Recent content by Eric Belcastro

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    Find remaining vertices of cuboctahedron.

    I figured out how to find them, it was fairly easy. I just used a quaternion rotation matrix and rotated about the known vertices according to the known rotation symmetry of a cuboctahedron and did this a few times, generating new vertices, and all was well. I also wrote one of the coordinates...
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    Find remaining vertices of cuboctahedron.

    *note - this is not a homework problem. I have the locations of three vertices of a regular cuboctahedron with edges of unit length (all vertices are length 1 from the center). They are (1,0,0), (1/2, sqrt(3)/2, 0), (1/2, sqrt(3)/6, sqrt(2)/2) or in spherical coordinates (1, 0, pi/2)...
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    Other Should I Become a Mathematician?

    Yes. Thinking in terms of operators / vector spaces is really what is new to me. Now that I am starting to connect the dots, the vector space approach is starting to make more sense to me, which is good, because quantum mechanics seems to make explicit use of it.
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    Other Should I Become a Mathematician?

    Ahh. That is about as lucid a tie in from quaternions to vector space as I could ask for. I am going to actually write that down in my notebook and keep it in mind, as I am studying vector spaces now (Hermitian operators, pauli spin matrices, etc.) and keep wondering what the specific...
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    String Theory predictions

    Not too complex? Explain that nicely? The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next - by Lee Smolin Agree or disagree, it really is a perspective that is worth reading, comprehending, and considering.
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    Other Should I Become a Mathematician?

    Noncommutative analysis and nonncommutative geometry both turned up quite a lot, though geometry much more so. Thanks.
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    Other Should I Become a Mathematician?

    Certainly there has been much work done on the Clifford algebras, the algebras in general, hypercomplex numbers, etc. but I have never really seen a single publication dedicated to quaternionic analysis as I have real and complex analysis. I wasn't aware of the term 'noncommutative analysis'...
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    Other Should I Become a Mathematician?

    Well, once you all become mathematicians, could you please create Quaternion Analysis, (and hey, go for Cayley/Graves/Octonion Analysis if you are feeling really brave) because Complex Analysis is just not cutting it. Us folks really need you mathematicians to help us out on this one.
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    Double-Slit experiment in Quaternion Quantum Mechanics?

    After beginning studies in the mathematics of quantum mechanics, this is what I am starting to notice. I prefer quaternions, though I noticed that the way non-commutative operators have been used with pairs of complex numbers is basically the same thing, as you said. It would seem to me to be...
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    Scale Relativity

    + Hi Peter, I sympathize, and share your interest for Nottale's theory. I do believe that it is a worthwhile path of study, and am open to any specific critiques of the theory, as it is indeed a work in progress - though I find it more promising than the alternatives at the moment. I...
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    Introducing the PF Library!

    I see what you mean. It would be nice for a community forum to go at it. Lot's to teach, lot's to learn...
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    Introducing the PF Library!

    A great idea - though members might want to consider not recreating entries needlessly that are explained well in wikipedia. It's not hard to find endless arrays of physical and mathematical concepts explained there.
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    Sciam Partnership: Member Discount!

    In am one who has a very low post count, but has signed up for a subscription. The reason I have a low post count is simply that I am a relatively new formal student of physics, and wish to learn more before I enter into serious conversations about many of the subjects I am interested in, as I...
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    Scientific American Subscription 20% off

    Well, either which way - I'm glad your forum is getting recognition, I hope your work is rewarded Mr. Bernhardt. Now to the forum - May the conversations be lively.
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    Scientific American Subscription 20% off

    - Well, I ordered it. I figured I might as well give it a try for a year. Eric
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