On Thu, 2011-03-03 at 14:52 +0100, Fabrizio Giudici wrote: > On 03/03/2011 02:03 PM, Miroslav Pokorny wrote: > > > > But are they constantly reinventing how they define or express > > formulas etc ?
Yes. Obviously there is an issue of scale. This is not constantly on the scale of minutes, hours, days, weeks, but it is constantly on the scale of years and decades. > It depends on what you mean for that "constantly". For instance, at some > point in history quaternions were not invented. At that point, if you > wanted to do 3D transformations you could, but it was cumbersome > (because of some problems related with trig functions going to infinity > for certain angles). Then somebody invented quaternions, and somebody > else was able to remap the 3D thing in a much cleaner form. Now, the > quaternion thing for 3D has been done, and probably there's no more need > to simplify that theory. But they could be useful for something else too > and somebody might be going to discover it. > > Note that quaternions weren't invented on that purpose, so the guy that > was able to redefine 3D transformations was able to find the better > solution probably because it was curious about learning "new languages " :-) Quarternions (even octonions) have found their place in graphics and rendering, but not physics so much, there everything is 4-vectors, at least for large scale things like atoms and galaxies. On smaller scales you tend to need 11 or 26 dimensional spaces. > BTW, if I'm not wrong (but I'm entering a foreign field to me) Stephen > Hawkins was able to improve his cosmological models with a very similar > approach (probably, with quaternions too?), avoiding "singularities" If you look at Weinberg's classic text on Relativity from the late 1970s all the equations are based on using coordinate systems. Then someone noticed the subject of differential geometry and all the same models could be expressed in different ways without reference to a specific coordinate system. A huge step forward. It also had a huge effect on the quantum gauge theories: particle physics moved forward about 20 years in 6 months. The LHC is only now testing some of the theory that came out of that period. BTW You know Maxwell's Equations -- there are usually 4 of them in most texts, but take a peek at http://www.zpenergy.com/downloads/Orig_maxwell_equations.pdf it even mentions quarternions. Using 4-vectors it is just a single equation. Moreover it is naturally in agreement with special relativity -- it had to be if you think about it. It's all about the serendipity as much as hard work, which is why knowing functional programming and logic programming properly helps your imperative programming. To get back on topic . . . :-) -- Russel. ============================================================================= Dr Russel Winder t: +44 20 7585 2200 voip: sip:[email protected] 41 Buckmaster Road m: +44 7770 465 077 xmpp: [email protected] London SW11 1EN, UK w: www.russel.org.uk skype: russel_winder
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