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    Square of Gradient!

    I would like to suggest perusing the literature of Dr. David Hestenes et al. regarding Geometric Algebra and Geometric Calculus. It soumds like you want to talk about the D' Alembertian and possibly Dirac's derivation of his equations as the inverse of 'squaring'. In what way would you interpret...
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    Is a Tesseract the only model we have for 4D?

    Buckminster Fuller questioned the orthogonal assumptions of multidimensional drawing and suggested instead, using 60 degree base vectors for x,y,z on one plane, with the fourth dimension as the altitude of a tetrahedron. He also preferred to refer to the second power of a number as 'triangling'...
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    Is the electron a photon with toroidal topology? - what is that?

    The question of whether or not a paper is legitimate science is not something that one should be asking others. Let tbe person who asked this question write down explicitly what they consider to be relevant criteria. Perhaps others could add their own set of criteria. It is also possible...
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    Is the electron a photon with toroidal topology? - what is that?

    Sometimes in order to move forward beyond something like The Standard Model, one has to backtrack and pick up a different idea thread such as Weyl's gravity ideas and gauge theory or the ideas of Kaluza and Klein. One should remember that the idea of photons being absorbed or emitted by...
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    Is the electron a photon with toroidal topology? - what is that?

    The nature of an electron has been a mystery since it's discovery. It is associated with EM radiation in atoms and in the creation of an electron and a positron by a gamma ray as it passes a heavy nucleus. So why not use gestalt type ideas and instead of creating light from electfons, create...
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    Why is GR and QM not compatible?

    See website and writings of Dr. Mendel Sachs.
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    Mendel Sachs' unification.

    I am familiar with Dr. Sach's papers, publications and books. He has a good website online. He does seem to recycle his papers a bit too much but then people do keep reinventing the wheel. He uses quaternions/spinors as a mathematical formalism that is applicable in both quantum mechanics and...
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    Hestenes' Geometric Algebra. What good is it?

    I know that Dr. Pertti Lounesto ( has expressed some disagreement with Dr. Hestenes regarding Geometric Algebra and Geometric Calculus, but one can't walk three roads at the same time and Dr. Hestenes has done a good job of designing a mathematical...
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    Musings on the physicists/mathematicians barrier

    You are not alone. See THE VECTOR CALCULUS GAP: Mathematics not= Physics by Tevian Dray and Corinne A. Manogue (24 September 1998) ( BRIDGING THE VECTOR (CALCULUS) GAP by TEVIAN DRAY and CORINNE A. MANOGUE...
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    Quaternions in QM

    James Clerk Maxwell originally used quaternions in his work on Electromagnetism but there was a dispute/difference of opinion regarding their use that led him to use vectors later on. As Dr. David Hestenes points out in his many writings on Geometric Algebra and Geometric Calculus, quaternions...
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    Directed Integration and the Fundamental Theorem of Calculus [Broken] [Broken] [Broken] Clifford Algebra to Geometric Calculus (1986) Chapter 7 / Directed Integration Theory 7-1. Directed Integrals...
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    Macroscopic vs. microscopic

    Several times I've listened to Brian Greene talk about string theory and say that General Relativity is a macroscopic theory but Quantum Mechanics is a microscopic theory. Do you think it could be otherwise? I know that this is an accepted "dogma" that is often repeated by others but I...
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    Why is quantum mechanics basically incongruous with general relativity?

    For a list of the incompatibilities between the General Theory of Relativity and Quantum Mechanics see Dr. Mendel Sach's website or his book "Einstein vs. Bohr". List on website: A) Principle of complementarity, implying 'pluralism', versus principle of...
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    We Should Work on Complining Book Lists

    It would certainly be a good idea to compile a list. I found as a result of visiting other libraries and Universities that there was some very good writing available that I would never have known about if I didn't travel and browse the shelves or ask people in other locations about. Living in...
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    Great Ideas

    I'm currently reading M.J. Adler's book "HOW TO READ A BOOK" (1940) and it's very good! It's the kind of thing I need and have been looking for. A lot of what Adler said in 1940 is just as true today. People, including myself don't know how to read a book let alone how to discuss it. This...
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    Creative (lateral) thinking to solve a complex problem

    I really enjoyed the solution to this problem when I first read about it in Mr. de Bono's writings. I know I would never come up with such a creative solution. How do you suppose the young woman might have arrived at such a brilliant solution? Have you ever seen something similar in real life or...
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    What else Albert einstein's contributions in optic and photonics?

    Albert Einstein, Ann. Phys. (Leipzig) 33, 1275 (1910); english translation: "Theory of Opalescence of Homogeneous Liquids and Mixtures of Liquids in the Vicinity of the Critical State", in Colloid Chemistry, J. Alexander, ed. (Rheinhold, New York, 1913), Vol. I, p. 323.
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    What else Albert einstein's contributions in optic and photonics?

    Re: quantised energy being due to Planck. I'm not so sure about that. I want to say yes and no. Planck employed quantised energy in his equation but it was Einstein that put forward the radical idea of quantising the elecromagnetic radiation field comparing it to a gas. The notion of a light...
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    Misunderstanding in physics

    What causes the greatest misunderstanding in physics? LANGUAGE! Physicists talk about "Solid states" when they know there are no solids and atoms are mostly empty space. Astronomers talk about seeing the sun move across the sky when they know very well that it is not moving across the sky...
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    Studying a subject

    I actually saw a paper in a journal along the lines of the original post here but I can't recall what journal it was. I'm thinking it was FOUNDATIONS OF PHYSICS.
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    What are quaternions

    Maxwell's original formulation of Electromagnetics was in terms of quaternions but there were several individuals such as Gibbs and Heaviside who questioned the necessity and pragmatics of using quaternions and promoted a version employing only VECTORS. The dispute got quite heated with insults...
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    Great Ideas

    I'm currently reading Adler's GREAT IDEAS OF THE WESTERN WORLD (1990's version) and I really like the idea of being able to 'listen in' on the GREAT CONVERSATION as it occurs throughout the great books. Adler's dialectic approach is one thing that would be useful for young people to experience...
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    The most interesting physics book

    Einstein's Clock's Poncare's Maps is good if you want to get a full context big picture of where Einstein's Paper "On the Electrodynamics of Moving Bodies" fits into the world scene of the early 1900's. A.I. Miller did something similar in his writings but not on such a personal level. There are...
  24. L

    Studying a subject

    I question the overall line of reasoning here. I also question the first sentence. Let me rephrase it using "parallel lines" rather than "math". When we study something, say parallel lines, we learn accepted axiomatic ideas. Aren't those very ideas what define parallel lines? This sounds strange...
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    Non-Logical Logic

    From the start there is clearly a confusion based on the use of the word logical for rational. All this about 1 rock + 1 rock = 2 rocks is rock logic. There are very defined boundaries. A sheep is or is not a sheep. It can't be sort of a sheep. How about lateral thinking and WATER LOGIC...
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    Classical physics and h

    For anyone interested in Professor Edwin Jayne's writing I'm posting this URL. In the paper STATUS OF NEOCLASSICAL RADIATION THEORY, Professor Jaynes models an atom with a quadratic interaction Hamiltonian and mentions a uniform integral of the...
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    A New Kind Of Science

    A NEW KIND OF SCIENCE is written in a SCIENTIFIC AMERICAN style and is actually a very good introduction to the subject. If it weren't for the numerous personal remarks Mr. Wolfram peppers throughout the book, I would recommend it to one and all. However, as it stands, it's a big ad for amateur...
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    A New Kind Of Science

    Surfing the net I came across a few reviews. Scott Aaronson's review at [Broken] echoes some of my own views. When I was reading A NEW KIND OF SCIENCE Wolfram's numerous claims to some kind of intellectual propriety or...
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    A New Kind Of Science

    Stephen Wolfram's A NEW KIND OF SCIENCE is the biggest disappointment I have ever experienced in my reading. If his book was a program it would be analogous to making a long journey to the edge of the universe in search of the meaning of life ony to be left in the end asking 'That's it?' Nada...
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    The most interesting physics book

    At the moment, I think SIMILARITIES IN PHYSICS by John N. Shive and Robert L. Weber is the most interesting and informative physics book I've read although I really like Poincare's writing in his THE FOUNDATIONS OF SCIENCE volumes and Mach's THE SCIENCE OF MECHANICS. What I find interesting in...