Saturday, April 28, 2012
Is Pseudospherical Pseudovector of Four Colors a Pseudoscience
Is Pseudospherical Pseudovector of Four Colors a Pseudoscience
L. Edgar Otto 28 April, 2012
I wonder if we can find a more elementary proof of the four color theorem. Or for such recondite theorems in general as some have suggested this is an example of how we know pseudo scientist
One of the bloggers I follow cited this monomania with the four color theorem said as much in a post of yesterday. I found it put forth in an exchange in the comment section of Kea's blog and not knowing better I added in a post my take on the use of colors as such. In the process where they were studying certain aspects of angles they exchanged a program called geoalgebra which I took a look at and recently found it a pleasant way to enhance my digital pictures beyond the limitations of symmetry in paint.
I understand the problem cannot be solved as we do not know somewhere out in the flat plane, or prove we may not find say a fifth color. I understand the problem was solved by a computer by inelegant brute force computations of the possible cases but not beyond a certain point was needed- and there was other deep math methods involved as those who are familiar with the methods are well aware.
Once in the late 60's religiously buying copies of New Scientist in Cambs I would work out the recreational math puzzles and this problem was one. Intuitively I adequately understood the problem because from my view the answer given for the diagram was wrong- how can a great science magazine be wrong I asked myself. It was in the next issue that an apology to the readership was given. I merely saw the problem not as colored regions but those as points in a connected graph- to approach also from another method albeit a much more trivial one than the modern proofs.
Now in the Geogebra I noticed the conics through five points button and of course this intuitively relates to so many things my patterns of five in the quasic grid or say Galois and in general the vague idea of five dimensions and so on. As I said I see Pitkanen's work as related to a form of hyperbolic geometry and am not sure it is or he sees it this way. To see the pictures in some degree of motion is more instructive than still pictures in general, less working dynamics in the dark.
But what I do not know is if this program has a limitation of these five points as only a matter of programming or if it is one of the intrinsic properties of numbers, including how we see the math to program vectors and so on. Can someone with better training tell me what I am seeing here and if I should be seeing much more? I begin to wonder if there is some reason I do not get direct discussions on my work itself when I see very uncivil discourse between those who demean or defend theories. All these words and no one has bothered to challenge me in the work itself, why? when I have seen some on line I understood judged or given the appearance their idea was soundly trounced and they vanish in disgust or perhaps embarrassment.
Now it occurred to me to draw the five points on the grid (hmmm I should try this with the hex grid somehow) but to compare the quasic and the natural right to left ordering. The ordering within any five is irrelevant to the resulting quadratic, that is the natural system always results in the span of parallel horizontal lines- or in some cases we have sloping pairs of lines for the orthogonality of things is preserved as a principle even between the hyperbolic world (and its mirror) and the quasic world or plane, (brane). This of course is as if we embed an Euclidean plane in a hyperbolic space much as Rene Thom with his catastrophe universal topology embedded elliptical space in the Euclidean on in his, yes, controversial Universal Topology of say 1974 or so, meaning in someones eyes this was pseudoscience at least in its conclusions for say animal behavior.
Now I have said, for example in the gene reading theory that the 25th and 35th depending on how one counts is the initiator and terminator in the quasic grid of the codons. Interesting things happen in the drawing in the order and beyond say so many multiples of 5 not reaching the entire plane of 60 or 64, the program stops working or cannot see beyond. Nature may be quasi quantized this way. It would make sense the distinguishing of the fermions and bosons and so on to be from such principles as Pitkanen-Otto or Thom seemingly restrictions from the geometrical formalism. Certainly the genes seem to allow both the uniqueness yet continuity of an inheritance line of individuals- most likely at the fundamental level including the spherical space views- much as if the duality of particle and waves, or the triangles and squares (orthogons and simplexes in the dimensional analogs and yes the 2 + 2 or 3 + 1 arithmetical aspects of four space views in the physics as well as mirror quantization intrinsically and not just some idea that is said to be justified by a principle of handedness as chirality applied to say half or doubled particles. In fact if we understand the mechanism the string idea of spin identities this too in depth would confirm this sort of general topological and looping gravity as quantized at least to the five fold principles of a unified theory.
Now in the count the hot and cold colors that I enhanced the drawing with, there is a new color I drew brown although in principle there is the possibility or uncertainty of a fifth in one drawing but that could be because of my choices or ordering of colors or say the idea of that higher number of superimposed Euclidean dimensions such as the ten, eleven or twelve as a favored description in these times of higher spaces that involve higher spaces of compacification.
Note I tried to arrange some color pairs as if to let the hyperbolic regions stand out as if in depth and suggest there are non transparent regions thereby as a sort of hyperbolic Venn diagrams to show the points of intersection.
Now why or where are their spinnors and what in a more general theory where we have declared limitations too soon can we ground the ideas of the quantum and qlassical (GR like analyses included) of physics that as a unified theory has been asleep to foundational progress for decades now? None of this will undermine some earlier gains in views and methods so the debate on such ideas is one of a matter of just artful views and quite beside these ideas to make further progress in understanding.