The Law of Existence – Part 2

Law of Existence – continued

In my previous post, I promised to illustrate how the Laws of Thought, as they are used today, emerge naturally from the Law of Existence. Time to make good on my promise.

In a comment left by reader SelfAwarePatterns he mentioned that he didn’t see how the Law of the Excluded Middle (LEM) was rendered false by the Law of Existence. He’s absolutely right – it’s not false, and indeed it’s very naturally present already within the Law of Existence. What is false however, is the ‘closed’ interpretation of the LEM which says that a Thing only ever is or (exclusive or) is not. That is clearly false, and to use the example he gave:
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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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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.

The Incredible Persistence of Life

persistence_of_nature_cropped

I saw a long tangle (several meters) of creeper vines outside that have grown along the ground and begun to spread over a large expanse of sheet metal. And it got me thinking: left alone for twenty or thirty years, and this sheet of metal will be completely hidden by vegetation. First the tangled vines will trap and accumulate dead leaves (preventing them from being washed elsewhere in the rains), dust and all sorts of organic material. This will form a kind of ‘mud’ or soil within which future seeds can grow – from dandelion seeds to seeds dropped in bird poop or whatever. These seeds will grow and their roots will spread across the sheet of metal, thickening and holding the soil ‘mat’ together even more. The metal underneath will keep this living biomass separate from the rest of the Earth so that we could hypothetically lift it off years later.

Life is the truly impressive, perpetually changing, form of ex-sistence as I’ve been looking at it. Persistence – genuine persistence, not apparent persistence – it seems to me, is made possible by perpetual ‘difference’ or change, so that Life is somehow more persistent (“per ex-sistence”) than the rest. Of course, it could be argued quite rightly that the metal sheet is just as persistent as the biomass, but it does seem somehow of a ‘lower order’ don’t you think? Like repetitive change being less impressive that non-repeating change. The atoms vibrate back and forth within the crystalline structure of the metal – a repetitive process and quite boring. But the organic matter has vibrating atoms, surely, but also moving atoms, bouncing atoms, and an exchange of atoms, incessantly!

Being persistent does not make it unstoppable. If it stops here, on planet Earth, I am fairly certain that there will be Life elsewhere, and perpetually (or at the very least until the end of the Universe). But that being said, our Life is precious to us because it is the only life we will encounter within our lifetime – hopefully we’ll explore other planets, but I certainly won’t live to see it – and so we have a responsibility to encourage its growth, nurture its variety and maintain its balanced environment.

What do you think? Does living matter somehow have more je-ne-sais-quoi than non-living matter?

Set theory, Mereology, boundaries and continuity

With this notion of wuji, or apeiron, or continuum, or whatever, the whole idea of set theory never sat well with me. The null set (the set which has no members) doesn’t quite make the cut. Consider the continuum – perfect homogeneous Everything – and you realize, like the definition of apeiron, it is limitless, or has no boundaries. Thus it cannot be contained and so cannot be a member of a Set – ‘the set of Everything’ for example. Then I thought about the boundaries. These boundaries are the only way to distinguish something within the apeiron. So instead of thinking of sets, I thought of boundaries within a limitless whole. Being infinite, the first boundary is actually a bisection, splitting everything in the middle. without actually ‘cutting’ anything.

Think of it like a strip of paper with black on the reverse side, white on the other side facing you. If you give that paper a half-twist, you are now differentiating the strip into half-white, half-black. The first thing in a continuum would be a Point which, in 1D, requires two boundaries So a second half-twist (I would opt for an un-twist actually but I’ll get to that) is needed. Sure enough, you now have a ‘segment’ of the strip-continuum which is clearly black in the middle and white on either side. So what we know about a Point’s position in a line is that it is not the point to its left and not the point to its right. The twist and un-twist is so that you have the truth value ‘within’ the boundaries:

---|>0---0<|---   (my crude graphic of two NOT gates facing each other)

This got me thinking further: What is the smallest number of boundaries required to enclose a 2D region? I realized that three line segments joined as an equilateral triangle was the most basic enclosable region. So a 2D region is enclosed by three 1D regions. Then a 3D region is enclosed by four 2D regions. This was a trend that allowed me to reaffirm my earlier concept: a 0D ‘region’ is ‘enclosed’ by one transformation – the zero-D Reflection, Not.

Let nB = the minimal set of boundaries required to enclose a region in the nth dimension. |nB| is the number of boundaries within that set. nBm where m is the index of nB sets

0B={Not}, |0B|=1

1B={0B1, 0B2}, |1B|=2

2B={1B1, 1B2, 1B3}, |2B|=3

3B={2B1, 2B2, 2B3, 2B4}, |3B|=4

nB={n-1B1, n-1B2, n-1B3, …, n-1Bn+1}, |nB|=n+1

So the smallest 3D region is delimited by four 2D regions. This is, of course, the tetrahedron, which can be made by four planar ‘cuts’. A triangle can be ‘cut’ out of paper using three cuts. A segment of string can be made with two ‘cuts’.

So, also, I discovered another field of study in mathematics called Mereology – the study of wholes and their parts. There is mention of Alfred North Whitehead – a strong proponent of Process Philosophy, which is very strongly similar to the rationale that I’m using on this site. Everything is a process, or act of transformation.

Well, once again, this is a short entry, but more to think about… Hope you enjoyed it!

More on Numbers

I’m still troubled by the notion of a number with relation to discrete vs. continuous, Rational vs. Real, etc.

Why? Because you can’t even talk about a number on a continuity which is infinite. There is simply no such thing, because there is no ‘thing’ upon which to attribute a number.

The mere fact of using a number implies, implicitly, difference from the whole – the continuity.

Consider a wrinkle. If we say that a wrinkle on a line – a crest or vertex – is different from the rest of the line (even though it’s ‘made of’ that line), then we can number it – count it.

However, when we want to talk about “the continuous number line,” i.e. the Real Numbers, then that is our first mistake because we are using numbers (implicitly discrete things) to describe a continuous thing. This is why we end up with infinite decimal expansions and transcendental numbers which go on forever. When we reach the ‘end’ of our decimal number, we’re merely wrinkling the continuity according to a well-established algorithm in order to obtain the next decimal in the infinite expansion!

When we compare a line segment (discrete), say, a circle’s diameter, to a continuous entity (the circumference) then of course we come up with the impossibly-finite ‘number’ pi! We’re comparing apples and oranges!

The two cannot be ‘com-paired’, paired-off against one another.

Let’s think about the sets to be paired-off:

“L” Line segment:

The ‘set’ which describes that segment is a single number – its length – which we take to be a countable set of wrinkles which are of a pre-established size.

“C” Circumference:

The ‘set’ which describes the circumference, we assume, is also a number. That number is a countable set of wrinkles of the same pre-established size as the segment’s wrinkles.

When we pair-off these sets of wrinkles, we see that you can almost pair-off “L” to “C” three times, but just not quite. In the gap, we see we could fit another wrinkle which is ten times smaller than the wrinkles of the set “L”. But again, not quite. Now you can fit four more wrinkles which are a hundred times smaller than the wrinkles in “L”. So that’s 3.14, but again, not quite. And so on.

You cannot com-pair sets of the same-sized wrinkles! But by creating smaller wrinkles we’ve ‘broken the rule’ – our initial assumption.

Now that we’ve broken that rule, the problem can be turned the other way around: say “C”is discrete – let’s say there are exactly 24 wrinkles of a chosen size which fit around the circumference of our circle.

Well, since you can arbitrarily choose the size of wrinkles for your sets, then you can choose to say that the set “L”, the diameter, also has exactly 24 wrinkles… or 8-ish so that “L” is exactly 3 times smaller than “C”.

Heck, at this rate, you could even say “L” has only one wrinkle in it, a big one which exactly spans the diameter of your circle.

But you see the nonsense here? There are no rules. We’ve made assumptions which cannot hold, and we’re trying to compare two things of fundamentally different natures!

In this view, I understand where Norman J. Wildberger is coming from when he says that he doesn’t ‘believe’ in Real numbers. His sense of pure, mathematical Truth is offended by those ‘irrational’ infinite decimal expansions and I think it’s because we threw out consistency (fixed wrinkle size in my example) for the sake of making an answer to the wrong question.

Now, that being said, I also understand that we need a way to describe a circle, because, though continuous, they clearly exist, and there are things which can be said about them which we might use to describe them. In addition, I also seem to come up against continuous things which make it impossible to avoid comparison between these two opposing types. So unlike Wildberger, I’m not ready to throw the baby out with the bathwater just yet.

Definitely needs more thought though…