Don't Know

Just spent the weekend trying to fix some code, when as almost always I find the solution, it took so long because I was looking in the wrong place (to quote Indiana Jones).

Isn't this the NP problem. Its also Turing. Its also the whole problem of finding better algorithms, of which there are proofs. If you could do it quicker wouldn't you? Perhaps you can develop heuristics to speed up the search, like not looking in the same place twice. But it seems problems always manage to get around your heuristics.

The fundamental problem that lies in a problem is that you must solve it, and there is no getting around that. There seems to be some fundamental entropy.

Yet and this is the point you can never know what that is before you try the problem. Even the search to discover the entropy is itself a problem with entropy.

Isn't this "don't know" a much greater truth about the world.

In the thinking of Frege et al you can derive a formula, procedure, proof to derive truth. Once you know this formula you can derive truth again and again. This encourages the idea that all of truth can be encode in formulae. But if you try this you will end up in contradictions due to self-reference. Which is the SRH of this blog. Russel took apart Frege with the "Set of All Sets" paradox. And Godel in turn took apart Russel with his Beq paradox (I am not provable). What looks like the strong arm of certainty becomes pathological when it is turned against itself through self-reference. The better your proof system, the more catastrophic your paradox.

So in the end we "don't know" and never will. Its not a pessimistic statement, its just a glass half full statement. We still have half a glass. We are still able to discover things. But like the "Infinite Employment Theorem" we can never know when the things are all discovered. Ultimately we can only know when all the things are discovered by discovering them, and who is to say we don't discover something new tomorrow. Time must be open ended then, because there must always be time to discover new things. If time was to stop, if a conclusion existed, then we enter the world of paradox.

One approach to SRH is to assume there was a way to find the number of theorem T in advance of counting them. But it will end in paradox because its isomorphic with all the other totalistic type problems. Metrics about the Self are impossible. #TODO.

It is interesting that this "don't know mind" is equated with the True Mind in Zen Buddhism. What is about to happen is genuinely unknown. The Present Moment is full of potential. When we lose sight of this sensitivity of the moment to new occurrences, perhaps a faint bird song occurs or subtle fluctuation in our mood, then our mind has become corrupted and faded.

It seems if there is one rule of this universe that pervades everything from conscious experience through to Science through to Logic and Computation it is the "Don't Know."

So does that mean we now know something, that nothing is absolutely knowable or unknowable? Well we know for sure right now whether we know something, but to expand that to universal status is where the don't know comes in. I know I am writing this blog, that is an empirical certainty, you doubt that you end up undermining your own doubt like Descartes. It seems smart to use your powers of reason to start doubting, but via SRH the more powerful your reason the more powerful the catastrophe for your doubting project when you realise that to unreason reason is a contradiction. You start with reason, or doubt you end with reason or doubt. And so Descartes knew at the very outset of his doubting, and Kant at the very outset of his Critique that they had Doubt and Reason, and they were not going away. As Hegel points out what is the point of using Reason to examine itself, if it is faulty then your conclusion it is faulty will be faulty. So we know at the outset what we know. The problem, the "don't know" begins the moment we start to expand that from Now in any direction. 

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