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.

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!

Back to Physics

While it is fun to philosophize and make stuff up about “Wu” and zero-dimensional reflections, at some point, this has to tie-back to ‘real’ reality – the actual, physical world of physics and matter.

I mean, seriously, what is this ‘zero-dimensional Reflection’ I keep talking about? How can a reflection be ‘of itself’?

Firstly, starting with absolute, conceptual Nothing, in order to ‘cordon-off’ a part of Nothing, it needs a boundary of some kind. This boundary is ‘made of’ the same ‘stuff’ as Nothing, which at this point we realize is Everything.

Supposing that this Nothing/Everything is stuff (I’m not yet talking of Matter though), then this boundary we need must do something to this Nothing/Everything to make it different from itself somehow (so that we may consider whatever is inside that boundary to be different from Everything ‘else’). But by the definition of Everything, this boundary is also part of Everything, so it must be of the same stuff. So a boundary, which does something, and yet is something, can only be a Transformation (a ‘mathematical function’ or operation). Transformations are the only ‘thing’ which satisfy the above three criteria, namely: A) are immaterial, B) can be something, C) can do something – that is to say, transformations can act on other transformations, producing new transformations (transformed transformations, so to speak), and yet all-the-while being immaterial. This means we have an immaterial Nothing-yet-Everything.

My first postulate: Everything is Energy, and that Energy is Transformations-operating-on-Transformations, infinitely.

But a Transformation isn’t a thing – it’s a description of a thing, right? Yes and no. Yes, of course it’s a description. When two different things are being moved in exactly the same way, how do you describe what’s happening to them? The action taking place is independent of what it’s acting upon, and is therefore a distinct thing.

There’s a first problem though: Just because something can change, doesn’t mean it does. There is no implication or proof of actual transformation – Action. Since Transformations are operations, they have an input and an output. The input, being other Transformations, infinitely recursively, as well as the output being another Transformation, means that Everything is inter-dependent and poised in a pregnant moment of indeterminacy. But you have to think about it a little further. There’s no Space, and no Time, so what kind of Transformation can possibly exist in a dimensionless space? I know only of four ‘fundamental’ transformations, as enumerated in Geometry:

  • Translation
  • Rotation
  • Magnification (a.k.a. Scaling)
  • Reflection (inversion)

The first three all require at least one dimension, since all three require three bits of information – that is to say, they are all vectors requiring a line of action – a dimension. That last one, however, and interestingly enough, is possible in a zero-dimension space. Reflection, in zero-d space, is simply an existential ‘inversion’ – Something either is or it isn’t. It is the Boolean NOT operation of sorts. Being an operation, it has an input and an output. Most mathematicians sorely dislike paradox, so would instinctively reject the possibility of a single NOT where its input was tied to its output. The equivalent of “This statement is False”. But, even if I were to accept the rejection of paradox, and say ‘No NOT operation may have its output as its own input’, what of three NOTs in a loop? Two NOTs effectively cancel each other out, they are semantically equivalent to ‘is’, so the third NOT’s output is it’s input. This happens for all odd-numbered NOT-loops. It seems paradox is unavoidable. I personally think this particular paradox is not a problem but, better yet, an answer to the problem ‘Just because it can, doesn’t mean it does’ as we will see with my second postulate.

I’ve come to call these two forms of zero-d reflections The Static and The Dynamic. The dual-not-loop is The Static. It is stable. The single-not-loop is The Dynamic, and it is ultimately unstable because it is a paradox in the sense that it is indeterminable. If the value or state of these three Reflections were to be evaluated, then at each ‘attempt’ to evaluate the Dynamic, the Static would be either/or (like ‘either 1 or 0’).

My second postulate: There is Action so long as The Dynamic cannot be evaluated.

This is like some kind of Reality-Computer, or a scratched-record. At each encounter with the ‘glitch’, it starts again, oblivious of its previous attempts. “Ok, the Static is one. The Dynamic is –glitch-. Ok, the Static is zero; the Dynamic is –glitch-. Ok, the Static is one…” Another analogy I feel is suitable is that of the programmer’s “infinite While loop”:

while(True){       Do stuff;}

 

But consider why I claim that the Static alternates. Why wouldn’t it just stay ‘one’ each time around? Well, if it did, then we wouldn’t be ‘different’ from the previous evaluation attempt. This violates the very possibility of ex-sistence. Further, ‘staying’ at a value is only half way around the loop. You cannot go backwards around the loop (to do so is to go anti-NOT-wise, i.e. not-not, which is The Static). And finally, the interdependence of all these transformations (you will see when we get into higher dimensions) makes it impossible to ‘stay the same’ at each evaluation.

It’s a pretty tall claim, to say that the paradox of the single-not-loop creates a sort of evaluatory context in which the dual-not-loop actually happens, but that is precisely my point – A transformation must have an outcome, it must happen. If it does not happen at all, then there is no Transformation to speak of. It ceases to be a Transformation at all.

My third postulate: Entropy is anti-Energy, where Energy is ‘having the quality of being different to itself’ and Entropy is ‘having the quality of being not different to itself’.

The Dynamic is pure Energy – the degree to which something is different to itself at each evaluation, and The Static is pure Entropy – the degree to which something is not different to itself at each evaluation. By ‘the degree to which’, one can consider ‘having the quality of’. By ‘different to itself’, I mean ‘of a knowable value’. The Dynamic, at any moment is neither True nor False, and so is the slipperiest of fish – it cannot be pinned down, cannot be determined or identified, so is ultimately different to itself instantly and eternally. The Static, in contrast, is the very opposite – it is either True or False. It cannot help but be something at some point – at any instant you look at it, it is something.

I believe (naïvely?) that this definition of Entropy isn’t too-far-removed from the present ‘accepted’ definition, and can still be used; only that Entropy now becomes the conjugate of Energy. A hot body has Energy because its internal state (its displacement on the axis of Time) is changing vigorously. A cold body has Entropy because its internal state is quite stable (lesser displacement on the axis of Time). As the two bodies meet, Energy and Entropy are exchanged and Equilibrium is attained. I use the word Entropy to describe a sort of anti-Energy. Potential Energy is pure Entropy – pure Static – the transformation hasn’t happened yet and it is highly self-similar, highly stable. Kinetic Energy Is Dynamic Energy, where a body in motion has a high degree of self-difference.

The notion of Rotation now seems plausible. Imagine a cylinder with one half (lengthwise) painted Black, and the other White. If you were to spin the cylinder around its length axis, but watch it from above, you’d see it alternate White-Black-White-Black, etc. This ‘rotation’ of existence, of ‘is-ness’ is what I’m talking about. Further, the closed-loop transformation in zero dimensions seems to be the smallest possible ‘entity’ – the Point.

My fourth postulate: Two N-dimensional Reflections are one (N+1)-dimensional Rotation.

So a Point in 0D is in fact also a Point in 1D. This is because it is a 1D Rotation. However, a line (being the first dimension) is defined to be the infinite collection of Points. So how does one Point differentiate itself from its two neighbouring points on a line? Simply by its boundary: the Reflection. Each Point on a Line is a Reflection of its neighbour. This re-affirms the ‘alternation’ of the Static, because at each evaluation, one Point must be NOT its neighbour. This is of course a 1D Reflection. According to my fourth postulate, two of these 1D Reflections are in fact a single 2D Rotation. So in fact, The Static is 0D, 1D and 2D. Continuing the reasoning, each 2D Point distinguishes itself from its neighbours by being 2D Reflections of them. Once again, using the fourth postulate, 2D Reflections are 3D Rotations. The fourth postulate is all-the-more striking when you consider the 2D Reflection/3D Rotation example:

Draw a triangle on a piece of paper, each vertex numbered. Then draw a vertical line (to represent the line of reflection) a little further away. If the paper is folded along the vertical line, and a new triangle is drawn where the two halves of the paper meet, with each numbered vertex of this new triangle corresponding to each original vertex, then you’ve successfully created its exact Reflection on a 2D piece of paper. But in Folding, you effectively did a half-Rotation in 3D space.

So The Static is a 3D Point also. This reasoning can be extended indefinitely (until proven otherwise), using the fourth postulate. But we’ve said that Rotations are vectors. So Points are Vectors also? Every Point in 3D space can be represented by a vector of norm 0 – that is to say the Zero Vector. This seems to contradict my separation of the first three ‘fundamental’ transformations from the fourth one. But in fact, it doesn’t. Ultimately, when down at the null dimension, the notion of magnitude or intensity is meaningless (the norm of a zero vector, being zero). Essentially, this means that, at zero dimensions, all four types of transformation become one and the same – the ‘pure’ transformation: “NOT”.

My fifth postulate: The Point is the Zero Vector in all spatial dimensions, and all spatial dimensions emerge simultaneously because of the Point.

So where does Matter come in? Matter has Mass, and Mass, it is currently thought, is but the distortion of space-time by Gravity. Space-time is the ensemble of Space and Time as a collection of axes – Three of Space, One of Time.

The following need to be determined:

  • What, really, is Time? Where is it?
  • What is Gravity in this context of Transformations?
  • Can dimensions be bent/distorted and if so, How?

What is Time? I adhere to the reasoning that Time is just the observation of change. There is the further, more human sense of Time which is irreversible Time. But, consider change happening. Take an oscillation, for example. The notion of periodicity requires a notion of comparison (because we need to know what happened before, to see it happen again). When considering ex-sistence, what exists must be different to everything around it, and constantly. If we were to take the periodicity of a Point as the prime frequency – the highest clock-speed that this ‘Reality Computer’ could attain, then every transformation must happen at a slower speed, but there must be change that happens at irregular intervals for something to ex-sist, otherwise there would be no ‘t=zero’ marker for our Universe to begin from. Any periodicity that is a multiple of the base frequency is nothing more than a different clock – and no notion of ‘when’ or ‘how long’ can be obtained. The slower clock-speeds just become the next level of comparison. What is needed is both aspects of Time: periodicity and irregularity. The Static and The Dynamic.

My sixth postulate: Time emerges alongside all spatial dimensions, and exists in all dimensions.

So we now have the three (and plausibly many more) dimensions of Space as well as Time. However, these Points, regardless of how Static or Dynamic they are, remain Points – not Things, not Matter. I’m still struggling to understand how a dimension itself could be bent or curved, but I suspect that it is this kind of transformation of a dimension (which, as we’ve just established, is just more transformations) that results in the ‘appearance of Mass’ through (sub-Plankian?) gravitational distortions of space-time, and therefore Matter. More to come later…

Reflections on Reflections: “IS”, not “IS NOT”

“Not” is about the only way I can think of expressing the concept of a zero-dimensional Reflection. By ‘Reflection’ I mean opposite, except that in zero-D, there is no position – maybe ‘inversion’ is more appropriate? In Zero-D, something either IS, or IS NOT. But if you think about it a little further, you’ll see that “IS” can be constructed from two “NOT”s – just like the bistable flip-flop in electronics. So “IS NOT” is actually three “NOT”s in a loop – which can be reduced to one “NOT” with its input tied to its output. This is the final, self-inverting, supremely astable paradoxical “Strange Loop”.

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A Breakthrough?

If you’ve read along this far, you’ll have noticed how mercurial these matters can be. And, like mercury, madness isn’t that far away…

Well, I feel like I’ve hit something with such resonating truth, such obvious obviousness, that I know this is it! Now, to extract it while avoiding insanity is the hardest part – I don’t want to get high on my own fumes, so to speak. If, at any point, you feel like I’ve strayed into crazy-town, please, please let me know where you think that fork in the path lies – where did I begin to talk nonsense?

OK, let’s get started:

Continue reading “A Breakthrough?”

Time-lapse and human-centric scales

In a breathtaking video on the various forms of coral in the Great Barrier Reef, Daniel Stoupin breaks us out of our human-scaled sense of Time and shows us what he aptly calls “Slow Life.” Before going any further, please take a look – not only is it edifying but it is beautiful:

http://vimeo.com/88829079

Another incredible documentary is The Private Life of Plants – the BBC documentary narrated by the inimitable Sir David Attenborough, which shows, through time-lapse footage the incredibly ‘intelligent’ movements of plants as they grow and feel about.

Our sense of scale is so limited by our own experience that trees seem immobile, but slow down time, and you’ll see these ‘creatures’ move around, adapt and change to their surroundings. We’re so stuck inside our own heads that there are things we rarely get a chance to consider…

Anyway, ponder, consider, and appreciate the wonder of life on every scale…

Numbers?

Difference being discrete, and our definition of Existence (as opposed to the more unattainable “Wu”), then, can be counted. In my first post I said “Wu” was zero.

Well, the first difference from Wu is one, so we could write:

0-1=-1

But ‘negative one’ is just a place holder, an expression of the absence of one. That absence is ‘felt by’ the Wu. But we are not the Wu, we are the 1, so in a weird way:

0-1=+1

Or, more comfortably: 1-1=0.

But that ‘absence’ is not to be ignored! As a matter of fact, it’s crucial.

Look at astrophysicists racking their brains at what Dark Matter could possibly be.

It’s only ‘Dark’ because they can’t measure it or observe it – and yet they noticed it – because the behaviour of our Universe was too strange without it – an absence of information is still information. -1 says “there used to be a one there” and we know how big it was too.

Our Existence, defined because of difference, is the reference point from which to measure Wu. Sure, we may not be able to measure all of Wu (is it infinite?), but we can certainly measure between here and over there.

We need to start thinking of ‘negative space’ like the artists do – the ‘pauses’ in music, the material removed from marble sculptures, the unoccupied space of the canvas. We don’t know what Wu is, but we know it’s there, in the gaps. But it’s also here, the ‘stuff-of-us’.

Difference being something discrete gives rise to the Natural Numbers (but let’s not forget zero!). We also have the Integers and Rationals. But what about the Real and Complex numbers? Quaternions and Octonions and so on?

Well, mathematicians state that the Real numbers are uncountably infinite, so infinite that they are infinitely continuous. Hmmm. Sounds a lot like Wu to me.

The continuity of Real Numbers pretty-much covers any and all dimensions. Wait. What? So Time is continuous? That’s pretty mind-boggling right there. Time, a sequence of events or changes, is continuous?

It’s hard to imagine a continuous flow of changes – especially since we just said that Difference is discrete!

Sure, compared to “Wu”, something is discretely different, but Time (being the observation of change) has to be discrete, because any change has to be discretely different from its previous state (it’s either different or it isn’t). So for a continuous yet discretely changing time-line, changes are continuous, but their “differences” are infinitesimally discrete. Isn’t that the same as ‘continuous’?

I’ve thought myself into a corner with this one… or I’ve come full-circle. Yes, Time is continuous. Or instead, Time doesn’t exist. Only change is continuous.

Is rate-of-change constant or varied? Without Time, one would be tempted to say ‘rate’ of anything is impossible. But that would be false. A rate is the ratio of the number of events occurring compared to another number of events.

One set of changes could be ‘faster’ than another (8 changes for every 4 of the other means it’s twice as fast). Well, by that comparison, we’ve just realized that rate-of-change is varied, by definition. Obviously – if everything changed at the same ‘rate’, then there would be no ‘rate’ to speak about.

Well, enough of that for now – on to more thinking. Leave a comment if this made you ponder…