Logical statements may come across as being immensely impressive, as being impossible to argue with, but they don’t mean anything, not really. With regard to the ideal (or formal) world that our statements necessarily assume they can mean something, but since the formal domain assumed by logic doesn’t exist anywhere apart from in our imaginations this doesn’t actually count for anything. Whatever we show to be true with respect to the logical world that we have assumed in order to be able make our statement in the first place is of precisely zero significance.

 

 

This is extremely hard for us to appreciate – it’s like saying ‘nothing is real’, only we’re not saying that at all. What we’re saying is that ‘nothing logical is real’, that ‘no logical description has anything to do with what is being described’. This doesn’t make sense to us because we could take it to be the case that our descriptions of the world are at least partially true, that they have at least a degree of substance to them. We believe that we’re certainly not too far off as regards ‘knowing what’s going on’ with stuff, we are – in our daily lives – wholly convinced that we’ve got the measure of who we are and what this thing called ‘life’ is all about.

 

 

To say that linear (or logical) space is ‘positively curved’ is to say that it always comes back to its own point of origin. It means that the domain in question is a closed one. We could think about this in terms of walking around in a circle – in one way it seems that each step is taking me further away from my origin (this is what I experience is being the case, after all), whilst in another (and more profound) way however each step that I take is taking me back towards to my origin. Apparently, I am moving away from ‘where I was’ and progressing towards ‘where I’m going to be’; apparently, I’m ‘escaping heroically from my own past’, but in reality this isn’t the case. In the Continuum of Logic there is always – we could say – this continual ‘virtual-or-subjective escaping’ going on – we always seem to be escaping from our own point of origin, our own past, but we never are.  It never ever happens that we do escape, but we keep on believing that it is possible all the same. That’s what we’re playing for, after all; that’s what we’re always trying to pull off.

 

 

On the one hand there is the continual feeling that we are moving away from a central point, whilst on the other hand there is the actual reality of our situation, which is that we are continually turning back towards the centre. We’re moving for sure, but not away from the centre. We could think of the situation of a planet moving around its sun, or a satellite orbiting around a planet – we’re in a state of movement it’s true, but at the same time we’re not ever getting anywhere. In the Continuum of Logic (or the System of Thought) all movement is circular, as we have been saying – we perceive ourselves to be moving boldly outwards from a ‘centre’ or ‘point of origin’ when this isn’t true. The reality of our situation is that we can never get away from the centre, the reality is that we are the prisoners of this centre (or – as we could also say – extensions of it).

 

 

All logical statements manifest this duplicity, this hidden contradiction. The whole point of a logical statement is that it goes somewhere, the whole point is that it actually says something, and yet well we to closely examine what’s going on here we did find out fat, as we asserted right at the beginning of this discussion no logical statement ever gets anywhere, no logical statement ever gets anywhere because the continuum of logic is continuingly ‘turning in on itself’ with the effect that it never gets away from itself. This is what makes the Continuum of Logic into a continuum. The COL is essentially a geometrical point that has been tautologically extended (or spread out) in all directions -the whole (supposed) domain is therefore nothing more than this same point replicated or reproduced an infinite number of times and so of course we’re not ever going to get away from it. There’s nowhere else to go…

 

 

Another way that we could talk about this self-contradictory situation is to say that it is exactly the same as travelling along the face of a mobius strip. A mobius strip (or loop) is a kind of topological oddity in that it appears to have two surfaces (or two faces) whilst actually only having the one. The reason it seems to have two faces (rather than just the one) is because the strip is kinked – it has a twist in it so that the one face gets to act as if it were two. If we travel along the ‘outside’ of the mobius strip then we end up on the ‘inside’ and if we travel along the ‘inside’ then we end up on the ‘outside’ – the surface that we’re travelling along is constantly turning in on itself (just as the moon in orbit around the earth is constantly turning in on itself) and what this means is that our apparent movement is actually only continuous looping. The ‘inside’ of the strip is also the ‘outside’, and so what this means is that there isn’t really an inside or outside – there can’t be such a thing as ‘only an inside’ (or ‘only an outside’), after all. Opposites have to come in pairs. What we’re saying here therefore is that the thinking mind doesn’t take us ‘out there’ into reality (despite all appearances), but rather that it’s nothing more than a deceptive mobius loop.

 

 

Linear or logical space is a ‘deceptive mobius loop’ because it is constantly ‘turning in on itself’ without this being visible to us. If the North Pole and the South Pole (which is to say, the plus and the minus) were two totally different things, then the movement from the one to the other would constitute genuine honest-to-goodness change, but the point is that North and South are only theatrically opposed, as Alan Watts puts it. We’re pretending that there are two things (one of which leads onto the other) but really there is only the one. This is what Alan Watts calls ‘The Game of Black and White’ –

 

Again, this is a problem which comes from asking the wrong question. Here is someone who has never seen a cat. He is looking through a narrow slit in a fence, and, on the other side, a cat walks by. He sees first the head, then the less distinctly shaped furry trunk, and then the tail. Extraordinary! The cat turns round and walks back, and again he sees the head, and a little later the tail. This sequence begins to look like something regular and reliable. Yet again, the cat turns round, and he witnesses the same regular sequence: first the head, and later the tail. Thereupon he reasons that the event head is the invariable and necessary cause of the event tail, which is the head’s effect. This absurd and confusing gobbledygook comes from his failure to see that head and tail go together; they are all one cat.

 

The cat wasn’t born as a head which, sometime later, caused a tail; it was born all of a piece, a head-tailed cat. Our observer’s trouble was that he was watching it through a narrow slit, and couldn’t see the whole cat at once.

 

 

We say therefore that North and South are two separate things (which would mean that the transition from the one to the other would be real rather than virtual) but since North is the mirror-image reflection of South and South is the mirror-image reflection of North, this means that any type of movement we imagine to be going on is always going to be strictly ‘virtual’ in nature. In a mobius loop virtual change is the only type of change there is or ever could be.

 

 

There’s no such thing as an ‘absolute UP’ or an ‘absolute DOWN’ – the two are completely interchangeable. It’s like ‘here and there’ – when we’re here then here is ‘here’, but when we’re there then there is ‘here’. Here and there are relative terms but in order for the game to work (the game of Black and White) we have to see them as absolutes. In order for the game to work we have to see something as being true that totally isn’t (i.e., we have to take something seriously that is actually quite absurd). In order for us to be able to play the Game of Black and White it is essential that we have no awareness of the essential relativity of our knowledge about our situation but if we don’t have this ‘awareness of relativity’ then we don’t have any awareness at all. ‘Playing a game’ means being profoundly unconscious, therefore, and when we are unconscious in this way then we will be under the influence of the illusion that we are ‘in control’ whilst actually the exact reverse of this is true.

 

 

By buying into the apparent movement away from our (supposed) point of origin we make ourselves blind to the principle of the ‘Identity of the Opposites’, which makes us into the slaves (or playthings) of these opposites. We don’t play the Game of Black and White, the Game of Black and white plays us and the way that the game of B & W plays us is by getting us to go around and around in a mobius loop whilst believing that we’re getting somewhere, whilst believing that we are stuck escaping from our point of origin (which means ‘escaping from our history’). Every logical statement we could ever possibly make takes for granted a particular context, in that context is the ‘formal world’ (or ‘game’) that we have started off by talking about. This formal world or game is nothing mysterious, nothing strange – it’s simply the situation that comes about when we (in our imaginations) separate [+] and [-] (or UP and DOWN) and say that they are distinct or unrelated things. The ‘context’ that we assume is simply polarity, in other words – everything (without exception) gets sandwiched between [+] at the one end and [-] at the other. All statements, all literal descriptions, all theories assume polarity and the thing about this is simply that polarity isn’t real.