Saturday, November 26, 2005

Aristotle and the Logic of the Natural World

Aristotle's logic, especially his theory of the syllogism, has had an unparalleled influence on the history of Western thought. It did not always hold this position: in the Hellenistic period, Stoic logic, and in particular the work of Chrysippus, was much more celebrated. However, in later antiquity, following the work of Aristotelian Commentators, Aristotle's logic became dominant, and Aristotelian logic was what was transmitted to the Arabic and the Latin medieval traditions, while the works of Chrysippus have not survived.

First and formost one should be drawn to the very highlighted statement emblazoned at the top of this blog.

PLato saids,"Look to the perfection of the heavens for truth," while Aristotle saids "look around you at what is, if you would know the truth"

I have to move quick forward here and reveal why the thinking is quite intense in terms of what such logic would have been revealling by "looking around you at what is." While I recognize this basis implanted in the natural world, such divisions arises from what had already existed. What we could accesss, as tangible realities of the ideas around us. "From whence they come?"

So maybe a list of the maths involved so far? If we can wrap these maths then what had we done from the perspective of the natural world? Would such creation of a new math help here?:) I have an idea, but all that thngs that currently exist and that will exist are already here. We just have to access them right? So what would support such adventures froma philosophy that had endured to realites of the natural process from the logic of a math? What math would this be?:)

  • Algebra

  • Geometry

  • Trigonometry

  • Calculus (single variable)

  • Analytic Geometry

  • Linear Algebra

  • Ordinary Differential Equations

  • Partial Differential Equations

  • Methods of approximation

  • Probability and statistics

  • Real analysis

  • Complex analysis

  • Group theory

  • Differential geometry

  • Lie groups

  • Differential forms

  • Homology

  • Cohomology

  • Homotopy

  • Fiber bundles

  • Characteristic classes

  • Index theorems

  • Supersymmetry and supergravity

  • K-theory

  • Noncommutative geometry (NCG for short)

  • So the idea is that Plato and Aristotle stand together, as a basis of what is happening in our world now. Between those of science and the resulting needs for experimentation. The roads to lead from the underlying avenues of philosophical thought, that would include math develoepment.

    Now how is this possible you ask? How is it possible such logic coud have been so revealling of nature that we would strive to find it's meaning in patterns underlying the nature of this reality, are actually abstract rules of engagement, that had been developed through philosophical thought? How so?

    If we look at the number of mayh creations what uses are these when moved into the basis is of the natural world? Would you not think these modes of thinking would be tempered by such logic, that math would find it's birthing as to the need for such expressions from this natural world?

    So part of the realization is that the creation of the math had to have already existed in the forms of natures response, and that such access gained to these ideas, are worth noting as a means to what already existed in nature. That is my logic:)


    So is there a method to the madness of all these tidbits of information that would wrap all of this in a easy way to divine the logic of the natural world? Is it beyond comprehension? I don't believe so, or why would I waste my time as a lay person, to move into this world of a higher standard of abstract thought and developing sciences, to wonder about the origins of the nature of this reality and the cosmolgical equivalent of asking what happened in that beginning of creation?

    Would it be so subtle that such logic woud have been driven to ask where this beginning was, and what roads had currently lead all these minds to this very question.

    Some act very safe, and walk safe ground, by what methods are currently tangible in our assessments, while other are quite adventurous. Some ask, that you stay in line, with current experimentation or suffer the wrath of deriving illusionary tales of ideas, that had not matured yet, as to the feasibility to what will express this logic of the natural world.

    Betrayal of Images" by Rene Magritte. 1929 painting on which is written "This is not a Pipe"

    So mine is a simple philosophy, that holds complex variables. A simple painting, that holds a thuosand words?:) To me Math is like that, yet I am deficient in all the logic it had to bear down on the natural processes in this world. While my collegues are simple folk, I recognized the diversity of that group that Lubos and Clifford belong too. This is the origins of my statement. I understand as well, about the crackpostism that follows aether rejuvenation, yet I see the graviton as a member of that spacetime fabric.

    Is this enough to speak on the creation and fabrications we like to embue to that natural world? Is it enough to understand these concepts, and find such roads leading too, are the very fringes of what is known and came from a brighter light that shines from behind us, to those shadows on the wall?

    1 comment:

    1. Dear Plato,

      Lubos Motl deleted the following comment to his blog:

      Nigel said...
      Dear Lumos,

      Consider Heisenberg's crackpotism that Wolfgang Pauli discredited with an anti-Heisenberg campaign. It is a piece of paper with an empty box on it and reads: ‘Comment on Heisenberg’s Radio advertisement. This is to show the world that I can paint like Titian. Only technical details are missing. W. Pauli.’

      Dr Woit explains: ‘With such a dramatic lack of experimental support, string theorists often attempt to make an aesthetic argument, professing that the theory is strikingly ‘elegant’ or ‘beautiful.’ Because there is no well-defined theory to judge, it’s hard to know what to make of these assertions, and one is reminded of another quotation from Pauli. Annoyed by Werner Heisenberg’s claims that, though lacking in some specifics, he had a wonderful unified theory (he didn't), Pauli sent letters to some of his physicist friends each containing a blank rectangle and the text, ‘This is to show the world that I can paint like Titian. Only technical details are missing.’ Because no one knows what ‘M-theory’ is, its beauty is that of Pauli's painting. Even if a consistent M-theory can be found, it may very well turn out to be something of great complexity and ugliness.' - Dr Peter Woit, ‘Is string theory even wrong?’, American Scientist, March-April 2002,

      Danny Ross Lunsford’s major paper, published in Int. J. Theor. Phys., v 43 (2004), No. 1, pp.161-177, was submitted to but was removed from by censorship apparently since it investigated a 6-dimensional spacetime which again is not exactly worshipping Witten’s 10/11 dimensional M-theory. It is however on the CERN document server at, and it shows the errors in the historical attempts by Kaluza, Pauli, Klein, Einstein, Mayer, Eddington and Weyl. It proceeds to the correct unification of general relativity and Maxwell’s equations, finding 4-d spacetime inadequate: ‘… We see now that we are in trouble in 4-d. The first three [dimensions] will lead to 4th order differential equations in the metric. Even if these may be differentially reduced to match up with gravitation as we know it, we cannot be satisfied with such a process, and in all likelihood there is a large excess of unphysical solutions at hand. … Only first in six dimensions can we form simple rational invariants that lead to a sensible variational principle. The volume factor now has weight 3, so the possible scalars are weight -3, and we have the possibilities [equations]. In contrast to the situation in 4-d, all of these will lead to second order equations for the g, and all are irreducible - no arbitrary factors will appear in the variation principle. We pick the first one. The others are unsuitable … It is remarkable that without ever introducing electrons, we have recovered the essential elements of electrodynamics, justifying Einstein’s famous statement …’ D.R. Lunsford shows that 6 dimensions in SO(3,3) should replace the Kaluza-Klein 5-dimensional spacetime, unifying GR and electromagnetism: ‘One striking feature of these equations ... is the absent gravitational constant - in fact the ratio of scalars in front of the energy tensor plays that role. This explains the odd role of G in general relativity and its scaling behavior. The ratio has conformal weight 1 and so G has a natural dimensionfulness that prevents it from being a proper coupling constant - so this theory explains why ordinary general relativity, even in the linear approximation and the quantum theory built on it, cannot be regularized.’

      Lunsford also shows that this correct unification discredits the cosmological constant. This is a far more rigorous unification of Maxwell and GR than the Kaluza-Klein 5-d unification, and its suppression proves the paranoia of string theorists who control I think they genuinely think that I'm crackpot and indeed everyone who thinks differently should be exterminated, at least from You have to pity them.

      At least if I'm a crackpot, I don't delete other people's papers. The damage done by some string theorists who censor is not crackpot so much as paranoia: Tony Smith is suppressed not for opposing string theory, but for resolving problems with it without using the mainstream mess M-theory!
      5:37 AM said...
      Tony Smith’s CERN document server, EXT-2004-031, uses the Lie algebra E6 to avoid 1-1 boson-fermion supersymmetry:

      ‘As usually formulated string theory works in 26 dimensions, but deals only with bosons … Superstring theory as usually formulated introduces fermions through a 1-1 supersymmetry between fermions and bosons, resulting in a reduction of spacetime dimensions from 26 to 10. The purpose of this paper is to construct … using the structure of E6 to build a string theory without 1-1 supersymmetry that nevertheless describes gravity and the Standard Model…’

      I wonder why this sort of work is excluded by the string theorists who censor arXiv? Could it be that THEY are the paranoid ones?

      Peter Woit says he doesn’t like the claims made for the Calabi-Yau manifold being beautiful, and that 11-d supergravity doesn’t predict anything testable. If there is useful science in M-theory, mainstream string theorists have had a decade to find it! More likely, it’s a dead end, like Kelvin’s vortex atom or Maxwell’s elastic aether. Just because Kelvin and Maxwell were top mathematicians as well as physicists, did not make their speculations correct.

      String theorists should study Kelvin’s vortex atom and Maxwell’s aether to see the fate of paranoia-type defence of crackpotism. Science can’t cover up the ineptitude of famous people endlessly.
      5:50 AM

      However, Lubos did give a reason:

      7:06 PM

      Lumo said...
      Nigel: please accept my apologies for my having erased your comment about Lunsford's ingenious work. You have typed some very long URLs that destroyed the layout of the page when viewed separately from the rest of the blog. Please, everyone, never include strings without spaces that are longer than 60 characters or so. If you know how to fix the bug of the template so that it treats long string in a more intelligent way, let me know.


      Happy Turkey

      7:52 PM

      Nigel said...
      Dear Lumos,

      "... please accept my apologies for my having erased your comment about Lunsford's ingenious work. You have typed some very long URLs..."

      Thank you for saying something nice about Lunsford. The media always assumes radical ideas are treated with tolerance or awe in science, and the media is wrong.

      If anyone wants to check the Lunsford paper, CLICK HERE, it is a PDF file on CERN doc server:

      "EXT-2003-090" on CERN database: . You need to print it out not view it on screen as it isn't in scalable PDF type, but it prints out nicely. Or see the published version: Int. J. Theor. Phys. 43 (2004) no. 1, pp.161-77.

      Best wishes,

      6:50 AM