Hello Rick,

I'm cross-posting this comment I just left on Ben's page, with due respect to John Baez, who is not my cousin in real life, because it deals with octonions.

A story:

They say my uncle is crazy, and cousin John tells me some family members wanted to lock old Uncle Octonius up in the attic, but I think he is only eccentric because he's seen the universe, and knows its secrets. For years we thought he just wouldn't associate with the other family members at all, but somehow we worked out how to do it safely. You see; Octonius is very persuasive, and can make people do almost anything - so he can't be trusted, or rather no one person can ever see him alone. And when we send two, they always disagree on what was said. Therefore; we always visit Uncle Octonius in committees of three. But; the first time a group of us visited, he insisted that he must see all the family members - with equal frequency - and that there always be someone in common between any two visits. Luckily; this worked out, because there are seven of us.

The thing is; Octonius is incredibly wealthy and knows the secrets of the universe, but we were all so afraid of him that we never knew why he seemed so crazy. You see; he always liked to break the laws of algebra - or insist on things being backwards sometimes - whenever we tried to use the associative and commutative rules to simplify expressions for him. But we never understood why that was, until we attempted to rank ourselves - thinking that both the greatest and slightest within our family needed to be included, within each committee, to assure trust. Then Octonius explained that committees follow a rule that is non-commutative, and then if you include everyone at once things become non-associative, because there can be disagreements between members or committees - but there is also a hierarchy or ordering of and within any committee.

Though we are still not sure we can trust him, Uncle Octonius tells us this is as fair as it can be, and now he is teaching us the secrets of the universe. So who could complain? I'm glad cousin John didn't let the others lock him up in the attic, or we would never have learned of his vast wealth and untold secrets.

end of story

Jonathan

    Hi Jonathan,

    Cute story. The only problem I have with it is "You see; he always liked to break the laws of algebra...". Not the case. The general algebraic rule for multiplication e_i * e_j = sum k: p_ijk e_k encompasses commutative, non-commutative, associative and non-associative algebras. It all comes down to the structure constants p_ijk.

    Rick

    Or structure variables p_ijk(x) in my variable torsion picture, at every point x in S^7.

    Excellent!

    You two certainly know how to spice up a story. I like both of your answers. And though it might be tough to work into the story, that's part of what makes our 'crazy' old uncle so interesting. But if we had decided he was crazy, and just left it at that, we never would have learned of his incredible wealth.

    But I think I clearly conveyed that he likes to be in charge, and makes the others do things his way. And as you both just said, in the final analysis he never really broke the law. He just bent the rules, to have a little more play, and ultimately made the others play the game by his rules.

    All the Best,

    Jonathan

    always weak dear Jonathan Dickau and the bad team so Rick,Lisi,Tom,Christi,Florin,and the friends .Your strategy show us your weak generality.In fact you are not intresting and your reasonings still less. You utilize bad startegies just for the monney and the vanity.You are not scientists.You are just business men thinking that all is permitted just because you are limited.Fortunally that you are in team and furthermore with algorythmic tools.The pity is still a weak word for your poor team. It is even not an antithesis in fact.It is just business and marketing. I don't know me, make an other job or I don't know me, study for example.

    You are not competent , so why you insist with your octonions ? just to make surf and to live in california with a lot of dollars.Let me laugh . If you were skilling, yes , but no, you repeat always the same stupidities.In fact you are not general, so how can be your details ? even the entropy you do not understand, so how can you understand its entropical distribution on the arrow of times. In fact you confound waht is the objectivity and the subjectivity. In fact you do not understand the determinism and its physical laws. So how can you understand the 3 vectors and the scalar? the evolution is unknown for you, you do not understand neither the principle of equivalence, nor the newtonian mecanic and its universal proportions. In fact you superimpose with pseudo parallelizations and you insert irrational reversibilities. All these extrapolations are not rational and dterministic. It is evident that the game is even not interesting because you repeat always the same things.So please increase your team or buy scientists, general please because there I don't evolve :).

    Jonathan , you are just skilling for the strategies, not for the rational part.Increase your team please, just for me, too easy there dude.

    Regards and sphericaly yours, Steve Dufourny Jedi of the Sphere and inventor of the Theory of SPHERIZATION ......eureka !!!

    and Mr Durham who is lost now in the meanders of irony.

    Jonathan and Mr Durham are in a bar of 11 dimensions, the team of bad angels is lost in its own stupidity. Mr Dufourny Steve, him, Jedi of The Sphere, inventor of the Theory of Spherization fights the bad with universal wisdom and universal sincerity.:) revolution spherization !!!

    2 months later

    I had to breeze through the conservation of Octonion energy and momentum in my essay due to the length restrictions. I attach below a snippet from the book I am writing that covers the derivation of the conservation equations in more detail.

    It sure would be nice to get some grant money to finish the book and further my ideas, especially now that I am recently unemployed and would have the time to work on it if I do not get another engineering job.

    Dreamingly yours,

    RickAttachment #1: R_Lockyer_book_chapter_10_preliminary_snippet.pdf

    a month later

    • [deleted]

    • Post #96

    Please see http://theoryofeverything.org/wordpress/?m=201301 for links to a Mathematica demonstration that completely links E8 and octonions to AESToE (AG Lisi) extended SM particle assignments. It generates all 480 permutations of octonions and links them 2:1 with E8.

    Greg

      Please use the link help page for web links so the blog home page doesn't get messed up.

      [this post can be deleted]

      Greg,

      I do not put much thought into E8 because its O connection is made to the 480 representations. As I said in my essay, the 30 ways to roll out 7 H subalgebra triplets from 7 distinct non-scalar basis elements are nothing more than aliases. But beyond this, there is no proper algebraic method for their simultaneous application (E8 single reality?), unless you want to increase the total number of non-scalar basis elements to 7*30. There is nothing algebraically new provided by any of the 30 possibilities. An analogy would be my calling you basis element Greg today, but deciding to call you Larry tomorrow, it does not change what you essentially are, just how I choose to enumerate you in order to distinguish between you and someone else. This is why I suggest picking one of the 30 and running with it, and see little physical distinction/importance provided by the full set of aliases.

      The E8 connection to all 30 does nothing to convince me otherwise. Physical reality *is not* symmetry groups, physical reality *exhibits symmetry*. I think this distinction is lost on many SM aficionados. Most symmetry abstractions have a multiplicity of physical/geometric application, making it suboptimal to look outward from a symmetry perspective in one's methodology for discovery of a TOE.

      I looked at your link. Your (presume) description of the construction of the 16 ways to roll out O for a given set of 7 triplets was not complete enough to judge, not knowing how you enumerated them. Perhaps there is additional information off the entry page. The simple essential and thus fundamental method is what I called in my essay the 3:4 Morph Rule. Starting with any valid O definition, you can create another by changing the handedness of all 3 H subalgebras that include a common basis element, or changing the handedness of all 4 H subalgebras that exclude one basis element. There is a plethora of ways to represent any single O algebra with a directed Fano plane. So if you are trying to gleam the variability in O through categorizing the various ways to draw a Fano depiction, you are over-complicating things.

      Rick

      " Physical reality *is not* symmetry groups, physical reality *exhibits symmetry*."

      That is an excellent and profound statement, Rick. Physically it agrees with the relativistic prohibition against a privileged frame of reference.

      Tom

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