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The Algorithmic Complexity of Empty Space

When we engage in the ubiquitous human activity of thinking and talking we skip along from thought to thought, from word to word, without ever noticing the space in-between. After all, why should we concern ourselves with what lies in-between two thoughts, or two words – aren’t the thoughts or the words themselves the important things?



Each thought or word seems to be a ‘nucleus of meaning’, a precious nugget – however small – of something significant, something substantial, something that stands out positively against an all-pervasive background of insignificance, or ‘blankness’. The assumption is that the thoughts or words are meaningful (i.e. they have something to say) and the back-ground, the back-drop, isn’t meaningful, it doesn’t have anything to say.



This is the way things have to be if the message in question is to make sense – if the background were to be as meaningful as the foreground then there would be no point in thinking anything, no point in saying anything.



The convention where we look at the foreground as being the significant thing, the thing to be taken notice of, is sometimes spoken of in philosophical parlance as a ‘positive’ viewpoint. The foreground is positively emphasized and the background is de-emphasized, ignored, excluded from our attention. When we adopt this convention then it is the definite statement, the accentuated or emphasized element, which is seen as being the significant content. This is ‘where it’s at’, this is where it’s happening. This is where our attention is to be fastened.



This is fine as a convention, but it is just a convention (which is to say, we chose to look at things this way, but we didn’t have to). We could have chosen to look at things the other way around – the ‘photographically-reversed’ way around, so to speak – so that our attention is not exclusively captured or monopolized by the high-lighted elements, by the ‘foreground’. This other, culturally unfamiliar viewpoint has been referred to as the ‘negative’ way – the via negativa.



The via negativa is the province of poets, intuitive thinkers, ‘natural philosophers’, and mystics. Mystics have always maintained that ‘silence is greater than sound’. As John G. Bennett says –


Silence only appears empty when you are looking for sound, and if you don’t find sound, you say that there is no sound there. But if you enter into silence, you become aware that sound is an intrusion. You realize how much greater silence is than sound, the same way that you realize that the emptiness that has no attributes is very much greater than any attribute.



Modern physics now says the same thing, only in a different language. We can give a few examples to demonstrate this. In the spectrum of electromagnetic radiation those waves that have a longer wavelength (which is to say, the grosser vibrations) carry or embody less energy than the shorter (or finer) wavelengths. Thus, as every physics student knows, a gamma ray carries far more energy than a radio wave: radio waves have a wavelength of 10-1 M or greater and have an associated energy of 2 x 10-24 Joules, whilst Gamma radiation has a wavelength of 10-11 M or less and has an energy of 10-14 Joules, which is greater by a factor of one hundred billion.



As the wavelength tends to zero the associated level of energy goes up and up, and what this tells us is that when the wavelength reaches the lower ‘limit’ of zero then the associated energy levels must be absolutely astronomical. When the wavelength actually reaches zero then this is the finest (or ‘subtlest’) form of vibration. It is a ‘fine’ as opposed to a ‘gross’ disturbance of the underlying medium – so fine in fact that it is not a disturbance at all…



When there is no disturbance of the underlying medium then there is nothing apart from the medium. So what appears to be a loss or a lack (i.e. a lack of disturbance) unveils or reveals the medium that up to now we were wholly oblivious to. Thus from a philosophically ‘positive’ point of view silence is seen as being merely a lack of sound, and so not of any interest at all, whilst from the negative perspective we can see that when the disturbance is not there to distract us we can catch a glimpse of what it was that was being disturbed.



So, just to give a familiar example, if we say that the ‘disturbance’ is an ocean wave, then on a very calm day when there is no disturbance and our attention is no longer ‘captured’ by the drama of the waves then we are free to notice – if we will – the ocean itself. And without any doubt, we will then see that the ocean itself is greater than the minuscule ripples that pass across its surface.



The astronomically high level of energy associated with the medium is indicated by values ascribed to what is called ‘zero point energy’ – according to the Wikipedia entry on the subject this value has been calculated (on the basis of Quantum Electrodynamics (QED) and Stochastic Electrodynamics (SED), as having a value of 10113 Joules per cubic meter. David Bohm was one of the first physicists to talk about the significance of this sort of interpretation, and embrace the world-view that comes with it –


Space is not empty. It is full, a plenum as opposed to a vacuum, and is the ground for the existence of everything, including ourselves. The universe is not separate from this cosmic sea of energy.



The same reversal of expectations that we see with energy can be found when we look at information. Exactly the same picture, exactly the same ‘unexpected result’, emerges. Algorithmic information theory gives us a way of looking at this: when we have a ‘single level of description’ of the world we only have a limited amount of information available to us as a result and when we have more than one level of description the information available to us increases.



According to this theory (also known as the theory of algorithmic complexity) the more unrelated (or discontinuous) terms are needed to describe or specify an object, the more complex that object is. In the Wikipedia entry on algorithmic information theory, it is equivalently said that “the Kolmogorov complexity of an object, such as a piece of text, is a measure of the computational resources needed to specify the object.Kolmogorov complexity, the article goes on to state, is named after the Soviet Russian mathematician Andrey Kolmogorov.



The higher the degree of complexity associated with an object, the more information that object may be said to possess. We might assume that an ‘obvious’ sort of an object (i.e. an object that can be described straightforwardly in black-and-white terms) might have a higher information content than a more ‘diffuse’ or less-well defined object would do, in which case it would be reasonable to expect that the least well-defined (or most ‘diffuse’) situation would have the lowest information content associated with it. Empty space – as being the most undefined and diffuse situation possible – would then be expected to have zero information content.



When we apply the theory of algorithmic complexity however this gives completely the opposite result – obvious or well-defined objects have the least information in them, whilst empty space – which is the underlying medium which we might say is ‘configured’ or ‘modulated’ (or in other words  utilized) to give rise to well-defined objects – has the greatest amount of information in it. If we were to reflect on the matter, this result makes perfectly good sense since if the underlying medium (i.e. space) is capable of containing (or facilitating) any conceivable form, then it must necessarily have a higher information content then any of these particular specified forms.



Furthermore, we can say that since space can accommodate or facilitate all possible forms or structures (i.e. there is quite clearly no limit to the number of different types of forms that it can contain) then it must be true that empty space has an infinite information content (or to put this another way, the algorithmic complexity of empty space is infinite).



Talking about information or lack of information is therefore really just a way of talking about openness versus closure. An open situation by its very nature is accommodating (or adaptable) to anything, without any exception whatsoever, whilst a closed situation can only accommodate or adapt itself to that particular configuration of possibilities that it has been specifically defined as being adaptable to. Thus, openness (or empty space) must have an infinite information content associated with it precisely because it is ‘unspecified’.



Algorithmic information theory has only been around since the nineteen sixties and the advent of computational science, but the same principle is elegantly expounded in Verse 11 of the Tao Te Ching, which is reckoned to have been written about 2,500 years ago.  Ursula K. Le Guin’s modern (1998) version of this verse is as follows –


Thirty spokes
meet in the hub.
Where the wheel isn’t
is where it’s useful.

Hollowed out,
clay makes a pot.
Where the pot’s not
is where it’s useful.

Cut doors and windows
to make a room.
Where the room isn’t,
there’s room for you.

So the profit in what is
is in the use of what isn’t.



What we think of as empty space, or ‘formlessness’, is not therefore the absence of information but an endless profusion of it, a bottomless well of it, an inexhaustible reservoir of it. To any student of Taoism it becomes very clear indeed what we are talking about here, even though we can’t actually talk specifically about it! In Verse 6 of the Tao Te Ching we read –


The Tao is called the Great Mother: empty yet inexhaustible,

It gives birth to infinite worlds.

It is always present within you.

You can use it any way you want.



Our Western ‘positive way’ of thinking finds this very hard indeed to understand because we see things exactly backwards – we see space as blank and sterile and the world of definite objects as being the only place where value, substance and fruitful possibility can ever be found. In contrast to the Taoists, we see empty space as being quintessentially ‘useless’ – it is just a blank canvass, waiting for some external creative principle to come and write upon it. The furthest thing from our thinking is that the notion that this empty space might be the actual creative source of everything itself and that there is no need for any external principle or authority.



This fruitfulness, this over-flowing fullness or plenitude, is testified to by what is called by physicists ‘quantum foam’ – the frenetic coming-into-being and almost immediate annihilation of a multitude of various high-energy ‘virtual particles’. These highly energetic virtual particles boil out of empty space and then disappear back into it, without cease, and so empty space is their ‘mother’, just as it is the mother of everything else.



The ‘playful creativity’ which brings particular (or particulate) existence into being out of the ‘indefinite’ cannot really be said to take place in a specific place at a specific point in time however. The womb of empty space does not precede its productions in time. It cannot be said to take place ‘at the beginning of things’ because time itself is a limiting factor and empty space is empty of all limitations – it is empty of both space and time.



To look at the transition from formlessness to form as being an event which occurs at a location in space and time is to take what has been produced (i.e. the space-time continuum) as being the primary reality, which is obviously a back-to-front way of looking at things. When ‘we tune into’ a vanishingly tiny portion of space, at a particular point in time, and catch a glimpse of the strange world of quantum foam it may look as if the origin of this activity is located securely within space and time but really of course space-time is an artifact just as the foaming virtual particles are artifacts.



From our ‘local’ perspective it looks as if something has been ‘created’ (i.e. produced miraculously out of nothing) but were we to look at this ‘the other way around’ then we would understand what we are seeing as an implosion of possibilities, a collapse of an infinitely high energy / infinitely high information state into incredibly degraded version of itself, a type of astonishingly ‘inferior copy or analogue ’. This is not the marvelous act of Divine Creation spoken of in the first pages of the Book of Genesis but the Fall. This is descent from a greater to a lesser condition, such that what we call ‘creation’ actually represents a tremendous collapse of possibilities – a degeneration (or weakening) of the original reality.



This general process is known in Gnostic theology as emanation – which is where the Source produces an attenuated or lesser version of itself, which can then go on to produce an even more attenuated version of the original. Each copy thus takes us further and further away from the source. In both Gnostic and Cabbalistic metaphysics, the cosmos is created via a lengthy series of such emanations, ‘culminating’ (from our point of view!) in the material universe with which we are familiar, and unreflectively assume to be the ‘primary reality’.



Lacking the Gnostic viewpoint, and the richly complex body of mythology that it has generated, we look apon our estate as material beings living firmly within the restrictions of space and time as being the very pinnacle of creation, the most wonderful possible news, the most fantastically unexpected result ever. It is not therefore given to us to understand that this everyday thought-bound consciousness of ours isn’t really ‘the pinnacle of evolution’ at all, but an astonishingly attenuated emanation of the Source, and that the space-time universe isn’t the ‘be all and the end all’, the alpha and the omega, but a stupendously over-simplified version of a transcendent reality that is frankly inconceivable to us.



William Gough (1988) sees matter as ‘frozen light’, or, we might say – light which has forgotten its own true nature –


For Bohm the content of “empty space” is thus more than “zero point energy.” It is “light” which he considers not only energy but also information, i.e., the content, form and structure necessary to create meaning from that which is apprehended. “Light” is the means by which the entire universe unfolds into itself. “Light” exists – it just simply is and transcends the present structure of time and space. It forms the unity or background whose information content has the capacity for immense diversity. All matter is a condensation of “light” into patterns that move back and forth at average speeds which are less than the speed of light. Matter can be considered frozen “light.”



In the same way, our ‘material’ (or ‘passively-identified’) everyday consciousness may also be said to be frozen light. We too have forgotten our true nature as consultant psychiatrist and undercover mystic Arthur Guirdham says here in his autobiographical A Foot in Both Worlds (1975) –


The great cosmic disaster of the fall of man was echoed in our own birth. I have felt it in dreams as I plunge through the darkness. The light reaches behind me until it is no more than the memory of a single star. The fall of man is re-echoed in physics. Matter is the slowing down of aeons congealed and inert in what we call the inanimate. And even as we descend in the Fall and in our birth, so we ascend after what we call death. Without the impediment of flesh we are more sensitive to the magnetic pull of the spirit. It draws us back, through the seven worlds and the seven levels of consciousness, till we are joined not to a personalized God conceived of as a monument to our own littleness, but to a silence which is immense because it is the extension of our own divinity.



What seems meaningful or important or valuable to us in our daily lives only seems to be so because it is in some way an echo of an echo of an echo of an echo of what we have long since forgotten – our own true nature. All we have left in our fallen state is the reflected and distorted memory of that single star, that single point of light. According to the Sufi mystics, when we are attracted to material objects or material goals, it is because in some ‘unconsciously symbolic’ way we are reaching out for what we have so long ago forgotten. That is the only way we have left to us of remembering who we really are, and yet this in this distorted or displaced form of ‘remembering’ we forget even more – in holding on all the more tightly to our precious thoughts and ideas we lose sight of the infinitely creative and infinitely expansive space that always exists between them.



By focusing all the more on our ever-proliferating ‘positive projections’ we lose our vital connection with the intrinsic space that is to be found freely available (and in never-ending abundance) in all the neglected nooks and crannies, in all the places we never think to look.







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