The Deep Symbolism of the Mobius Strip

The Mobius Strip

If ever there was something which merited the name “God” in my eyes, it would be the Mobius Strip. But I don’t believe in a personal, let-alone sentient, god. I’d be far more inclined to call it “Tao” instead. Buddhists might call it “Om” (or “Aum”). Mathematicians should call it “i” (the square root of negative one), but there are even more examples in Mathematics (the involution, the half-rotation, inconsistency, contradiction, “not” or the symbol ¬). Electronics circuits represent it as the inverter whose ouput feeds back into its input. Philosophers might call it “contradiction” or more formally the “paradox of self-reference” epitomized in the Liar Paradox:

“This statement is False.”
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Strange and relative thinking: two examples


On Infinity and Boundaries:

You have to understand that if you have an infinite “expanse” of sameness that is unchanging, and that you (I say ‘you’, but I mean ‘it’ or ‘unknown’ for the time being) cause a Thing to exist from that sameness, if it is to ‘exist’, then it must necessarily be perfectly bounded; and if it is perfectly bounded, then, reciprocally, so too is the ‘infinite’ sameness (which is now clearly not infinite).
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The Universe as an Analog Circuit

We intuitively describe an object’s ‘tendency’ to remain as it is, in terms of how it was before. Talking of Time and memory, we perceive the past, but in a physically objective world outside of us, if everything is transformations, then Time is bogus – illusory. We only perceive it as a ‘rate of change’, but a change-per-change is all that really exists, and so our notion of Time is relative, obtained by comparison between two rates of change.
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The Present is “Not” – a Transformation Ontology

When you think about transformations, how they exist ‘en soi’ (they are, independent of origin or basis) because to exist is to be different, and to be different is to transform (or be a transformation), and given that Matter is, ultimately, Immaterial ‘Energy’ – which is just another word for transformation (even ‘potential’ energy is just self-cancelling transformations – two collinear but anti-directional vectors of identical magnitude are ‘potential’ vectors, which, if either is ‘rotated’ so that they are no longer collinear, thereby become ‘actual’ vectors, kinetic energy).

As I’ve said elsewhere, the first, ‘basest’ or most ‘atomic’ transformation is the zero-dimensional ‘reflection’, which we humans call “not” – i.e. the logical negation/inversion. This transformation is physically imperceptible to us except in one dimensions – a Rotation. Leptons ‘have’ spin. I’d go even so far as to say they are spin. Even neutrinos are said to “have half-integer spin” –Wikipedia.

But even the ‘self’ is a zero-dimensional ‘reflection’ defined as ‘not’ (“I am not my reflection” or “I am not you”). Thoughts, though I haven’t actually done this yet – but intend to – may well be ‘representable’ as transformations also. If so, they arguably ‘are’ transformations. This is contentious and I’m more than willing to work more on this! Though I am by far not the only one to think of this – just look at Douglas Hofstadter’s “I am a Strange Loop”.

And even further (and this one makes me uneasy), the Present, our ‘now’, is the boundary between Past and Future, and being ‘not’ either one, can be conceived as the transformation (reflection) of the future into the past. Like a single half-twist in a strip of paper travelling along it, what’s ahead is the ‘potential’ future – i.e. ‘unknown sameness’, ‘self-cancelling transformations’ – ‘potential energy’. What is behind the twist is the past, also ‘unknown sameness’, or ‘self-cancelling transformations’ – but being subjected to a reflection, it is forever ‘not’ the future. If the future is ‘zero’ (a digital analogy), then the past is ‘one’. And the present is the transformation ‘effecting’ the past.

All of reality can be broken down to transformations, and the very essence of Time – the quality of temporality – is expressed in the ‘liar’s paradox’ aspect of a self-reflecting ‘not’: “This statement is False (‘not’ true)” can be expressed as a recursive inversion x=-1/x, which resolves into x2=−1 – i.e. the mathematical constant ‘i’. “i” expresses a rotation just as -1 expresses a reflection (where a reflection in a given dimension is a rotation of 180° through a higher dimension). The ‘irresolvability of i’ is temporality. The ‘direction’, or historicity of Time arises in the irrevocable transformation of future into past (where past is not-future and future is not-past).

The past does not ‘exist’ – it has existed. The future does not ‘exist’ – it has not existed. Only the present ‘exists’ because it is the ‘act of existence’ itself – a transformation.

Finally, the old subject-object dilemma is resolved/united via that strange transformation “not” – the subject is not the object; the observer is not the observed. The interaction between the two happens via the reflection “not”. This harps back to the quantum-mechanics problem of the ‘observer effect’ (see the “Quantum Mechanics” sub-heading in this Wikipedia article).

I’m really sorry, but I just can’t make peace with how all-encompassing this damned transformation is! It’s freaking everywhere, and yes, I am aware this smacks of confirmation bias… but I can’t help it! Which is why I need your help. How viable is all of this? Is this utterly nuts? Think about it and get back to me, please!

Thank you for reading.

In-between-ness

This zero-D Reflection is a strange bird…

The very existence of a boundary to separate a space in two gives rise to a higher dimension in which both can exist. In zero dimensions, a Thing bounded by a Reflection (“Not”), then (and I know the words are dangerously wrong here) has a kind of ‘inside’ which is not ‘outside’. Strictly speaking, this ‘inside’ is no longer even in the apprehensive realm of whatever is ‘outside’ – precisely because of the boundary which ‘shuts the door’ to the ‘inside’. It is clearer in 2D and then you can roll-back the analogy to 0D later:

Think of a circle – an enclosed section of 2D space. To a 2D observer, that circle is closed and has a boundary. Because it is closed, then the 2D observer might conclude that the circle has an ‘inside’ – but has no way of getting to it, unless one of two actions are taken:

1) Using a special 2D scalpel, the 2D observer ‘cuts’ the circle open. By doing this, it has reduced the circle to  a 1D line – an object in a lower dimension than the observer, and so both ‘inside’ and ‘outside’ can be observed (though arguably both ‘inside’ and ‘outside’ are lost, the moment the circle was ‘cut’)

2) Trying to ‘step over’ the boundary. Like trying to jump a fence – the only way to do this is to briefly traverse the 3D realm, only to land ‘inside’ the circle. But because the observer is 2D, now ‘inside’ the circle, then the observer loses all apprehensive ability of ‘outside’ the circle. It’s either-or.

The Reflection in a dimension, I’ve said elsewhere, has a special property in that it is a Half-Rotation in a higher dimension. So to pass from ‘inside’ to ‘outside’ (and vice-versa) you have to be subjected to a higher-dimensional Half-Rotation. But you’ll start and finish in the original dimension. What if you wanted to stay above 2D? Well, you’d have to ‘not’ complete the Half-Rotation. You’d have to do a Quarter-Rotation of sorts. This is obvious when we consider that the third axis of 3D is 90° perpendicular to the other two, but it’s also beautiful when we consider that some Thing both Is and Is Not in a higher dimension. So back to zero-D, where what can be said of a Thing is that it “Is” or “Is not” – in 1D then you can ‘see’ both.

Consider this line: —–IS—–<NOT>____ISN’T____<NOT>—–IS—–

The ‘region’ bounded by both those ‘not’ Reflections, is invisible (incomprehensible) to a 1D observer. We see it because we’re in a higher dimension.

Time and Change

Stop. Stop every single thing. Freeze. Freeze Time itself.

For us, as humans, we wouldn’t be able to see anything because the photons have stopped and therefore aren’t reaching our retinas, but even more, our own neurons have stopped.

That doesn’t mean nothing exists absolutely – Everything still is, just frozen – but it does mean that nothing ‘intelligibly’ exists – i.e. we can’t say that anything exists.

This illustrates the distinction between static difference (existence) and dynamic difference. The latter I playfully renamed ‘persistence’ to “per-existence”, intending to load the word with two meanings: ‘per’ as in ‘miles per gallon’, here meaning ‘change per change’; and ‘per’ as shortened ‘persistence’, thus meaning ‘persistent existence’.

But let’s stay in this static existence for just a bit. We’ve only been here for one ten-umptillionths of a microsecond. Oh, wait, my mistake. We’ve actually been frozen like this for seventy-eight gazillion millennia!

This illustrates the following: Without ‘change-per-change’ our reality ceases.

But what about ‘Real’ reality – the one that exists regardless of consciousness? Surely there must be something that remains, no?

Well, boundaries still exist, just as the boundaries between colours in a static painting, and those boundaries are still transformations. Or are they?

“Static” functions – one-shot transformations are absolutely meaningless! f(x)=x2, for example, has an input, ‘x’, and an output ‘f(x)’.  f is absolutely meaningless in an absolutely static state because it’s truly either-or: either we have the input, (‘before’ the transformation, in which case there is no transformation because it has not yet ‘been’) or we have the output (‘after’ the transformation – a concept that is only relevant because we have memory of ‘before’, which is clearly impossible in the absolute static instant – so again there is no transformation because it has already ‘been’).

But, and I don’t want to seem glib here, it is a simple fact that stasis means no-change, and change means transformation, and so, stasis – absolute and total stasis – means absolute and objective (i.e. independent of whether there is a conscious ‘observer’ or not) non-existence. Nothing exists Statically (in both senses: “Nothingness” is Static, and “No Thing exists in stasis”).

Since we exist, and since there is change, then there is no absolute stasis. This means that the only stasis possible is relative stasis: i.e. either repetitive change or self-cancelling change -> a dynamic ‘not-not’.

Strangely, this also means there is no static, one-shot difference – only continuous difference. Something is different only ‘so long as’ it is – and then it is not, unless it is ‘differently different’ – different in another way.

As an aside:

This ties back to my thoughts on the Real Projected Line (I hate that name!):

A is ‘not’ nothing. B is ‘not’ A and ‘not’ nothing. Here, B is ‘differently different’ to A because if it was simply ‘not different’ to A, then it would be A.

Also, this means that there was no ‘static’ before-big-bang, and there will be no static ‘heat-death’ at the end.

This means that a state of absolute annihilation (the Dynamic not-not of the entire Universe) will have the lowest possible entropy (i.e. the entire system has only one configuration where it can be considered the same) and yet will also have the highest possible entropy because every configuration of the Universe leads to the same state.

This mind-blowing ‘truth’ is HUGE: “Energy is neither created nor destroyed”

This states that energy is eternal (has no beginning and no end) – it always has been and always will be – which means that Absolute Static Non-Existence has never been nor ever will be. Non-Existence is absolutely impossible! Absolute Stasis is impossible.

Transformations exist because they always have and always will – Energy is(are) transformation(s).

 

So let us consider Total Continuous Annihilation -> the only (the Truest Possible) True Zero. This, if all transformations were vectors, could be a state where all vectors were paired-off with their opposite, resulting in continuous no-change.

We have a conflict here: how can continuous no-change be considered in any way different from Absolute Static (that thing we’ve just established is impossible)? No Change is the definition of Absolute Static.

If the ‘output’ of a function is the same as the ‘input’, can we really consider there to have been a function at all? I think not. There neither ‘was’ nor ‘will be’ since the input and the output are the same.

Let us now investigate the Dynamic: Let us consider a transformation so absolute that no matter how fast you ‘query’ it, the result will always be wrong – it will always be ‘not’ what you think it is, it is immeasurable. Absolute Dynamic change is Absolutely ‘Not’ itself. This transformation’s output is Absolutely Undeterminable, which means its input is also Absolutely Undeterminable.

Here again we seem to be faced with no-change where the input and the output are the same – (except that it’s not).

Well, I will leave you with this thought: What if the entirety of Reality is the self-Reflection, “Not”, whereby locally everything is continuously changing so that at no ‘point’ can Reality-as-a-whole be ‘frozen’ and ‘said to be x or y or z‘ – i.e. that it is immeasurably different at every instant? And what if, at its smallest core, Reality was composed of “Not-Not”s -> the ‘atoms’ of Reality. To split one of these (i.e. all of existence stretched-out and ‘exhausted’ at the end of the Universe) would re-start a new Big Bang (or two?). Chew on that, and I’ll continue to work on this new topic of scale – how to distinguish between Reality-as-a-whole and Reality-as-an-atom. Leave me your thoughts!