New Mathematical Recreations

New Mathematical Recreations

L. Edgar Otto  31 January, 2013   

Like the theory developing where the speculations of physicists are in dispute at the frontiers of issues of philosophy and decoherence and information in the interpretations of the quantum theory, I see a parallel in the evolution of their thinking describing what I long ago considered as physical and philosophical levels beyond our simple idea of a space time continuum at the time (1964) what I have referred to as the Ultranscontinuum in these matters of decoherence, consistency, many worlds, twisters, and the role of information.  To this I add the deeper view that we may complicate things further by the states and phases in theory of consciousness and the observer, at least structure wise- that is a deeper generalization of ideas like Gell-Mann to which we leave the physical continua to go toward the philosophic ones... then the symmetry of things discussed in those of quasi-quality I now style N-branes.  Perhaps on this level we may find ways to understand better the various views that arise in our first unification theories of everything.

But what is our reaction when the gods of physics in themselves are in dispute and wage wars of doctrines if not to address the issues of our time, perhaps write a new myth that too decoheres at things integrate or focus over time?

Entering the waxing of the fish month in a sea of chaos again I so will arise to post more formally, and with certainty to present a formal paper on the more important issues of the nature of numbers in these books I have not posted in this bare sketch with many of my informal drawings included that the unity and beauty of it all in its cold objectivity has been enhanced as to the directions I have gone or may go in my inquiry.  The books do show what we have to have in more advanced significant state steps while the breakthru resolution still escapes us.  (perhaps not some of us but how do we show this to those who are in the evolving as some sort of needed or not needed observers?)

On top of this the epistemology is not neglected as a core part of the philosophic views... the question of typing and the desire to keep the keyboard in the portable phones valuable as in the Blackberry 10 insight rather than the touch- yet the information as a physical focus in relation to heat and entropy in the retrieval of memory or in the forgetfulness - that is the desire to go beyond the shifting needing apps to navigate the ergonomics of private experience.  We are more sophisticated in our touch than the distribution of energy by just two binary fingers. 

So too the grounding of our subjectivity not that different in the measure of efficiency as if a machine unto ever deeper levels of breakthru grounds for understanding the nature of quasiclassical contiguity in matters of our analogs beyond the acceptance of what that was abstract now the familiar physical of theory- again, the breakthroughs intuited as needed but not yet explained how.  The need for new insights, a new Newton or Dirac, not asked in a way that this extension is even asked or realized.

The idea of dark matter is deep into our actual workings of our mind.  I wonder in particular about Hawkings boxes which to me are just Coxeter on certain regions of space containing singularities or not, if in what sort of box, observers aside, do we find a unifying theory as to if the old cat or kitten is dead?

The quasic idea addressed long ago that conclusion in metaphysics of similarity and absolute identity of certain indistinguishable objects in a way that is just not accepted as with phase space where in one point we may describe the totality.  We need this space of a little wider generalization to keep the reality of it in our heads as we exist in this world.

Some of my other titles for would be posts included:

Playground and World   a reference to the Vietnam era and what in our personal experiences constitute boxes of singularity or continua of excluding them...  all the see saws and swings, the spinning roundabouts (I forget the name but throwing a tennis ball on one shows clearly interesting paths) and other physics as prime by us monkeys on the jungle gym imagining flying with the light or vibrating in some ideal lattice as if an electron, or perhaps another universe full of sentient beings if we looked deep down into a fundamental particle- Sagan like or right out of Superman comics of the 50's.

I have issues now that might threaten my newly found stability which do take their toll on the energy to try to write formally.  This sort of thing I feel also wastes vast resources of how we should live in relation to our shared government. It may also waste people as well as new and hopeful projects.

In the dream while typing I dropped and cigarette that started an ember around a whole in the sheet and I jumped out of bed forgetting my phantom typing and trying to recall it or paste it into the real world and that of my pc- well, I reached for the paper and pen the old fashioned way.  In Darling's book I found a bit of humor that ends in the mathematician seeing his bed catching on fire, saying ah there is a solution, then rolling over and going to sleep.

The campus and green illustration was a fanciful yet fractal island like structure, as is the quasi superposition of prime patterns of artificial life that resolve in directions past chaos, a plan to imagine what it would be like to work in one and what details of travel between them, where can we view the ocean... perhaps if we made mazes including the energy to heat the building, fire walls (as all could catch fire adjacent), and the communications between them- it would be more difficult in the physical world to breach the security of those in the commons so in academic freedom sheltered- but would it be an interesting place to commit to memory so as to navigate and to live, or are square and round things a better way to go physically and spiritually?

New Epistemology and Reasonably New Nature of Chemical Bonding  As I said needing a separate post, this applies also to that point in the development of a single mind beyond the chaos not found in quantum theory as to its quasic centering (but that only on the three prime physics level so far discussed) and the self, autism in particular... in the actual engagement with the external world and the communications distinguished in messages between them.

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The Directive Prime

The Directive Prime

L. Edgar Otto    30 January, 2013

I continue a burst of creativity that is hard to take the time in its complexity to post.  It would be a series of posts with clarity in our existing problems in the physics and would explore new directions of what even to myself for the moment is among my most radical of speculations.

Part of this is my checking out of three significant books in the popular literature.  The end of the last century suggests to me that such books, despite the viewpoint of the authors in their apologies, are made to promote some thesis and gain support from a wider audience of people and experts in the field.  The entry into our new century and the flowering of the computer age is one of brave new speculations itself.  Sometimes these seem to reach too far and have their detractors.  One outstanding enterprise is the attempts to understand better the nature of consciousness as the final frontier of our current research.  Another was a debate on the acid test of a philosophy, thus of physics, as to the nature of determinism and free will.

But one of the books put the bare facts in a way I found very accessible in which to relate ideas in the trends I already have developed from a different view- and together I am under the spell that these things fit together much more close than the mysterys still there in say, number theory.  I do not know how someone else may see this book without some background or exposure here and there to these issues of number theory and physics- but I suspect it is not a hard as we think should we desire to inquire about these things.  Still, if nothing else, I see the relevance and even urgency in the debates as to how we see the world and society, ourselves if we are free to design our own evolution.

One was from Roger Penrose, The Emperors New Mind   this I missed from that significant last century decade although I have seen, and respect highly, his work on the nature of reality in that big volume of which some of it seems to have its forerunner in this book.

The next one was The Bit and the Pendulum  by Tom Siegfried which concerns the New Physics of Information and which made comments on Penrose in the area of the exploration of consciousness.

But there are fewer and fewer books in the library and I do not have the luxury of internet access time at the moment.  I checked out one on html 5 web design again but have not had time to work with it, just for something to keep my mind occupied.

David Darling, PhD has a book called The Universal Book of Mathematics  which I checked out for the familiar pictures of certain recreational mathematics photos- and it listed many things not yet solved in number theory-  I did not know for example there was not algorithm for n-onomoes greater than 8 as they will include holes.  I would have posted commentary on some of the puzzles in new light but these as useful for my digital art drawing led to some striking ideas to develop.

I had further insights into what Conway's game of Life has to do with so many issues we debate now in the universe.  One of these animations called Langford's Ant was particularly interesting in after ten thousand iterations or so it as and "attractor" begins an endless highway-  now it may be true that the numbers needed in continuous physics are complex numbers but these can be discrete also in my view- the animation fits well with my general idea of a third or quasic physics perspective.  These have a direction chosen in the quasic plane.

Another thing is what there is of pattern orders in the distribution of primes,  two pictures and these have different properties when merged in the paint transparency of the symmetry involved- after all, the rules of how the ant moves is one of its right angle changes of direction.  But more than this the parity in a plane, being different if seen as a brane of flatness than in depth is independent of the outcome of the animation.

From the playing with these prime patterns I give two radical ideas or interpretations.  One I call the Imagomnium which as to do with what seems to be the pseudosphere or Gabriele's horn shape I imagine as if a barred spiral galaxy. Of course we imagine shapes in the clouds of patterns, oddly it is easy in the Ulam spiral to merge things that suggest faces as it the case on different resolutions of craters as on Mars.

The other seems to go well with the general evolution of the universe in terms of what is the nature of dark matter and how we see from observations how it may relate to galaxies.  But itself it would mean little without the clarity and view of Penrose on his ideas of the relation to gravity and entropy.  I note that Penrose respects "Beauty" as some higher ingredient found in some theoreticians- he discusses his own states of mind, for example nothing coming from his subconscious as in dreams.  This evolution I style the Ubrane, for Ulam.

On top of this I had a significant dream which concerned drawing and typing, alas these did not go directly to the computer but raised some rather interesting questions as to communication possiblilites and does seem to give the psycho-dynamic views of Jung more weight as part of the new physics as well  his steam engine synchronous model  of the mind.  Yet he did state a synthesis of ideas that may not resemble those of the science of his day alone- still the quasic unification does not necessarily suggest that beyond science if it is read carefully.

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Entropy, Information, Imago

Entropy, Information, Imago

L. Edgar Otto      29 January, 2013

I return now to a more mathematical recreational stance, to view the history and body of the literature and concerns from the new perspective.  I found this a pleasant and interesting activity of inquiry in which seeing how in the questions and search for possible unified and new physics general directions for a theory of everything various theoreticians intuitively sense a direction yet stuck on the details of method wherein in viewing the goal it remains illusive as if they beat their heads upon a wall or the wall recedes and twists away from them on something like what we first glimpsed in perspective of Western art as the projective plane.

I also had to look up terms and ideas in the library of things I have read or heard about observing the conversation in discussions on the internet.  What is a D or p-brane? What does the term moonshine mean added to the Monster groups?  Luckily I found these summarized in a few places to which the filling in of ideas and connections, a unified view in new light, I found inspiring and easily linked as I referred to what I could Google off line in my mind.  But it also was the reading of those popular authors that I have not encountered who wrote at this time of change as our theories of the last decade developed rapidly, their glowing sense of clarity outside of that time where some issues are now obsolete in their search for a formal and unified speculation as an act of communication and creative thinking.

The p-brane idea based on natural but vague dimensions is flawed from my view where dimension is so ill defined so I did not miss much from the training or influence of such ideas- after all my grasp of string theory came before the M theory as any other physics based, like quantum theory, on some ideal of hidden and even inaccessible generalizations as if 'Magic" or 'Mystery'.  The D-brane is a little more interesting dealing with loops and open ends and things- but this idea too would work a science outside the mystery as if the universe as a computer or informational simulation may ignore if anything exists outside it be that the idea of an absolute nothingness after all, or some intelligent designer as a theory or perhaps a personal being as with any of our ideas that also try to refer to 'consciousness' which of course the observer is part of things in teleological systems theory.

If there is no more certain philosophy in these hierarchical and inellegant recursive systems (which as looping and infinite regress can be used legitimately and elegantly) we can find the same theoretician endorsing another that supports his view yet rejecting that which challenges his view... using the same data and impressions from a wider view what appears contradictory at worse at best is a missing of each others point. 

Lisa and Lubos are the standing our example of the day in defense of these core theories of which each in their presentations shores up the core of their methods, takes fundamental stance to the same inquiry into a theory of everything or not for the working awakening of frontier ideas realized by the brane methods- Lubos is consistent in applying these stances to the debate of what grounds the earlier just quantum ideas.

Aware of some advanced problem like decoherence as well the hierarchy of things, not so much as that beyond the two modern physics, we can look back at earlier generalizations and new directions from it (such as chaos science).  We can say that ultimately, as with Maxwell's demon, Newton's system itself will not hold unless it is ultimately ground in the quantum ideas of uncertainty.  So too the quantum theory is grounded by something higher of which I have called quasics.  The debate between these creative scientists would do well, if only for the design of the logic's sake, to have at least an overview of creative philosophy that they are not blind to states of their stances.

Various generalizations of space, configuration or phase spaces, the idea of information as a part of the picture as if a half physical realm as much as things like energy and matter, the idea of time and applying complex number methods to it - or radically so for all the variables such as momenta-  the ubiquity of Hamiltonian methods that seem to apply remarkably to so many diverse areas of the physics as if our most general idea of space and time, this also bequeaths the problem so set up that it is a concern and one that as science may be clouded if limited to existing levels of methods and generalization to which we may state the problem yet not be lead toward a solution. No wonder we approach the problem politically so as to  solve the Gordian knot with the blade.

To this end, and pulled out of the air as these terms are too new even for a poet inventor reluctantly of words,  beyond the idea of energy, then entropy, I chose imago- already a term used in group psychology.  But it is the specific new light on certain recreational puzzles and patterns (after all mathematics is a word derived from knowing and patterns)

thus the issue of what is shape say compared to volume- more the grounding as my word stereonometry even over but hinting at the mystery or Metaphysics is the joy and promise of joy in new comprehension- that and a higher respect for the actual individual inquirers ancient and modern.

I give the readers a puzzle, imagine the impossible triangle as of Penrose (of which we should not underestimate the value of mathematical recreations or game theories and so on)  These are nine cubes in a triangle as if the tops of them may be walked on unclear if we are going up or down.

Now, of the 30 cubes so colored find a rational solution that their face colors match.  Hint: Contemplate my 9 of the 15 cubes extended in depth direction from 6 of the others in the bicolor matrix I offered my the last post.  Can the matching be only there in the abstract higher space also in such a way they match only from this view?  After all, so much of this quasi-physicality or half real issues is this question of what we imagine as real or concrete in the so called optical illusions.  My illustration for this post is just an uncolored example of them in a pleasing but double cross eyed array.

Now formally (especially our concepts of topology or what structural patterns may exist at least inside black holes as this quasics solves the mechanism of what contained in various shells or surfaces describes the relative volumes as structure and information, and what I have called the Phoenix level of the workings of energy) what concepts are we to develop here even as a simpler example than the general case of such shape matching?  It seems to me a joy also that in the collection of ideas and conjectures in number theories, even in what seems as simple as the counting, a unifying stance and new concepts hidden in the patterns, arises.

Perhaps, we face the general great speculative frontier beyond these patterns or coincidences, ultimately representations by primes beyond their randomness and chaos, into and thru the new physics to an even higher level- one that has natural and unique restrictions not to be asserted so to save our theories such as the uniqueness of the patterns of 6 x 6 that arise in our bilateral slicing of regions of space as part of the integration of such facts.

The simple question of why a mirror reverses right and left but not up and down has a long history as with many things foreshadowing in quantum theory Carrol contemplated this.  From what perspective may we regard other (elliptic for example) equations as of slower convergence than the golden irrational?

Is it not enough to apply the monster moonshine ideas not as a matter of suggest deep connections between different mathematical approaches then this suggested but remains a mystery, that the same concept and all its variations as we increase or leave behind some idea of dimensions at the moment, applies to protons, particles, creative structures like black holes and the description of the atom as to the periods of elements?

If there is any such great speculative frontiers to be seen within the Omnium, ideas like the similarity of parts broken down or fit together describe the whole so ultimately we treat these various conceptions of what happens at a singularity or point as if nothingness and their generalization, the null points of creativity, this is creative and vital philosophy- things like baby universes in the sky or in the zero point ideas of an atom beyond its balances wherein we discuss some idea of transfer of energy or heat, or a little more sophisticated uncertainty and momenta that obviously grounds nuclear arsenals as an experiment hard to dispute, philosophy indeed, but as projects of science let us call it what it presently is: "M" is for metaphysics.

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