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- #What do rational numbers help us understand install
- #What do rational numbers help us understand free
This is where the arguments become more qualitative, but it is very easy to see a multi-dimensional fractal structure to the Universe, from cosmic web to galaxy to star to planet to molecule and so on to the depths of our understanding of physics. I have seen some promising work into a generalized Standard Model that allows the metric signature of the quaternions or octonions to vary, which can describe some results of General Relativity.Īlso, complex and hypercomplex numbers have very interesting properties under iteration. If the quaternions are extended to the octonions, all sorts of connections to the Standard Model arise. Further analysis on the imaginary component of this quantity yields a relation identical in structure to the Heisenberg Uncertainty relation.
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Taking the square of a differential quaternion, one finds the invariant interval of special relativity in the real component. As a simple case, the quaternions are very much like Minkowski space, with a metric signature of (+-). It is useful to think of a quaternion as being represented by Q = t + I.X, where t is time, X is a 3-vector representing space, and I is the imaginary unit of quaternions, (i, j, k). There are a number of interesting properties of quaternions that are reminiscent of the structure of space-time. I realize I'm being vague, I apologize for that. TeX all the things Chrome extension (configure inline math to use delimiters) MathJax userscript (userscripts need Greasemonkey, Tampermonkey or similar)
#What do rational numbers help us understand install
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#What do rational numbers help us understand free
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