 yarrow stalks or by the equally random throw of three coins. The result of this method is, incontestably very interesting, but so far as I can see it does not provide any tool for an objective determination of the facts, that is to say a statistical evaluation, since the psychic state in question is much too indefinite and indefinable. The same holds true of the geomantic experiment, which is based on similar principles.

We are in a somewhat more favourable situation when we turn to the astrological method, as it presupposes a meaningful coincidence of planetary aspects and positions with the character or the existing psychic state of the questioner. In the light of the most recent astrophysical research, astrological correspondence is probably not a matter of synchronicity but, very largely of a causal relationship. As professor Max Knoll has demonstrated the solar proton radiation is influenced to such a degree by planetary conjunctions, oppositions, and quartile aspects that the appearance of magnetic storms can be predicted with a fair amount of probability. Relationships can be established between the curve of the earth's magnetic disturbances and the mortality rate that confirm the unfavourable influence of conjunctions, oppositions, and quartile aspects and the favourable influence of trine and sextile aspects. So it is probably a question here of a causal relationship, i.e., of a natural law that excludes synchronicity or restricts it. At the same time, the zodiacal qualification of the houses, which plays a large part in the horoscope, creates a complication in that the astrological zodiac, although agreeing with the calendar, does not coincide with the actual constellations themselves. These have shifted their positions by almost a whole platonic month as a result of the precession of the equinoxes since the time when the spring- point was in zero Aries, about the beginning of our era. Therefore, anyone born in Aries today (according to the calendar) is actually born in Pisces. It is simply that his birth took place at a time which, for approximately 2000 years, has been called ‘Aries’. Astrology presupposes that this time has a determining quality. It is possible that this quality, like the disturbances in the earth's magnetic held, is connected with the seasonal fluctuations to which solar proton radiation is subject. It is therefore not beyond the realm of possibility that the zodiacal positions may also represent a causal factor.

Although the psychological interpretation of horoscopes is still a very uncertain matter, there is nevertheless some prospect today of a causal explanation in conformity with natural law. Consequently, we are no longer justified in describing astrology as a mantic method. Astrology is in the process of becoming a science. But as there are still large areas of uncertainty, l decided some time ago to make a test and find out how far an accepted astrological tradition would stand up to statistical investigation. For this purpose it was necessary to select a definite and indisputable fact. My choice fell on marriage. Since antiquity, the traditional belief in regard to marriage has been that there is a conjunction of sun and moon in the horoscope of the marriage partners, that is, ☉ (sun) with an orbit of 8 degrees in the case of one partner, in ☌ (conjunction) with ☽ (moon) in the case of the other. A second, equally old, tradition takes ☽ ☌ ☽ as another marriage characteristic. Of like importance are the conjunctions of the ascendant (As) with the large luminaries.

Together with my co-worker, Mrs. Liliane Frey-Rohn, I first proceeded to collect 180 marriages, that is to say, 360 horoscopes, and compared the 50 most important aspects that might possibly be characteristic of marriage, namely the conjunctions and oppositions of ☉, ☽, ♂ (Mars), ♀ (Venus), As and descendant. This resulted in a maximum of 10 per cent for ☉☌☽. As Professor Markus Fierz, of Basel, who kindly went to the trouble of computing the probability of my result, informed me, my figure has a probability of 1: 10,000. The opinion of several mathematical physicists whom I consulted about the significance of this figure is divided: some find it considerable, others find it of questionable value. Our figure is inconclusive inasmuch as a total of 360 horoscopes is far too small from a statistical point of view.

While the aspects of these 180 marriages were being worked out statistically, our collection was enlarged, and when we had collected 220 more marriages this batch was subjected to separate investigation. As on the first occasion, the material was evaluated just as it came in. It was not selected from any special point of view and was drawn from the most varied sources. Evaluation of this second batch yielded a maximum figure of 10.9 per cent for ☽ ☌ ☽. The probability of this figure is also about 1: 10,000.

Finally, 83 more marriages arrived, and these in turn were investigated separately. The result was a maximum figure of 9.6 ☽ ☌ As. The probability of this figure is approximately 1: 3,000.

One is immediately struck by the fact that the conjunctions are all moon conjunctions, which is in accord with astrological expectations. But the strange thing is that what has turned up here is the three basic positions of the horoscope, ☉, ☽ and As. The probability of a concurrence of ☉ ☌ ☽ conjunction and ☽ ☌ ☽ amounts to 1: 100,000,000. The concurrence of the three moon conjunctions with ☉,☽, As has a probability of 1: 3x10¹¹; In other words, the improbability of its being due to mere chance is so enormous that we are forced to take into account the existence of some factor responsible for it. The three batches were so small that little or no theoretical significance can be attached to the individual probabilities of 1: 10,000 and 1: 3,000. Their concurrence, however, is so improbable hat one cannot help assuming the existence of an impelling factor that produced this result.

The possibility of there being a scientifically valid connection between astrological data and proton radiation cannot be held responsible for this, since the individual probabilities of 1: 10,000 and 1: 3,000 are too great for us to be able, with any degree of certainty, to view our result as other than mere chance. Besides, the maxima cancel each other out as soon as one divides up the marriages into a larger number of batches. It would require hundreds of thousands of marriage horoscopes to establish the statistical regularity of occurrences like the ☉,☽, and As conjunctions, and even then the result would be questionable. That anything so improbable as the turning up of the three classical moon conjunctions should occur at all, however, can only be explained either as the result of an intentional or unintentional fraud, or else as precisely such a meaningful coincidence, that is, as synchronicity.

Although I was obliged to express doubt, earlier, about the mantic character of astrology, 1 am now forced as a result of my astrological experiment to recognize it again. The chance arrangement of the marriage horoscopes, which were simply piled on top of one another as they came in from the most diverse sources, and the equally fortuitous way they were divided into three unequal batches, suited the sanguine expectations of the research workers and produced an over-all picture that could scarcely have been improved upon from the standpoint of the astrological hypothesis. The success of the experiment is entirely in accord with Rhine's ESP results, which were also favorably affected by expectation, hope, and faith. However, there was no definite expectation of any one result. Our selection of 50 aspects is proof of this. After we got the result of the first batch, a slight expectation did exist that the ☉ ☌ ☽ would be confirmed. But we were disappointed. The second time, we made up a larger batch from the newly added horoscopes in order to increase the element of certainty. But the result was ☽ ☌ ☽. With the third batch, there was only a faint expectation that ☽ ☌ ☽ would be confirmed, but again this was not the case.

What happened in this case was admittedly a curiosity, apparently a unique instance of meaningful coincidence. If one is impressed by such things, one could call it a minor miracle. Today, however, we are obliged to view the miraculous in a somewhat different light. The Rhine experiments have demonstrated that space and time, and hence causality, are factors that can be eliminated, with the result that acausal phenomena, otherwise called miracles, appear possible. All natural phenomena of this kind are unique and exceedingly curious combinations of chance, held together by the common meaning of their parts to form an unmistakable whole. Although meaningful coincidences are infinitely varied in their phenomenology, as acausal events they nevertheless form an element that is part of the scientific picture of the world. Causality is the way we explain the link between two successive events. Synchronicity designates the parallelism of time and meaning between psychic and psychophysical events, which scientific knowledge so far has been unable to reduce to a common principle. The term explains nothing, it simply formulates the occurrence of meaningful coincidences which, in themselves, are chance happenings, but are so improbable that we must assume them to be based on some kind of principle, or on some property of the empirical world. No reciprocal causal connection can be shown to obtain between parallel events, which is just what gives them their chance character. The only recognizable and demonstrable link between them is a common meaning, or equivalence. The old theory of correspondence, was based on the experience of such connections- a theory that reached its culminating point and also its provisional end in Leibniz' idea pre- established harmony, and was then replaced by causality. Synchronicity is a modern differentiation of the obsolete concept of correspondence, sympathy, and harmony. It is based not on philosophical assumptions but on empirical experience and experimentation.

Synchronistic phenomena prove the simultaneous occurrence of meaningful equivalences in heterogeneous, causally unrelated processes; in other words, they prove that a content perceived by an observer can, at the same time, be represented by an outside event, without any causal connection. From this it follows either that the psyche cannot be localized in space, or that space is relative to the psyche. The same applies to the temporal determination of the psyche and the psychic relativity of time. I do not need to emphasize that the verification of these findings must have far-reaching consequences.

In the short space of a lecture I cannot, unfortunately, do more than give a very cursory sketch of the vast problem of synchronicity. For those of you who would care to go into this question more deeply, I should mention that a more extensive work of mine is soon to appear under the title ‘Synchronicity: An Acausal connecting principle’. It will be published together with a work by Professor W. Pauli in a book called The Interpretation of Nature and the psyche.

Source: Atom and Archetype, The Pauli- Jung letters.

Photo: Moon, Venus and Jupiter in conjunction, seen from Eastern Asia.

Jabberwocky

2009-03-15T13:33:00.000-07:00

Jabberwocky literally means nonsense and it was the author of this poem who gave birth to a new expression of nonsense. I' m not sure if Lewis Carroll was really autistic as some people suppose but I' m sure this is a really autistic assumption. I regard this poem as above translation either in Greek or in English. For some of the meaning of words you can look at 'Jabberwocky', Wikipedia. Maybe in the future I'll try giving an explanation if this is worthy and I'm sure I'll write a nonsense poem myself. I believe there are two categories of nonsense poems. An author or a poetry critic should always know about a poem which of the two categories it belongs to, the 'good' one or the 'bad' one. What is the final clue? I guess a sentiment of acceptance and, moreover, the elapsed time.

'Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.

"Beware the Jabberwock, my son!
The jaws that bite, the claws that catch!
Beware the Jubjub bird, and shun
The frumious Bandersnatch!"

He took his vorpal sword in hand:
Long time the manxome foe he sought—
So rested he by the Tumtum tree,
And stood awhile in thought.

And as in uffish thought he stood,
The Jabberwock, with eyes of flame,
Came whiffling through the tulgey wood,
And burbled as it came!

One, two! One, two! and through and through
The vorpal blade went snicker-snack!
He left it dead, and with its head
He went galumphing back.

"And hast thou slain the Jabberwock?
Come to my arms, my beamish boy!
O frabjous day! Callooh! Callay!"
He chortled in his joy.

'Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.

Jabberwocky

Les Mystéres du Château du Dé

2009-02-13T19:46:00.001-08:00

"A throw of dice will never abolish chance."

The film

Les Mystéres du Château du Dé (The Mysteries of the Castle of Dice) is a 1929 film directed by Man Ray. It depicts a pair of travellers setting off from Paris and travelling to the Villa Noailles in Hyères. At 27 minutes the film was the longest that Man Ray directed during his career. (Les Mystères du Château du Dé)

Plot

Mannequin hands hold a pair of dice. A castle is perched on a hilltop. Below it, a posh, modern villa. Meanwhile, far from Paris, two men with masked faces play dice in a bar. They decide to drive to Paris. Country roads, hills, fences. The posh "chateau" appears again: meticulous garden, fancy interior, odd sculptures. And at home? "No one, NO ONE." For the next two days, masked figures play dice, frolic by the pool, perform exercises with a ball. Two new figures arrive. Masked. They search and find the dice. They dance. Mannequin hands hold a pair of dice. (by David Carless)

Synopsis (by Man Ray)

To the Viscountess of Noailles. I dedicate these pictures which can never reveal the extent of her kindness and charm. How two travellers arrived in St. Bernard, what they saw in the ruins of an old castle on top of which a modern-time castle stands. The travellers: MAN RAY, J.-A. Boiffard.

The missing link

Villa Noailles

The cubist garden

The Villa Noailles is an early modernist house, located in the hills above Hyères, in France, built for the Vicomte de Noailles and his wife, Marie- Laure de Noailles, both starring in the film. Throughout the 1920s and 1930s, the Noailles were important patrons of modern art, particularly surrealism. They were friends of artist-filmmaker Jean Cocteau, they supported film projects by Man Ray, Salvador Dali and Luis Bunuel, and commissioned paintings, photographs, and sculptures by various artists, such as Pablo Picasso and Joan Miro, whose sculptures are depicted in the film.

Portrait of Marie- Laure de Noailles, Salvador Dali.

Personal comments

I don't know what Man Ray really meant by his statement, that a pair of dice cannot abolish chance. This is certainly a non optimistic- surrealistic statement. It may imply a fatal love affair. It may also refer to the idealized picture of Marie de Noailles. However, the film has all the characteristics of a surrealist film. The heroes are faceless, and the scenes succeed each other in an 'acausal' order creating the 'dream effect', that surrealism cared a lot about. There are also the surrealistic symbols, like the mechanical hand, the masked faces, the stars, or Picasso's and Miro's artifacts. Nevertheless, the focus of the film around the Villa Noailles and its inhabitants shows the strong affiliation surrealism used to have with the bourgeoisie of its time. But, of course, surrealism was first of all an art movement, and this Man Ray's film is lovely.

More:

A downloadable version of the film at UbuWeb.

The verb to reverberate

2009-01-25T12:23:00.001-08:00

Oscar Dominguez's 'Never', in the 1938 Surrealist Exhibition.

The tie between the object and space-time.

In our age we regard space and time as inseparable. In fact what we experience as space-time is what we see with are eyes and hear with our ears. But what we really see is the distance between things, that we call space, and also the change of position of two objects moving relatively to each other, that we conceive as time. We may even listen to time, when a clock is ticking. If we want to measure how much time has elapsed we count the ticks, or equivalently we measure the journey of the sun in the sky. In any case, objects define space, and relatively moving objects define the meaning of time. This is why space-time may be regarded as a secondary aspect of a deeper reality, because without objects space-time is inconceivable, it doesn't exist at all.

The object and the deeper reality.

So we can say that space-time is a measure of distance between still or relatively moving objects. We need an object as a reference frame, for example a pillar, to measure the distance of other objects. However, we also need some boundaries that space-time is confined within. When we look at the sea for example, we need the distant mountain range or even the spherical shape of our planet to conceive the limits of ‘so much water not leaking anywhere’. The same thing happens with space-time. We cannot have a definite notion of it without some boundary conditions. It seems that space-time is itself a non compact object lying within a compact one, like a glass-of-water. But at the same time the landscape or what we call ‘the vacuum’ is the background relative to which we measure the motion of things. We also need a background upon which things are suspended, even space-time itself. How strange this is- something lying on nowhere! Because if there exists some symmetry between space-time and things, then we need the notion of the vacuum as a deeper, fundamental reality through which this symmetry is manifested.

Reality and the symbolic order.

The relation between objects and space-time has been a common preoccupation in art. A painter knows that a different juxtaposition of elements in a painting can create a different sense of space and time within the painting, and gives another perspective to its meaning. Surrealists used a paradoxical juxtaposition of objects stemming from the unconscious, in order to distort space-time and to provoke an uncanny feeling. The objects the surrealists used where ‘personalized’, meaning that they were personal expressions or interpretations of the fundamental objects or symbols of the soul. Since these subjective interpretations rely on an objective and fundamental reality, they can refer to anyone and establish a universal effect. These universal objects or symbols, are what Jung called archetypes. According to him, the objects and notions of our everyday world are reflections of a universal unconscious, which he called the collective unconscious. This collective unconscious reminds me of the previously discussed notion of the background or the vacuum. In modern physics the vacuum is full of virtual particles created by vacuum perturbations. Physics instead of archetypes uses mathematical symbols, like operators, vectors, spinors, tensors e.t.c. in an abstract space, and symmetry relations between the fundamental properties of matter.

The verb to reverberate

Can space-time or a deeper implicate order be realized only through symbols? It’s true that our senses and mere experience can’t perceive what lies on a deeper level of consciousness, where all objects have a symbolical representation. It is also important to realize that within this deeper level, we form the shape of reality and things, using our state of mind and conditions of reasoning. Words are as much powerful as other abstract symbols, including mathematical symbols, archetypes and even strange surrealistic forms. As a matter of fact, it is always our consciousness (or unconsciousness) a background or a vacuum upon which we use our creative imagination, establish the connection between objects and built our conception of reality. The verb to reverberate for example seems like an entity that haunts our mind and body, and bounces back and forth fulfilling the emptiness of our silent existence. The realization and rationalization of this, I believe, can establish the deeper connection between reality and what we think reality is.

Links:

Sound symbols and surrealism

The sympathy of things

2009-01-20T08:35:00.001-08:00

Salvador Dali, Melting Space-Time, 1975-76

In my previous post I wrote about the Huygens's effect, that is 'Sympathy of clocks'. He originally explained the effect with the air currents created by the pendulums and flowing between them. He later attributed the effect to the beam's imperceptible motion. But, someone could thing, if the beam didn't exist what would have happened? The plausible answer is nothing, because without a beam the clocks wouldn't have anything to suspend from. Nevertheless, in our case it is the word 'nothing' that we are going to deal with.

Air currents

Huygens abandoned the idea of air currents because the phenomenon could still take place when the pendulums were isolated inside boxes. Of course, if we use electrically charged pendulums instead, and (not metallic) boxes, we will see again an interaction. This time it will not be air currents but electromagnetic 'currents', i.e. fields. Aristotle was the first to talk about an imperceptible means filling up space, which he called aether. Later on, Michelson and Morley showed that the electromagnetic field doesn't need a means to propagate (how peculiar really). The notion of the strange aether was replaced by that of quantum vacuum, which is also strange, because it is not empty at all.

The beam (and its imperceptible motion)

In physics, things can interact without having some sort of visible or tangible 'beam' to hold them together. This beam can be abstract, like a 'beam of light'. Light however can be very material, since this is one of its two aspects, the other being a wave. Waves are also of a material nature, less tangible though. We see that the notion of 'imperceptible motion' that Huygens was talking about, has to do with our ability to perceive the means of interaction. In our case the beam could be light particles or more generally force carriers that mediate between things, causing attraction or repulsion. This definition explains the word 'imperceptible' but still cannot explain the way another force acts, namely gravity.

Space- time (and the background)

Einstein regarded space- time as the final culprit for all interactions. Gravity, in his opinion, is not a force but the result of space-time geometry. Using his own words: "When forced to summarize the general theory of relativity in one sentence: Time and space and gravitation have no separate existence from matter. ... Physical objects are not in space, but these objects are spatially extended. In this way the concept 'empty space' loses its meaning..." (Albert Einstein). What Einstein implies here is that space-time not only exists but also is the unifying material of all things, connecting or even creating them with space- time disturbances. What is also important is that space- time serves as a background relative to which position and motion of objects can be perceived. It's like a painting, where the background plays the role of a fundamental layer upon which the perspective of images is established.

The interconnectedness of things

One of the first to assume a unity of things was David Bohm, who used the notions of a Hologram and of an implicate order to explain reality in a fundamental level. He said: "The notion that all these fragments are separately existent is evidently an illusion, and this illusion cannot do other than lead to endless conflict and confusion. Indeed, the attempt to live according to the notion that the fragments are really separate is, in essence, what has led to the growing series of extremely urgent crises that is confronting us today..." (David Bohm, Wholeness and the Implicate Order, 1980). According to him, even space- time is an illusion created by thought. He also introduced the meaning of a quantum potential, as a possible background or generator of all fields.

The sympathy of things

What we saw is that we cannot have things not connected. We may separate them but this separation is phenomenological, since they remain deeply connected inside a vacuum or a 'space- time'. Indeed, the vacuum, in a quantum mechanical sense, is far away from being empty. It is full of the imperceptible motions of virtual particles and it forms the 'ground' that things can be suspended. But there is also another clue. What is the role of the participator in this cosmic drama of interconnectedness? Is this sympathy a notion corresponding to a real natural phenomenon or is it just a word expressing human emotions? Because, if space- time (or vacuum, aether, quantum potential if you prefer) really exists, then we should realise that we are part of a unity inconceivable for the time being and that we may find ways of communicating with and transforming things that we have never experienced before.

References:

http://www.spaceandmotion.com/quantum-physics-mechanics-david-bohm.htm

Sympathy of clocks

2009-01-15T16:45:00.000-08:00

(A Letter from Christiaan Huygens to his father, Constantyne Huygens)

"While I was forced to stay in bed for a few days and made observations on my two clocks of the new workshop, I noticed a wonderful effect that nobody could have thought of before. The two clocks, while hanging [on the wall] side by side with a distance of one or two feet between, kept in pace relative to each other with a precision so high that the two pendulums always swung together, and never varied. While I admired this for some time, I finally found that this happened due to a sort of sympathy: when l made the pendulums swing at differing paces, I found that half an hour later always returned to synchronism and kept it constantly afterwards, as long as I let them go. Then, I put them further away from one another, hanging one on one side of the room and the other one fifteen feet away. I saw that after one day, there was a difference of five seconds between them and, consequently, their earlier agreement was only due to some sympathy that, in my opinion, cannot be caused by anything other than the imperceptible stirring of the air due to the motion of the pendulums. Yet the clocks are inside closed boxes that weigh, including all the lead, a little less than a hundred pounds each. And the vibrations of the pendulums, when they have reached synchronism, are not such that one pendulum is parallel to the other, but on the contrary, they approach and recede by opposite motions. When I put the clocks closer together, I saw that the pendulums adopted the same way of swinging. In addition, I took a square table of three feet, one inch thick, and put it between the two [clocks] so that it touched the ground below and was so high that it entirely covered the clocks and in this way, separated one from the other. Nevertheless, this synchronism remained as it had been before, over whole days and nights; even when I perturbed them, it was reestablished in a short time. I plan now to get them well in pace while they are far apart, and I shall try to determine the distance to which the sympathy mentioned above extends. From what I have already seen, I imagine that it will be out to five or six feet. But to obtain a greater certainty of these things, you shall have to wait, please, until I have examined them further and found out their origin more precisely. However, here we have found two clocks that never come to disagree, which seems unbelievable and yet is very true. Never before have other clocks being able to do the same thing as those of this new invention, and one can see from that how precise they are, since something so small is needed to keep them in eternal agreement."

Huygens's story

The first person to discover the notion of synchronization was Christiaan Huygens, who was the inventor of pendulums clocks, revolutionizing the measurement of time, and was searching a way to calculate longitude for naval navigation. While lying in bed in sickness, he was watching two pendulum clocks swinging. He noticed that no matter the initial phases, the clocks tended to couple in an opposite way, that is an anti-phase state. He used the term odd kind of sympathy to explain this phenomenon, and he originally explained it with the air currents circulating between the two pendulums, but he would later attribute it to 'imperceptible movements' in the beam from which the pendulums were suspended.

What is synchronization?

There is a nice definition of synchronization found in the book 'Synchronization, A universal concept in nonlinear sciences', written by A. Pikovsky, M. Rosenblum, and J. Kurths. According to the authors, synchronization is an adjustment of rhythms of oscillating objects due to their weak interaction. There are two things here we can observe. The first is that an oscillation or vibration is the essence. There is not a single thing in the universe that does not vibrate, including vacuum. The second thing is the meaning of weak interaction in a sense that strong coupling makes one or more of the oscillating components of the system to lose their autonomous character. (This means that the definition is shortened to autonomous oscillating objects).

What is not synchronization

As the authors say, resonance is not synchronization. Resonance happens when a system oscillates at maximum amplitude, due to external driving periodic forces. An example of resonance is a magnetic pendulum that oscillates in the electromagnetic field of an electromagnet. If the field stops, then the oscillator stops, due to friction. Strong interaction is again not synchronization. For example, if we tie two pendulums together with a rope, then we have a unified system rather than two autonomous oscillating objects.

What really is sympathy?

Huygens originally spoke about sympathy. He finally explained the phenomenon using the beam as the medium connecting the two clocks and synchronizing them through the energy transfer of forces. In fact, all things in the cosmos, not just clocks, are connected with forces, since there is at least one force omnipresent connecting objects through mass, namely gravity. So there are no things in the universe without 'feeling' sympathy for each other. But is it sympathy a causal effect that we feel after an event takes place, or is it this sympathy that causes (or alters) the event? Is the notion of a force, capable of explaining all kinds of this interconnectedness of things or we miss something out there that connects things without being transferred? There is still the case of quantum entanglement, a unique case of synchronization, where entangled particles can interact or interconnect with each other, instantaneously. In such an interaction, the force hypothesis is not the case, since we would violate causality (the cause-effect chain of time) and locality (the speed of light limit in space). Can some other properties of nature, more than those described by the present mathematical formalism, lead us to an another and more complete understanding of nature? What other means of interaction could exist or what other way of interpretation could we find for this sympathy? I mean to be explained by numbers and words.
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Appendices

Synchronization in nature

In fact, coupled oscillators are ubiquitous in nature, for example the synchronized flashing of fireflies, the chirping of crickets, or the pacemaker cells that regulate heartbeats. We can also have synchronization in the case of the circadian (daily circle) of living organisms which is regulated by illuminance, or the menstrual circle of women entrained by the phases of the moon. But is it here again some case of an external driving force? If humans were to inhabit an another planet without a moon or with a different period of revolution around the planet, what would happen with the menstrual circle of women? Would it stop? Would it be different? Are both phenomena connected with a deeper rhythm or symmetry in the cosmos or is it us that we see some kind of connection?

Developments after Huygens's discovery

In the middle of the nineteenth century, in his treatise 'The theory of sound', William Strutt, (Lord Rayleigh 1945) described the phenomenon of synchronization in acoustical systems, when organ- pipes begin to sound in unison. He also described the phenomenon of quenching (oscillating death), when, in extreme cases, the pipes may reduce one another to silence. Later on, in 1920, W. Eccles and J. Vincent applied for a British Patent confirming their discovery of the synchronization property of a triode generator. A few years later Edward Appleton and van der Pol replicated and extended the experiments of Eccles and Vincent and showed that the frequency of a generator can be synchronized by a weak external signal of a slightly different frequency. These studies were of great importance because triode generators became the basic elements of radio communication systems.

Modern research

Huygens had never succeeded using his findings for his original cause, that is longitude measurement in the sea. Nevertheless, his findings led to the study of nonlinear science and synchronization. Researchers from the Georgia institute of technology reproduced the Huygens's effect and found out that his explanation was correct. The anti-phase coupling of the clocks is due to energy transfer through the suspension beam and its movements, while the in-phase state can also be produced but with difficulty because of counter-parting friction effects. The glory of Huygens's observations was a new way and also a new field of studying synchronistic phenomena in nature, since the previous mentioned scientific team is currently working to find a single law that would apply to all coupled oscillators and predict their synchronous or anti-synchronous movement.
=====================================================================================

References:

Synchronization, A universal concept in nonlinear sciences, book

The Georgia institute of technology page about Huygens's effect.

The Relativity of a Hypothesis

2009-01-12T14:45:00.000-08:00

For most of us, the existence of God is a matter of faith. Faith, could somebody say, is a human property outside human logic. However, I believe that faith lies within our logical system, including bivalence (contradiction) as a legitimate fact. For example, if we accept that God exists, then how can we explain the fact that we perceive it? These of course are logical assumptions. In fact, our belief in God, and generally to the supernatural, is due to an interpretation that we gave some time in the past, about the things we didn't understand, and that evolved through history to consist a 'metaphysical reality' of ours. As a matter of fact, faith belongs to our logical system (or vice- versa), as a 'truth without proof', and indisputable hypothesis.

The process of logic

"As you set out on your journey to Ithaca..."

(Constantine Cavafy, Ithaca)

In our logical proof we use assumptions (hypotheticals) that we regard axiomatically correct and we use them in order to come to conclusions (sequences) through some legitimate logical assumptions. However, by considering a hypothesis true beyond any reasonable doubt, we build a reality that, as soon as the results of our assumptions prove themselves contradictory, can be irrational or even absurd, without us being able to reduce this absurdity.

The omnipotence of hypotheticals

"I'm sure that someday I'm going to die,
but I tend to doubt this all the time."

In the last sentence, we see the basic property of hypotheticals, their a priory acceptance. Hypotheses have a really 'divine' origin, since we accept them as true in the first place. We can also defy them, but even so, we accept them as a 'deeper essence' of our logic. This not accidental. Logic stems from the deeper structure and functioning of our brain. We first 'think', and then realize what we thought about. This is why we instinctively attribute a metaphysical meaning to our thoughts, that is our hypotheses too, since they seem to come from a 'kingdom of no space and time'.

The principle of bivalence

'Something can be black and white,
but not right and wrong'

A hypothesis is in force, independently of being right or wrong. So, two hypotheses can be ambivalent or lead to contradiction, which we have to face without leaving out our necessary assumptions. In the previous hypothetical sentence (protasis) we realize the contradiction, while the hypothesis exists independently. Perhaps, something cannot be right and wrong at the same time, but the hypothesis exists, even if it cannot be proved right or wrong.

A logical paradox, by Lewis Carroll

In his paradox, Lewis Carroll uses three hypothetical sentences for his heroes.

A) Carr is out
B) Allen is out
C) Brown is in

And the logical sequences

If Carr is out, then if Allen is out, Brown is in.
If Allen is out, then Brown is out.

Uncle Joe wants to prove that Carr must be in. He then starts a conversation with Uncle Jim, making the assumption that if Carr is out, then, if Allen is out, Brown is in. But then he shows that if Allen is out, Brown must be out. This way he leads the conversation to a logical contraction, proving that Carr must be in.

Reduction to the absurd

'Can God create a stone that cannot lift?'

Following the example of Lewis Carroll, we can now come to this classical 'God paradox'. We can analyze the problem using the following list of hypothesis- protasis:

Α) God exists
Β) God is omnipotent
(C) God can create a stone that cannot lift.

We make logical sequences:

If (C) is true, then if (Α) is true, (Β) is not true.
If (Α) is true, then (Β) is true.

We see how fast we led ourselves to contradiction. (Β) is true and false at the same time. Now, if we change the third hypothetical (C) to be 'God cannot create a stone that cannot lift', then we also have a contradiction. Consequently God cannot exist.

The relativity of logical assumptions

Why something can't be right and wrong?

In the previous examples, we saw how vulnerable logic is. We discussed the total force of hypotheticals. But if God as the 'ultimate hypothesis' exists, then He can't be omnipotent, otherwise He cannot exist. So, if He does exist, then his power must be relative. The next question of course is: Relative to what? I could say relative to the power of our understanding the rules of our logical assumptions within our own system of logic, where, as I have already said, faith is a true, although ambiguous, component. I could also say that we need Him in the same manner that we need all our 'true without proof' hypotheses, because, in any other case, that is if we start out annihilating hypotheses, our system of logic will become rather short. I guess what we really miss is a relativistic eye, so that we see ambivalence not as a contradictory, but as a complementary aspect of our logical system.

---This post comes as a reply to my previous post,

A logical paradox, by Lewis Carroll. ---

A logical paradox

2009-01-05T07:04:00.001-08:00

"What, nothing to do?" said Uncle Jim. "Then come along with me down to Allen’s. And you can just take a turn while I get myself shaved."

"All right," said Uncle Joe. "And the Cub had better come too, I suppose?"

The 'Cub' was me, as the reader will perhaps have guessed for himself. I’m turned fifteen—more than three months ago; but there’s no sort of use in mentioning that to Uncle Joe; he’d only say "go to your cubbicle, little boy!" or "Then I suppose you can do cubbic equations?" or some equally vile pun. He asked me yesterday to give him an instance of a Proposition in A. And I said "All uncles make vile puns". And I don’t think he liked it. However, that’s neither here nor there. I was glad enough to go. I do love hearing those uncles of mine 'chop logic,' as they call it; and they’re desperate hands at it, I can tell you!

"That is not a logical inference from my remark," said Uncle Jim.

"Never said it was," said Uncle Joe: "it’s a Reductio ad Absurdum".

"An Illicit Process of the Minor!" chuckled Uncle Jim.

That’s the sort of way they always go on, whenever I’m with them. As if there was any fun in calling me a Minor!

After a bit, Uncle Jim began again, just as we came in sight of the barber’s. "I only hope Carr will be at home," he said. "Brown’s so clumsy. And Allen’s hand has been shaky ever since he had that fever."

"Carr’s certain to be in," said Uncle Joe.

"I’ll bet you sixpence he isn’t!" said I.

"Keep your bets for your betters," said Uncle Joe. "I mean"—he hurried on, seeing by the grin on my face what a slip he’d made— "I mean that I can prove it, logically. It isn’t a matter of chance."

"Prove it logically!" sneered Uncle Jim. "Fire away, then! I defy you to do it!"

"For the sake of argument," Uncle Joe began, "let us assume Carr to be out. And let us see what that assumption would lead to. I’m going to do this by Reductio ad Absurdum."

"Of course you are!" growled Uncle Jim. "Never knew any argument of yours that didn’t end in some absurdity or other!"

"Unprovoked by your unmanly taunts," said Uncle Joe in a lofty tone, "I proceed. Carr being out, you will grant that, if Allen is also out, Brown must be at home?"

"What’s the good of his being at home?" said Uncle Jim. "I don’t want Brown to shave me! He’s too clumsy."

"Patience is one of those inestimable qualities——" Uncle Joe was beginning; but Uncle Jim cut him off short.

"Argue!" he said. "Don’t moralise!"

"Well, but do you grant it?" Uncle Joe persisted. "Do you grant me that, if Carr is out, it follows that if Allen is out Brown must be in?"

"Of course he must," said Uncle Jim; "or there’d be nobody in the shop."

"We see, then, that the absence of Carr brings into play a certain Hypothetical, whose protasis is "Αllen is out," and whose apodosis is "Brown is in". And we see that, so long as Carr remains out, this Hypothetical remains in force?"

"Well, suppose it does. What then?" said Uncle Jim.

"You will also grant me that the truth of a Hypothetical—I mean its validity as a logical sequence—does not in the least depend on its protasis being actually true, nor even on its being possible. The Hypothetical, "If you were to run from here to London in five minutes you would surprise people," remains true as a sequence, whether you can do it or not."

"I can’t do it," said Uncle Jim.

"We have now to consider another Hypothetical. What was that you told me yesterday about Allen?"

"I told you," said Uncle Jim, "that ever since he had that fever he’s been so nervous about going out alone, he always takes Brown with him."

"Just so," said Uncle Joe. "Then the Hypothetical, "if Allen is out Brown is out" is always in force, isn’t it?"

"I suppose so," said Uncle Jim. (He seemed to be getting a little nervous, himself, now.)

"Then if Carr is out, we have two Hypotheticals, 'if Allen is out Brown is in' and 'If Allen is out Brown is out,' in force at once. And two incompatible Hypotheticals, mark you! They can’t possibly be true together!"

"Can’t they?" said Uncle Jim.

"How can they?" said Uncle Joe. "How can one and the same protasis prove two contradictory apodoses? You grant that the two apodoses, 'Brown is in' and 'Brown is out,' are contradictory, I suppose?"

"Yes, I grant that," said Uncle Jim.

"Then I may sum up," said Uncle Joe. "If Carr is out, these two Hypotheticals are true together. And we know that they cannot be true together. Which is absurd. Therefore Carr cannot be out. There’s a nice Reductio ad Absurdum for you!"

Uncle Jim looked thoroughly puzzled: but after a bit he plucked up courage, and began again. "I don’t feel at all clear about that incompatibility. Why shouldn’t those two Hypotheticals be true together? It seems clear to me that would simply prove 'Allen is in'. Of course it’s clear that the apodoses of those two Hypotheticals are incompatible— 'Brown is in' and 'Brown is out'. But why shouldn’t we put it like this? If Allen is out Brown is out. If Carr and Allen are both out, Brown is in. Which is absurd. Therefore Carr and Allen can’t be both of them out. But, so long as Allen is in, I don’t see what’s to hinder Carr from going out."

"My dear, but most illogical, brother!" said Uncle Joe. (Whenever Uncle Joe begins to 'dear' you, you may make pretty sure he’s got you in a cleft stick!) "Don’t you see that you are wrongly dividing the protasis and the apodosis of the Hypothetical? Its protasis is simply 'Carr is out'; and its apodosis is a sort of sub-Hypothetical, 'If Allen is out, Brown is in'. And a most absurd apodosis it is, being hopelessly incompatible with that other Hypothetical that we know is always true, 'If Allen is out, Brown is out'. And it’s simply the assumption 'Carr is out' that has caused this absurdity. So there’s only one possible conclusion. Carr is in!"

How long this argument might have lasted, I haven’t the least idea. I believe either of them could argue for six hours at a stretch. But, just at this moment, we arrived at the barber’s shop; and, on going inside, we found——

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A Logical Paradox was written by Lewis Carroll, and appeared in the July 1894 issue of Mind. It is republished here from the following address:
http://fair-use.org/mind/1894/07/notes/a-logical-paradox