- The notion of "free will" is well-defined to the satisfaction of just about every rigorous theorist. We can prove mathematically that every algorithmically finite system will perceive itself to have something exactly analogous to "free will", it is a simple consequence of mathematics. The internal uncertainty is mathematically required in any context, but a context always exists in which there is no uncertainty for the same system.
- The human mind is algorithmically finite by every mathematical test for such things. These tests work on "black box" systems; their efficacy does not rely on having any knowledge of the system internals. There is no test for the opposite -- the best one can assert is that the nature of a system is inconclusive -- but this inconclusivity does not seem to be a necessary assertion in this case.
- The brain is computationally inferior to modern silicon in every aspect except one: memory reference rates, which the human brain outstrips silicon by about three orders of magnitude for conventional hardware. The mathematical definitions of general intelligence (see Hutter et al) that have been proven in the last few years and are generally accepted proscribe an implementation that is bound by effective reference rates. We can reengineer silicon to address this, but until very recently not much effort has gone toward this outside of narrow supercomputing domains; a lot of this is the result of basic architectural differences between the human brain and silicon process technologies.
- Among rigorous theorists (i.e. not philosophers playing semantic games and waxing eloquent), consciousness is generally agreed to be a necessary emergent property of all large-scale systems capable of algorithmic induction (the generally proven architectural model of intelligence in mathematics). This is not the "big question" that it used to be, but you dismiss it out of hand and assert that it is something extra and mysterious. Since the architecture of the human brain is a very good match for algorithmic induction (its structures and behaviors map very well into what is expected in that model), it should not be surprising then that the human brain expresses consciousness. Note that quantum mechanics is orthogonal to intelligence and therefore consciousness; QM is purely time-domain, intelligence is purely space-domain, and you cannot translate time-complexity into space-complexity (though you can go the other direction).
Those are my off-the-cuff technical remarks without having read the entire article yet. We now have a fundamental understanding of intelligence and intelligent systems in mathematics that we have never had even five or six years ago. What is interesting is that our understanding now makes it patently obvious why everything we came up with previously was incorrect. The truth is far more elegant and slightly stranger mathematically than what has long been imagined. It surprises most people to discover that we never had a general mathematical basis for intelligence in the 20th century to work from.
You will be hearing a lot more about this in the next three years or so. It still has not filtered out of the hardcore research circles, though it IS moving into development phases.
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- The notion of "free will" is well-defined to the satisfaction of just about every rigorous theorist. We can prove mathematically that every algorithmically finite system will perceive itself to have something exactly analogous to "free will", it is a simple consequence of mathematics. The internal uncertainty is mathematically required in any context, but a context always exists in which there is no uncertainty for the same system.
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I had not heard of any 'mathamatical' description of free will. Do you have any links to this?
I find it interesting that the 'internal uncertainty is mathematically required' in any context. That goes along with the two excerpts I posted in post 16.
I don't quite follow how the same system can then have a different context wherin there is no uncertainty. It seems to me that if someones actions are entirely predictable then one can suppose they don't have free will? (although I guess you could construct some scenarios like something with lab rats where their environment pushes them down very predictable paths)
"Note that quantum mechanics is orthogonal to intelligence and therefore consciousness; QM is purely time-domain, intelligence is purely space-domain, and you cannot translate time-complexity into space-complexity (though you can go the other direction)."
Well, so you are concuring with what is in this paper, in that consciousness arises from physical interactions. I am unaware that it is universally agreed upon that quantum mechanics is responsible for Consciousness, rather that it is thought that it has to be a part of any explanation. And I believe at a singularity it is theorized that it might be possible to go in the other direction (space/time). Could be wrong about this...?
I don't know what memory reference rates are (memory I assume), or how they are calculated, but it seems to me that there are a great deal of problems with HOW these computing rates are calculated. (see my example on babies and the chess graph) Because they operate in different ways.
You admit that almost everything that was previously constructed to explain Consciousness has been incorrect, and that a lot has still not been worked out, yet find fault in that I find Consciousness very mysterious. I don't think the issue is very clear cut in mainstream science at all.
However, obviously you are well versed in these issues, I would appeciate your comments on the computing section of this paper...
you equivocate between a narrow definition of intelligence and consciousness.
your "faith" requires that consciousness be material.