On Thursday, May 26, 2022 at 9:52:49 PM UTC-7, zelos...@gmail.com wrote:
> torsdag 26 maj 2022 kl. 17:24:48 UTC+2 skrev timba...@gmail.com:
> > There is a sort of convergence that occurs at unity.
> > This is a matter of physical correspondence, philosophy, and mathematics.
> Mathematics do not care about physical correspondence, that is for physicists
> > To unify is to make one.
> > To unite is to join together.
> > We see that mathematics has done this but that this junction has to be kept tender.
> > How is this?
> > We reuse the same numerical format to represent the continuum that was used to represent discrete concepts.
> > This is done not only by choice but out of necessity. There is but one difference between the two and that is the decimal point.
> > This little dot marks a new unity reference. It comes at the convenience of the digits in distinction to the geometer's way of simply fixing his dividers at a handy workable span for the amount of material he has to work upon. The little dot does nothing in these physical terms. Yet it establishes the ability to work arithmetically upon the continuum. It does reuse the natural value with the slightest augmentation. Other than this augmentation, however, there is nothing left but a natural value. This interpretation is starkly different than the standard one which leans upon the elderly rational value. There lays a fault. The simplicity of the structural interpretation is exposed. It is a superior format in that its simplicity is intact without the complications that rational analysis requires, some of which is dubious at best.
> >
> > To me a source of conviction is ultimately to go back to primitive forms. Above is a digital analysis on the reuse of the modulo-10 value. Few are attracted to those sorts of arguments,though their work will be done in those terms should instantiation be called upon. Yielding back to the primitive form we will see that the continuum ultimately asks for direct graphical transcription. In other words the concept of representation by this form actually lacks any unit other than the value itself, which cannot really even be called a value at this primitive stage. Giving up as much technology as possible a piece of twine cut to the length of say the length of a pole in order to transcribe that pole length could stand as a reference to be copied or transferred say to groups of men who are to cut such poles from the woods. As to how many poles each group should cut: this is a discrete figure, and each group could be given a number of pebbles in a bag along with the string to account for what is asked of them. Of course other figures could be augmented, but this is a simplistic example explaining the distinction between the discrete and the continuous. As the man in charge of the bag fumbles through the stones and sees that there are some left to go to what degree did he just bump into the rational value without ever encountering division? Here we see the dirty reradixer in primitive form. This sense of the modulo exception is perhaps not even perceived by the reader here. If there were five stones in the bag then the work is honestly done in fifths. No division was necessary; no five was uttered; yet it occurred as an exception, and then they hauled the logs to the work site.
> >
> > That these two distinct forms happen to overlap in our numerical representation is a tender point. It is as false as it is true. As to what the unit is upon the continuum that affords such a number: here physical correspondence is done away with by the mathematician in modernity. In a time when physics is stumbling and mathematics contains provable ambiguities within its base; as to why the subjects were trifurcated in the first place when many of the best practiced all three as if they were one; I see that we are engaged in a progression; that humans really do have a very difficult time finding the truth. We do in fact start from a blank slate and rely upon the transfer of previous generations of knowledge which we habituate into in order to proceed along a path. So long as ambiguity has been absorbed and even enforced under threat of failure the necessary tension has us shooting ourselves not just in the foot, but in the head. Somehow we survive the wound and keep trying, but progress is minimal.
> >
> > The obvious answer is to break the old rules and reject the old rulers. They filtered out the best who challenged their false paradigms. Rejection is done that easily. The notion that something else quite fundamental remains to be exposed by humans or possibly our offspring AI; something that humans' linguistic abilities simply cannot muster; this would be the greatest hope and yet the simplest explanation as to why physics flounders and mathematics continues its burgeoning accumulation.
> >
> > I've already offered up polysign numbers as an instance of overlooked mathematics. They do beget their own version of emergent spacetime with unidirectional time through the family
> > P1 P2 P3 | P4 P5 ...
> > thanks to a natural breakpoint in the product behavior.
> >
> > Time has been cast as an open problem. Polysign does indeed have something to say about it as well. To what degree is time embedded within mathematical argumentation may be a workable problem. Under this guise concerns that all our work actually takes place in the physical continuum will have to be a basic concession of all of mathematics. A lack of physical correspondence is problematic. Mathematics thus far has failed to recover the spacetime continuum. In that this is the basis that is under discussion is it appropriate to burden mathematics rather than physics with its development? By definition a basis is that primitive. It is that which we work from. In other words physics is to take place upon a continuum that is mathematical in nature. This is the ideal form that we all seek. As objects in or of the basis we cannot hope to gain direct access to its developing parts or mechanisms as we are built out of those things. As we work with intangibles the guessing game ensues.
> >
> > While I don't see polysign numbers as the end of the progression I do realize that they are a necessary step along the way. They fly in the face of the first cosmological principle; isotropy; and expose that spacetime is in fact structured. In the marriage of continuous and discrete entities something may be left to construct still. This is the ideal situation, and I am attempting to give it away here, so to speak. Could you stew on a mixed modulo augmentation to the progression so that not only the sign of P1 is modulo one but that the component value is as well? Likewise the modulo two nature of P2 then extends into its magnitude, and so forth up the chain. What is different? Certainly P1 does come out discretely as its decimal point is not operative. It can exist, but it does nothing to the first interpretation of its value. In some ways this is congruent with our computers and even our writings which come out discretely.
> >
> > This is possibly a view of the natural value as P1. P2 certainly does go continuous as well. Strangely this modulo interpretation comes out fairly consistent with existing mathematics. Perhaps then we can come around to the P2 as a two component value differently? It does seem like a more unified value. Almost as if they are more free-standing entities; individuated entities, but that is just a gross sensitivity. A P3 value is three all the way under this intepretation. Its three components modulo three and three signs... is it simply a triplicate numerical format? There is nothing new there; just that they are right on top of each other. Far be it for me to handle this level of complexity. Call in the mathematicians!
> > On Tuesday, May 10, 2022 at 9:13:35 AM UTC-4, Timothy Golden wrote:
> > > It seems uncontroversial at first.
> > > Discern unity on the continuum
> > > versus unity in discrete terms.
> > > The problem opens up considerably.
> > > That these two take the same representation '1' within our numerical representation is problematic.
> > >
> > > Set theory is supposed to address this, yet the natural values are formally a subset of the real values. This has been vetted by eons of mathematicians, right?
> > >
> > > Having gone through the long way around through the generalization of sign, which uncontroversially I have named polysign numbers, and early on in the past tense, we arrive at a treatment of number as sx, where s is sign and x is continuous magnitude. Sign is of course discrete in its quality; the real numbers being the two-signed numbers, and but for the introduction of a non-travelling identity sign (the zero sign) polysign are consistent with the real number in its present form. Of course three-signed numbers require attention, but if you focused long enough you would bump into them as the complex numbers in a new suit, and realize along the way that the real number is not fundamental. I don't mean to drive you into polysign, but it is this route of thought which leads me to the present interpretation. Having generalized the sign of the real number to what degree am I burdened dealing with the continuous magnitude of it?
> > >
> > > Along the way operator theory is encountered. Polysign come with sum and product algebraically defined in Pn. Geometry comes along for free through the balance of the signs. No Cartesian product is necessary. They are extremely close to the polynomial form, but already they possess their modulo sign character from their composition and so the ideal of abstract algebra, seemingly the curriculum where polysign are intersecting, that ideal is not necessary. That confusing load is gone, along with other confusing details such as the obfuscation of closure and the need to introduce real value coefficients. No. The real value is P2. P3 sits alongside P2 as a sibling; not as a child. Operator theory is directly falsified within the curriculum of abstract algebra, though possibly patchups are underway. Meanwhile their treatment of sum and product as fundamental I agree is sensible, though the term 'ring' is poor.
> > >
> > > Ultimately we see that mathematics has crossed up a fundamental distinction between operators and values and treats compositions of the two as if they are fundamental values. Instances of these include the rational values such as one fifth as well as the irrational values such as the square root of two. In hindsight the irrational value is foisted upon the student as a foil to the foibles of the rational value so quickly that there is no time to look back upon the problem. Firstly, division is not a fundamental operator. Secondly there is a lack of closure of the rational value. To what degree the rational value constructs the continuum versus happens to fit upon it can be taken as a matter of discussion. Clearly the camp that I have landed in is either deleted from current theory or has never even existed.
> > >
> > > The continuous and the discrete are distinct. The operator and the value too are so distinct that such blurry claims as modern mathematics makes deserve our scrutiny. Here I think we can lay a boundary where mathematics left philosophy.
> > >
> > > That we are near to discussing physical correspondence too at this early level of theory is good. This is as it should be; the three as one.

If mathematicists don't need physicists
what about one who invents a mathematics?