You may remember, from a long time back, that there was a “Science Gate” episode at the New Forest Observatory.  You can read about it here if you scroll down to the section “Godcidentals”.

I was contemplating the “Science Gate” episode when suddenly a whole bunch of thoughts and ideas flooded in.  I don’t think I have lost the plot (but unlike my Dad I don’t have a piece of paper to prove it) but here’s the basic idea anyway.

Can computers think about themselves?  Well as they cannot think, then it is quite obvious that they cannot reflect on their own existence – but we can!
It is this ability of the brain to reflect upon itself, our ability to hold a conversation with ourselves, in our head, that makes us unique.  Can some animals “think things out”?  Almost certainly. Does that mean that some animals may feel “spirituality” – it disturbs me very deeply to say, yes quite possibly (elephants for example).
When you hold a conversation with the voice in your head, your brain is acting anything but like a digital computer (as we currently know it).  I am 100% certain that the brain does not operate, even at some deep/low level as a quantum computer – but I think it is quite clear that it does not operate as a simple “Turing Machine”.
The ability to hold a rational conversation (or irrational if you prefer) with the voice in your head is intriguing.  Is the voice “in there” or is it “out there”?  I think it is clear to most of us that it is “in there” but you can see that for people who “hear voices” that it could be perceived as being from “out there”.  Having this constant companion, which for some people is more detached from “self” than others is extremely interesting.  Some call this companion their “Muse”.  I think it is the whole basis of spirituality and religion.  It is what gives (some of) us the feeling, or belief, that there is something that is bigger than us, something that is more knowing and more powerful than us.  The ability of the brain to ponder itself introduces a recursive property to brain function which I don’t think we’ve even begun to explore.  I believe that one of the consequences of this “recursive” nature of brain operation is that (some of us) can work with the infinite, and juggle not only infinite quantities, but even higher orders of infinities (Georg Cantor), and that is quite an achievement for a blob of grey matter that is of very finite size and composition.
And therein lies the link between God, the infinite, spirituality, and madness.  Whom the Gods would destroy, they first make mad, as the saying goes.  Most (if not all) of the mathematicians/physicists who spent too much time contemplating the infinite (and in particular the Absolute Infinite), basically lost the plot.  A few of the great mathematicians (Godel, Cantor, possibly Boltzmann) believed that the absolute infinite, the Ein Sof, was indistinguishable from God.  Possibly so.  Our brains seem capable of handling the “sub-infinities” and their properties, which is in itself quite remarkable for a small blob of grey jelly.  This ability to contemplate such enormous quantities, quantities well beyond anything in our day to day experience, is what could lead to the feeling that there is something much bigger than us and more knowledgeable than us.  It enables us to feel awe when we look up and appreciate what vastness there is when we view the Milky Way.  And it is this feeling of awe that can also be interpreted as a feeling of spirituality that eventually leads to us trying to “normalise” these anything but normal thoughts by grounding them in our man-made religions.
I believe the Ein Sof will always be just beyond our reach, even with our near infinitely powerful recursive brain.  The Ein Sof may, or may not even exist – and as the Ein Sof is very likely what we call God, the same goes for God as well.  BUT, whatever the ultimate limitations regarding the potential of that lump of grey matter in our heads, I think it is very clear that we are not using even the tiniest amount of its actual capabilities in our day to day activities.  Even though our pathetic mathematics and Physics stretches most of us to our intellectual limits, it will only be when we understand the full potential of the recursive ability of our brains that we will make the next great leap forward. 
Some of the Ancient Greeks believed that you could “think anything out” – basically you didn’t need to perform any experiments at all, you could do all the experimentation in your mind.  I now understand what they were saying.  So some guys a few thousand years ago had already worked this stuff out – amazing!!
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