Post by Timothy GoldenPost by Timothy GoldenThe newb, young as he was, did have access to quite some documentation on the internet, which had access to since his younger years. His curiousity was spawn during an overheard breakfast conversation at a diner between a stranger and his friend in the next booth. "The plates must have heated at high voltage, and the dielectric between them changed somehow. That's the only way I can explain the drop in frequency, and it still is that way now even with the thing running cold." Not a bit of it made sense to the boy, but he could tell they were discussing electronics, and that nobody in his family spoke a word of the stuff. Indeed, they almost treated it as if it were voo-doo. When you turn the switch and nothing happens it's time for a new one. This was the golden age that they lived in. It still is next to impossible to actually make a transistor, and yet the devices by the millions entered every gadget, from a toddler's crib toy to the grave of granddad Johnson, where a little solar panel illuminated the grave at precisely his time of death, coordinated universal time, for about an hour. Sure, there was a fancy version that would compute the trajectory to Venus at his time of death if you wanted it to, and it would turn the LED bulb on for as long as you want; until the battery dies. Brownout detection, they called it. These things have more tricks and widgets built into them than a slice of pi.
To find them at the dump is common around here; not with all these smarts; not on a LED light charged by the sun, but soon, perhaps. I'm really hoping to see three phase motors coming in. Plenty of old DC motors, by the way. So many NiCad drills, NiMH batteries, and even abandoned LiIon. Is technocracy inhumane? Will culture run away? Or are we its slave now? Perhaps it would be wise to keep a wide stance.
Well, so what about those billiards? I was pondering random action, and some other had a quip of variation round about the same time; those billiards actually in their natural state not quite so stable as on that perfectly level felt top table to perfection; as if their own terrestrial makeup were of some other worldly sort.
Then too, the damn electrons, and who exactly ever claims them to be still ever in their lives? In this kinetic mess we are born? And Ohm's law, too? Why, the current here sir is zero, so I must be in an infinite voltage sort of place. My dielectric is quite excellent over here, sir. What a fine dry day it is. What will we do without any ground? Just use the case, sir. Sure, it could be sparking during a nuclear attack, and I've been meaning to ask that Ritter fellow about just how far a Boston blast will get? If I hook a water heating element to my antenna am I in danger of further vaporization? Is it a line of sight thing?
The decent into such places these days feels so well established to me, as the credibility of our own government long ago washed down the toilet drain like a fecal deposit. As if they could make us stoop any lower for it. Cry out in pain, and they'll feed you again. That, or take your circuits down, sir.
Amidst my free-flow of paranoid thinking; why does a chick-a-dee look over its shoulder at a bird feeder?
Then too: has the state known as the U$FG provided us sufficient cause for such thinking?
Certainly they have, sir. Over and over again, kind sir.
Still, upon angst over-loading what is a populace to do?
I guess we are going to find out then.
P1 P2 P3 | P4 P5 | P6 P7 | P8 P9 P10 P11 | P12 P13 | P14 P15 P16 P17 | P18 P19 | P20 P21 P22 P23 | P24 P25 P26 P27 P28 P29 | P30 P31 | P32 ...
which is simply a break after a series of primes, and clearly a non-prime following.
This is in terms of polysign ridiculously complicated, but it does mimic the first breakpoint found in polysign product behavior at P3|P4.
On the one hand the sequence has natural correspondence, but already polysign has turned it into general dimensional geometry.
The effects of mu, which is minus unity, do in fact become blurred at the primes. Even before the antimu blurred it slightly, but at the primes the effect swamps them. Every sign other than the neutral signed unity (nu) will dance through the series accurately and completely. The perfect symmetry of the geometry exposes a sort of observer problem; as if the initial signs can not be detected, other than nu, which does nothing, and in this regard one might even declare an observer problem on nu, which is to say that possibly neutral elements are undetectable; at least in product this would be true of nu.
Anyway, should such a structure be occurring the question could arise whether it is a language; a protocol; or could it be pure arithmetic? It seems more like a protocol, but to claim that it is artificial is not quite the case either. We'd like a source of structure, and if your natural numbers did carry such a thing inside of them then arguably we would grant them structure. Certainly mathematicians have bothered with prime numbers excessively in my opinion, and personally I never felt so compelled to chase them. In a way here under this interpretation they are the hum-drum numbers, with no harmonic excitability.
In this regard of observer awareness, the only thing that is not hum-drum about P4 is its + sign, which has a harmonic behavior. It is actually the first standout.
The awareness on the prime signs as observationally indifferent from one another, with the exception of nu; neutral unity; I am calling this muness, for while mu is well defined behaviorally there is symmetry amongst the other signs under product; they each will march through all sign combinations in an orderly way, and so an observer within this space would have great trouble assigning one particular one of them to be mu. For instance in P7 z equals sign two (+1) will take one through the signs:
z^n: (0,1,0,0,0,0,0), (0,0,0,1,0,0,0), (0,0,0,0,0,1,0), (1,0,0,0,0,0,0), (0,0,1,0,0,0,0), (0,0,0,0,1,0,0), (0,0,0,0,0,0,1)
at which point the structure wraps, and all but nu, and here I should specify this series usage above as mu first, though that detail is cryptically stated already, such details are necessary.
The part which has been overlooked is that within the nonprimes characters such as these still do exist. For instance in P8 signs one, three, five, and seven each possess muness. Those which do not are harmonically related to the signature. In P9 we see signs one, two, four, five, seven, and eight all have muness. Those who do not are three and six, these are providing the harmonic behavior of threeness, and possible some improved nomenclature could be introduced here.
Because the geometry of polysign numbers are automatically demanded as what has traditionally been described as n-1 dimensional, via the law of balance that the sum over the signs of a unity value is zero, thus demanding the balance of the simplex vertices as the sign rays emanating from the center of the n verticed simplex for n-signed values. Yet can you see the arbitrary nature by which these rays become assigned? This is a similar awareness; As we march through the rays as powers of mu we will have the first order of them established, yet no actual chirality rule exists.
Returning to the simplicity of P3, which are a new form of the complex numbers, though they are behaving by the same rules that build the real numbers as P2 via polysign, we can reexpose the puzzle in Cartesian form: without the chiral rules and conventions by which we develop the plane as a horizontal x axis with positive to the right, and a vertical y axis positive upwards, there is no actual way to determine the negative imaginary axis from the positive. An observer within the complex plane will exist in a bilateral symmetry, other than some choice of convention to arrive at.
In this regard the polysign spaces have additional character to their general dimensional geometry. Strangely though, all the way up in P9, we see just three higher types, which simply stem from the factors, and under this thinking in P11 there are just the original two 'higher types' which are muness and nuness, and this is true of all the primes.
Following this lead the orderly types within this 'higher types' awareness are the factorial signatures. P1, P2, P6, P24, P120, P720, etc., and this is a bit different that the breakpoint style construction I offered before, which I think overlooks the muness of the non-primes and focused on those primes as generational.
There is nothing false of the original series of Pn, and without Pn these 'higher type' sorts would not become available. The issue of chirality is always very interesting but I don't see how polysign breaks through any differently than the Cartesian system. If anything the puzzle is exacerbated by the pure geometrical symmetry in Pn. Of course the usual criticisms of the Cartesian way hold from the polysign perspective, which regards the Cartesian product as unnecessary.
Post by Timothy GoldenI can see that in some regards this is backwards thinking, but then we are elements of this universe; we are prisoners of spacetime; we are observers, and possibly with no direct access to the basis upon which we exist. With indirect means we attempt to decode a system which has yielded us as conglomerates of elemental forms which we keep refining, to the point that the elements are no longer elemental, and so the farce is upon us. But this is the state of the art, and prior to this time we might have only earth, air, fire, and water in our thinking. Certainly we have come a long way, but to try to take it all in is a bit much.
One of the compelling details of polysign is the behavior of mu as it can step through the coordinates; something missing from other forms. Linear algebra comes close with its e to the n sort of thinking, but mu does the job from the algebra, and gets an arithmetic product to boot. It is far more primitive. So this thinking in mu does offer subtle guidance.