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How the gaia hypothesis links in with the spurious history of maths logic + computing

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  1. Synesthesiac
    Premise: Consciousness gives rise to the brain and material reality in a way as of yet we are not entirely sure.


    George Carlin - The Planet Will Be Fine - We may not. The Gaia Hypothesis.


    George Calin predicting the gaia hypothesis by the end. Such an open mind it came intuitively to him, and this intuitive effect relates to the intuitive feeling the scientists I mention below felt. Brilliant speech, from a brilliant mind.

    Why do such great open minds get it? Yet greed driven materialists fail to realize the bigger picture of what the gaia hypothesis implies this meddling with nature is doing?


    http://en.wikipedia.org/wiki/Gaia_hypothesis

    The Gaia hypothesis, also known as Gaia theory or Gaia principle, proposes that all organisms and their inorganic surroundings on Earth are closely integrated to form a single and self-regulating complex system, maintaining the conditions for life on the planet.


    The theory in a succinct 15 minute clip here. Please watch it, it's a brief summary of very important scientific paradigm shift away from previously mechanistically deterministic "selfish" gene theories of evolution.
    BBC Four Beautiful Minds - James Lovelock
    http://www.youtube.com/watch?v=8ndlznLb0Fc


    Epigenetics [< Documentary] is the study of environmental factors on gene expression, and also our physiological states such as stress and other things that result from states of mind, based on environmental factors play a far bigger role on inheritance and (maybe at a stretch) speciation than evolutionary theory (Dawkins, selfish gene). Which is the basis for the Gaia Hypothesis. Its not in conflict with evolution, Darwinian selection still plays a role, but the role seems pretty limited.


    There are two forms of Gaia theory, weak gaia theory and strong gaia theory. The weak gaia theory is pretty much just saying that the earth and the organisms within it are an interconnected system with feedback loops and therefore capable of self-regulating up to a point, widely accepted. Strong gaia theory argues for the system to be considered an emergent type of organism in its own right arising from the complex actions of its smaller constituents, and some take it further and talk about consciousness also being such an emergent property.


    There IS something to be said about a wholistic approach vs. reductionism. The key concept here is that of emergent properties we notice in all of nature. Biology is an emergent property of chemistry, which is in turn an emergent property of physics. From a reductionistic standpoint, if we knew the state of all the subatomic particles in a system we should be able to tell which gazelle the lion will eat. However, such a notion is laughably absurd--you simply cannot know the nature of the system by pure reductionistic methods. You have to accept that there's a lower limit to the units in the system, a basic component that cannot be split.


    This isn't a concept unique to Lovelock. Steven J. Gould said much the same thing in his critique of evolutionary biologists/paleontologists atomizing organisms into their constituent characters and trying to figure out what advantage each character offers the organism. You can't do that-organisms live or die wholesale. The notion of a lobster dying, but "crusher claw with relatively weak dentation" surviving is nonsensical. You've got to look at the organism's position in morphospace as a whole--meaning that the organism, not the trait, is the "pixel" of evolution, as it were (there are exceptions; however, this is the general rule).


    The Gaia Hypothesis states, in essence, that the unit of ecology is the planet as a whole. You've got to understand all of the feedback loops and the nonlinear interactions--something biology has been slow to do and which paleontology, to the best of my knowledge, has not adopted at all. And nonlinear dynamics cannot be fully understood by analyzing the parts--that's a basic concept in nonlinear mathematics.


    Weak gaia is just systems theory applied to the earth and makes good sense, while the strong version is highly controversial to the scientific community. Thus highly interesting to a scientific sceptic :)

    Within gaia theory it's quite reasonable to assert earth shows traits of an organism in its own morphospace/scale of existence, even if in a different environment from typical organisms as we recognise them. It's also quite reasonable to note that it could share similarities to conscious entities instincts for survival. Making it a self correcting system, with complex defence mechanisms for its long term survival, that would encompass all the earth bound sciences, from biology, natural selection, geology, micro-biology, atmospheric physics, climate change, quantum physics, the biosphere, etc, all working in symbiosis.

    The true complexity and interconnectedness of which we don't currently understand, but should strive to as scientists.

    But, the scope of the theory goes further still, in its scope and scale.


    I guess the above argument comes down to how you define nonlife. And if you know the answer to that, in the context of a galactic in extent gaia hypothesis, then you deserve a nobel prize. In fact, more than that.


    But you will need materialistic proof of some sort to be accepted by mainstream science, especially in the physics area, as it currently stands. The greatest most intelligent minds that walked this earth in terms of understanding the machinery of the universe were likely Albert Einstein and Godel, I still think to this day. We would be wise to take a historical note of what Einsteins later years were spent doing and what conclusions he came to, as the scientific community ran off and made 'mainstream' with a set of his theories he himself was deeply uneasy with. Einstein and Godel seemed to reach similar conclusions, but seemingly one of them coped better with the implications of this than the other in the end.


    There seems to be other criteria to win a Nobel in the last twenty to thirty years in physics, or any one of its closely related mathematically constructed cousins. The historical perspective with through which these following statements should be viewed is made imminently.

    * Mathematically eloquent abstractions wrapped up in space time and tied with a topological knots of re-ified infinities seems to meet the criterion.
    * Trying to find truth in further and further materialistic reductionism (to the detriment of any interdisciplinary wholistic considerations)
    * Patterns in data discovered that fill a hole in a long standing particle physics problem that lead us further down the rabbit hole of reductionism, looking ever deeper for something that is likely not even underground.
    * Cosmological scale discoveries that add vague credence to the possibility that the 96% of the universe we simply have to assume is there for the Big Bang theory to work somehow tell us something of any significance to the universe at large, its dark matter on top of fudge factors on top of epicycles; and all predicated on extraneous extrapolation of perturbation theories inferred mass + gravity of solar system bodies applied to the universe; as if the immensity of the universe is impervious to our solar system bound gravitational sample bias.
    * Theories that can not be tested experimentally, even if they tie a nice "theory of everything" knot in the gaps of current shortcomings seem fair game if complex and confusing enough.



    The solid mathematical foundations that a lot of these modern day Nobels are awarded for, have a slightly darker and mirkier past in a historical context. And in fact, the whole materialist myopic view of linear maths as revealing deeper and deeper truths to us about the universe is fatally flawed from the get go. It's a story of how some of our most intellectually stimulated minds untied the previously cosy relationship the universe seemed to have with the certainties of mathematics, and how these facts have been acknowledged but largely ignored. It's a story of how such deep questions being asked back then of such high importance resulted in the fact that when some of the greatest minds of the time engaged their mind with such questions their brain dare not look away from the evidence that perplexed them so much, and how pursuit of meaningful answers to these issues pushed them first to the brink of insanity, then over to madness and suicide.


    But for all the humain tragedy of great minds lost due to seeking meaning from life from maths and logic, what they saw is still true - the intellectuals at the time that took over the consensus opinion, assigning Einsteins work greater credibility than the original creator himself did, whilst in the case of Godels work largely ignoring it; so to this date we have yet to inherit at large the conclusions they themselves made.


    Now, the world that they saw, we still stand at the frontier of as much as they did over fifty years ago.


    George Cantor (1845-1918) was a religious professor of maths who started a paradigm shift in the world of established maths and science, that maybe he did not appreciate at the time. The profundity of a brand new question, not based on previous knowledge or even a similar school of thought in maths at the time; he asked himself "how big is infinity"?


    It’s just an incredible feat of imagination. It’s, to me, the equivalent of taking mind enhancing drugs for that era (1800-1900) Others before him, going back to the ancient Greeks at least, had asked the question but it was Cantor who made the journey no one else ever had, and found the answer. But he paid a price for his discovery. He died utterly alone in an insane asylum.


    The question is what could the greatest mathematician of his century have seen that could drive him insane?


    Cantor had auitary hullicinations from a little boy that he attributed to god as calling him to maths. So for Cantor, his mathematics of the nature of infinity had to be true, because God had revealed it to him.


    Cantor soon discovered he could add and subtract infinities conceptually, and in fact discovered there was a vast new mathematics opening up infront of him - maths of the infinite. This out of the boxing thinking had revealed something special, and he could feel it as a sort of profound insight into the nature of maths he was previously blind to.


    By 1884 Cantor has been working solidly on the Continuum Hypothesis for over 2 years. At the same time the personal and professional attacks on him for his heretical "maths of the infinites" had become more and more extreme. Due to this, the following may of that year he had a mental breakdown. His daughter describes how his whole personality is transformed. He would rant and rave and then fall completely and uncommunicatively silent. Eventually he is brought here to the NervenKlinik in Halle, which is an asylum.


    Even after concerted further effort he could still not solve the Continuum Hypothesis, he came to describe the infinite as an abyss. A chasm perhaps between what he had seen and what he knew must be there but could never reach. He realised that there’s a way in which in order to understand something you have to look very hard at it but you also have to be able to sort of move away from it and kind of see it in a kind of wholistic context, and the person who stares too hard can often can lose that sense of context.


    After the death of a close relative, Cantor went on to say that he "could no longer" even remember why he himself had left music in order to go into maths. That secret 'voice' which had once called him on to mathematics and given meaning to his life and work. The voice he identified with God. That voice too had left him.


    Here I divert from Cantor, because if we treat Cantor’s story in isolation it does little to bridge the gap in the idea that Cantor had dislodged something was part of a much broader feeling of that time. That things once felt to be solid were slipping. A feeling seen more clearly in the story of his great contemporary- a man called Ludwig Boltzmann.


    The physics of Boltzmann’s time was still the physics of certainty, of an ordered universe, determined from above by predictable and timeless God-given laws. Boltzmann suggested that the order of the world was not imposed from above by God, but emerged from below, from the random bumping of atoms. A radical idea, at odds with its times, but the foundation of ours. Ernest Marc one of the most influential er philosopher of science at that time stated: 'I cannot see, I don’t need it, they do not exist so why we should bring them in the game.'


    Worse than insisting on the reality of something people could not see, to base physics on atoms meant to base it on things whose behaviour was too complex to predict. Which meant an entirely new kind of physics – one based on probabilities not certainties. Boltzman worked tirelessly at his idea irrespective, and as Boltzmann got older and more exhausted from the struggle, he'd get mood swings, mood swings that became more and more severe. More and more of Boltzmann’s energy was absorbed in trying to convince his opponents that his theory was correct. He wrote, “No sacrifice is too high for this goal, which represents the whole meaning of my life.”


    The last year of Boltzmann he didn’t do any research at all, I’m talking about the last 10 years. He was fully immersed in a dispute, philosophical dispute, tried to make his point – writing books which were most of the time the same repeating the same concept and so on. So you can see he was in a loop that didn’t go ahead. By the beginning of the 1900’s the struggle was getting too hard him.


    Boltzmann had discovered one of the fundamental equations, which makes the universe work and he had dedicated his life to it. The philosopher Bertrand Russell said that for any great thinker, “This discovery that everything flows from these fundamental laws… comes”, as he described it, “with the overwhelming force of a revelation: like a palace emerging from the autumn mist, as the traveller ascends an Italian hillside,”

    And so it was for Boltzmann. But for him, that palace was at Duino in Italy, where he hung himself.


    A new generation of mathematicians and philosophers, were convinced if only they could solve the problem of the nature of infinity Maths could be made perfect again.

    Godel was born the year Boltzmann died 1906. He was an insatiably questioning boy, growing up in unstable times. His family called him Mr Why.


    What Godel later showed in his Incompleteness Theorem is that no matter how large you make your basis of reasoning your axioms, your set of axioms in arithmatic there would always be statements that are true but cannot be proved. No matter how much data you have to build on, you will never prove all true statements.


    There are no holes in Godels argument. It is, in a way, a perfect argument. Thus the present tense of this paragraph, it stands impeach-ably strong to this day. The argument is so crystal clear, and obvious.


    To this day, very few want to face the consequences of Godel. People want to go ahead with formal systems, and Godel explodes that formalist view of mathematics that you can just mechanically grind away on a fixed set of concepts. There’s a very ambivalent attitude to Godel even now a century after his birth. On the one hand he’s the greatest logician of all time so logicians will claim him but on the other hand they don’t want people who are not logicians to talk about the consequences of Godel’s work because the obvious conclusion from Godel’s work is that logic is a failure - let’s move onto something else, as this will destroy the field.


    Godel too felt the effects of his conclusion. As he worked out the true extent of what he had done, Incompleteness began to eat away at his own beliefs about the nature of Mathematics. His health began to deteriorate and he began to worry about the state of his mind. In 1934 he had his first breakdown. But it was after he recovered however, that his real troubles began, when he made a fateful decision.


    Almost as soon as Godel has finished the Incompleteness Theorem, he decides to work on the great unsolved problem of modern mathematics, Cantor’s Continuum Hypothesis. Godel, like Cantor before him, could neither solve the problem nor put it down - even as it made him unwell. Again, the mind so engaged the brain dare not look away from the evidence that perplexed the mind so much. He calls this the worst year of his life. He has a massive nervous breakdown and ends up in a sanatoria, just like Cantor himself.


    Alan Turing is the next person to enter this brief history. Turing was most well known for breaking the Enigma code; but he is also the man who made Gödel’s already devastating Incompleteness Theorem even more devastating.


    Computers being logic machines was Turings predominant world view, and he showed that since they are logic machines incompleteness meant there would always be some problems they would never solve. A machine fed one of those problems, would never stop. And worse, Turing proved there was no way of telling beforehand which these problems were.


    With Gödels work there was the hope that you could distinguish between the provable and the unprovable and simply leave the unprovable to one side. What Turing does, is prove that, in fact, there is no way of telling which will be the unprovable problems. So how do you know when to stop? You will never know whether the problem you’re working on is simply fundamentally unprovable or extraordinarily difficult. And that is Turing’s Halting Problem.


    Startling as the Halting problem was, the really profound part of Incompleteness, for Turing, was not what it said about logic or computers, but what it said about us and our minds. Were we or weren’t we computers? It was the question that went to the heart of who Turing was.


    This tension between the human and the computational was central to Turing’s life – and he lived with it until, the events which led to his death. After the war Turing increasingly found himself drawing the attention of the security services. In the cold war, homosexuality was seen as not only illegal and immoral, but also a security risk. So when in March 1952 he was arrested, charged and found guilty of engaging in a homosexual act, the authorities decided he was a problem that needed to be fixed.


    They would chemically castrate him by injecting him with the female hormone, Oestrogen.
    Turing was being treated as no more than a machine. Chemically re-programmed to eliminate the uncertainty of his sexuality and the risk they felt it posed to security and order.
    To his horror he found the treatment affected his mind and his body .He grew breasts, his moods altered and he worried about his mind. For a man who had always been authentic and at one with himself, it was as if he had been injected with hypocrisy.


    On the 7th June 1954, Turing was found dead. At his bedside an apple from which he had taken several bites. Turing had poisoned the apple with cyanide.


    Turing had passed, but his question remained. Whether the mind was a computer and so limited by logic, or somehow able to transcend logic, was now the question that came to trouble the mind of Kurt Godel.


    Having recovered from his time in the mentally unstable sanctum. But by the time he got here to the Insititute for Advanced Study in America he was a very peculiar man. One of the stories they tell about him is if he was caught in the commons with a crowd of other people he so hated physical contact, that he would stand very still, so as to plot the perfect course out so as not to have to actually touch anyone. He also felt he was being poisoned by what he called bad air, from heating systems and air conditioners. And most of all he thought his food was being poisoned.


    Peculiar as Gödel was his genius was undimmed. Unlike Turing, Godel could not believe we were like computers. He wanted to show how the mind had a way of reaching truth outside logic. And what it would mean if it couldn’t.


    So, why so convinced was Godel that humans had this spark of creativity? The key to his belief comes from a deep conviction he shared with one of the few close friends he ever had, that other Austrian genius who had settled at the Institute, Albert Einstein.


    Einstein used to say that he came here to the Institute for Advanced Studies simply for the privilege of walking home with Kurt Godel. And what was it that held this most unlikely of couples together. On the one hand you’ve got the warm and avuncular Einstein and on the other the rather cold, wizened and withdrawn Kurt Godel. The answer for this strange companionship comes I think from something else that Einstein said.. He said that "God may be subtle but he’s not malicious." And what does that mean? Well, it means for Einstein is that however complicated the universe might be there will always be beautiful rules by which it works. Godel believed the same idea from his point of view to mean, that God would never have put us into a creation that we could not then understand.


    The question is, how is it that Kurt Gödel can believe that God is not malicious? That it’s all understandable? Because Gödel is the man who has proved that some things cannot be proven logically and rationally. So surely God must be malicious? The way he gets out of it is that Gödel, like Einstein, believes deeply in Intuition - That we can know things outside of logic, maths and computation; because we just intuit them. And they both believed this, because they both felt it. They have both had their moments of intuition, moments of sudden conceptual realisation that were by far more than just chance.


    Einstein talked about new principles that the mathematician should adopt closing their eyes, tuning out the real world you can try to perceive directly by your mathematical intuition, the platonic world of ideas and come up with new principles which you can then use to extend the current set of principles in mathematics. And he viewed this as a way of getting around the limitations of his own theorem. He no longer thought that there was a limit to the mathematics that human beings were capable of. But how could he prove such subjectives?


    The interpretation that Gödel himself drew was that computers are limited. He certainly tried again and again to work out that the human mind transcends the computer. In the sense that he can’t understand things to be true that cannot be proved by a computer programme. Gödel also was wrestling with some finding means of knowledge which are not based on experience and on mathematical reasoning but on some sort of intuition. The frustration for Gödel was getting anyone to understand him.


    Gödel was trying to show what one might call mathematical intuition of the kind we see in the brains of Synesthesia Savants such as Daniel Tammet in current times, and he was demonstrating that this is outside just following formal rules. What he had shown was that for any system that you adopt, which in a sense the mind has been removed from it because it's you that's used to lay down the system, but from there on mind takes over and you ask what’s it’s scope? And what Gödel showed is that it’s scope is always limited and that the mind can always go beyond it.


    Here’s the man who has said, certain things cannot be proved within any rational and logical system. But he says that doesn’t matter, because the human mind isn’t limited that way. We have Intuition. But then of course, the one thing he really must prove to other people, is the existence of intuition. The one thing you'll never be able to prove. It would be synonymous in many regards to trying to prove the strong version of the gaia hypothesis.


    Because he couldn’t prove a theorem about creativity or intuition it was just a gut feeling that he had and he wasn’t satisfied with that. And so Gödel had finally found a problem he desperately wanted to solve but could not. He was now caught in a loop, a logical paradox from which his mind could not escape. And at the same time he slowly starved himself to death.


    Using mathematics to show the limits of mathematics is…is….is psychologically very contradictory. It’s clear in Gödel’s case that he appreciated this - his own life has this. What Gödel is, is the mind thinking about itself and what it can achieve at the deepest level.


    It's a paradox of self-reflection. The kind of madness that you find associated with modernism is a kind of madness that’s’ bound up with not only rationality but with all the paradoxes that arise from self-consciousness from the consciousness contemplating it’s own being as consciousness or from logic contemplating it’s own being as logic.


    Even though he’d shown that logic has certain limitations he was still so drawn to the significance of the rational and the logical. That he desperately wants to prove whatever is most important logically even if it’s an alternative to logic. How strange and what a testimony to his inability to separate himself - to detach himself from the need for logical proof; Gödel all of all people.


    Cantor originally had hoped that at its deepest level mathematics would rest on certainties, which, for him, were the mind of God. But instead, he had uncovered uncertainties. Which Turing and Godel then proved would never go away; they were an inescapable part of the very foundations of maths and logic. The almost religious belief that there was a perfect logic, which governed a world of certainties had unsurprisingly unravelled itself.


    Logic had revealed the limitations of logic. The search for certainty had revealed uncertainty.


    The notion of absolute certainty, is, there is no absolute certainty, in human life, in maths, in logic neither in science. The only certainty that has withstood the test of time to date is; that what we think is certain and true has a limited axiomatic scope, and the conscious mind is the only force in the universe that can transcend proclamations of truth by virtue of conceptualising and defining its limited scope, thus transcending certainties to higher values of truth it itself previously set the scope of. In this regard, focussed right by powerful minds, it's self transcendental, and could maybe eventually (if the trend continues) reveal a realm approaching the maths and dimensions of the infinite, where the amount of axioms nears the infinite and where logic and turing machine computation as we recognise it simply fails and we end up with a conscious universe of immense complexity, the complexity of which our current maths, computer models and materialistic sciences can't even detect or comprehend.

    Maybe such an immensely universally complex system already exists. And maybe its the field of consciousness everything in the existing universe shares. We just have to reach a higher state of consciousness and awareness to become aware of the conscious attributes of things we don't typically ascribe consciousness to. Everything is alive, just at different levels all relevant to each others level of conscious transcendance.


    Bzzzzzt. Reality check. Thats the dream.


    But if consciousness in its normal form is indeed non computational, non algorithmic and not based on logic (incompleteness theorem) associated with turing machines then how are we ever going to try to understand it in terms of them without just tying ourselves up in knots made of the same paradoxes that drove the aforementioned geniuses mad?

    And how can we solve the mystery of consciousness if neuroscientists do indeed have the cause and effect the wrong way round? It seems explaining consciousness with reductionist examining of brain function is a fruitless, but yet noble, quest many have embarked on. Consciousness is universal.

    To finish, applying Godels theorem more vigorously to current dominant paradigms could have such a catalysing effect in developing new, mathematically sound theories, based on more creative functions of human inspiration.

    I revel in scientific unknowns and theories being falsified and replaced by a better theory, personally. I have no pet theory I'm emotionally attached to.

    But some would likely end up having breakdowns comparable to the ones mentioned above, if say the Big Bang theory was proved wrong or statistically impossible based on the sort of scientific reasoning we would subject to other areas of science, or evolution insignificant in the large scheme of things, what would the reaction be? I get a lot of religious zeal when I dare argue with cosmologists, always on the attack implying an emotional attatchment to their theory. I don't know how their egos could handle it ... and if we should be sensitive or blunt.

    The problem is that today, some knowledge still feels too dangerous.
    Because our times are not so different to Cantor or Boltzmann or Gödel’s time.
    We too feel things we thought were solid, being challenged, feel our certainties slipping away.
    And so, as then, we still desperately want to cling to belief in certainty.
    It makes us feel safe.
    At the end of this journey the question, I think we are left with, is actually the same as it was in Cantor and Boltzmann’s time.
    Are we grown up enough to live with uncertainties?
    Or will we repeat the mistakes of the twentieth century and pledge blind allegiance to yet another certainty?

Comments

  1. rawbeer
    This was a great read! Thanks!

    I often find myself thinking of the fact that logic is limited by dualism - the concept of Unity, of One, is unbearable to logic because, in logic's view, One is either something to be broken down into smaller units or something to be added to another One to create a set of units. "Logic abhors unity" just as nature abhors a vacuum. And so no logical thought can pass beyond the pillars of dualism. Logic and reductionism simply have no use for the concept of One, other than as a starting point for some operation (when in fact it is an end point).

    Therefore the ultimate expression of logic is the paradox of two things being one, or one thing being two. Absurdity is the ultimate expression of logic and is the essence of modernism, because it is the end-point of logical, reductionist thought. The only escape from the modern absurdity it to reverse our course and seek holistic conclusions...by pursuing reductionism we are like the stubborn traveler moving further and further down the wrong road.

    Anyway I need to read more about these poor geniuses and their explorations!
  2. Synesthesiac
    A lot of it is not textbook knowledge. They tend to publish the good points of what the contributed, not the personal bads. Even wiki is bad at giving a good picture. But when you read the books of people close to them the true nature of the story becomes more clear.
  3. Calliope
    A quick question about how you understand the concept of organism related to the Gaia hypothesis, and some semi-random suggestions about your ideas Syne. Just some things to think about really, not arguments for or against. :)

    So, first:
    What are the properties something must have to count as an organism? I ask because while I find the weak version of GH appealing and true (though how useful, I dunno) the strong version, it sees to me, owes us an account of just that, and giving one may lead it into trouble. Roughly put, one property an organism needs to count as such, i think, is a means of self-replication. Not sure if this shows the strong GH is a non-starter, but I can't get my head around how Gaia has this. Perhaps I'm going wrong here, but it is something that has puzzled me.

    A suggestion: don't leave out the impact Russell's discovery of the paradoxes in Cantor's set theory (the set of all barbers who shave everyone who does not shave themselves!!) either as part of the reason Cantor became so despondent, or as a central cause of the enormous amount of debate and work on the foundations of mathematics in the early 20th century. It was very troubling to Cantor, but many other mathematicians as well, and it influenced among other things Hilbert's program to formulate a finitistic and, in your terms, mechanistic, formulation of mathematics, in order to circumvent the uncertainties introduced by taking completed infinities to actually exist (see Hilbert's "On the Infinite" if you are not already familiar). This then of course ties back into your comments about Gödel's incompleteness results.

    About which a further comment:
    I'm not sure this has any particular effect on what you want to say about incompleteness or what it may show us about the (purported, lol) non-mechanistic, non-Turing-machine nature of consciousness, but I wanted to suggest being a bit clearer in describing what Gödel actually showed. He did not show that there are some truths that cannot be derived or proved in a system of logic. What he showed was that for any system of logic sufficiently rich to model arithmetic, there will be sentences formulable in that system which, *if* the system is consistent, will not be derivable in that system, yet will be obviously true to anyone who has the concepts adequate to understand what they say. But it it always possible to generate from such a situation a expanded system in which they are provable. So we get a picture of an ever expanding outward set of systems of logic which can capture these truths, even though they can, so to speak, never catch up.

    Most people understand Gödel to have, with these results, definitively shown that Hilbert's program was completely undermined. I am inclined to agree, but there is a very intersting book (and some papers as well) by Michael Detlefsen (Hilbert's Program) who argues this is mistaken. I can't reproduce his arguments here, they are too complex and long, but Mic makes a petty good go of resuscitating at least some central elements of Hilbert. You might be interested to have a read. I'm not clear in my mind what consequences would follow from Mic being right about this, in particular for the idea that Gödel shows us we can't be turing machines, but it is at least suggestive that some kind of computational model of mind is possible, at least insofar as it is the incompleteness results that are a linchpin in arguing the contrary.
  4. Calliope
    A quick question about how you understand the concept of organism related to the Gaia hypothesis, and some semi-random suggestions about your ideas Syne. Just some things to think about really, not arguments for or against. :)

    So, first:
    What are the properties something must have to count as an organism? I ask because while I find the weak version of GH appealing and true (though how useful, I dunno) the strong version, it sees to me, owes us an account of just that, and giving one may lead it into trouble. Roughly put, one property an organism needs to count as such, i think, is a means of self-replication. Not sure if this shows the strong GH is a non-starter, but I can't get my head around how Gaia has this. Perhaps I'm going wrong here, but it is something that has puzzled me.

    A suggestion: don't leave out the impact Russell's discovery of the paradoxes in Cantor's set theory (the set of all barbers who shave everyone who does not shave themselves!!) either as part of the reason Cantor became so despondent, or as a central cause of the enormous amount of debate and work on the foundations of mathematics in the early 20th century. It was very troubling to Cantor, but many other mathematicians as well, and it influenced among other things Hilbert's program to formulate a finitistic and, in your terms, mechanistic, formulation of mathematics, in order to circumvent the uncertainties introduced by taking completed infinities to actually exist (see Hilbert's "On the Infinite" if you are not already familiar). This then of course ties back into your comments about Gödel's incompleteness results.

    About which a further comment:
    I'm not sure this has any particular effect on what you want to say about incompleteness or what it may show us about the (purported, lol) non-mechanistic, non-Turing-machine nature of consciousness, but I wanted to suggest being a bit clearer in describing what Gödel actually showed. He did not show that there are some truths that cannot be derived or proved in a system of logic. What he showed was that for any system of logic sufficiently rich to model arithmetic, there will be sentences formulable in that system which, *if* the system is consistent, will not be derivable in that system, yet will be obviously true to anyone who has the concepts adequate to understand what they say. But it it always possible to generate from such a situation a expanded system in which they are provable. So we get a picture of an ever expanding outward set of systems of logic which can capture these truths, even though they can, so to speak, never catch up.

    Most people understand Gödel to have, with these results, definitively shown that Hilbert's program was completely undermined. I am inclined to agree, but there is a very intersting book (and some papers as well) by Michael Detlefsen (Hilbert's Program) who argues this is mistaken. I can't reproduce his arguments here, they are too complex and long, but Mic makes a petty good go of resuscitating at least some central elements of Hilbert. You might be interested to have a read. I'm not clear in my mind what consequences would follow from Mic being right about this, in particular for the idea that Gödel shows us we can't be turing machines, but it is at least suggestive that some kind of computational model of mind is possible, at least insofar as it is the incompleteness results that are a linchpin in arguing the contrary.
  5. Synesthesiac
    Planets are self replicating. Not only are we made up of the elements that result from fusion in stars but the planets are too, as sagan says, we are recycled star dust.

    The universe did not start with a big bang. Thats a fanciful fairy tale and a testament to the malleability of maths as a form of truth and logic when applied to a material, yet plural, universe.
    http://en.wikipedia.org/w/index.php?title=Plasma_cosmology&oldid=88918621#Overview

    Materialism is ultimately a philosophy based on belief, not evidence.

    Nice info, thanks. I still consider Godels incompleteness theorem the last thing of value a philosopher added to the progress of science.

    I know :)

    Despite my concise readers digest version above. The theorem is obvious, intuitive almost ;) . And it's quite obviously un-impeachable in it's brilliance, profundity and simplicity. Irrespective of it's deeper meaning relating to the matrix of maths and logic material science is precariously predicated on.

    Godel took Occams Razor and sharpened it with the power of his mind.

    "Any intelligent fool can make things bigger and more complex... It takes a touch of genius --- and a lot of courage to move in the opposite direction." - Albert Einstein

    Which is really what this thread is getting at, the power of the mind and consciousness over any mathematical, logical system and resulting physical science; Einstein seemed to realize this in his later years even as the scientific community ran off and made 'mainstream' the science truths and mathematical absolutes he himself was deeply uneasy with.
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