Doctrines of Space & The Calculus L. Edgar Otto 12-21-11
Encountering these first works in the original and understanding them in the historical context, I ask if Riemann foresaw so much that could be developed into physics- what of the ideas of Lebesgue? For one thing, although I find the standard theory more and more inadequate and absurd especially in the mixing of chiral senses as a source of mass- that Lebesgue grounds the idea of Feynman in the reading of his simplified graphs (and in the concept of higher variations in space structure that is the sums of infinite paths depending on quantized space of integration functions in the more general sense) that we can rotate the Feynman graph 90 degrees for the interchange of field and particle mediation and descriptions. See Lubos here today. Lebesgue turns Riemann's axes for a Brane or Plane around. But can we say then that the calculus of Lebesgue foreshadows the work of Feynman? Or is there an essential step to be made where great thinkers have to find the way in a sea of chaotic thought in a climate of mentors where Nobel Laureates beget Nobel Laureates and the universities lead society in uniform continuity found between the teacher and the student as an enterprise of awakening?
Today, in thinking about the geometry of it, for example I could say that Lebesgue in a sense my own views of space- a quasic distance from the quantum ideas on it. This is very close for he is concerned and asks questions I have asked and said things about that may make one wonder why he felt the need to write it down when the world might certainly see it as vague or pointless to do so or at least not needed to make the point that perhaps only becomes clear at some future time. I do have an inkling that others around him in the dialog did talk about and inspire some of the questions on the mathematics of the time- so again in the context of a lonely genius I may attribute him too much- that is the reaction from admiring students or the rebellious ones who go further in the iconoclasm than the modest desires of their teachers, as in politics.
Today I had some questions for Pitkanen, for he too is foreshadowed in Lebesgue in that there is such a concept of more general space. But it seems those questions synchronously begin to be answered here. For I was wondering where I differ and Pitkanen differs from such calculus in the matter of if his distances between a multi-sheeted geometry (which I imagine more general than Riemann's multi-ply concept of space sheets and re-entrant polyhedral densities if there is multiply connected and distinct surfaces or volumes that include such a point) if there is in a sense between is a quantum concept of distance or a quasic one- for such ideas of abstract distance apply equally well to the undifferentiated concepts of what is a plane or a sphere in the geometry. I note the general idea, as if a proof by construction and alas a geometric or topological picture by Lebesgue considered over just the abstract algebra, that Pitkanens intuition of further levels of a Planck constant, a hierarchy, a fractal like and quasic recursive idea as a possibility, seems to be suggested as a solid grounding in Lebesgue's calculus. But this is not clear, even in the standard physics where perhaps we need further fundamental constants to explain the mass horizon at singularities, that in a narrow and even Diracian nilpotent view, even a rarefied space only of scalars that the idea of a Zero Point energy or minimum level for measure of such things as some assure us the string theory finds for its grounding scales- is an idea not developed enough in our alternative or standard theories- it is perhaps an independent idea from the application of matter and gravity in standard unification models. It is thus universal but does not contain much accessible meaning in the details. Zero point energy is a viewpoint and perhaps goes against deeper ideas of mirrors in absolute spaces such the very general ones described by p-adic theory. But I have not address the Maxwellian question in Pitkanens post- just the earlier one of Is TGD integratible now that I understand such Lebesgue boundary ideas and the primitive idea of applying this to quark confinement as a foundational theory of standard unification that is not even as deep as the topology described. Of course I ask about such distance as if the types are virtual or real, coincident, as perhaps anything we may observe in a mirror.
The hallucination question is inspired by the treatment by Lebesgue of the idea of sets and certain shared points in an interval on a line- this is a case where we ask about the axiom of choice which is independent from the ZF axioms. We know biologically that such a jumbling of our content of consciousness in the way the chemistry and structure of the brain works in animals is necessary that with things a little out of focus one finds the clarity otherwise lost into the background- a matter of cycles and balances. But the choosing of these point like solutions in infinite sets is after all done by such a method of focusing.
Now, a further point, a political one, for those who find it expedient to delay the advancement of science and discourage enquiry in the details. Is our technology a threat, say in the biological sense- of course I personally think to evolve viruses in a lab (and the government asked rather than warning professors not to publish some method of decoding or they to be arrested for early computer ciphers) that the details of such study not be posted in the name of making it easy for terrorists. Well, it has been known for sometime now we can make any virus artificially in the lab (my objection is that in the banishing of diseases those kept in labs have invariably escaped to make epidemics- so what is the zero tolerance for such weapons?) Nevertheless, in the long run it is the very knowledge that would make the cure for such biological's less a threat. The knowledge that will make us all mutually safe as a group or society from the power of even one of its malcontents for each soul is potentially such a malcontent on which there is less likelihood of defense save the containment by ignorance of all free people. Still, just as we had underground testing of the atomic era- we all drank Strontium 90 a children and worried over Polio, it seems to me that given the proper theory we can simulate such tests or effects and evolution of viruses without the direct need to rattle our sabers for the show when other than to find deep wisdom need not do the experimental proofs. But this is a philosophy of science that to a great degree, accepting the idea of historical conflict, Darwin like and Lemark like also, socially, that a people can think ahead for possible surprises- that is be predictors of events that are based on sound science and not just lost down chaotic paths of no return for the good of what in the future is the best of probable outcomes and places where new thought becomes new freedom.
I was going to ask Pitkanen what was his objection to the gauge theory concepts but that has become clearer to me in these more advanced views of space anyway. I just doubt quantum ideas grounding the escape from its confinement of physics enough. I guess we all have private styles if not private languages- even not as poets. So part of it is learning the Pitkanen speak. I think I have addressed some of these questions he asks and tries to use earlier terms to expand on the ideas and the terms. Magnetism, flux tubes, and so on... all the quantum terminology too... I think the Maxwellian part, considering his residual flow in nature, and the explanation of monopoles, and the Diracian idea of a shorting of such forces by at least one monopole, explained by the arithmetic patterns (if not just the counting that is the province of finite things rather than congruences of measure and non-overlapping congruences as refined by Whitehead) by my refinement of the quasic plane where the x and y cannot simply be rotated about the same information. This is a step a little further than the space and presumably a calculus there too of Lebesgue's view of integration of surfaces.
New Scientist has this article- and we certainly need better ways to discuss these concepts of dark-x ,x = matter, energy, fluids etc... sometimes too common a word does not convey the relationship or depth of an idea as we all try to use them for it is not proven the link to what Pitkanen says if the opaque matter if it exists but something exists on many scales... see here, like so many things the established powers go to great lengths to save the face of their complicated but questioned or failing theories- conspiracies (even the great Godel felt this in his eccentricity and that part of the Integer book is a little too speculative for me still) may or not be conscious or linked as they censor and confine our promisingly bright people or damage them where they can only so far fulfill noble expectations that are worthy and help us all. Those who care are cannon fodder for those who do not and it is not clear that anything on this lower level of us great apes really matters to any higher power or each other- or for that matter all our children's futures. We have yet to make a world where morally and ethically at least we become ourselves a higher power not long out of the absurdity of vandals sacking settled people- but we should not be ashamed of our origins for they go back very far and the next stage here in the world for us can hold wisdom to come that is not that far away.
It would have been great to talk one on one to people like Pitkanen over these shared issues in a world of research especially in serious universities and political and social, environmental climate where merit is valued, and a world of enquiry is possible. The young grow lazy and expect much when the cost of existing is much greater than the cost of living yet everything is free.
I wish I had a little more time and was a little further along sooner.
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