THE JUDGEMENT
In the case of Atomistic Enterprises Inc. vs. Plato & Ors, this honorable court wishes to commend FQXi for providing and maintaining courtroom 1764 for the proceedings.
In deciding this case, the court is pleased that both counsel founded their arguments on geometry, in keeping with the late Hon. Judge Galileo's admonition that in constitutional conflicts, geometry is supreme, as he said and I quote, "He who attempts natural philosophy without geometry is lost - Galileo Galilei, Dialogo, Opere 7 299 (Edizione nazionale, Florence, 1890-1909)". However, counsel misdirected themselves in not equally heeding the admonition of the late Hon. Judge Wheeler, which *prima facie* must equally apply to geometry, the science of space in that "... even the SPACE-TIME continuum itself - DERIVES its FUNCTION, its MEANING, its very EXISTENCE entirely - FROM ... binary choices, BITS". (capitals for emphasis and can be read separately). Indeed, if they had done so this case would not have been so protracted or even arisen in the first place.
Taking counsels' addresses, submitted exhibits and other testimonies into account, including at least two from expert PhD witnesses in the persons of Howard Baum and Carolyne Devereux on the question whether "Existence/Non-existence" can be regarded as a 'bit' which was answered in the affirmative, this honorable court now finds as follows:
1) As there is no dispute between parties that the fundamental objects of geometry would 'have no part', being not further divisible, we uphold both counsel's submission. POINTS are the fundamental units of geometry, BUT so are MONADS.
Courtroom audience: (murmurs)
Court sheriff: Silence in court‼
Both counsel: Your honor, how can we BOTH be correct?
Judge: (turning to audience) Further murmurings may attract contempt charges...
(turning to both counsel) Have counsel disregarded the 'reducing middle' of Peter Jackson and the 'interplay in a cosmic dance' of Jonathan Dickau? I continue...
2) Points are geometric objects of zero dimension. Their attribute of "non-existence" does not make them a geometric fiction as Plato has pointed out during proceedings.
3) Monads can be regarded as extended 3-dimensional geometric objects of Planck dimension conferring extension to that entity which we call space, even as there can logically be no spatial interval between them. All that has extension must exist. Therefore monads have the attribute of "existence", which they exhibit discretely.
4) As noted by the late Judge Wheeler, citing various authorities, information in terms of expressed binary choices underlies reality. The court holds that reality cannot be hindered from expressing its constitutional right to this binary choice, which it may freely express in the manner of existence/non-existence, and which from paragraphs 2 and 3 above is to say monad/point, representable by the binary digits, 1 and 0 respectively. The experts' opinion therefore indicate that a point can be a 'bit' after all, notwithstanding its non-existence and contrary to Plato's earlier answer during cross-examination.
5) The expression of the binary choices in paragraph 4 is the fundamental event in this universe. All other events are secondary patterns to this, no matter how seemingly complexly contrived and expressed.
6) The fundamental 'it', the basis of substance is a discrete expression of binary choice 1. All other extension/structure in the form of lines, surfaces and bodies are composite, no matter how seemingly complexly contrived and beautifully expressed like Antony Ryan's Fibonacci series, and no matter whatever other attributes like mass, charge they claim to have acquired. All these acquired attributes can be decomposed into the fundamental structure/event.
7) As regards, the issue of motion, the court finds that this is a phenomenon whereby in the line of motion of a body, monads discretely convert sequentially to points, while in the opposite direction points convert serially to monads, both events occurring simultaneously and equally in obedience to an action-reaction principle. This makes motion describable in incremental steps as has been advocated by Leibniz and Newton in their development of Calculus (testimony from Jeff Baugher noted with thanks). *dx* in calculus is therefore a discrete manifestation of binary choice and is equal to the Planck length, not more and not less. On the other hand, *dt*, i.e. duration for a monad to annihilate to a point or for a point to transform to a monad, cannot be smaller than the Planck time but can have larger values, possibly including being a real number. This allows for variable speeds. Indeed, if counsel had cultivated a reconciliatory attitude, they could not have found otherwise.
When a body flush at an origin A moves to a destination B, assuming without conceding, that the fundamental objects of geometry can only be of zero dimension, from whence does the increasing extension between the moving body and the origin emerge? A question for the relational view with points having zero dimension.
Similarly, assuming without conceding that the fundamental objects of geometry can only be extended objects, whither those objects as the extension reduces between the moving body and its destination? Have they not collapsed to points of zero dimension? A question for finite geometry and substantivalism.
Motion is therefore digital, without the necessity to resort to mathematical but unphysical tools like those of Cauchy and Cantor in order to bypass Zeno's paradoxes of motion. A bypass that ends up giving us the headache of distance to destination *tending* to zero, fractioning of distances beyond the Planck limit and no discernible first or last step taken during motion.
So when next you drive your car, take a walk, see a bird fly, a fish swim or even nod your head to some music, consider that that which you are witnessing is the conversion of extension to points and points to extension.
8) On the possibility of superposition of states. While this may apply to composite things, we find no evidence before us that this will be available to things having no parts, as subtly hinted also by Leibniz in paragraphs 7 of his Monadology, and I quote, "It doesn't make sense to suppose that a monad might be altered or re-arranged internally by any other created thing. Within a monad there's nothing to re-arrange, and there is no conceivable internal motion in it that could be started, steered, sped up, or slowed down, as can happen in a composite thing that has parts that can change in relation to one another". Indeed, evidence of superposition of states by any 'it' can be taken as evidence that that 'it' is composite. Ian Durham's testimony although a possibility is therefore not applicable to the instant case, while that of Georgina Parry is upheld.
9) As regards rumors that what decides whether a centrifugal force would act between two bodies in *constant relation*, would not be the bodies themselves, since they are at fixed distance to each other, nor the space in which they are located since its whisperings that it is a participant and not a nothing are ignored, but rather by a distant sub-atomic particle light-years away in one of the fixed stars according to Mach's principle, or in its alternative by the cosmic background radiation or a local inertial frame as suggested by Giacomo Mauro D'Ariano and Philip Gibbs respectively, in which reference frame the *constantly related* bodies' circular motion can then be realized, all in a bid to deny space its geometric constitutional rights to participate in motion, are respectfully noted but are unconvincing to this court in the light of evidence that points and monads are now to be seen as binary states.
10) As to counsel's plea to rename Point road, Extended Point Highway, the court declines to do this. That there is no victor and no vanquished in this suit is obvious, *res ipsa loquitur*. Rather, for his remarkable insight we name the bridge linking the two roads, "Wheeler's Bridge", for providing an opportunity for that much needed handshake across the theoretical physics divide.
11) We thank some of the friends of the court, *amicus curiae*, not earlier mentioned, Alan Kadin, Marcus Arvan, John Merryman, Michael Helland, Joe Fisher, Eckard Blumschein, Basudeba Mishra, Edwin Eugene Klingman, George Gantz, Roger Granet, Anton Biermans, Hoang cao Hai, Antony Ryan, Hon Jia Koh, Henry Lindner, Patrick Tonin, Helmut Hansen, Vladimir Tamari, James Hoover, Zoran Mijatovic, John Selye, Domenico Oricchi, Andrej Rehak, Vladimir Rogozhin, Armin Shirazi , Sreenath, George Kirakosyan, Hugh Matlock, Vijay Gupta, Stephen Anastasi, Thomas Howard Ray, John Maguire, Yuri Danoyan, Adel Sadeq, Steven Sax, Brian Ji, Jayakar Joseph, Israel Perez, Michel Planat, Than Tin, Don Limuti, Chenxi Guo, Douglas Alexander Singleton to mention a few.
12) In the matter of Atomistic Enterprises Inc. vs. Plato & Ors, this is the considered judgement of this honorable court. Details of this judgement may be posted later on viXra.org or arXiv.org.
THANK YOU.
*This is a Classical judgement. For future Quantum versions see people like Armin Shirazi, Don Limuti and Gordon Watson.