MMXI Happy 2011 everyone... not much but some stray thoughts and perhaps an adjustment to new comprehension and ways to see the world anew. I am not sure if all this amounts to matter as knots of space or knots in space-but either way the mystery seems to me now more of what is physical in our assumptions as to what is physics and real. A find distinction then between the concerns as quasiphysical and quasimetaphysical. I am amazed we can know so much about nature with such abstract models to apply and touch it- what we regard as real.
Life may be defined as that which binds or is bound within itself hidden parts and is aware of it; in this sense each of us is equal to a universe.
Enigma 1 - Basically, the idea of something material as primary that includes some form of vacuum- the sole metaphysical principle Peter Rowlands [PR] stated as such in his book, the muon and all that is not muon as vacuum together form such a particle. But could we not regard this as only a state of matter?
Enigma 2 - [PR] discusses a sort of symmetry breaking wherein 4 space is reduced into 2 space by considerations of the a Klein's bottle. The point is that it exists only in four space but in three space it intersects itself (and a glass one will in that sense hold water). Again, these that topological ideas apply to concrete physics is something I have not considered although I realize some of my methods as simple as the subject were rather difficult to solve let alone see as concrete thus I am amazed but now see the core strength of how some folks believe in depth to some of the various abstract theories.
The Klein's bottle is made of two Moebious strips (of two space). [PR] states that the intersection is the description of a muon as stated above. I had thought such a thing about possible holes observed in the cosmic background but not as more than an abstract model. (back later...)
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Wow, I just noticed some interesting new posts by Kea and some comments to one of my diagrams! So I posted this comment:
Kea,
I am quite honored you quoted my diagrams. Sorry, I just try to google my brain and forget there is so much is now on the internet.
In fact I knew the problem was difficult but I did not think my math recreations applied to these sorts of theories.
From my view this amounts to writing matrices in at three space notation. My labels help keep things strait. What of the other possibilities of the Vn's of which there are 15? and in the Conway matrix there are two others that form such a cube? Now I have to wonder how much of the codes apply.
On some level the assumption that generations have increasing mass is after all an assumption that at first approximation does seem like a linear method.
I wrote to Gardner about the cubes and it was discussed all over the bulletin boards long before I had a computer (as he replied that we could all share in the fun) and Conway's was published in Scientific American shortly thereafter. But I do not want to take any credit for anything someone else has achieved, sorry if somehow I stepped on your toes.
I found another solution of one form instead of three for one of Conway's puzzles he said was very "elegant". And Coxeter, my mentor, said Conway thought in 24 dimensions (he only 8). I see you can think in high dimensions judging from your next posts.
I am really nobody at all. Now I have a keen interest in seeing what you have done :-)
Thank You, The PeSla
http://pseudomonad.blogspot.com/2010/12/theory-update-28.html where you can find a very kind reply to this comment.
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As I was saying, stray ideas, I find Rowlands comment that we can have a string theory without strings interesting! I am not sure I like the idea of Dirac of a filled negative space and this symmetrically extended to the quarks as if we have some sort of classical theory on sterioids. In any case the intersection in a Kleins bottle he called a "singularity" but really, it is more as if the classical radius or something like it is a singularity as defined and not ultimately a point.
Nevertheless, Rowlands treatment of space and (what amounts to the idea of so many particles as measured by a number of point electron charges) that as far as scaling goes the h, G, and c of things show these physics values are not fundamental seems to me right on. But should we agree it is all 3+1 (reduced to 2+1, thus 4 into two space)? He explains the signs, +++- but there ++--, and Penrose shows it ++++, something I imagine if we regard the quarks as one higher particle pair ud... then yes the diagonals are important. But there seems other principles of space that helps shore up this direction and measure, discrete or not, of matter. A world without gluons or Higgs particles as significant, of light as the center of things a little less so. I do suspect we can think of a purely 4D world topologically and beyond that. (I begin to think as pairs there are really only five generations from a general natural group idea- but some restrictions on math and group properties do not apply on any less of a generalized theory of space as a limitation.
I suppose this for now amounts to some sort of corpuscular view which as physics may indeed imply the primacy of light, and bar h, and G. Are the leptons really unbound quarks (Rowlands?) Can we now say vaguely some part of the world makes sense of the relatively continuous and absolutely discontinuous?
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I not that my use of the world creation and creativity (let alone used and in Creationism or Hoyle's creation field, needs to be finely distinguished. The quasimetaphysical would not require more than a vague undefined vacuum for a sense of concrete creation of objective things in the world from this sideways life force-like view.
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Now the chemical links from science daily I posted on two articles I thought about that these could naturally link - of course it is but theory to which experiments or what we know of the properties to show what structures are possible or not.
If we can add metal to one or more bond of a NH4 molecule and we can define alloys as in the other article as one metal surrounded by 20 others like Au, could we not add something to the bonds, a third metal? To say guild Ag, with Au, then to add Pt? Perhaps this may explain why such a mixture of the right proportion would lead to violet! In any case the symmetry and geometry involved is relevant to our topological discussions here in a world of mere 3 and 4 space matter.
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I almost wrote a song but it was a little too close in the music to another one.
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I found a neat new thing (put on the illustration above) of three interlocked double straws. It has rather interesting symmetry in that from the plane it has a direction of what is over and what is under in one spin direction, but in the z axis it maintains one direction even if you flip the "triangle" over. Of course the whole structure can be mirrored- but what a delightful ignoring of three space.
This differs from the Borromean rings in that if you remove one the other two stay together. But what this means is that if we shift them to the center we get a jack of sorts that is really the basis for diamonds rather than just perpendicular orthogons. It is a diamond or hexagonal like space. Now is it not amazing that we cannot see such small crystals but can determine they would have such structures topologically from say connecting toothpicks on the human scale of things?
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I find one thing I do not quite understand in Rowlands- 10 20 35 and so on as a vector base that leads to 20- 120, 35- 175 in the quarks. I note these are analogs of Pascal's triangle in 3 space but cannot quite see how to put them into the quasic view of things, yet.
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Kea's remark earlier I find very interesting for my idea of space is also an embedding of all the alephs on a skeleton of say lines and other linear things. Thus we have to deal with the transcendental on which we define connected regions as in how Coxeter treats rotations and reflections. Even in the clear extension or analogs to Pascal's triangle from the dimensional view from some given dimension I get the feeling we can find holes there, or centers not covered by the integers- but who is to say given such "spaces" hidden within our calculations and commensurable measures that they are full or not even with such possibilities. I added a comment but hope it does not bother him, I like how he thinks:
Kea
I found it interesting the Egyptians, I think, approximated pi by 256/81. 2^4/3^3 which fit their needs.
You probably know all this. Of course the sum of the subcells of a hypercube = 81 as the fourth level of the expansion (2+1)^n is of course 3^4. The Orthogons (and anti-orthogons).
But such things still are in the realm of some sort of modern numerology for me. In general if we think of points all connected to each other it is a simplex space- but I find it interesting you in later posts treat 81 as 81 dimensions. It was not easy to eventually see the chessboard as 6 dimensional, that is = 64.
Once reviewing a thesis for just a look at repeated lines and spelling and so on for a string theory professor (wow, I learned a lot doing it but did not know much of the theory). He eventually got me aside to show him all this algebra of the Pascal analogs. Alas, he did not get tenure here.
Such algebra is indeed as important as any of our ideas from the geometry viewpoint.
ThePeSla
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You know, I just cannot get over the naive idea that perhaps in some of these analogs there are indeed analogs to say the icosahedron (fifth degree equations or not) in higher dimensions. We really do not know why we may run out of mathematical properties- that is not the deep reasons. Note: I love that idea Kea quoted that involved 5 branes- we are all beginning to see something more of what space and physics is, I imagine.
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