Remember what the dormouse said: Feed your head!
An Epistemological and Quantitative Framework for understanding the Structure and Function of the Quantum and Cosmic Worlds is presented in an overview. The envolution and involution of the Universe, a refined and more sophisticated and integrated model of cosmic and quantum evolution is also illustrated within this Framework. The current generally accepted model of the universe, the Lambda-CDM model, is turning out to show major conceptual and perceptual cracks, as the result of recent “crisis in Cosmology” using Euclid, Hubble, Webb (JWST) telescopes and other instruments to measure the hypothesized constant of the Hubble tension H0 by using the assumed Newton’s and Einstein’s Universal Gravitational constant G. Moreover, the current Standard Model of particle physics is incomplete and has epistemological deficiencies and faux-mysteries that block a better understanding of the underlying processes of the Quantum world. The Formatics Framework is a Framework for understanding the process and structure of the Universe at both the Quantum and Cosmic scales, avoiding speculation of ersatz concepts such as “dark energy” and “dark matter”.
In formulating how and why the Universe works, Gestalt Science is a methodology that can be used to better understand the structure and function of existence. Gestalt Science: Comparative Science and Relational Complexity is a way of researching and modeling dynamic and informational physical processes. The four domains of knowledge: science, mathematics, information science, and envolution (functional evolution) are used to integrate models of dynamic structures in a functional, contextual, and wholistic manner. Formatics is a Gestalt Science Framework for unifying the cosmic and quantum worlds.
The ANSATZ: A SYSTEM FOR REASONING
The Formatics Framework via the 27 Non-Abelian Finite Simple Sporadic Groups and their 355 maximal subgroups suggests that there is a “finite quantum pool” in the form of the Cosmic Background Radiation that forms the Dynamic Discrete Finite Quantum basis for Existence.
There is two ways of doing a scientific calculation according to Enrico Fermi: either have a clear physical model in mind or have a rigorous mathematical basis. For a coherent and effective modeling of science phenomena, one needs to integrate four knowledge domains.
In Gestalt Science, I posit that you need to have four things:
1) a solid informational Framework,
2) clear physical models,
3) a rigorous finite mathematical basis,
4) a flexible envolutional and involutional model.
In Gestalt Physics matching physical phenomenon with mathematical and informational concepts through an envolutionary (structural and functional) lense is the first order of business. The 27 Non-Abelian Finite Sporadic Simple Groups form a total order (on the whole number line) and can be thought as forming a pre-order for the universe, with each group representing an underlying finite scalar field of existence. With this discrete finite Framework, specific physical informational dynamic concepts such as quarks, neutrinos, leptons, bosons, various “forces” are assigned to informational atoms in a relational context by careful analysis and synthesis.
Conventional physics has a major problem, although quantum mechanics is very accurate in the small, and general relativity is fairly accurate at the star system level, there is a total mismatch between the two models and at the galaxy scale and beyond, these models are hopeless and contradictory in their predictions. The over reliance of vague notions of physical and mathematical continuity and limits, has formed a cul-de-sac in understanding.
“Do not worry about your difficulties in mathematics,
I assure you that mine are greater.” –Albert Einstein
These 27 Non-Abelian Finite Sporadic Simple Groups (in some sense, information atoms) can be relationally interconnected to form a partial order lattice underlying dynamic physical reality. From a informational and mathematical perspective the 27 Sporadic Groups form a Finite Total Order.
For example, seven of the simple groups are part of the Leech Lattice. Each of those seven Simple Groups can be assigned to an epistemological and informational concept, within informational and physical relations and processes. The following groups are assigned to an informational atom corresponding a physical dynamic concept. The Leech Lattice can be seen as being embedded in the Higgs Field in the form of the Monster Group (M).
Conway 1 (Co1): Z Boson, Conway 2 (Co2): W- Boson, Conway 3 (Co3): W+ Boson, McLaughlin (McL): Tau Lepton, HigmanSims (HS): Muon Lepton, Suzuki (Suz): Down Quark, Janko 2 (J2): Electro-Magnetic Center.
Each of these finite information atoms form dynamic physical and informational relationships. Bound, constrained by maximal subgroups the Sporadic Framework dynamically delineates and forms the quantum foundation and cosmic roots for the universe.
In the Standard Model of particle physics, “time” is treated as a linear, continuous parameter that is part of the spacetime continuum described by Einstein’s field equations. The Standard Model itself, which governs the interactions of subatomic particles, does not provide a mechanism for the emergence of time; rather, time is a backdrop against which these interactions occur. Time in this framework is fundamentally simple and universal, without internal structure, and is invariant under Lorentz transformations which mixes the general notion of time with the three spatial dimensions depending on the observer’s relative motion. Inherent in the Lorentz transformation is “the one di-mension of Time.” This assumes infinity based on differential and integral calculus, assuming smoothness and continuity, as being physically valid, despite the obvious contradictory notion of Planck’s discrete quantum scale in [HBar]. It has been established that the Standard Model is incomplete. The simplistic and over general notion of one infinite di-mension “time” can be refined.
Notion of Time in Mathematical and Information Symmetries
In contrast, when considering groups like the Finite Simple Sporadic groups, the concept of time can embody more complicated and structured properties, akin to informational and mathematical notions of symmetry, antisymmetry, gyrosymmetry and asymmetry. Sporadic groups, which are among the most exceptional and complicated finite structures that are characterized in abstract algebras, do not represent “time” as a simple (continuous and smooth) and infinite (infinitesimal) concept of one dimension but provide a framework for understanding different “discrete and finite kinds of time.” The 27 Sporadic Groups serve as a Total Order framework (in a finite integer domain), which is a pre-order for existence. Moreover, the Framework, called Formatics, serve as a dynamic partial order for the universe. For example, using the 15 Supersingular values of the Monster’s Sporadic Group Primes (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 67, 71) one can build up a relational understanding of physical concepts using the 27 Sporadic groups as information atoms. As examples: 1) the Mathieu 11 Sporadic group is an information model of the proton, 2) the Mathieu 12 Sporadic group is an information model of the neutron, 3) the Janko 1 Sporadic group is an information model of the electron, and 4) the Thompson Sporadic group is an information model of the weak force. All 27 Sporadics can be assigned a physical meaning related to quantum phenomena, forming a finite network of relations characterizing the partial order lattice .
Sporadic Groups and Mathematical “Time”
Sporadic groups are a distinct series of finite simple groups and uniqueness and intricacy are analogous to more refined versions of “time” where time here refers to the unfolding of symmetrical/asymmetrical properties and transformations of the quantum world. In addition, the 17 Finite Families of Lie Simple Groups, on the other hand, serve as the embedding foundation for the cosmic world and the Sporadic groups Framework.
In this (finite) Framework, “time” could be conceptualized as the progression through sequences of symmetrical states or transformations, each represented by finite information group actions. These groups’ actions can be akin to transformations that evolve a system from one dynamic state to another, revealing symmetries/asymmetries and patterns not evident in simpler systems that rely on the simple Shannon entropy. This conceptual version of “time” aligns with mathematical exploration into highly structured and layered phenomena, where symmetry/gyrosymmetry/antisymmetry/asymmetries play a crucial role in group and Moufang loop transformations via maximal subgroups, subgroup direct products, semi-direct, semi-simple and cyclic embeddings of “time”.
Connection to Physics
Although the 26 finite Lie Sporadic groups have not been directly linked by conventional particle physics to modeling physical time, Lie groups are fundamental to the Standard Model. Thus, indirectly, the Sporadic groups (which are Lie groups), with their simplex and orthogonal structures, embody abstract but finite mathematical properties. These properties are more refined and represent sophisticated models and symmetries/asymmetries in physics. The 27th Sporadic group, the Tits group, which is neither a Lie group nor a subquotient of the Monster group, breaks the symmetric constraints of the Standard Model (U(1) x SU(2) x SU(3)). Understanding the symmetries and asymmetries in particle physics, the field extensions beyond the Standard Model are enhanced by correspondences drawn from the Supersingular prime values associated with 27 Sporadic groups and the 17 Simple Families such as G2(q), 3D4(q3), 2E6(q2), 2F4(22n+1), E6(q), E7(q), and E8(q) that serve as information bases and constraints for star systems, neutron stars, and black holes.
Gestalt Science related blogs: The Di-Lemma, Gestalt Science, Reimagining, Feynman, That Relational Thing, The Digital Sand Reckoner, Towards Quantum Formatics, The Ring that Binds and Grinds, Prime, On the Question of Learning Words, One Ring that Binds Them All, The Functional, Within the Edge of…