Paper 1: Taking a Pragmatic Position for Describing Objects, Time, Space, and Making an Extra-Model of Them
Keywords:Physical Objects, Model Time, Model Space, Local and Nonlocal, Conceptual Model.
This Paper 1 introduces a tentative Formalism, which is detailed in a separate Paper 2, and tested there on two cases studies of Time dilation. Paper 2 titles: Practical application of the composite Modeling Units, and an exercise on emulating the mathematics of Time dilation in a relative velocity or gravity situation.
We touch exclusively at the way we describe the physical Objects in human terms, whilst the true Objects, as well as true Time and true Space, remain unchanged. The particular Formalism we propose is geometrically-blind, so it needs to work in parallel with regular human Observing-Modeling of the Objects.
A good question is why we should complement our regular geometric picture of the Objects, and also think of them as our Formalism does. The possible advantages are: a much intuitive and practical handling of the human Nonlocal; a plain reading of human Objects and of their Relationships in terms of elementary Logics; a common Modeling frame for the formal light-like, and for the Closed and Local Massive-like Objects we have in the Model.
We may also gain some independent hints on the human Observing-Modeling in general. The Geometry of our own body qualifies Closed and Local, so it is much similar to the one of regular Objects we want to Model. As a matter of fact, our body makes a concrete Observing-device, thus we qualify as a very particular case of Observer-Modeler of the physical World.
We want to conserve such a concrete and well-established human position with regards to the Objects, but we want also to generalize it. Thus we attempt extending our naí¯ve Geometric perceiving of the World, and see where it leads.
Section 1 focuses on Geometry, and proposes a logically-inverted Geometry B as a natural complement of our regular Point-based Geometry A. Then we explore the idea of a composite Model Object made of both a Local and a Nonlocal part. We base on a double Point-Of-View, which reflects formally our new A-and-B Geometry.
Section 2 investigates the Point-Of-Views, as a second key element on which we base any human Observing-Modeling of Objects. We propose a pragmatic Absolutism-Relativism classification of the Model Parameters. This depends plainly on where we Modelers want to set the Point-Of-View, and basically makes a practical tool for reproducing the objectivity of an Object, and the objectivity of the Observation.
Section 3 checks the implications, and handles pragmatically the human conceptualizations of Time and of Space. The scope is very small-minded, and we declare openly not to know what those items are. Instead, we formalize a Model Time-like and a Model Space-like to start working practically with our Objects. This requires introducing a human notion of Time which is discontinuous, and thus very particular to our Nongeometric Modeling of Objects.
Section 4 anticipates the two kinds of composite elementary Objects that we can formalize based on the components above. They are made of a geometric-like body A-B, which includes a Logic A-B and a special Time-like function on board. We specify our Objects as being concrete and to conserve as usual. We can however explore the effects of the Logic, so we get a flexible Modeling Unit, which can take different configurations, and emulate different kinds of Objects.
The full Procedure appears in Paper 2. Below we simply suggest a possible handy visualizing of our composite A-B Objects. We also provide a few practical indications on how they work and behave formally in the Model. The whole refers to the well-knows Point-Mass scheme. Operatively, we build an equivalent which is Nongeometric and contains two-Slabs A-B, where A emulates the solid core of a regular Object. Then we set our two key-standards, which are the elementary Model Objects of the kind of Proto1 or Proto2.