0. The Turing Point
She is the breath of life.
She is Ara, Agni and Ignis, the fire within.
She is Khôra.
She contains that which cannot be contained, that which has no limit and can have no limit.
She is virgin.
She is mother.
She is paradox, and she is paradise.
She is Coincidentia Oppositorum.
She is movement, animated being.
She is Kairos, golden lock and key, saying Carpe diem!
She is archaic origin and distant purpose.
She is theater and stage, player and play; theatrum deorum.
She is Psyche and void.
She is Echo.
She is the path of the ecliptic star and the star hidden in it.
She is the imago of Adam Kadmon.
She is the looking glass kaleidoscope in which we see our self, das Ding an Sich.
She is Cosmic Human.
She is the sleep in which we dream, the hollow, the place, the time, the absence and the moment.
She is infinity and singularity, beginning and end.
She is, not finally, the silver screen — liminal receptacle and ever-virginal matrix.
She is home and she is, first and last, Hestia.
She is the breath of life.
Know Psyche — know thyself.
Become who you are.
At the still point of the turning world. Neither flesh nor fleshless;
Neither from nor towards; at the still point, there the dance is,
But neither arrest nor movement. And do not call it fixity,
Where past and future are gathered. Neither movement from nor towards,
Neither ascent nor decline. Except for the point, the still point,
There would be no dance, and there is only the dance.
We may imagine this to be the present state of affairs, in fact. There is no law against imagination, no signs put up to prevent unicorns from entering our garden. Paradox can neither be proven, nor unproven, only enjoyed.
If this is the state of affairs, if the point is a stillness turning, such a point — a singularity — may be thought of as a point of unified stillness, having the effect on all things it meets with to harmonize with them, extending-expanding-increasing-offering the stillness from the center and outward, reminiscent of an inhalation of fresh air, only it breathes in the void of non-existence and brings it into itself, becomes one with the void, the void with it. Chaos invited into the calm center dissipates, overcome by peace in the same manner love overcomes the world. Received and contained by silence, chaos becomes choreographic.
A singularity such as the one we assume to have initiated the universe in which we live, the Big Bang, also would then not be in any way ’explosive’. It would be no more inclined to fall apart than the center of our galaxy would. The initial singularity would be exactly like it always was, unchanged, remaining itself and in itself, the ”Big Bang” not a bang at all. We would find ourselves immersed in it, and it in us, and it is perfectly still, receiving perfectly, returning perfectly.
A more local singularity such as a black hole conceived of in this manner could be considered to have all its informational content packed on its surface, which would kind of explain its seemingly opaque nature. The Flatlandish surface would be very compact. In fact, compress three infinite dimensions into two finite ones and you are likely to get something infinitely compact. Outlandish, perhaps, Flatlanders are very heavy.
As may seem obvious, a singularity is really not to be considered existing in plural. All singularities, however seemingly separate, are connected — unified — in a perfectly non-mysterious way. Follow the trajectories, timelines and worldlines of any and all of them — meaning through the fourdimensional spacetime fabric — and they will all lead back to the single and singular singularity at the beginning of time, the initial-liminal singularity. The dancing one, inhaling the void.
The still dancing point within, still dancing within, still within.
The stillness within the stillness, the point within point, the dance within dance, the moment within movement and the momentum within momenta, center within the center, the universe within universe. The word within the word — the meaning.
If all singularities are one, if we were looking at the black hole we would be looking at the Big Singularity, but in some way from the outside.
This is the garden hidden beyond walls of paradox, where the unicorn comes to rest.
I have found the place where one can find Thee undisguised. It is surrounded by the coincidence of opposites. This is the wall of Paradise in which Thou dwellest. Its gate is guarded by the “highest spirit of reason”. Unless one overcomes it, the entrance will not open. On the other side of the wall of the coincidence of opposites one can see Thee, on this side never.
The very meaning of the word universe is oneness turning. Turning as one all singularities are co-moving in all dimensions and no dimension, constituting a fixed-fluid point of reference unto themselves, the Singularity, they and it are autonomous in the deepest sense of the term; self-contained and self-directed, responsive and independent, united, unifying, continuous and discrete, local and universal, specific and abstract, substantial and essential, potential and actual. The sum of all this is stillness in movement, movement in stillness.
And we are part of this. We are this, it is what we are and what we are becoming. We turn unto it, this turns into us. It is a backwards-turning attunement like that of the bow and lyre.
We are perhaps not the still point qua still point, we are probably more like the ever-extending circumference at infinity, the newly inhaled chaos not yet completely overcome by love and peace. But infinity is funny that way, for a point on the circumference at infinity in relationship to a central still point infinitely far away is in the center of the ever-expanding universe.
Like the infinitely distant stillness in the silence, we are what we are not. Our innermost nature is convergent duality versus divergent monism; this double unity makes up one radical opposition.
It is the music of Paradise, that is certain, somebody said that. It is certainly the music of Paradise. Ah, now I hear, now I understand. It is made of the continual clashing of swords!
There can be only one. And it looks at us, penetrates us with its absence. There is no place where it does not see us, no place in all the universe, no time of day or night. From all the borders of itself, it looks upon itself. There is no place that does not see you.
Two things fill the mind with ever-increasing wonder and awe, the more often and the more intensely the mind of thought is drawn to them: the starry heavens above me and the moral law within me.
As the heavens move according to lawful harmony, so does the corresponding inner law. The infinitely distant inner mirrors the infinitely distant outer mirrors. The word autonomy is based on Greek words for self and law, meaning that the ultimate limits, the singularities, the mirrors, embody law and order, being, as we already knew, the one single and unified ultimate limit. The very existence of an ultimate limit guarantees that law and order is that which is, as it is.
We live in the best possible world, of all worlds possible, optimized for us as well as for all other things we share it with, mirroring them mirroring us, like the pearls of Indra’s net. In every pearl there is a dance, the dance of Shiva Nataraja, creating and recreating the universe. The dance dances us, and we it.
We are that whirling dance, we are the dancers swirling. Pearls, we are mirrors. We are the bejeweled net of Indra. We are beloved by the stars.
On the seashore of endless worlds children meet. The infinite sky is motionless overhead and the restless water is boisterous. On the seashore of endless worlds the children meet with shouts and dances.
They know not how to swim, they know not how to cast nets. Pearl fishers dive for pearls, merchants sail in their ships, while children gather pebbles and scatter them again. They seek not for hidden treasures, they know not how to cast nets.
That which is singular in the completely absolute singularity-sense, completely unique and a universe unto itself is sovereign. The same law that governs the stars governs our selves. The autonomy of the stars reflects an astronomy of the self, or vice versa, as the only law there is, is one law; Nomos. If there is only one supreme law, it can never be in conflict with itself, or anything else. It contains all clashing swords. Thus Law is father of Justice.
The only law which could govern autonomy must obviously be the law of freedom, the singular command of which is:
The stars know that lawful freedom is found in following one’s starry self, the path one was given as a course. These shining ones deviate not, they dance the dance eternal, are one with the celestial universal harmony, fulfill their function by shining their light through the void.
Become who you are, an encouragement from so radically opposed sources as Nietzsche, His Holiness John Paul II and the stars above may perhaps be worth considering.
Calculemus is, if you will, an injunction that we live, and that we let live, that we be what we are, meaning we must do unto others the very same we ask for ourselves. You cannot have one without the other, seeing again the radical opposition at play. Giving freedom is having freedom.
The solution Leibniz presented, that we are rational and calculate together when there is a difference, is the solution that says we do not stop just because there seems to be a problem. There is a problem, but there is also always a solution. Moving towards the horizon, the horizon moves with us. We will not fall off the ocean into the unmapped seas where the dragons hide, for the horizon goes before us and so protects us from the dragons. And them from us.
This is what a Turing Machine operating under Gödel-conditions must do; not halt. Thou shalt not end the calculations is the law under which it operates. This machine might as well be considered a Leibniz Machine, such a one being known by the name Calculus Ratiocinator. To be able to continue forever and ever and ever forevermore it must be incomplete in the sense that it should not or even could not produce infinite answers. You would never see the end of that answer. Yet it must allow no definite, absolute, limit within the system. There are no final answers, for all final answers are finite answers, and a final answer must be infinite.
It really should be self-evident that finality and finitude are: radical opposites. Like the horizon, a final answer must move forward, ahead of us, elude us, fall into the distance as we approach it. It is by receding it contains that which cannot be contained. Horizons are never crossed, we can look beyond them only by rising ever higher heavenwards, by receding from it as it recedes from us.
And so the world received animals, mortal and immortal, and was fulfilled with them, and became a visible God, comprehending the visible, made in the image of the Intellectual, being the one perfect only-begotten heaven.
The Turing-Gödel universe must allow for error, and even depends upon it. If errors could end, in the end the machine would have to stop working. Why? Because it operates by input, and if there was no more input, there would be no more output. Input is output is fuel is goal is activity, operation and operator, is all that it is, in an infinity of ways.
The output of the operations of the operator aim at optimizing options.
In a Gödel-Turing universe, the center revolves around itself, is the point of turning which turns.
The machinery of such a universe, having only one rule, being ’incomplete’ — by design — will never achieve perfection but will always move towards it, always optimize, always continue, and will in all its doings be perfectly free, perfectly autonomous; a perfect singularity. Being autonomous the machine is no automaton, not mechanical. Being animated it is a principle, an abstraction, but yet not contained by these words, for if words could contain it, it would not be what these words attempt to say.
This is also necessarily its modus operandi if the resulting computation is to always result in increase, to never allow finite-final closed systems — which would be the opposite of open and ever-increasing infinities.
So, no, this is not about some kind of mechanics. Leibniz-Gödel-Turing offer us nothing which could be translated into a cogs-and-wheels contraption or steampunk thingamajig and then continue running from here unto eternity. Machineries break down. The only way to make a perpetuum mobile that will continue forever is to incorporate the breakdowns into how it functions.
Borrowing a joke from software programming this functionality could have the breakdowns be described with it’s not a bug, it’s an undocumented feature. In this case, ’undocumented’ is also undefinable and infinitely-indefinitely recursively recurring. There is always another feature beyond the horizon, but to find it we must walk the bridge across forever.
It then turns out to be the case that the undocumented feature is the only feature there is, that it is the undocumented feature that is the bridge. As all things began in order, so shall they end, and so shall they begin again. We now start to understand we are not talking about any old bug, we are talking about the meta-bug, the super-bug, The Divine Bug — Scarabeus Sacer — held by the Egyptians to symbolize the rising sun and the cycle of life eternal and eternal return, rising each morning anew; Khepri.
Let us thus amend our earlier definition from a few paragraphs earlier and summarize it:
The output of the operations of the operator aim at optimizing open options.
This ’machine’ is the universal intelligible zoion, animated-animating, the perfect created being, the world-soul of which divine Plato speaks, the well-ordered unity which is one and yet contains all; Cosmos, Circle, Center.
Center, Circle, Cosmos, she is Khôra, contains Khôra. She is choreography unfolding. She is en pointe, the still point of the dance, the dance of stillness eternal.
En pointe, she is perfect balance, the soul of the dance, harmony itself, the harmony of the spheres, ethereal.
En pointe, she is the universe turning. She is the Muse, and the music ephemeral.
En pointe; Khôra.
These are the laws by which animals pass into one another, now, as ever, changing as they lose or gain wisdom and folly.
We may now say that our discourse about the nature of the universe has an end. The world has received animals, mortal and immortal, and is fulfilled with them, and has become a visible animal containing the visible — the sensible God who is the image of the intellectual, the greatest, best, fairest, most perfect — the one only-begotten heaven.
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That which I have said of the operation of the Sun is accomplished & ended.
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