Wednesday, July 27, 2011
SOMAMore and the Foundational Theorem of Arithmetic
SOMAMore and the Foundational Theorem of Arithmetic L. Edgar Otto July 27, 2011
I have made some progress orienting these objects and discovered some interesting things along the way I shall present here today. My questions of uniqueness are fundamental and foundational in the sense of the nature of arithmetic and primes. But be warned- at this level I have questioned some rather fundamental things we have held to for a long time now and have accepted the authority of such proofs.
I quite imagine this will give some a sense of vertigo or perhaps make them question their sanity. Or in the case of Hawkings, debate in his wisdom the why of the universe- if there is M theory without strings then how can his string ideas think there is no God? Or is he looking again for one? But the field of exploring is now so wide that it will take us rather long and if we ask the purpose of why we are here, well that joy of exploration and struggle to know will satisfy that question of purpose for awhile.
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Post to Matti having an existential moment:
The universe becomes more like the theories you imagine it to be.
I am just a pigment of your imagination in the landscape your are painting.
"He whom the gods would destroy they first make mad..." Seneca I think...
SUSY is not the zombie, just the zombie animates the SUSY.
Now, if someone asks what I smoke or did I take my meds - My first reaction is to let them teach me how such chemicals work- they do not have a chemical imbalance but an ontological zombie imbalance.
But symmetry is not the key to balance... we do get intoxicated from all the intense beauty and the depressive hangover that comes before the storm or breakthru.
Feel, feel the fragile flesh and drink in your reality and the actuality of others- hold a child for you are only trusted and gentle with it.
In half of infinity it is clear that where were are we can see things as half full or half empty.
Some here think they can put meat on the bare bones of symmetry group theory with magical incantations of five space and make the zombies walk.
Narrow minds are not even relatively prime in their constipated but half truth logic.
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Well, I ran out of paper and have been putting things on whatever is blank - so things are a little messy.
*1 We all seem to have a SUSY of sorts but not in the standard description and it may not suggest there are s-particles for example. Then again we are on the border lime of octonion multiplicative inverses. That part of some of the theories are obsolete now does not mean they are wrong, they have their worth and place still in our quest for a unified physics.
*2 I imagine other ways we may find the reason for fractional charges than those suggested by simple mixing. It has to do with the 4x4 matrix and how we see it, a unification but not of the style envisioned by Einstein and 32 in group theory for electromagnetic and gravitational fields. Such complements or inversions are close to the inversion of the notions of such space and dimensions as notions, We fail to balance these notions- Thus we must unify the various approaches like that of braiding or the centering in a multiverse of Conway matrix Cw quasic positions.
*3 From a more modern view I find the Minkowski idea of the distortion of space by mass a little contrived and no longer exciting as a fundamental principle. Einstein pointed out the 4x4 matrix as having ten places of rest (presumed gravitational) of the 16 and did say the question of dynamos and spinning things were to still be answered. We should look deeper than imposing on some matrix these values that connect mass and so on- but we can also say that such values may be interpreted as zero plus or negative time in a different way than just the imaginary part of some sense of a light cone. Particles faster than light while not necessarily particles are an intimate part of this picture to resolve. How we treat these sixteen elements (and where I have used pixel unit cell or quasic region I now call them "elementals"(e:) for the span of things and "filamentals"(f:) for the depth of things in the "Firmament" (r:). Clearly the inversion of notions of the Conway Matrix Cw and the Kea type braiding is a sort of unification of very basic ideas.
*4 The universality of laws stand as a relativistic principle but only if generalized
to a elemental centered movable Conway Field where laws can be different and creative on the lower levels. If we rewrite or upgrade physics fundamentally we have to so do the mathematics too.
*5 The uniqueness and proofs of the fundamental theorem of arithmetic does not hold or is not complete enough to describe the nature of numbers. For at a zero elemental it is not clear ab-cd = 0 where things are "relativity prime". Co-prime is ambiguous at the zero elemental.
*6 Part of the difference between pi and e is seen in the fraction expansion to involve these general concepts of numbers and the quasic field as regards to the virial number two or four and the natural or the odd sequence.
*7 The quantum consequence of a series of natural numbers is not as deep as the structures of this new view of what can be deduced from the current arithmetic.
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I am a little under the weather today, storms and hard to sleep with the thunder and other things so I should have posted the concepts here a little better. I may clean it up some later or make a new post. The comment to Pitkanen needs to see the post it applies to in order to understand the meaning better. That and Kea's terms like Zombie SUSY. But having to redefine on a page each time some term is as bad as having to use the standard terms as the truth which tells us nothing new. One thing for sure our alternative new constellation of scientists all have a SUSY of sorts and are all bothered by the situation as are the standard scientists- yet I see that again we have all made progress, in victory and the uncertainty of new views of a completion. I am very optimistic. Heck to question these fundamentals most certainly may invoke ideas of crackpottery but not if we are happy and wise to find the happiness in ourselves and not the confusions of others.
* * * More Comment to Pikanen:
Nice Poem Ulla :-)
As I said on a post- Matti- we all seem to have some form of SUSY but It is still not clear (to me) if there are say, s-particles as such.
We need a new concept of such things as mass and gravity- On the face of it your use of primes is rather far above the standard ideas which perhaps gets use sufficiently to octonions and mirrors if we consider real multiplicative inverses.
As I said, Victory all the way around including the established experimenters. Only now we have a little writers block some project of enquiry seemingly abruptly finished, chrysalis before our sprouting of new wings.
Or (Nice metaphor Ulla, Cicadas coming out of the ground and leaving so many skins of theory shed clinging to the trees.)
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Interesting Articles on the Sci Mags
An interesting series which seems to make Hawking a sort of philosopher...surely he has insights that puts him forward into these long considered human concerns. What is on the other side of a black hole long after from all perspectives it has evaporated and yet persists? One thing for sure we are not finsished with knowledge only that of our day and a vast new awakening awaits us.
This alone should show us how much we need a slightly wider view of what matter is if we are to understand the why behind the technology that works and in its proof makes sense. An important article here if you read between the lines and non-linearity, after all it is not just a matter of choosing what entity needs be Majorana or not- but how we organize perceptions and information.
This is a cleaver yet retro idea and does ask us to define better what is an indivdual and species. Yet there are other ways the mutation systems are contained in an organism of so many cells. Applied biology would also benefit from more unified and system levels of theories on analogous scales. These distinctions cannot be the only model and may vanish after their assertions that give us a reality check for current models.
A little sociobiology here, the ten percent poor always with us- Perhaps the handedness of snail shell ratios, and just perhaps the underlying general direction into the idea of dark matter- energy. Well, 15% of the voting population did after all initiate the American Revolution.
Scientific truth is not necessarily the fad tipping point as consensus and peer review and in chaos-science some mutations or new species might try but not survive the organization of say four established powers short of a major disaster.
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*8 Whatever the theories in view of the wider application of what we imagine as uniform laws across the universe but more general, the concept of limits as if two points are vanishingly close in the equations leading to a grounding that is in principle Pythagorean, assumes things that compacts theories to this narrower view before we cleverly modify them- this is especially true when we jettison the smaller values of higher differentiations in a world where our concept of distance at least from some central perspective is not as clear cut as we imagined- This is not to say that underlying all things is an ultimate Euclidean substratum although that is there- but the effect for awhile at least for this realization with the mathematical details of foundations is as if we once had to choose or discover if the nature of physics was Euclidean or non-Euclidean (which we do not as all geometries logically rise or fall together). Why does a spinning object spin the space around with it? You see, we need a more fundamental explanation than what is given if we chose to look for one. Such jettisoning works to some extent because (beyond the symmetry of equations implied but are really non-necessity in the general cases as we try to equate different representations and models) because of the 1/2 real limit of the unit or zero pixel (elemental unit) of the quasic field. Riemann turning the directions of zero and infinity on end in his sphere has also to reckon with the multiverse of such privileged centered or not centered space positions. While the math of say general relativity is cleaver in its use of analytic geometry to choose where something shifts axes and coordinates- it is not general enough.
If in our general concern with what is unique and if that uniqueness in meaningful or worth the saving then based on what other than a natural intelligibly of primes to which nature has no problem with large numbers and things do not loop or are inelegantly recursive iterated unto potential and perhaps actual infinity, then what defines uniqueness if primes cannot? If we say that any number beyond 2 can be the sum of primes it is a unique property but only a small part of the general picture of what could be unique yet in general uniform throughout the reality.
* * *
primes, what are they?
p-adic, l-adic, m-adic
so many different
forms and functions
giving us the structure
Maybe it takes a little madness to make us truly human?
To hear the song?
Humans are not gods, perfect
humans have emotions that guide us
I saw an old house
grey, with many failures
but so big
it contained many beds
I didn't know
The kids and their families
they told me without words
about their admiration
happiness and joy
joy, joy and happiness
and so much more
You were busy, meeting all those people, talking to them,
your friends, living in your heart.
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