May 06, 2017

Incompleteness provides a theology to the machine

Dear Dr. Puri,

Of the various concepts of God that other people hold, I find yours particularly friendly. I accept that the universe is larger than we are, and that whatever mysterious thing it is, everything and everyone is ultimately grounded in it. I don't doubt the universe, as such. If this counts for you as my accepting "God," in this sense I do.

It's when we get to God-as-personage that a polytheistic mythology seems much wiser to me than any of the monotheistic portrayals of such a God. The universe presents many faces. Those who believe they've seen the face of a greater being than themselves may well have; but the hierarchy of greatness
in a universe so large may well extend far beyond any being which would display its face to any human being. To believe that the next step up in greatness from myself is the whole universe would be a horrible presumption of ego. I am not, emphatically, the next best thing to the universe. And the whole universe, if it could speak, has far better things to do than to speak
to me.

May 4, 2017


Fair enough though we have different senses of the use of the word innate. If I say all humans have an innate language ability or if I say that humans are innately good, this does not require any meditation or introspection on the humans' part. Perhaps you are right but practically this excludes most humans who are toiling 60 hours a week for survival and do not have the luxury of meditation. Hence, it is an non-egalitarian innateness. But perhaps God who gave us this innateness is also non-egalitarian. Thank God, that those like Buddha and Christ were egalitarians.

May 4, 2017
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I wonder what 'greatness' really is. To me there is nothing greater than the sweet chirping of the bird with the backdrop of the sound of the sear where I am right now. Or to observe dew on a blade of grass early in the morning. If there is a God then all Her creation must be as beautiful and as great than any other. So, the notion of greater makes no sense. The same holds if there are many gods or no gods but nature. Every species is important and necessary, so none is greater than any other, neither is any part of the universe or any body greater than any quantum particle. This is why I oppose notions like "higher consciousness" and "cosmic consciousness". I just don't see why they are greater than a deep breath I take on top of Mount Kilimanjaro.

May 5, 2017
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Responding to your continuous use of incompleteness as a necessary feature of mechanism, I find it very interesting. You have mentioned the Turing test. What about the halting problem? Is it something like incompleteness. A machine can go on at least for a long time, if not infinitely, with the process in the halting problem, by constructing other machines to carry on the task, by producing another machine and so on recursively. In this regard what about the human mind, can it pass on the task to future after its end because of its mortality? Or is it the mortality a constraint that makes the human mind incapable of grasping incompleteness. I know I am all over the place. I had written some vague paper on this. I will dig it out and send it to you. You can comment if you get time.

May 5, 2017
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Did I? I don't really believe in the Turing test. But it is another topic. It is related. If we accept Church Turing thesis, we can derive incompleteness from the halting problem. I might explain this in more details later.

We can summarize all this by the fact that we begin to understand that we don't know what numbers and machines are capable of. Even very elementary arithmetic appears to be quite transcendental, and explainably so with Mechanism.

The difference between true and false in arithmetic is a bit like the border of the Mandelbrot set: definite, but very complex. For example:

I think human grasp incompleteness. They might not like it, but that is emotional. He makes us very modest.

Machine grasp also incompleteness, they too can prove their own incompleteness. It is "Gödel third incompleteness theorem", that Gödel promised to prove but never did, probably because Hilbert and Bernays will prove it in 1937. Then Löb generalized it beautifully.

My problem is that, when I explain those things, I need to explain a bit of mathematical logic. It is not well known, and frequently misunderstood. Even a great guy like Penrose was wrong on Gödel, and as deter physicists to dig on that issue, alas.

OK. I will read them.

We will have opportunity to come back on this. Incompleteness is a lucky event for Mechanism, as it kills the possible reductionist conception that we might have on machine and number. In fact, I want argue that incompleteness provide literally a theology to the machine, and that it is close to the neoplatonists and neopythagoreans (and many other mystics). It is also testable, because it put strong constraints on what the physical appearances can look like.

In a sense, this leads to a sort of "strong atheism", as there would be no Creator, nor Creation. But in another sense, this leads to a universal machine "neoplatonist" theology, with an "Inner God"  looking like a universal dreamer which can't avoid losing Itself in an (arithmetical) web of "dreams". There is also an "Outer-God", which might be just the arithmetical truth (which transcend us, but might, or not, be a personal god (open question)).

The amazing possibility, is that the inner god can wake up. But it is not clear to me, at this stage, if that provides It with an advantage or an handicap, to survive on the "terrestrial plane".  I still try to figure that out.

May 5, 2017
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Quite beautiful, Priyedarhsi!

It is particularly worrying when "religious" attitudes cause people to turn away from the beauties of this very particular and differentiated world, in pursuit of some presumed other place. Especially so given the various threats to this world by the stresses of population and misuses of technology. One might hope that at least in religion one would find those who would care for our garden. Far too often we hear from those who consider themselves religious their hope that this world will end, that some "purer" one be revealed. Much as they claim worship of "the Creator," they wish creation to have a do-over.

By "great" I had in mind physical scope. If our Sun is a god, as some have supposed, how small must it be before the galaxy -- and that one of how many millions? Still, William Blake's "infinity in a grain of sand" is one of the finer insights. Yet again, is not your deep breath on top of Mount Kilimanjaro enhanced by the commanding view from a great summit?
Best regards,

Thanks! I understand now. Of course it is the small in the scope and scape of the grand that makes it beautiful. I was really thinking of William Blake while writing what I did.I am totally unmoved by miracles such as the parting of the sea as each day I get up and get through with my activities and am still alive is a miracle. Fauja Singh is a miracle (If you know who he is).

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