**A new quantum logic: Back to square one**

(continued from here)

**A mystery now confronts us. **Have we uncovered an unexpected broken symmetry hidden in the multiplication operations of trigram patterns? In an attempt to answer this question we are going to use an indirect approach and revisit some basic themes. These themes include: the definition of multiplication; dimensional numbers and multiplication; magnitude, scalars and scaling; direction, vectors and sign; commutability; inversion and reflection; and the all-too-often-present conflation.**(1)** We can anticipate that it will take several posts at minimum to carry out this investigation.

**My suspicion is that the culprit here** is conflation and that what we have uncovered is not truly a broken symmetry but rather a clandestine error of conceptualization. The origin of our difficulties lies in the way we have been psychologically conditioned to view multiplication by that ubiquitous villain, conflation. Let’s see if we can unravel this labyrinthine deception.

**To begin we need to go back** to the fundamental polarity which defines two directions of a single dimension. *Positive* and *negative* lie at the root of our difficulties. Are we to view these two as asymmetric or symmetric? This is the basic question we must answer before addressing any of the other issues which grow out of this confusion. From a purely geometric perspective the two are symmetric. It is only when we attach names and numbers to the poles that they begin to appear asymmetric. This is a trick of algebra and language. It is, I think, a fallacy of mind.**(2)**

**And convention is undeniably an accessory to the fact.** We ourselves

*choose*names and other special distinguishing characteristics with which we label the directions and poles. Convention is humanly determined though nature has its own arbitrarily determined preferences as well.

**(3)**

(continued here)

**Image: **Three classes of levers. By Pearson Scott Foresman [Public domain], via Wikimedia Commons

**(1) A seeming hodgepodge** but all significantly related to one another.

**(2) Even the ancients** had no difficulty balancing weights and objects about a fulcrum. They were masters of intuitive geometry and the building arts. Also one of the reasons the rationalists of the Age of Enlightenment had so much difficulty in accepting negative numbers may have been that their geometry seemed not require them despite the fact that their algebra clearly demanded them. Better the devil you know and all that.

**(3) Consider, for example,** its preference for the L-form over the D-form of amino acids in metabolism.

© 2014 Martin Hauser

**Please note -** This is a beta post meaning that the content and/or format may not yet be in finalized form. A reblog as a **TEXT** post now will contain this caveat to warn readers to refer to the current version which appears in the source blog. This note will not however appear in a **LINK** post which itself accomplishes the same. Thank you for not removing this statement and for your understanding. :)

## Paul Dirac on mathematics and progress in physics

The steady progress of physics requires for its theoretical formulation a mathematics that gets continually more advanced. This is only natural and to be expected. What, however, was not expected by the scientific workers of the last century was the particular form that the line of advancement of the mathematics would take, namely, it was expected that the mathematics would get more and more complicated, but would rest on a permanent basis of axioms and definitions, while actually the modem physical developments have required a mathematics that continually shifts its foundations and gets more abstract. Non-euclidean geometry and non-commutative algebra, which were at one time considered to be purely fictions of the mind and pastimes for logical thinkers, have now been found to be very necessary for the description of general facts of the physical world. It seems likely that this process of increasing abstraction will continue in the future and that advance in physics is to be associated with a continual modification and generalisation of the axioms at the base of the mathematics rather than with a logical development of any one mathematical scheme on a fixed foundation.

dirac diracing it up

"Quantised Singularities in the Electromagnetic Field", Dirac 1931, proceedings of the royal society A

I do believe Dirac was making a valid point here.

**Addendum, September 10, 2014**

I feel compelled to make an additional comment/clarification here. The statement “dirac diracing it up” is not mine nor do I agree with it, either in content or tone. It seems to me in some sense derogatory. But when reblogging posts I rarely remove comments others have appended, not without very good reason (which to me is not simply because I disagree with a remark.)

Let it be known by all that Paul Dirac was one of the great theoretical physicists of the 20th century. He made significant contributions to the early development of both quantum mechanics and quantum electrodynamics and shared the Nobel Prize in Physics for 1933 with Erwin Schrödinger “for the discovery of new productive forms of atomic theory”. He did work that forms the basis of modern attempts to reconcile general relativity with quantum mechanics. He was also a gifted mathematician who was the Lucasian Professor of Mathematics at the University of Cambridge.

I have good reason to suspect that the individual who actually made the remark noted above has come nowhere close to any of these achievements. I personally find the remark disrespectful to the memory of one who was an important contributor to the development of both modern mathematics and physics.

Waves in superconductors were the inspiration for the Higgs boson, but they had remained almost as elusive as their particle physics equivalent - until now

Special vibrations, working effectively as the mathematical equivalent of Higgs particles, shake superconducting material cooled to nearly -273 degrees Celsius to slow down pairs of photons travelling through them, making light behave as though it has mass.

Image: Higgs mechanism. ”Mecanismo de Higgs PH”. Licensed under CC BY-SA 3.0 via Wikimedia Commons.

**A new quantum logic: Symmetry and asymmetry - I**

(continued from here)

**Physics considers symmetries quite important** as they often carry in concealment laws of nature. Asymmetries are important too. These are at times broken symmetries which physics also makes much of and which can instruct us in important ways as well. We will look at what appears to be one of these broken symmetries and attempt its demystification. We will be describing what must surely be one of the most basic asymmetries of dimensional numbers, one which involves the most fundamental polarity of nature. Could this be one of the earliest broken symmetries? And could dimensional numbers be the fount of symmetry, asymmetry and broken symmetry alike?**(1)**

**The way mandalic geometry views symmetry** differs slightly from the way physics does. This must be explained before we attempt the broken symmetry demystification mentioned above. To accomplish this we will need to discuss a number of other topics, including that of the rotation group of the cube, composite dimension, isotropic and anisotropic space, variant perspective, and invariance under Planck scale interchangeability. We have a long road ahead of us before we reach the fabled Fortress of Broken Symmetry and attempt to penetrate its formidable encasement.

(continued here)

**Image:** The ceiling of the Sheikh-Lotf-Allah mosque in Isfahan, Iran. By Phillip Maiwald (Nikopol) (Own work) [GFDL or CC-BY-SA-3.0], via Wikimedia Commons

**(1) ****Within mathematics symmetry in geometry **is very closely linked to group theory. Mandalic geometry at its current stage of development is concerned principally with the symmetries and asymmetries inherent in the cube, sphere, and their extrapolations to six dimensional space, or rather to the composited 3D/6D space of the mandalic cube and mandalic sphere. Wikipedia has an excellent introductory article on groups in mathematics which can be found here. An equally excellent article dealing with both symmetry and symmetry breaking appears in The Stanford Encyclopedia of Philosophy. For a discussion of the relation between groups and graphs I think you can do no better than this original tumblr post.

© 2014 Martin Hauser

**Please note -** This is a beta post meaning that the content and/or format may not yet be in finalized form. A reblog as a **TEXT** post now will contain this caveat to warn readers to refer to the current version which appears in the source blog. This note will not however appear in a **LINK** post which itself accomplishes the same. Thank you for not removing this statement and for your understanding. :)

## The way I see it

**The Second Law of Thermodynamics is** a law only a simpleton would follow. But nature is no simpleton. Slow, perhaps, but it has had billions of years to perfect its laws. I think we can be certain its laws work quite well and are a lot less simplistic than this Second Law regarded as sacrosanct.

**Did physics never hear about** energy gradients that traverse and work across different dimensions? It seems not. Well nature has. Nature has not only heard of such energy gradients, it invented them. Probably quite early in the history of the universe because a young universe striving for self-sufficiency hasn’t much of a chance without them. So it learned early on how to juggle multiple feedback circuits all at once. Nature as juggler.

**Science generally doesn’t like to juggle** a whole lot of parameters and variables all at once, mainly since it’s not very good at doing that sort of thing. So a lot of conclusions end up out of context of reality and as a result quite simplistic. Nature prefers holism. Throw the entire stash of variables at it and it will deal with them all simultaneously - - - somehow it just does.

**Do not construe from what I’ve said here** that I am anti-thermodynamic in general. I object to it only as an end scenario for the universe. The main problem with the Second Law as I see it is that it takes into consideration only a single energy gradient, spreading the energy involved throughout all of space which it imagines to consist of only three dimensions, everywhere homogeneous and isotropic. We live in an age of holo-homogenization and the Second Law also follows suit. Throw into the mix the possibility that the universe as we know it may not even be a closed system and the odds that it will suffer demise from absence of a heat energy gradient becomes even less likely.

**Still, the Second Law is the law least likely** to be overturned by physics in the next hundred years. Due to the long reach of its many tentacles it has insinuated itself throughout much of modern physics. Physicists simply do not realize the gravity of the situation, that this overly simplistic Second Law is holding physicists and physics alike hostage.

Image: Turquoise Eyes by thepeachpeddler CC BY 2.0

© 2014 Martin Hauser

**Interlude 4**

**The mathematical structure** upon which mandalic geometry is based is the mandalic cube/hypercube. This maps a combined 3D/6D spacetime in which the 3D and the 6D aspects are both superimposed and composited, resulting in a mandala. In three dimensions this mandalic spacetime can be represented in configuration of either a cube or a sphere but owing to the discretized quantum nature of Plank scale spacetime these two are in fact congruent. In other words, point for point the mandalic cube/hypercube can be superimposed upon the mandalic sphere/hypersphere. In reality the two are one. It is only our rational minds that insist on distinguishing them.**(1) **

**More precisely it presents** as a set of four nesting cubes or spheres which in their interactions create the hypercubes or hyperspheres. It is as though the mandala is formed by nesting Chinese boxes, placed one within another, with the stipulation that all the discretized points of each “box” are able to functionally interact with any and all those in all the other “boxes” and to interchange location with any of them in the spacetime defined by mandalic geometry.**(2)** For particle physics this may entail in some sense or other the exchange of quantum numbers.

**One of the most essential characteristics** of mandalic geometry is its seamless holistic nature, all parts of which can nevertheless be extracted conceptually and rearranged in countless different manners. This results in a discretized probabilistic spacetime which seems not to respect any requirement that insists on restriction to a given dimension. Not only are the parts of the mandala interchangeable but this interchangeability can take place in any number of different dimensions both *concurrently* and *consecutively* (both terms which I believe must ultimately be given new definitions in the context of this geometry.)**(3)**

**More specifically, instantaneous jumps can occur,** for example, from two dimensions to three dimensions or from two to four or three to six and vice versa. This is not simply a conceptual trick of the mind. Nature itself participates in all these maneuverings described and many more. This is one of the characteristics of nature that makes quantum events appear so strange and unsettling, demanding that we view them in a probabilistic manner.

**(4)**

**Image: Stacking boxes - **GRIMM’S kleiner Kistensatz blau-grün (Small Set of Boxes, blue)

**(1) In truth though,** to view mandalic spacetime in terms of *either* a cube or sphere is almost like the way stars in the night sky are viewed in terms of constellations which are really no more than conceptual areas grouped around patterns which represent the shapes that give the name to the constellations. Though not quite because the points mandalic geometry describes *do* bear multiple real relationships in mandalic spacetime. They are just not fixed in the sense that the points of a cube or sphere are and there is a lot of *nothingness* between them other than these relationships, more that is than seems apparent between stars in a constellation.

**(2) Up till now** only the cube/hypercube form has been described in this blog but previously the sphere/hypersphere form was described in detail in blindmen6.tumblr.com. The first in that series of posts can be located here.

**(3) The mandalic configuration imposes** upon spacetime a gradient between actual and potential. Similar to the way in which the yin/yang gradient works in both Taoist philosophy and mandalic geometry, this actual/potential gradient possesses bidirectional and multidimensional capabilities which trigger a layering of a probability distribution on reality and have significant effects on how time is expressed and experienced. This being so, it would seem that the traditional definitions of *concurrence* and *succession* are inadequate in the context of mandalic geometry. The entire notion of sequence may need to be reeevaluated, more stringently even than Einstein did in his special theory of relativity. This subject will be addressed in greater detail in future posts.

**(4) For a good discussion regarding the tesseract** or four-dimensional hypercube see here. Keep in mind though that the mandalic cube we are describing in this blog is a 6-dimensional analog of the cube and therefore all the more complex in its construction.

© 2014 Martin Hauser

**Please note -** This is a beta post meaning that the content and/or format may not yet be in finalized form. A reblog as a **TEXT** post now will contain this caveat to warn readers to refer to the current version which appears in the source blog. This note will not however appear in a **LINK** post which itself accomplishes the same. Thank you for not removing this statement and for your understanding. :)