Monday, August 16, 2010
Earlier today I saw this article on New Scientist which seems another in the breakthrough ideas for the new physics.
Only Rowlands seems to try to bring the foundations of physics down to the intelligibility of number theory in ways I see it. The depth of a shadow figure of many dimensions is not what it seems on the surface of things in our span of space. I saw it as if linear structures as polytopes and the curves of space within them that correspond to the aleph numbers of Cantor. In this article there is a more general depth called the super-cardinal numbers and in many respects the next intelligible breakthrough in debates on line with very good young logicians is the notion that some ideas may exceed cardinality. Of course the central question of where is the continuum seems in the realm of the questionable to some and in this article part of a choice- yet are not there finite things in this world? Certainly the fundamental laws of arithmetic need modification at the foundations and should not be abandoned as the world for what certainty we judge is there is intelligible in the correspondences of the finite and infinite. One does not have to choose between notions that are both part of this world- save for steppingstone theories.
Of course this question of why mathematics matches the world so well, why it is intelligible and as a quasi-principle 1+1=2 has a feeling of certainty at least on the human scales is one we know how to ask when we add something to the equations such as the cosmological constant in the calculus by Einstein or for that matter the way we define a complex number. Certainly there was something wrong with the disconnect between addition and multiplication, logically- and Boolean wise the difference in idempotent and nil potency, to me a rather quasi-potent thing. That particular notion of arithmetic is one I questioned here and gave an alternate view, more more of a scalar world where those operations are the same. The axioms of these operations and the suspension of blind faith in our logic can find deeper intelligibility and certainties that are based on reason more than faith and can prove it as well as reason.
In the illustration above there are five pentagonal dipyramids joined by triangular prisms (a more stable way to do it with the materials I used). Being that the spheres are alike in color and the sticks are the same I found hard to see as to their stacking. If I cannot do so as an intelligible creature then the universe should also have a real effect materially with its own natural blind-sight. Thus as we stack such geometric entities as if the lesser symmetries of DNA like objects we find a flexibility (would we have the geometry of DNA so crystalline rigid?) yet it is not some extreme idea of intrinsic randomness. Stacking the pentagonal prisms or even pentagons is a reduction and a trivial statement of angles easy to see but not in the true depths and grasp of what space is and its potentials.
So, such new connections in high level and unlabeled general particles permit new permutation parameters for the shifting of the senses of circles and helices. The external conditions or chemical groups do have the ability to label things, turn them on or off, shift them back to the overall developmental design.
* * * Next day:
This concept raises the question of what we mean by scale such as what to expect from persistent finite entities in the color complexity of labels that keep the ground to higher dimensional structures. Is it meaningful really to insist at what scale, be it Planck or otherwise, some string or particle phenomena exists? Is it meaningful moreover to say some lesser numbers are improbable to the point of non existent compared with sampling the number line for transcendentals? In a sense from this relaxed by restrained view and hidden generalization of numbers like the partition numbers and colors and flavor environs and structure of some particles we find at a certain threshold of being unities on all scales on how physics works and in a sense is the quasi-proofs in a quasi-world.
I find it interesting in mammal cells those beyond the first 32 cannot be cloned into more than one individual- that is the fifth dimension of representation. Also at that threshold the vague inter-structure on all levels of the non-degenerate encoding's make it possible that the mammal cell can also make the RNA (new scientist article) much like the general living idea that proteins can influence the development of other proteins in a sort of prion way where the reduction to preons as an idea in the nucleus really breaks down as a simple idea on some continuous energy or entropy universal scale.
* * * Later Next day:
I was to begin this post with an idea- that we age and grow past our toys- I mean it is not our technological toys that for some make them feel alien to the world they knew at the time- such toys really are gateways to costly programs, games, and some fleeting memories like nostalgic family photos meaning very little to others.
In physics, although I could find some old technology in rummage meets even if there is little left there of the old radio days to see or hear or those to speak with, it is rather late to finally have the fulfillment of such wishes now just the memory of a wish for its own sake. I do not see some of the new toys as more than the popular consensus of the way things are and are to be desired- not strategically critical as if more refined sugars or drugs far from the subtle differences of the rituals of the times- indeed, old war movies and how dependent we were on oily propeller planes and state of the art now junk design cars.
In this explorations of physics I feel so much ahead of any toys or ideas that may be part of the times I could have been born in- and today I think perhaps, just perhaps, there are some toys we can take with us.
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