Dear Prof Yanofsky,
Good essay on Structures of the mathematics and number systems required for explaining this Universe or Multiverse...
Your observations like...
1. "Since we have no contact with possible other universes, the question of the existence of the multiverse is essentially metaphysics." And "Rather than saying that the universe is very structured, say that the universe is chaotic and lacks structure. The reason why we see so much structure is that scientists act like a sieve and pull out only those phenomena that are predictable. They do not take into account all phenomena; rather, they select those phenomena they can deal with."
2. "science predicts predictable phenomena"
3. "Despite these failings of our explanation for the structure, we believe it is the best candidate for being the solution."
4. "in the middle of the 19th century, physicists started using complex numbers to discuss waves. In the 20th century, complex numbers became fundamental for the study of quantum mechanics."
5. "the octonions as fundamental and all the other number systems as just special subsets of octonions. The only number system that really exists is the octonions. To paraphrase Leopold Kronecker, "God made the octonions, all else is the work of man." The octonions contain every number that we will ever need"
6. "This is similar to what we are doing in physics. We do not look at all phenomena. Rather, we pick out those phenomena that satisfy the requirements of symmetry and predictability. In mathematics, we describe the subset with the axiom that describes it. In physics, we describe the selected subset of phenomena with a law of nature."
7. "As physics progresses and we become aware of more and more physical phenomena, larger and larger classes of mathematical structures are needed and we get them by looking at fewer and fewer axioms."
8. With the final concluding sentence... "Rather than looking at the universe, we should look at the way we look at the universe."
Are really excellent.
It leads to a question, while describing some portions of Universe, if some mathematical structure is used, later we find some undefined area or singularities.... We will be left with no alternative except to find those singularities, is it not? Or can we change the structure of mathematics to find a better solution...
Here in Dynamic universe model an attempt was made to find a singularity free tensor mathematics, which provides a solution to many of the present day Physics problems.
Many papers and books were published by the author on unsolved problems of present day Physics, for example 'Absolute Rest frame of reference is not necessary' (1994) , 'Multiple bending of light ray can create many images for one Galaxy: in our dynamic universe', About "SITA" simulations, 'Missing mass in Galaxy is NOT required', "New mathematics tensors without Differential and Integral equations", "Information, Reality and Relics of Cosmic Microwave Background", "Dynamic Universe Model explains the Discrepancies of Very-Long-Baseline Interferometry Observations.", in 2015 'Explaining Formation of Astronomical Jets Using Dynamic Universe Model, 'Explaining Pioneer anomaly', 'Explaining Near luminal velocities in Astronomical jets', 'Observation of super luminal neutrinos', 'Process of quenching in Galaxies due to formation of hole at the center of Galaxy, as its central densemass dries up', "Dynamic Universe Model Predicts the Trajectory of New Horizons Satellite Going to Pluto" etc., are some more papers from the Dynamic Universe model. Four Books also were published. Book1 shows Dynamic Universe Model is singularity free and body to collision free, Book 2, and Book 3 are explanation of equations of Dynamic Universe model. Book 4 deals about prediction and finding of Blue shifted Galaxies in the universe.
With axioms like... No Isotropy; No Homogeneity; No Space-time continuum; Non-uniform density of matter(Universe is lumpy); No singularities; No collisions between bodies; No Blackholes; No warm holes; No Bigbang; No repulsion between distant Galaxies; Non-empty Universe; No imaginary or negative time axis; No imaginary X, Y, Z axes; No differential and Integral Equations mathematically; No General Relativity and Model does not reduce to General Relativity on any condition; No Creation of matter like Bigbang or steady-state models; No many mini Bigbangs; No Missing Mass; No Dark matter; No Dark energy; No Bigbang generated CMB detected; No Multi-verses etc.
Dynamic Universe Model gave many results otherwise difficult to explain
Have a look at my essay on Dynamic Universe Model and I request your esteemed opinion...