From: Stephen Speicher Subject: Re: against mathematica Date: Tue, 19 Sep 2000 22:16:06 -0700 Newsgroups: sci.math Summary: [missing] On 20 Sep 2000, John Baez wrote: > Stephen Speicher wrote: > > >The result has to do with the triality automorphism of the group > >Spin(8), and its relation to the Clifford algebra CL_8, for which > >an error was corrected by Lounesto in a previous post. Having now > >read the result, it is not at all obvious to me why Lounesto > >believes this result to represent the most important discovery in > >the past 75 years of mathematics, however I remain open to his > >explication as to the reasons why. > > Can you tell me what the result says, since Pertti seems unwilling? > > I know a fair amount about triality, so the bare statement may be > enough. > The triality automorphism of the group Spin(8) is a restriction of a polynomial mapping Cl8 -> Cl8 of second degree, actually a product of two affine linear mappings: trial(u)=trial_1(u)trial_2(u), trial_1(u)=0.5(1+e_12...8)<{[(e_8ue_8**-1(1+e_12...8))^e_8]e_8**-1}(1+w)>0,6 +0.5(1-e12...8), trial_2(u)=(3-w)[(u(1+e_12...8))^e_8]e_8**-1(3-w)**-1. The triality corresponds to the octonion product x o y = 1 of x,y E R8 with e_8 as a real axis and w=ve_12...7**-1, v=e_124 + e_235 + e_457 + e_561 + e_672 + e_713. Stephen sjs@compbio.caltech.edu You can always tell a pioneer by the arrows in his back. Printed using 100% recycled electrons. -------------------------------------------------------- ============================================================================== From: Stephen Speicher Subject: Re: against mathematica Date: Wed, 20 Sep 2000 11:54:47 -0700 Newsgroups: sci.math On Wed, 20 Sep 2000, Pertti Lounesto wrote: > Stephen Speicher wrote: > > > On 20 Sep 2000, John Baez wrote: > > > > > Stephen Speicher wrote: > > > > > > >The result has to do with the triality automorphism of the group > > > >Spin(8), and its relation to the Clifford algebra CL_8, for which > > > >an error was corrected by Lounesto in a previous post. Having now > > > >read the result, it is not at all obvious to me why Lounesto > > > >believes this result to represent the most important discovery in > > > >the past 75 years of mathematics, however I remain open to his > > > >explication as to the reasons why. > > > > > > Can you tell me what the result says, since Pertti seems unwilling? > > > > > > I know a fair amount about triality, so the bare statement may be > > > enough. > > John brings forth one of the main obstacles in communicating > new scientific discoveries: Intelligent people are satisfied with > their present state of knowledge, and believe that they know > "a fair amount" already, although they do not know what they > do not know. Thus, people who don't even have an objective > estimate of their state of knowledge, are ready to utter: I know > "a fair amout" already. > I disagree with John about quite a number of things, but this characterization of him does not seem correct at all. John Baez is not only very erudite, but he shows a willingness -- nay, an eagerness -- to learn from others when they offer him knowledge. Perhaps you are attributing to him personally a trait inherent in all new discoveries; an inevitable intellectual hurdle to be jumped in order to appreciate something truly new. You cannot expect immediate understanding and acceptance of any radical knowledge. > > The triality automorphism of the group Spin(8) is a restriction > > of a polynomial mapping Cl8 -> Cl8 of second degree, actually a > > product of two affine linear mappings: > > > > trial(u)=trial_1(u)trial_2(u), > > > > trial_1(u)=0.5(1+e_12...8)<{[(e_8ue_8**-1(1+e_12...8))^e_8]e_8**-1}(1+w)>0,6 > > +0.5(1-e12...8), > > > > trial_2(u)=(3-w)[(u(1+e_12...8))^e_8]e_8**-1(3-w)**-1. > > > > The triality corresponds to the octonion product > > > > x o y = 1 of x,y E R8 > > > > with e_8 as a real axis and w=ve_12...7**-1, v=e_124 + e_235 + e_457 + > > e_561 + e_672 + e_713. > > From my experience about revealing my earlier discoveries, > I can predict that John will, if he acts like a usual scientist, > utter that he can now estimate signifigance of my discovery, > before he has explored the new territories opened to him > by my discovery (= years of jewellery to be found). > I know nothing about these previous attempts, but if your discoveries were rejected out of hand, then I can understand your reluctance. However, a new opportunity presents itself here, and if you refrain from teaching us all the significance of your work, then I think you must bear part of the blame for the lack of acceptance of your ideas. Stephen sjs@compbio.caltech.edu You can always tell a pioneer by the arrows in his back. Printed using 100% recycled electrons. --------------------------------------------------------