Archive for the ‘scientific data’ Category

Godel 3

Monday, July 27th, 2009

So what is this Incompleteness Theorem?

At the beginning of the twentieth century, mathematicians assumed that all of mathematics was a created form [Constructivism] simply utilized to express relations between things, whether or not those things were present in reality. On that basis, it was further believed that if all of the rules of this creative form could be fully expressed that all of mathematics could be known, and all future assertions in mathematics could be determined true or false based upon the formal system developed to do such. An amazing attempt at this process was completely by Russell and Whitehead in the three volume set, the Principia Mathematica. Formalism or Constructivism was assumed to be reasonable, true, and the future of mathematics, and to some degree logic. For the formal system to be functional, it would have to correctly identify all true statements accurately, and create no contradictions [it would have to be both complete and consistent otherwise it would logically fail its purpose.]

Kurt Godel shocked the mathematical world be creating a short Proof, which demonstrated beyond doubt that all formal systems are necessarily incomplete. That in some manner a true statement can be introduced into the formal system, which the formal system could not identify as true. As it turns out, this Godel Phrase actually creates an infinite number of true statements that the formal system cannot identify as true, making any formal system necessarily incomplete, because, once the first Godel number/phrase is inserted, another [G’] is created, which continues without ceasing. Godel’s intense introversion led his announcement of the proof to be less than overwhelming, but other mathematicians of the day made the findings more public within the mathematics community.

Godel’s original proof made the concept of a formal system quite strict, such as the Principia Mathematica level of formalism. Perhaps had he stopped at that point, his work would be non-relevant to the questions of consciousness, but in a later version of his proof, he was able to so simplify the definition of a formal system, while retaining the result of the proof, that this otherwise esoteric bit of mathematics suddenly becomes substantial in a whole host of other intellectual inquiries. These true but unprovable statements, and their existence, have in Nagel and Hoffstader’s words, forever separated the concepts of “true” and “provable.” That is an amazing paradigm shifter for any of us.

Consider: is it not the case that a creative idea which in every way seems fresh, intriguing and true after receiving the insight, would not have been necessarily identified as “true” by your mind prior to that creative insight?

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Neuroplasticity

Sunday, April 26th, 2009

Although epiphenomenalism may be nearly assumed by many doctors and patients alike since it seems to match data related to impaired neurological function, some of the research in neuroplasticity likely refutes the entire concept of epiphenomenalism. Early research demonstrated that when people learn new skills, such as typing or piano, that areas of the motor cortex of the brain actually increase in size to match. Later research demonstrated new brain connections, after some forms of brain injury, sometimes form to areas of the brain which would otherwise have processed information from different areas of function. This process actually restores the lost functioning, even with different areas of the brain processing the information.

Although these studies were fascinating as they showed the neuronal connections and biological functioning of the brain changed as a result of essentially newly learned tasks, some researchers minimized the results with arguments that this was largely a unique ability for repair following injury. One of the more recent studies was a true paradigm changer. In this research, Tibetan Buddhist monks participated in functional brain imaging studies while practicing a compassion based meditation technique. The finding was astounding: monks showed a novel Gamma brainwave pattern in the frontal lobe, which correlated with the subjective sense of blissfulness. This brainwave pattern had never been seen in any non-pathological state before, and its presence and strength was only related to the number of hours of meditative practice. No other demographic factors correlated with the finding, which suggested a clear circumstance in which willed meditative practice altered brain function over extended practice.

Since epiphenomenalism requires that mental process is only an accidental byproduct of neuronal firing, there is no conceivable way that mental process could actually effect the biological structure. This latest research proves just the opposite: that mental process changes the biology of the brain. Clearly then, any form of biological monism cannot account for this research finding. A different model is needed which accounts for the research data.

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Psychiatry and Consciousness

Saturday, January 24th, 2009

One of the most amazing questions I’ve found is the mystery of consciousness. The quest to explore it drove me towards the study of psychology as an undergraduate, and towards psychiatry after medical training. Psychiatry, at least historically, had a depth and breadth that seemed to allow real exploration of questions of consciousness. After more than a decade in the field, and experience in academic and clinical psychiatry, it is truly peculiar to observe the minimal interest of my field in even asking the relatively hard questions. Many colleagues comfortably assume that all the questions of relevance have already been answered in the form of biology.

Until quite recently, consciousness was considered a taboo subject for research or consideration in mainstream academia. Not only ignored or defined into non-existence, the topic was considered quite dead until several authors began raising the timeless questions with new and serious discussion: authors such as David Chalmers, Roger Penrose, and Daniel Denett. The first two of whom used Godel’s Theorem as the starting point of their discussion on mind, brain, and consciousness. The discussion of the forbidden “C” word re-entered both public and academic life for the first time in decades.

David Chalmers has been credited with formulating the “hard question,” which is essentially the question of why is there mental experience at all. Or, how does the physical presence of a brain actually lead to subjective awareness, which he terms “qualia.”

Much more on Godel, Chalmers, Penrose and others later, but this essential question that Chalmers so perfectly framed remains the focus. Why indeed would a complicated physical system, such as a brain, necessarily result in subjective experience for you or for me? Answers to this question range from monistic versions of reality to dualism of various sorts. We’ll start this exploration looking at those two general models and later consider the limitations implied by Godel.

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