The concept of space is of fundamental importance to an understanding of the world of all possible realities, including the physical universe or digital world.
The conception of space is among the most insightful but the least known concepts. We are unaware if it is an ordering of realities or a conceptual framework or a subjective "pure a priori form of intuition" (the concepts of space and time are not empirical ones derived from experiences of the outside world—but the elements of an already given systematic framework that humans possess and use to structure all experiences, Kant, the Critique of Pure Reason)
Debates concerning the nature, essence and the mode of existence of space date back to antiquity, and a large disagreement continues between philosophers and scientists about what sort of things could be space.
If space is some fundamental substance, entities in itself, or states or processes or interrelationships, the causal ordering upon things, the ultimate causal framework of our interrelated world.
Historically, there have been Aristotelian space and time, Galilean space and time, Newtonian absolute space and time, Minkowski space, or Einstein's relative space and time, with contradicting ontologies of eternalism and presentism.
Space is commonly defined as a 3-dimensional continuum of things containing extension and positions, directions and distances. Paired with time, space is part of a boundless 4-dimensional continuum as spacetime.
In pure mathematics, space is a continuum of mathematical objects as data points with specific mathematical relationships. A space is a set (sometimes called a universe) with some added structure, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces.
In mathematical physics and engineering, space is modelled as a state space, or phase space, an abstract space in which different "positions" represent not locations, but states of some physical system, as a mechanical system or a dynamical system or control system or AI system. Say, in mechanical systems, the phase space usually consists of all possible values of position and momentum variables. In a phase/state space, every parameter or degree of freedom of the system is represented as an axis of a multidimensional space. As a whole, the phase diagram represents all that some system can be, and its shape can elicit the hidden patterns/qualities of the system. A phase space may contain a great number of dimensions.
Nevertheless, no philosophy, neither mathematics, nor physics, nor information sciences defines the notion of "space" itself, space at large, space in general.
What is Space in General?
While abstracting from the philosophical, mathematical and physical spaces, it could be generalized as an infinite and boundless hyper-dimensional continuum, an illimitable extension in all directions, within which every thing and entity and object and event and process is causally interrelated.
<W, C, F>, where W is the totality of all possible realities, C - the totality of all possible causes and effects, changes and processes, F - the totality of all possible causal transformations and mechanisms, mappings or functions
We define "space as a whole" as an ontological construct of Real or Causal Hyperspace (C-Hyperspace) underlying all the possible forms of spaces and state spaces, from mathematical spaces to physical spacetime to digital spaces.
The concept of C-Hyperspace is the world's space framework. Its powerset is the universe of all subspaces, including the empty space and the C-Hyperspace itself, as well as specific subspaces ordered by inclusion, mathematical spaces, physical spacetime, mental or cognitive space, social space, cyberspace, or digital AI hyperspace.
The Causal Hyperspace programming as the global causal hypergraph network is a key part of the World Model Engine Construct, the soul of the Global AI Hyperdimensional Computing Intelligence.
Making hyperintelligent machines demands modeling of the world at large, with all its possible realities and domains, hyperspaces and spaces, as ANNs' parameter/weight ML spaces.
The World's Hyperspace State Spaces: Ontological Hyperspace and Hyperintelligence
The World: all possible universes and realities, entities, relationships and interactions >
Real/Causal Hyperspace: the totality of causal variables, causes, effects and interactions >
Mathematical Space: the universe of variables (mathematical objects) with relationships (structures):
variables/objects: numbers, vectors, matrices, tensors, sets, functions, expressions, geometric objects, transformations of other mathematical objects, and spaces; concepts, axioms, theorems, proofs, and theories
Euclidean spaces, parameter spaces, linear spaces, topological spaces or manifolds, Hilbert spaces, or probability spaces
Structures: measures, algebraic structures (groups, fields, etc.), topologies, metric structures (geometries), orders, events, equivalence relations, differential structures, and categories (objects and relations)>
Physical Spacetime: the universe, matter, energy and fundamental forces/interactions; causal sets, causal structures, quantum gravity, from the Big Band to black holes causal singularities >
Digital hyperspace/Cyberspace: the digital universe of the internet, data universe, cyber-physical technologies >
Hyper-AI World: the intelligent metaverse of virtual, augmented and extended realities, artificial intelligence (machine learning, deep neural networks), hyperdimensional computing, AI hyperspace >
HyperAI is an open and shared AI metaverse ecosystem based on technologies such as applied and generative AI, metaverse, and Web3.0 to space and climate technologies, as pictured below.
All is to create a new space where the real world and the virtual world meet by integrating human intelligence, the internet, and emerging technologies as the man-machine AI hyperspace of hyperintelligent hyperautomation.
AI Space-Time-Matter-Information Compression
Time–space compression and matter-information compression refer to the altering of the qualities of space–time, matter-energy-information and the relationships between space and time, matter, energy and information due to the expansion of emerging technology.
Space-time compression occurs as a result of technological innovations driven by the AI technology that condense or elide spatial and temporal distances, including technologies of communication (Internet, quantum communication) and travel (rail, cars, trains, jets, spacecraft), driven by the need to overcome spatial barriers and speed up all causal cycles.
In computer science, data compression (source coding, or bit-rate reduction) or compression algorithms is the process of encoding data using multi-dimensional vectors as in the hyperdimensional computing as a benchmark for "general intelligence". There are many examples of AI-powered audio/video/image compression software including VP 9, NVIDIA Maxine, TensorFlow or MATLAB's IPT.
As to materials compression, a variety of AI chips as accelerators or massively parallel Intelligence Processing Units for AI and machine learning models as produced by Nvidia, AMD, Intel, Meta Platforms, Graphcore could have billions of transistors.
Cerebras's WSE 2 of the CS-2 AI system, with 7 nm fabrication process, has about 2.6 trillion transistors, which has 850,000 cores, while its brain-scale technology could run ANNs with over 120 trillion connections or parameters:
It is expected that the total amount of data that is stored on the internet and various storage devices could be essentially compressed and ordered as insightful information and valuable knowledge with causal hyper-AI compression algorithms.
The AI world is spreading in and out and speeding up with the speed of light and beyond.
