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Restoring Symmetry

Asymmetry is when the tide goes right out, leaving behind innumerable little rock pools scattered here and there, but no trace of the incomprehensibly larger body of water that left them there. We see the rock pools, but not the Ocean from which they came.

 

 

Rock pools are asymmetrical precisely because they are pools. A pool is defined as such by virtue of the fact that within the limits of the perimeter of what constitutes the pool there is water, whilst outside this perimeter there is not. This is a very basic kind of a concept and not in the least bit challenging for us to grasp. In fact, far from finding it difficult to grasp this kind of notion (which is the notion of the ‘excluding boundary’) we are very much at home with it. We are very much at home with it because our thinking process itself is founded upon this very principle.

 

 

Our thinking process is based upon the principle of the ‘excluding boundary’, which is another way of talking about asymmetry. Our thinking is categorical and the whole point about categories is that there is a very important difference – a crucially important difference – between what lies within the boundaries of the category and what lies outside of it. One way is very much not the same as the other way and this fundamental and irreducible lack of parity is what dissymmetry is all about.

 

 

Seeing everything on the basis of this enshrined cognitive dissymmetry is so much ‘taken for granted’, so unconscious, for us that we have a major problem seeing the way in which it is actually all quite arbitrary. This is only to be expected since the meaning of every single word we use (and thought we think) relies entirely upon the asymmetrical nature of our mental categories.

 

 

This can be illustrated with the simplest of sentences, such as “The fish swims in the sea.” Everything inside the category <fish> is the fish and everything outside of the category is not the fish. There can be no deviation from this at all – there cannot even be the slightest leeway in this regard. If there was a bit of leeway, a bit of a sense that the ‘divide’ embodied by the category was not perhaps quite as absolute as all that, then all sorts of surreal things start to happen. For the fish to do anything (let alone swim) it has to be definitely the fish (and nothing else) that does it. Otherwise, the whole meaning of the sentence is totally lost. Otherwise, the whole sentence starts to swim, not just the <fish>.

 

 

If for example both of the nouns in the sentence began to become a little bit imprecise, a little bit ambivalent, a little bit ‘less than absolute’, then we could have the sense that not only does ‘the fish swims in the sea’ but also that ‘the sea swims in the fish’. And if that were not confusing enough we could also have the sense that perhaps a bit of ‘the fish swims in the fish’ and ‘the sea swims in the sea’ is going on as well, just to add to the mix of possibilities. The problem is of course that the categories concerned are no longer water-tight and so there is nothing to stop a general ‘mingling’ taking place with regard to what is (or rather should have been) tightly contained by them.

 

 

And that is only the nouns! We also have the preposition <in>, the definite article <the>, and the verb <swims>. All of these constitute ‘categories in language’ and as categories all of them are unashamedly and unreservedly asymmetrical, which is to say, each defined possibility specifically excludes everything that is not it. <Swims> excludes all other verbs of movement such as <flies>, <runs>, <hops>, <jumps>, <climbs>, <burrows>, <bounces>, <dances>, and so on. <In> rigorously excludes, as a matter of course, <out>, or <over>, or <beyond>, or <above>, or <around>, or <amidst>, or <against>, or <behind>, etc. <The> excludes the indefinite article <a> which would if used significantly alter the meaning of the sentence in yet another way. So what this shows is that without the exclusive nature of the words we use to talk about or think about the world our understanding of that world would quickly become very strange indeed. The situation that then prevails is the one in which, as Anaxagorus has famously (and – with regard to our ‘common sense’ – controversially) said,

 

In everything there is a portion of everything.

 

 

It is not just our mental picture of the world that is founded upon the principle of dissymmetry (the principle of one way not being the same as the other way) – so too is the physical universe itself. The most essential, no nonsense way of looking at that most singular of events which is the creation of the physical universe is to say that it involves the introduction of dissymmetry into a situation where previously there was no lack of symmetry. This sort of thing is known therefore as a ‘symmetry break’. It is of course possible to get distracted, side-tracked, and generally bamboozled by focussing on the technicalities of what went on after the original symmetry break – which particles appeared first, in what order, for what period of time, what laws they obeyed, what their distribution was and what type of movement they might have had, and so on. We may then get caught up in all sorts of debates, discussions and arguments as to how exactly the process happened but whichever way we look at it it all comes down to the same thing – symmetry breaking. That’s all we really need to know.

 

 

The most basic symmetry break is the space-time continuum itself. The space-time continuum is the classic symmetry-break because in each of the dimensions it is made up of, to move in one direction is not at all the same as to move in the other, complementary direction. Each dimension is made up of two directions, two poles, and these poles (UP or DOWN, PLUS or MINUS) are defined by the fact that they are opposite to each other, which means ‘not at all the same. Each dimension in the continuum is a symmetry-break because each dimension (or each axis) is made up of an UP and a DOWN, a [+] and a [-] direction, and nothing else. Those two directions (which both equal the same axis) are ‘all that’s allowed’. Without the symmetry-breaks which these linear axes, these dimensions embody, there is simply no such thing as the space-time continuum.

 

 

Particles may also be said to exist by virtue of the asymmetrical situation inherent in the continuum. Particles get to be particles precisely because they represent a break in symmetry – the basic symmetry-break of ‘here but not there’ (where ‘here’ is not at all the same as ‘there’ and there absolutely isn’t any of that Anaxagorian funny business where there is ‘a portion of here in there’ and ‘a portion of there in here’). If a particle was symmetrical with regard to its location in space then it wouldn’t have a location in space; if a particle were to be ‘equally (i.e. symmetrically) here and there’ then as a result of being sublimely uncommitted in this way it would not be a particle. It would be delocalized and there is no such thing as ‘a delocalized particle – that is a contradiction in terms. In this case the ‘so-called particle’ would have ceased to exist within the strict terms of the space-time continuum and so we would not be in a position to say anything about it all, since our capacity to know something about it depends purely upon our ability to place logical limitations upon it, and say therefore what it ‘is’ and what it ‘isn’t’. If we can’t slap a boundary in place then what we are trying to know’ eludes us so completely that we can’t even really say that there was anything there to know about in the first place.

 

 

Particles can also be said to possess properties such as ‘charge’ and ‘spin’ which also represent breaks in symmetry – to be positively charged is not the same as being negatively charged, and having left-handed spin is not the same as having right-handed spin. ‘Movement’ too (like information relating to ‘location’ and ‘spatial distribution’) only makes sense once a symmetry break has been put in place such that ‘movement in the one direction’ is not the same as ‘movement in the opposite direction’. Everything we take for granted in the physical world rests upon asymmetry: as Erich Jantsch says, the physical universe is created (or unfolded) via a series of symmetry breaks starting off from the space-time continuum itself, moving onto the cosmic constants and laws, the elementary particles and continuing right up to the level of the macroscopic universe.

 

 

Behind both the physical universe and our mental picture of it lies logic. Logic itself is the quintessential symmetry break – the symmetry break behind all symmetry breaks. In logic everything rests upon the symmetry break of the two mutually exclusive categories <YES> versus <NO>. Thus, in the game of logic we start off with a premise, some sort of basic ‘given’, and then from this premise we can proceed to ask all sorts of questions, questions to which we can receive either <YES> or <NO> answers. Logic does not of course refer to any particular thing – it exists in the realm of the abstract, it deals in ratios of numbers, in sets of proportionalities that can be manipulated in accordance with precise and unyielding laws. Firstly, therefore, we ‘set up the game’ and then with the laws of logic we work out all the ramifications, the lawful development of that ‘taken-for-granted’ starting-off position. The ‘trick’ in all this is however that nothing ever comes out of the game that wasn’t already in it. Nothing comes out of the extrapolation process that wasn’t already there in the premise. If we reflect on it, we can see that there is absolutely no way that anything ‘new’ can ever come into the picture without breaking the strict laws that logic runs on – the laws that make logic into ‘logic’ in the first place.

 

 

If all the answers have to come back to us in the form of either <YES> or <NO> then we can see that this means that the starting-off position is being treated as if it is totally bang-on, totally ‘relevant’. Or to put this another way, the assumptions that lie behind this starting-off position are treated as if they are absolutely correct – they are, in other words, treated as if they are not assumptions at all. Thus, the fact that the premise upon which everything is based was ‘plucked out of thin air’ (or ‘freely chosen out of an unbounded range of possible assumptions’) gets utterly lost sight of once we start going down the road of developing or extrapolating those premises.

 

 

This is, as we have said, inherent in the nature of logic anyway – it was always going to be the case that the ‘groundless’ nature of our premise is going to be lost sight of just as soon as the train of logic pulled out of the station (logic being logic and not having therefore any time for any answers that aren’t either YES or NO). Logic is constitutionally incapable of taking seriously anything that does not agree with its assumed frame of reference, and so it is constitutionally incapable of questioning this framework (which is the extension of its starting-off position).

 

 

In order for us to be able to get any sort of intimation that this starting-off position is in fact resting precariously upon a foundation that can never be validated we would have to be open to an answer to our questions that lies outside of the narrow range of <YES> versus <NO> (both of which are only saying the same thing anyway, since both implicitly affirm the validity of the framework within which they make sense). But what form could information come to us anyway, other than in the form of ‘affirming’ or ‘denying’ statements? What kind of way could information be received by us to tell us that our premise isn’t in fact relevant to anything (unless of course it cheats by spuriously making itself ‘the centre of the universe’)?

 

 

This is not as straightforward a matter as it might seem. If a message comes back to me telling me that my premise (or my ‘framework of interpretation’) isn’t the right one, then the very fact that this message makes sense to me proves that my premise, my framework of understanding is the right one after all. Any information I receive that I can understand is confirming my basis, any message that makes logical sense to me is confirming my basis, and so the only type of information that would not confirm my starting-off position as being relevant would be information that I cannot understand, cannot interpret, cannot make any sense of whatsoever. But then the problem here is of course that I won’t spend any time considering information that I can’t understand – I will dismiss it immediately as being nonsense, which to me it is. Thus it is that the logical mind is immune to be proved wrong. It will only enter the debate if the debate is conducted upon the terms which it itself takes for granted and so – in this way – it has won before the debate has even got started.

 

 

What we are asking here is, “What does the type of information that exists outside of any all-determining frame of reference look like?” and the answer is of course that it doesn’t look like anything that we can recognize since ‘recognition’ essentially involves making a comparison with our assumed context of meaning. Every single word or symbol within our language system means something, otherwise why would we have it there? Even the word <nothing> means something; even the word <meaningless> has a meaning. So what we are looking for is a word that brings no meaning at all to the sentence it is being used in, which is clearly not a regular sort of a word at all. Robert Anton Wilson uses the word <MAYBE> in this connection and argues that by incorporating this inscrutable give-nothing-away <MAYBE> term into YES/NO logic we can break the stranglehold that classic Aristotelian two-term logic has on our thinking. <MAYBE> isn’t YES and it isn’t NO – it is ‘YES with a portion of NO in it’ or ‘NO with a portion of YES in it’. Far from adding to what we think we understand it subtracts, leaving us nothing that we can hold onto with any degree of certainty. This of course is not very satisfactory to us at all. Instead of being ‘cash in the hand’ that we can take away and bank, <MAYBE> is like a slippery eel that escapes from our grasp every time we go to grab it.

 

 

Classical Aristotelian two-term logic is the type of information that belongs to the closed world of the symmetry-break and, as we have said, there is no room in this virtual reality world for anything that does not agree with the framework. This then means that there is no room in it for radical uncertainty, which we can represent by the shorthand term <MAYBE> or simply [?]. Certainty is sure and certain in the way that it is because it corresponds exactly to polar coordinates in as many dimensions as there are axes in the framework – anywhere from 1 to n where n is a finite number. As long as I can read off the location of whatever it is that I am interested in (in terms of these all-determining axes) then the information that I have obtained as a result of this operation is certain – it is certain because it is completely encapsulated, because there is nothing ‘left over’. [?] on the other hand is radically uncertain precisely because it is does not in any way affiliate itself with any axis. If [?] did conform to some axis or other then it would immediately take upon itself some sort of ‘polar characteristic’, which is to say, it would be representable in terms of [+] and [-], where [+] and [-], quite simply, equal ‘the axis’.

 

 

Polar coordinates are all about the symmetry break because [+]/[-] is the symmetry break. [+]/[-] is ‘the axis’ because the axis exists solely in terms of YES and NO; YES/NO is the only type of ‘information’ it has to offer, the only type of information it traffics in. Thus we can say that [?] gives us a way out of the closed world of the symmetry-break by relating us back to the ‘open situation’ of original symmetry. [?], which we have also called ‘radical uncertainty’, denotes therefore the state of original symmetry, which is the way things were before the certainty-producing symmetry-break of logic ever occurred.

 

 

We could say that the logical world of the symmetry-break is a closed one because everything in it has to be related back to a particular set of assumptions (or a particular ‘arbitrary position’) as if those assumptions are somehow central (as if the position wasn’t arbitrarily chosen). Or we also could say that this world – which is the world created by the ‘continuum of logic’ – is a closed one because everything in it only gets to be there because it can be determined (or specified) in terms of a finite set of abstract axes.

 

 

All axes are necessarily abstract because they are only ‘one-dimensional’, because they don’t actually occupy any space. The whole idea of an axis is that every single point on it can be exhaustively specified, such that when we specify the position of any point on the axis we have said everything there is to say about that point. Anything that is absolutely defined in this way ‘takes up no space’. Space – though we might be unused to thinking about it this way – is equivalent to radical uncertainty. Emptiness is radical uncertainty. This does make good sense intuitively because it is, as we have said, only in the realm of radical uncertainty – which is the domain that is outside of any determining or specifying framework – that any genuine change (or movement) can occur. Without [?] there can be no such thing as movement; or as both Taoism and Buddhism assert, without emptiness nothing can ever happen.

 

 

When we are utilizing a determining framework (a mental symmetry-break) as a basis for understanding the universe then we relate all incoming information to fixed position we have arbitrarily adopted, in such a way that there is no means by which we may know that the fixed position is arbitrarily chosen. The system that is made up only of YES and NO answers is a closed one – all [?] answers have been edited out. The system (which is our everyday rational mind) is ‘devoid of all perspective’, devoid of anything that doesn’t agree with its starting-off assumptions. Because there is no perspective, anything could be true, and we have no way of knowing that it isn’t. On the other hand, once we open ourselves up to [?] information (which is information that is alien to the system) we regain perspective and so we can see that our assumption only is an assumption, that our ‘final viewpoint’ isn’t so final after all.

 

 

As soon as we pay attention to [?] information (which is to say, as soon as we stop automatically dismissing it) then we cannot help seeing that our supposedly exclusively true viewpoint is no more relevant or valid than any other viewpoint that we might have taken, and there are an infinity of other possible viewpoints. Our starting-off position, our basis, our unexamined premise is therefore relativized by this MAYBE information just as the no-nonsense YES/NO information which tells us about the location of a material particle would be relativized if the underlying symmetry-break were to be suddenly taken away. If the location of the particle is ‘here but not there’ (or ‘here but nowhere else’) then there actually is a real discrete particle, but if the presumed particle could ‘equally well be anywhere’ (i.e. if all possible positions are equally good) then this means that there simply isn’t any particle there. In the same way, if such-and-such an assumption is ‘no more true than any other possible assumption’ (i.e. if ‘all assumptions are equally true/equally untrue’) then this relativizes our basis to an infinite extent and so there is actually no basis there.

 

 

The premise that the train of logic uses to start off from on its journey is therefore not any sort of a genuine premise at all; it is a premise which can only be ‘retrospectively validated’, so to speak, by the spurious but ubiquitous argument that ‘it must be right because that is where we started from’. The logical domain is thus a world that only appears to be a solid, genuine world from its own assumed basis. It is a kind of virtual reality that only appears real when we agree to look at in a particular way – the way that it itself takes for granted. It is real only because we say it is.

 

 

Once we have agreed to look at things this way, once we have ‘bought the ticket’ and ‘climbed aboard the train’ and gone off happily on our illusory journey, then the virtual world that logic shows us is as solid as rock, it is as unshakeable as a mountain, as opaque and as impenetrable as a brick wall. And yet the whole set-up could just as easily vanish like early morning mist in the rays of the rising sun if we were only to move slightly away from our static and unquestionable stand-point – which is like a very worn-out (and somewhat malodorous) old armchair that we always sit in, for no better reason than ‘force of habit’, for no better reason than the fact that ‘we always have done so’.

 

 

The logical universe looks tremendously imposing when we’re sitting in the worn-out old armchair of the everyday mind but actually it is very cheaply constructed. It is cheaply constructed (like an inflationary economy) because it is based on a trick – it is all based on the trick of printing unlimited money by pretending that the position we have started off from was ‘the one and only possible position’. This completely untrue supposition is what makes the money of our ‘logical statements’ actually worth something, so that we can run away and buy stuff with them.

 

 

Huge results are possible on the short-term, but only at the cost of inevitable long-term collapse. The bank-notes we have unwisely printed in such huge amounts, and have been more than happy to throw into circulation, are made up of literal YES / NO statements. It is these literal YES / NO statements that we have used to make our world, the world we are so very attached to. And yet the thing we ignore in all this flurry of purposeful activity is that the logical banknotes, the literal YES / NO statements, aren’t really worth anything at all in real terms. They are ‘information-free’ because they were produced on the basis of a trick. They are ‘null and void’ because they are produced on the basis that our starting-off position is something that it flatly isn’t.

 

 

As a consequence of being ‘an information free zone’, the continuum of logic is a null-world – it is null because ‘nothing ever happens there’. As we have said, the only stuff to happen in the continuum of logic is the type of stuff that makes sense within it, the type of stuff that reflects its own assumptions about reality and these ‘assumptions’ always come down to what we might call a ‘static framework’. A symmetry-break is always going to be static – there’s no such thing as a flowing or evolving break in symmetry because the process of symmetry breaking essentially involves taking a ‘freeze-frame’ of reality.

 

 

The static nature of the symmetry break is clearly demonstrated by the indisputable fact that logic can never go beyond its own premise, or ‘leave its own premises behind’ – a symmetry break can never ‘go beyond itself’ because everything that happens after the symmetry break is determined by the symmetry break. Any developments that might seem to occur in the continuum of logic where actually already prefigured in the starting-off position, which is the ‘freeze-frame of reality’. It is all a tautology, albeit a very well disguised one. Thus, just so long as we are contained within the continuum, we can never get away from the program that underpins the whole simulation, any more than a player of a game can get away from the rules of that game, no matter how skilfully he or she plays it. No matter how fast we think we’re running, we are never getting anywhere; we’re ‘running on the spot’, we’re ‘trapped in the freeze-frame’ and the only type of freedom we have is ‘the freedom of the freeze-frame’, which is a ‘static surrogate’ of the real thing.

 

 

Symmetry-breaks split off ‘static universes’, they generate ‘rule-based simulations’ (or ‘games’), they create abstract virtual reality worlds that we can live in without ever realizing that they are only ‘pale copies of heaven’s original’. Symmetry-breaks produce entropically degraded versions of reality – versions or analogues which have been so cheaply produced that they are actually a mockery of the original, just as Satan was said – in medieval theology – (according to Gnostic authority and renowned science-fiction writer Philip K Dick) to have mocked God’s Creation with his spurious interpolations.

 

 

If an apparently acceptable inferior version of reality can be produced cheaply (at no cost at all, in fact) then there is absolutely no reason why this can’t be done again and again, over and over, ad infinitum. Because of the cost-free nature of this entropic process there is an ‘automatic proliferation’ of lower analogues or ‘inferior productions’. The market gets flooded with them, and no one knows the difference. We can relate this progressive process of repeated symmetry breaking to what Lao Tzu says in the Tao Te Ching

 

Tao gave birth to One,
One gave birth to Two,
Two gave birth to Three,
Three gave birth to all the myriad things.

 

This idea (either in the form of the production of a false or inferior world, or in involutionary series of ever-more attenuated versions of a Divine and Ineffable Reality) is a central one in both Gnostic and Kabbalistic thought. Cosmogenesis (or world-formation) via a series of emanations is a very ancient idea – more than this, the spontaneous production of lower analogues is what Jung calls an archetypal idea. A well-known example of this idea would be the way in which the Goddess Athena sprang with a war-cry from the head of her father Zeus, fully-grown and fully-armed.

 

 

Mystical literature is full of references to symmetry breaking. In the Emerald Tablet of Hermes Trismegistus (which is of unknown origin and age, but said by some authorities to date back to the second century after Christ) the first verse reads:

 

True, without error, certain and most true: that which is above is as that which is below, and that which is below is as that which is above, to perform the miracles of the One Thing.

 

 

In the Gospel of Thomas, one of the so-called ‘Gnostic Gospels’, Verse 22 contains an absolutely unmistakable reference to symmetry breaking (or rather, to the ‘undoing’ of the symmetry break):

 

Jesus saw infants being suckled. He said to his disciples, “These infants being suckled are like those who enter the kingdom.”  They said to him, “Shall we then, as children, enter the kingdom?” Jesus said to them, “When you make the two one, and when you make the inside like the outside and the outside like the inside, and the above like the below, and when you make the male and the female one and the same, so that the male not be male nor the female female; and when you fashion eyes in the place of an eye, and a hand in place of a hand, and a foot in place of a foot, and a likeness in place of a likeness; then will you enter the kingdom.”

 

 

By bringing our attention to the original symmetry break mystical (or transcendental) literature perennially seeks to ‘remind us of what we have forgotten’. Even just to understand the idea represents a radical challenge to the status quo since the symmetry break cannot afford to contain any reference to itself, since to do would necessitate mentioning (or ‘acknowledging’) the state of original symmetry. This is equivalent to the system of logic owning up sheepishly to the fact that it does not represent the final word, or to the rational mind admitting to itself that its authority is based upon nothing more than stubborn one-sidedness.  Logic cannot ever own up to its essentially provisional or relativistic nature (any more than the rational mind can admit to having its basis in absurd one-sidedness) because if it were to do so then ‘the game would be up’, and when the game is up then the little rock pool returns to the ocean. And when this happens, its limited idea of itself is entirely lost…

 

 

 

 

 

 

 

 

Author: Nick Williams

Nick Williams works and writes in the field of mental health and is particularly interested in non-equilibrium states of consciousness, which are states of mind that cannot be validated by standardized experiments or by reference to any formal theoretical perspective.

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