The Algebra of \"Everything\" by Rick Lockyer

Rick,

As a fellow physicist you know that the line between Maths and Physics was drawn by Galileo - Physics only existed after he set the experimental standard of applying a mathematical theory to reality. It's not my definition of Physics, it's Galileo's. Every theory starts as *just* a mathematical theory until experimentally verified and shown not to contradict known experimental results. Reproducing known theories by different means - which both you and I have done - meets the Galilean standard of Physics as the known experimental results are entailed (question answered).

In the Standard Model, the spectrum of particles and their coupling constants are added by hand from experimental results. Dimensional compactification defines a whole class of mathematical theories that seek to derive the particle coupling constants from the GR constants and a compactification scale. The 11D GR theory referenced in my essay is one of this class of theory and succeeds by *deriving* the full spectrum of particles so that they do not have to be added by hand - this is not present in the Standard Model or any associated principles. The GR scenario is uniquely defined mathematically by the occurrence of the spheres S0, S1, S3, S7 as physical manifolds and this is directly linked to the successful reproduction of known physics without any additional features that conflict with known physics. This includes the derivation of the correct Standard Model Lagrangian and QFT. These characteristics *are* unique.

The acknowledgement of "if and only if" in Godel's mathematical incompleteness is PRECISELY my point. It is conditional on integers, which is the case in classical physics for particle numbers. The calculation of the rest mass of the particles derived in 11D GR as topological defects is subject to Godel's mathematical incompleteness because of this "if and only if" condition. A mathematician would be stumped at this point, but as physicists who know that maths is just a formal language for describing reality, we are free to drop the "if and only if" condition of strictly using integers to denote particle numbers and switch to real numbers instead - the wave-function - mathematical incompleteness then vanishes. If you trace the mathematical consequences of this shift in the theory, you find that it is of the form of quantum theory. Hence, QT is not fundamental because I can derive it!

This implies that mathematical incompleteness is not so much a red herring, but the elephant in the room.

Michael

In the film spherewars by Spielberg,Steve the young Jedi has found an important thing, the force is with him. But the empire of the bad is there. The son of Yoda is his friend.

About the post:here is my humble point of vue of spherewalker.

all false !!! mike badteam ,the octonionic obliged comportment will not change the algorythms, deterministic. The aim is not to superimpose the maths without a real universal domain. In fact it is a good tool for computing.

you think what ? that you are going to insert balls now.Let me laugh band of comics.You are not skilling to ponder this kind of works.So what is the probelm. Mr Wilcszec is an universalist. Mr Tegmark also, Mr Guth also, Mr Penrose also, Mr Hawking also,Mr Witten also.so why you insist on the pseudo works,you do not respect the real searchers, you just imply strategy of strategical steal. In fact you know what ? I beleive that you do not permit the truths.Just because you confound a lot of things.It is simply an unconsciousness comportment.In fact you think that you are right. But no, there are a lot of probelms.

and you,Mr Witten , are you going to continue to act like that ? You fear for your 11d or what ??? If some persons of your team utilize several roads for the confusions about ball and sphere, frankly it is sad.and But perhaps that you do not know that they act like that?

Spherically yours

Rick,

I really had in mind, the so-called "pretty" maths of super-symmetry and string theory, whose "prettiness" has been used as justification for pursuing what has proven to be a pointless course for decades.

I have a preference for the geometric view of the same algebra, as it conceptually gives a big picture view which can guide the choice of direction to go in, and this is what the S7 geometric view of the octonions has done for me. An algebraic view is necessary to guide individual steps, and to conceptually check you don't step in anything nasty ;-), but can it really provide the big picture view of where to go next?

Your response on Godel's incompleteness strikes me as the exact opposite of what I meant. The classical physics theory over the integers is provably mathematically incomplete; the unbridgeable category divide between integer particle numbers and waves makes reaching a wave property from integer particles impossible in classical physics. So when a particle has a wave property, the classical physics theory is scientifically incomplete in the experimental sense that there-exists an observation that cannot be derived within classical physics. It is this specific sense of scientific completeness which can be addressed by dropping the "if and only if" condition of describing particle numbers by integers and instead use a real valued wave-function that incorporates the undecidable wave feature. The result is quantum theory - surely a very un-herring-like outcome?

Deeper philosophical points about "completeness" don't arise for this restricted experimental sense of scientific completeness; I use this term precisely so as to avoid the general notion of "completeness" which seems so vague you wouldn't know it if you found it.

No Space Shuttles out my window, just a buzzard if I'm lucky ;-)

Michael

PS. In my Sept 25 reply to Jonathan I give a view of Joy's frameworks in terms of topological mappings and particles as monopoles if your interested.

Hello Rick,

While the story goes that the Octonions are the weird and crazy old uncle whom everyone would like to hide away in their closet or attic; that is only partly true, and misses the point somewhat. Instead; the octonions are like the wealthy and eccentric old uncle, who almost nobody else in the family associates with, because they are intimidated by his freedom and power. Of course; the rest of the family is jealous, but they would never admit it, because then they would end up feeling a little less powerful themselves.

But we would all be a whole lot less wealthy, if it were not for the Octonions - which are the great granddaddy of all the other number types. However; the wonderful properties of those amazing octonions assure that the rest of the family emerges and persists as well. I rated your essay highly, because I believe in what you are saying - and that you said it well. Of course; I fully understand that you can't talk meaningfully about your subject without getting too technical sometimes, which you did, but so it goes.

All the Best,

Jonathan

Hmm,

Thinking on the above comment; I imagine you could make a detailed storyline out of it - where, for example, the rest of the family will only approach uncle Octonius in committees of three, but there is always a member of each committee in common. Such a dramatic approach might illustrate the kind of special respect the octonions demand. Just a thought.

But I like the idea of the Octonions being a wealthy and eccentric uncle (who knows untold secrets) better than a weird and crazy one, any day.

All the Best,

Jonathan

To continue;

Good old Uncle Octonius was one crafty old genius. The family insisted that the only way anyone in the family could be trusted to meet with him is if they went in committees of three. And of course; he insisted that - in order to be fair - there must be one member in common each time they send a committee. But how did he know that there would be seven committees? That crafty old guy must have planned it that way.

Of course; the committees are called quaternions - which is short for "It's our turn again." Anyhow; I'm just thinking out loud on your page.

All the Best,

Jonathan

If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

Mr Lockyer,

a very interesting essay. I remember a few years ago I was looking for math that would allow the multidimensional nature of space to be expressed with ease. I wish I had found Octonion Algebra then, but all I saw was quaternions. I imagine how hard it was to pack it all in 9 pages -- well done! I hope your essay will get the recognition it deserves.

Lisi , Jonathan,Tom ...are stealers ahahahah frustration +lack of general skillings=your comportment.

conclusion return at school ahahah spherization of balls and spheres ahahahah yes of course band of comics.

Steve score= 1001

bad teamscore = 0

in fact you are not cramped or pinched or troubled just between us. Because frankly , if you think that you are intelligent, let me tell you that frankly your sciences are weak, in a general point of vue of course. Cramped and pinched are weak words for your pseudo team of pseudos gneral scientists. I really suggest that you retrun at school you know. I don't know what are your foundamentals learnt at school during your young education, but frankly here in europe I beleive that our courses are better, but it is just a suggestion of course. Coordonates of nothing badband team. You are ironical Jonathan and Tom.

Study for your Phd instead of loosing your time with things that you do not understand in fact. Or change of option , take the marketing for example.

Each person at its place badteam of nothing for nothing.

I am parano ok ,but I have my reasons.

Regards

Mr. Lockyer,

Congrats to us all on having it over with!

Thank you for your response. You wrote, " Potential functions over a simplistic notion of space whose purpose more is to set the algebra, dimensionality and allow us to distinguish one point from another has always resonated with me more than say intrinsic curvature of space itself to describe Gravity. "

-?? did I understand you right?...If it does not curve, what's gravity?

I am very curious about your take on space. Like, there are many topological, geometrical, algebraical spaces whose characteristics and properties are mathematically defined. There is only one real thing. What do you think defines its characteristics and properties?

I imagine you must think that space has more dimensions than the observed 3. Otherwise, why Octonian Algebra?

Hello Rick,

Good old Uncle Octonius would be proud! Assuming no further vacillation; I wish you the best of luck in the finals. You deserve to be there!

All the Best,

Jonathan

Congratulations, Rick.

You have brought our crazy old uncle to the party. I hope he unleashes unimaginable havoc.

Joy

Mr. Lockyer,

congratulations on making the list of the finalists! It did not look so when I posted above. I am glad you have made it in the end.

Thank you for your reply and sorry for the delay. I needed a break from physics and enjoy the cluster of birthdays. So, for you it's all algebra and no curvature at all... I guess my visual approach requires geometry, but I do like it very much that your world is set in 8D.

Again, congratulations and good luck with the rest of the competition!

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