hythloday, 2 of ???

• one difference between us is the overall area we view this from... to me this is not just about mathematics, the idea of a priori, of self cause, it's bound up in religion, law, all sorts of things.  These mathematical debates are part of philosophy.  The Godel angle has to do with identifying there is a part of reason that computers cannot do, and Godel proved that.  that is a brick in the conversation I'm  having.  You want to talk just math... ok, but once again, that's just a subtopc
• that I barely make an argument?  what are you arguing against?  I am meandering?  I'm a skeptic, I gather t he extensions, then reflect on possible abstractions.  I try to make clear when I am showing something up for analysis, and when I have already made a conclusive analysis, and I'm also  generally rerunning "conclusive" analysis to see if I can trip it up.
• The relevancy of GIT to consciousness is merely that however humans arrive at their axioms, it's not from a rule system like second order logic, they use another method.  Furthermore, NOTHING could possibly arrive at them that way, the first rule system needs something else to establish it.  I am fine with that being good old trial and error.
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• 17:00) Russel?  why do I mention it... but you say possibly relevant
• I say I'm elevating living things' "understanding" or, alternately I see the phenomenon.  
• Doing this without foundation?  elevation, perhaps, but at least I admit it, but I also said I was just "seeing a phenomenon".
• I agree none of these things imply, or "speak to" human awareness... nor animal awareness, in and of themselves, those phenomenon are indicated by other experiences... HOWEVER, it's interesting that we, the starting set of aware things (in some sense)
• my interest is not in finding a platonic way to establish axioms, I'm fine with emperical systems, e.g. trial and error.  
• I don't have to defend the Penrose system, I'm just presenting it as interesting, I don't -believe- it.  The part I overlap is the use of quantum computing in brains, so I find it interesting that he says this is a way to establish axiom in a somewhat sure, platonic, pure, way.    That's kind of hopes and dreams mathematical logicians have... not me!  but it is an interesting thought
• agreement on "brains doing calculus", calculus is one way of describing what it's trying to estimate
• I think one issue with out discussion is, for example, the subtitle just the math discussion, because the argument I endorse of Penrose' and it's not just his, is the demonstration there is something beyond math as we currently understand it.  What I like about Penrose' technique is that unlike mystics and philosophical intuitionalist is that instead of saying "see, math won't do it" he's like, "we can expand out understanding of math".  He puts it as having access to a Platonic realm which is a bit too much for my taste, but I think that's can be seen as a metaphor for coming up with a mathematics of axioms.  It's just got to be a new field of math, that's what Godel showed, the Hilbert approach being limited to a traditional type of formalism that isn't sufficient.
• Regarding raising the importance of understanding, it's a bit more complex... it's also narrowing the scope of understanding... it works at the axiom level once you have reduced something to it's simple basis, but logic and reason work much better at the macroscopic level. Really, understanding is only useful for things that really and truly are "obvious"... it's what makes them obvious.
• if you believe in the qubit... if you think QM is just a statistical description and there are no superposed states really... then the qubit is impossible.
• quantum computer will have structural elements: of course, and it requires classical parts, but how will the parts be hidden from the user?  
• Forget Penrose, I'm saying that given our agreement on how brains work things out over time, quantum computing, while limited, is good at that type of thing.  Like catching something taking calculus... if you have a simple model that does approximations, plus a quantum computer, you can run the simulation a lot and take the most successful run.  Your answer won't be perfect, you're not using a perfect model... you BRUTE FORCED it, as we'd call.
• deep understanding and high level questions... I think answering how consciousness works is a pretty deep understanding sort of question.
• the point of using different types of logical thinking at different levels, C++, machine language, transistors, is that if something at a low level contradicts some higher level idea, then the higher level is "wrong", that is, something of an approximation.
• (~38:00) EXAMPLE: an turing machine doesn't model mechanical failure... it doesn't m odel corrosion, or being altered because of a cosmic ray, so if someone argued a computer was perfect, should run for ever, should never break from an infinite loop, for example, the transistor level will explain why THEY ARE WRONG.  You cannot "violate" a lower level.
• on heuristics vs analytics... this is my love as a programmer.
• evolution isn't going to wait around for QM... wtf does that mean?  HOW OLD is photosynthesis.
• 44:00) LEVELS
• the idea that quantum mechanics is low level
• level in computer design
• I don't think the brain is too analagous to a computer but I do think it can be made to do computation
• But cells have this kind of reactive analog to a computer too
• cells are RIDICULOUSLY COMPLEX
• the question of is the consciousness in the circuitry or algorythm, the stuff or the software... that's the question.  I vote the stuff.  The software flavors it.
• Wikepedia quote you emphasize.  THE SECOND incompleteness theorem.  You said to make evidence for the comment about arithmatic... on the page, also, I made the video with Oxford and Stanford characterizations... and the next sentence after the one you highlight.
• in the end you confuse me about the issue of proving axioms... some people thought we could, that's all.
• Penrose's argument is that Godel shows a rule system can't prove itself, that you always need another rule system to establish the one you are using, that you can prove in.  But it doesn't mean it's not possible to establish it with something different than a formal rule system as we now know it.  I'm fine with empericism... Penrose wants something more like a formal system still.
• math was undermined in terms of what was HOPED for it.
• I believe Godel proved it was free of INTERNAL contradictions.