**“Constructing the Universe from Scratch”**

A running commentary is being developed within my LinkedIn blogging area. Besides editing the overall document, the end notes will be using some of these reference materials below.

*****************************************************************Reference materials**:

https://en.wikipedia.org/wiki/Bifurcation_diagram

https://en.wikipedia.org/wiki/Law_of_Continuity

http://www.academia.edu/748956/The_pythagorean_relationship_between_Pi_Phi_and_e

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/propsOfPhi.html

http://sprott.physics.wisc.edu/pickover/trans.html

https://en.wikipedia.org/wiki/Clifford_A._Pickover

https://en.wikipedia.org/wiki/List_of_mathematical_symbols

Hales: http://arxiv.org/abs/math/9811071v2

https://en.wikipedia.org/wiki/Hopf_algebra#Cohomology_of_Lie_groups

https://en.wikipedia.org/wiki/Cellular_automaton

https://en.wikipedia.org/wiki/E_%28mathematical_constant%29

https://en.wikipedia.org/wiki/Euler’s_formula

https://en.wikipedia.org/wiki/Special:Search/Hierarchy_of_transfinite_cardinals

https://en.wikipedia.org/wiki/Euler’s_identity

https://en.wikipedia.org/wiki/Buckingham_%CF%80_theorem

https://www.google.com/search?q=Buckingham+Pi+theorem&ie=utf-8&oe=utf-8

https://www.quora.com/What-is-the-Penrose-number

https://en.wikipedia.org/wiki/Ultrafinitism

https://en.wikipedia.org/wiki/Names_of_large_numbers

https://en.wikipedia.org/wiki/Aleph_number

https://en.wikipedia.org/wiki/Finitism

https://en.wikipedia.org/wiki/Wreath_product

https://en.wikipedia.org/wiki/Spherical_coordinate_system

https://en.wikipedia.org/wiki/Taylor_series

https://en.wikipedia.org/wiki/Hyperreal_number

https://en.wikipedia.org/wiki/Wallpaper_group

*Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere* by **Edward S. Popko **

***********************

http://keithbriggs.info/documents/Keith_Briggs_PhD.pdf

Isoperimetric Quotient for Fullerenes and Other Polyhedral Cages Tomaž Pisanski ,^{†} Matjaž Kaufman ,*^{†} Drago Bokal ,^{†} Edward C. Kirby ,^{‡} Ante Graovac ^{§ }Inštitut za matematiko, fiziko in mehaniko, Univerza v Ljubljani, Jadranska 19, 1000 Ljubljana, Slovenia, Resource Use Institute, 14 Lower Oakfield, Pitlochry, Perthshire PH16 5DS, Scotland, UK The Rugjer Bošković Institute, Bijenička c. 54, HR-10001 Zagreb, POB. 1016, Croatia J. Chem. Inf. Comput. Sci., 1997, 37 (6), pp 1028–1032 DOI: 10.1021/ci970228e Publication Date (Web): November 24, 1997 b Copyright © 1997 American Chemical Society Abstract: The notion of Isoperimetric Quotient (IQ) of a polyhedron has been already introduced by Polya. It is a measure that tells us how spherical is a given polyhedron. If we are given a polyhedral graph it can be drawn in a variety of ways in 3D space. As the coordinates of vertices belonging to the same face may not be coplanar the usual definition of IQ fails. Therefore, a method based on a proper triangulation (obtained from omni-capping) is developed that enables one to extend the definition of IQ and compute it for any 3D drawing. The IQs of fullerenes and other polyhedral cages are computed and compared for their NiceGraph and standard Laplacian 3D drawings. It is shown that the drawings with the maximal IQ values reproduce well the molecular mechanics geometries in the case of fullerenes and exact geometries for Platonic and Archimedean polyhedra.

In the equations of general relativity, `G` is often multiplied by 8π. Hence writings in particle physics and physical cosmology often normalize 8π`G` to 1. This normalization results in the **reduced Planck energy**, defined as:

2π | E_{P}⋅ℓ_{P} |

*************

- natural number after zero.
*e*, approximately equal to 2.718281828459045235360287…*i*, the imaginary unit such that*i*^{2}= -1.*(square root of 2)*, the length of the diagonal of a square with unit sides, approximately equal to 1.414213562373095048801688.- Giunti M. and Mazzola C. (2012), “Dynamical systems on monoids: Toward a general theory of deterministic systems and motion“. In Minati G., Abram M., Pessa E. (eds.),
*Methods, models, simulations and approaches towards a general theory of change*, pp. 173-185, Singapore: World Scientific. ISBN 978-981-4383-32-5.

- Vladimir Igorevic Arnol’d “
*Ordinary differential equations*“, various editions from MIT Press and from Springer Verlag, chapter 1 “*Fundamental concepts*“. - I. D. Chueshov “
*Introduction to the Theory of Infinite-Dimensional Dissipative Systems*” online version of first edition on the EMIS site [1]. - Roger Temam “
*Infinite-Dimensional Dynamical Systems in Mechanics and Physics*” Springer Verlag 1988, 1997. - https://en.wikipedia.org/wiki/Ring_theory
- http://www.uwgb.edu/dutchs/symmetry/penrose.htm
- https://en.wikipedia.org/wiki/Continuous_function

THEORY OF *DYNAMICAL* SYSTEMS AND GENERAL *TRANSFORMATION*. GROUPS WITH INVARIANT MEASURE. A. B. Katok, Ya. G. Sinai, and A. M. Stepin.

Printing:

page 1= Printable PDF of this page only

page2 = Printable PDF of this page only

*March 20 George Polya* can rightly be called the father of problem solving in mathematics education. https://en.wikipedia.org/wiki/George_P%C3%B3lya

Notes: March 5, 2017

1. Virtual particles: https://en.wikipedia.org/wiki/Virtual_particle

2. Pertubation theory: https://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics)

3. Hamiltonian: https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)

4. Also Carlo Rovelli, https://plus.google.com/101505201345791903693

http://www.cpt.univ-mrs.fr/~rovelli/

TIME IS NOT WHAT YOU THINK IT IS

5. Richard Muller https://www.amazon.com/Now-Physics-Time-Richard-Muller/dp/0393285235#reader_0393285235

6. https://en.wikipedia.org/wiki/Cantor_function

7. http://physics.uoregon.edu/profile/jschombe/

**Notes (2016)**:

https://en.wikipedia.org/wiki/Planck_units

https://en.wikipedia.org/wiki/Planck_constant

http://abyss.uoregon.edu/~js/cosmo/lectures/lec20.html

http://www.pnas.org/content/103/28/10612.full.pdf Packing, tiling, and covering with tetrahedra J. H. Conway* and S. Torquato

http://doye.chem.ox.ac.uk/research/cluster_structure.html Jonathan Doyle, Cambridge

https://arxiv.org/abs/1608.00119

On inflation, cosmological constant, and SUSY breaking Andrei Linde

July 2016

finitum

http://abyss.uoregon.edu/~js/cosmo/lectures/lec20.html

Hartle-Hawking proposal

http://link.springer.com/article/10.1007/s40844-015-0001-6

On the problem of scale: a general theory of morphogenesis and normative policy signals for economic evolution

1.54 steradians = or ≠ a gap of 7.36∗

http://plato.stanford.edu/entries/spacetime-iframes/#LinProAbsSpa Robert DiSalle <*rdisalle@uwo.ca*>

space and time: the hole argument

http://plato.stanford.edu/entries/spacetime-theories/ Absolute and Relational Theories of Space and Motion Nick Huggett <*huggett@uic.edu*> Carl Hoefer <*carl.hoefer@ub.edu*>

Dr. *Claus Kiefer*. Institut für Theoretische Physik Universität zu Köln … 0221 470-4300 (secretary). Fax: 0221 470-2189. E-mail: kiefer@thp.uni-koeln.de

http://people.bu.edu/gorelik/cGh_FirstSteps92_MPB_36/cGh_FirstSteps92_text.htm

- Why Trust A Theory? from a conference,
*Reconsidering Scientific Methodology in Light of Modern Physics*, 7-9 December, 2015 - Study algebraic phenomena inhabiting the murky boundary between finite and infinite with Alexandre Borovik
- Study the tension between intuitive infinitesimals and formal mathematical analysis with Mikhail G. Katz (and David Tall)
*Crossroads in the History of Mathematics and Mathematics Education*edited by Bharath Sriraman, University of Montana- Wendy Freedman, University of Chicago, once director of the
*Carnegie**Observatories*in Pasadena, California, and an expert on the Cepheid variable whereby a star pulsates radially, varying in both diameter and temperature and producing changes in brightness with a well-defined stable period and amplitude. - Lewis Carroll‘s
*The Mad Gardener’s Song*includes the lines “He thought he saw a Garden-Door / That opened with a key: / He looked again, and found it was / A double Rule of Three“^{[7]} - Quantum Electrodynamics and Planck-Scale, Rainer Collier, 28 Sep 2017 arXiv:1710.00618v Institute of Theoretical Physics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany

**Infinity, infinitesimals, **dimensionless physical **constants,**hierarchy problem

- A smooth function which is nowhere real analytic
- Instanton
- Peter Mohr <WidmaierMohr@t-online.de> Cross sections at sub-Coulomb energies
- homotopy group of SU(2)
- topological vacua
- abelian gauge group
- Yang–Mills theory
- BPST instanton after its discoverers
- Alexander Belavin
- Alexander Polyakov
- Albert S. Schwarz
- Yu. S. Tyupkin
- pure gauge at spatial infinity
- nonrenormalization theorems
- perturbation theory
- Equations of motion are grouped under three main
*types*of motion: - translations, rotations, oscillations
- Robin Hartshorne
- The idea of T-duality was first noted by Bala Sathiapalan in an obscure paper in 1987[1].

W**ikipedia’s dimensionless qualities**

- Newtonian constant of gravitation
- Newtonian constant of gravitation over h-bar c
- Planck constant
- Planck constant in eV/Hz
- Planck length
- Planck mass On 20 May 2019, World Metrology Day, the world said goodbye to the original kilogram as the redefinition of the SI base units come into force.
- Planck mass energy equivalent in GeV
- Planck temperature
- Planck time
- reduced Planck constant
- reduced Planck constant in eV s
- reduced Planck constant times c in MeV fm
- speed of light in vacuum
- vacuum electric permittivity
- vacuum magnetic permeabilityy
- http://www.fields.utoronto.ca/people-and-contacts

**Period doubling bifurcation**

- …a fine string is maintained in transverse vibration by connecting one of its extremities with the vibrating prong of a massive tuning-fork, the direction of motion of the point of attachment being parallel to the length of the string …the string may settle down into a state of permanent and vigorous vibration whose period is double that of the point of attachment.
- Nonlinear dynamics: chaos are period doubling… intermittency, horseshoes and homoclinic orbits.
- chaos is always regarded as intrinsic randomicity of determinate dynamical systems.
- …attractor undergoes a
*period*–*doubling bifurcation*which converts it from a period-1 to a period-2 attractor. This*bifurcation*is indicated by the forking of the curve *The -coordinate of the Poincaré section of a time-asymptotic orbit plotted against the quality-factor .*- Poincairé (1) bifurcation theory (1885),
*The Future of Mathematics*(PDF) (Weil) (Wikipedia), Sphere, Homology Sphere (Evelyn Lamb, 2017) - On the scaling structure for period doubling (
**PDF**), Garrett Birkhoff, Marco Martens & Charles Tresser, Astérisque, Société mathématique de France, 286 (2003), p. 167-186 *Connecting period-doubling cascades to chaos*, Evelyn Sander, James A. Yorke 17 Feb 2010- ventricular fibrillation (VF) is an application of period doubling

Fourier transform transforms

- Fourier, Quantum Electrodynamics and Planck-Scale,Rainer Collier, 28 Sep 2017 arXiv:1710.00618vInstitute of Theoretical Physics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany

Euler exponentiation

- Euler, https://www.youtube.com/watch?v=IUTGFQpKaPU Yet, we ask, what are these people thinking when they voted for these equations:
- The Dirac
**equation**. 27,061 votes. 34% - Euler’s identity. 13,745 votes. 17%
- Pi. 9,937 votes. 13%
- The wave
**equation**. 3,761 votes. 5% - Riemann’s formula. 4,271 votes. 5%
- The Euler-Lagrange
**equation**. 3,176 votes. 4% - The Yang-Baxter
**equation**. 1,592 votes. 2% - Bayes’s theorem. 2,958 votes. 4%

- The Dirac

The logic of quantum indeterminacy

- https://en.wikipedia.org/wiki/euler
- https://en.wikipedia.org/wiki/Lists_of_mathematics_topics
- Doubly Special Relativity theory (DSR), loop quantum gravitation, the introduction of non-commutative geometries, the use of specially deformed Lorentz algebras, as well as several generalized uncertainty principles (GUP) in which the Planck momentum occurs.