Essay Abstract

Around two-thousand years ago, a book with texts by some of the philosophers of Greek antiquity was compiled. It contained an aphorism stating that «God is the Infinite Sphere whose Center is Everywhere and Circumference Nowhere.» Over the course of the centuries, this image of of an impossible sphere was adapted to no longer describe God, but to imagine the shape of the Universe. Using the dream-like quality of this impossible geometry as an argument, and a text by Jorge Luis Borges as a guide, the author follows a philosophical chain of associations that lead from one fundamental to another, from geometry to music to language to intelligence to paradoxa to spatial inversions to infinity. This tour d'horizon inspires the proposal of a novel geometric shape--the ‹spherene›--which may suffice the conditions called for in the aphorism, while possibly being globally hyperbolic. Maybe one day, we will learn that the Greek philosophers were right all along. The argumentative structure of the text assumes the form of a lemniscate, supporting the conclusion that fundamentals build on other fundamentals, organized in infinite loops. Notes provide alternate readings, supplemental information and sometimes little escapes.

Author Bio

Christian Waldvogel is a conceptual artist, architect and space researcher. His ongoing series of implemented thought experiments covers the timespan from the antiquity to an uncharted future, and topics ranging from particle physics and the shape of the universe to literature and philosophy. He engages in cooperations with the likes of biologists, astronauts, the Swiss Air Force, or the physicists at CERN, producing thought-provoking works in various media. Waldvogel holds an architecture degree from ETHZ and RISD, has exhibited in museums internationally, authored three monographs and served as a Co-Chair for the ESA Topical Team Arts & Science.

Download Essay PDF File

Dear Dr Christian Waldvogel,

FQXi.org is clearly seeking to confirm whether Nature is fundamental.

Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.

All objects, be they solid, liquid, or vaporous have always had a visible surface. This is because the real Universe must consist only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Only the truth can set you free.

Joe Fisher, Realist

Christian,

I loved your essay, as an Astronomer, as a Cosmologist, as a Physicist and as an Architect. I've published a model of coherent galaxy cyclic evolution which scales up to fit the complex CMBR anisotropies exceptionally well with a 'quasar' type dynamic with torus and orthogonal axial outflows encompassed by an etherial oblate spheroid. There are strong similarities with the spherine. I agree your analysis of a sphere and extend that to rotational dynamics and momentum distribution.

My present essay agrees; "geometry is not limited to what is visible. Electric fields can be described in geometric terms, as can gravity and everything that is wave-like.."

I also loved your incisive sentence; "The translation from one system to another, possibly incompatible system poses extraordinary and sometimes insurmountable difficulties, like trying to express a dream by means of architecture or forming a sphere from a sheet of paper." but think even insurmountable can be surmounted with a better approach to thinking, showing, as "Roger Penrose argues that the key to the reconciliation of Relativity and Quantum Mechanics is the human mind"

Also "Wittgenstein famously described the boundary of one's world as being set by the extent of one's language" so true, (and I'm sure you're aware of his affinity with the language of Architecture)

Though you wrote; "one may also find the theory unifying Relativity and Quantum Mechanics, although possibly written in an as yet undiscovered language." I hope you'll recognise my language - the problem is the language of architectural geometry is one most in quantum physics may not understand! (Declan Trails essay gives the matching maths and beautiful curve for them).

Most here may think your essay to etherial but not me. Beautifully done. I hope you don't find mine to mechanistic!

Very best

Peter

Dear Christian Waldvogel, ancient Greek philosophers were right when asserted:«God is the Infinite Sphere whose Center is Everywhere and Circumference Nowhere.»

I would add that space is the body of God, which we do not see, but which works wonders. According to Descartes, space is matter, and matter is space that moves. Thus, space is the foundation for constructing fundamental theories. The space has information, which is then realized in the device of the world. Look at my essay, FQXi Fundamental in New Cartesian Physics by Dizhechko Boris Semyonovich Where I showed how radically the physics can change if it follows this principle. Evaluate and leave your comment there. Then I'll give you a rating as the bearer of Descartes' idea. Do not allow New Cartesian Physics go away into nothingness, which wants to be the theory of everything OO.

Sincerely, Dizhechko Boris Semyonovich.

Christian,

A quite interesting essay. I would think that a Cosmology of Inversion might not just be a philosophical inversion but also a physical inversion, represented by an inverted big-bang, described through one equation by Martin Bojowald who suggested that the big-bang was not the beginning of everything but merely a transition -- the end of a previous universe collapsing into itself, a sort of a white hole rather than a black hole.

Does you inversion go beyond the interdependent systems of mind, perception and knowledge which you say at some point flip back onton themselves, like inversions, rings, and spherenes?

Your fundamental is the concept of inversion? My concept of fundamental might interest you as well.

Jim HOover

A sphere is a mathematical idealization that can be used to describe some objects. The Earth shape can be approximately modeled as a sphere for many applications, but it is not a sphere. We often represent atoms as little balls, but atomic surfaces are not spheres. I see no reason to believe that the Universe, a physical system would have an idealized mathematical shape. The reconciliation of relativity and quantum mechanics do not have anything to do with the human mind, and we do not need a "yet undiscovered language" to unify relativity and quantum mechanics.

Similar remarks about the 'spherene', adding that measured curvature in universe is not "constant negative". Infinite space either implies zero density (so there is no Universe) or an infinite amount of matter (which implies universe different from the observed).

Dear Christian Waldvogel, ancient Greek philosophers were right when asserted:«God is the Infinite Sphere whose Center is Everywhere and Circumference Nowhere.»

I would add that space is the body of God, which we do not see, but which works wonders. According to Descartes, space is matter, and matter is space that moves. Thus, space is the foundation for constructing fundamental theories. The space has information, which is then realized in the device of the world. Look at my essay, FQXi Fundamental in New Cartesian Physics by Dizhechko Boris Semyonovich Where is the assertion that through the surface of a closed sphere around every point in space is the stream of force equal to a constant value. If this consistency is broken to point moves so that consistency was restored.

Do not leave without attention New Cartesian Physics which wants to be the theory of everything OO.

Sincerely, Dizhechko Boris Semyonovich.

Christian,

I feel every concept contributes to an understanding of "fundamental," so I am reviewing my own sketchy evaluations to help my understanding and see if I have rated them. I find that I have not rated yours and am correcting that today. I feel that your essay lends an ancient wisdom to thinking on all realms of thought as I noted above.

Regards and good luck,

Jim Hoover

Dear Prof Christian Waldvogel

Wonderful OP words... "Around two-thousand years ago, a book with texts by some of the philosophers of Greek antiquity was compiled. It contained an aphorism stating that «God is the Infinite Sphere whose Center is Everywhere and Circumference Nowhere.» Over the course of the centuries, this image of of an impossible sphere was adapted to no longer describe God, but to imagine the shape of the Universe. ......."

I hope you will not mind that I am not following main stream physics...

By the way...Here in my essay energy to mass conversion is proposed................ yours is very nice essay best wishes .... I highly appreciate hope your essay ....You may please spend some of the valuable time on Dynamic Universe Model also and give your some of the valuable & esteemed guidance

Some of the Main foundational points of Dynamic Universe Model :

-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 GR on any condition

-No Creation of matter like Bigbang or steady-state models

-No many mini Bigbangs

-No Missing Mass / Dark matter

-No Dark energy

-No Bigbang generated CMB detected

-No Multi-verses

Here:

-Accelerating Expanding universe with 33% Blue shifted Galaxies

-Newton's Gravitation law works everywhere in the same way

-All bodies dynamically moving

-All bodies move in dynamic Equilibrium

-Closed universe model no light or bodies will go away from universe

-Single Universe no baby universes

-Time is linear as observed on earth, moving forward only

-Independent x,y,z coordinate axes and Time axis no interdependencies between axes..

-UGF (Universal Gravitational Force) calculated on every point-mass

-Tensors (Linear) used for giving UNIQUE solutions for each time step

-Uses everyday physics as achievable by engineering

-21000 linear equations are used in an Excel sheet

-Computerized calculations uses 16 decimal digit accuracy

-Data mining and data warehousing techniques are used for data extraction from large amounts of data.

- Many predictions of Dynamic Universe Model came true....Have a look at

http://vaksdynamicuniversemodel.blogspot.in/p/blog-page_15.html

I request you to please have a look at my essay also, and give some of your esteemed criticism for your information........

Dynamic Universe Model says that the energy in the form of electromagnetic radiation passing grazingly near any gravitating mass changes its in frequency and finally will convert into neutrinos (mass). We all know that there is no experiment or quest in this direction. Energy conversion happens from mass to energy with the famous E=mC2, the other side of this conversion was not thought off. This is a new fundamental prediction by Dynamic Universe Model, a foundational quest in the area of Astrophysics and Cosmology.

In accordance with Dynamic Universe Model frequency shift happens on both the sides of spectrum when any electromagnetic radiation passes grazingly near gravitating mass. With this new verification, we will open a new frontier that will unlock a way for formation of the basis for continual Nucleosynthesis (continuous formation of elements) in our Universe. Amount of frequency shift will depend on relative velocity difference. All the papers of author can be downloaded from "http://vaksdynamicuniversemodel.blogspot.in/ "

I request you to please post your reply in my essay also, so that I can get an intimation that you replied

Best

=snp

Hello :)

I like , of course they are the sphere :) do uou know my theory of spherisation with quantum and cosmological sphères Inside thisuniversal sphere in optyimisation of matter energy ? here is also my equation about matter and energy explaining quantum gravitation and DM E=m(b)c²+m(nb)l²

Best Regards and spherically yours from Belgium

5 days later

Dear Christian

If you are looking for another essay to read and rate in the final days of the contest, will you consider mine please? I read all essays from those who comment on my page, and if I cant rate an essay highly, then I don't rate them at all. Infact I haven't issued a rating lower that ten. So you have nothing to lose by having me read your essay, and everything to gain.

Beyond my essay's introduction, I place a microscope on the subjects of universal complexity and natural forces. I do so within context that clock operation is driven by Quantum Mechanical forces (atomic and photonic), while clocks also serve measure of General Relativity's effects (spacetime, time dilation). In this respect clocks can be said to possess a split personality, giving them the distinction that they are simultaneously a study in QM, while GR is a study of clocks. The situation stands whereby we have two fundamental theories of the world, but just one world. And we have a singular device which serves study of both those fundamental theories. Two fundamental theories, but one device? Please join me and my essay in questioning this circumstance?

My essay goes on to identify natural forces in their universal roles, how they motivate the building of and maintaining complex universal structures and processes. When we look at how star fusion processes sit within a "narrow range of sensitivity" that stars are neither led to explode nor collapse under gravity. We think how lucky we are that the universe is just so. We can also count our lucky stars that the fusion process that marks the birth of a star, also leads to an eruption of photons from its surface. And again, how lucky we are! for if they didn't then gas accumulation wouldn't be halted and the star would again be led to collapse.

Could a natural organisation principle have been responsible for fine tuning universal systems? Faced with how lucky we appear to have been, shouldn't we consider this possibility?

For our luck surely didnt run out there, for these photons stream down on earth, liquifying oceans which drive geochemical processes that we "life" are reliant upon. The Earth is made up of elements that possess the chemical potentials that life is entirely dependent upon. Those chemical potentials are not expressed in the absence of water solvency. So again, how amazingly fortunate we are that these chemical potentials exist in the first instance, and additionally within an environment of abundant water solvency such as Earth, able to express these potentials.

My essay is attempt of something audacious. It questions the fundamental nature of the interaction between space and matter Guv = Tuv, and hypothesizes the equality between space curvature and atomic forces is due to common process. Space gives up a potential in exchange for atomic forces in a conversion process, which drives atomic activity. And furthermore, that Baryons only exist because this energy potential of space exists and is available for exploitation. Baryon characteristics and behaviours, complexity of structure and process might then be explained in terms of being evolved and optimised for this purpose and existence. Removing need for so many layers of extraordinary luck to eventuate our own existence. It attempts an interpretation of the above mentioned stellar processes within these terms, but also extends much further. It shines a light on molecular structure that binds matter together, as potentially being an evolved agency that enhances rigidity and therefor persistence of universal system. We then turn a questioning mind towards Earths unlikely geochemical processes, (for which we living things owe so much) and look at its central theme and propensity for molecular rock forming processes. The existence of chemical potentials and their diverse range of molecular bond formation activities? The abundance of water solvent on Earth, for which many geochemical rock forming processes could not be expressed without? The question of a watery Earth? is then implicated as being part of an evolved system that arose for purpose and reason, alongside the same reason and purpose that molecular bonds and chemistry processes arose.

By identifying atomic forces as having their origin in space, we have identified how they perpetually act, and deliver work products. Forces drive clocks and clock activity is shown by GR to dilate. My essay details the principle of force dilation and applies it to a universal mystery. My essay raises the possibility, that nature in possession of a natural energy potential, will spontaneously generate a circumstance of Darwinian emergence. It did so on Earth, and perhaps it did so within a wider scope. We learnt how biology generates intricate structure and complexity, and now we learn how it might explain for intricate structure and complexity within universal physical systems.

To steal a phrase from my essay "A world product of evolved optimization".

Best of luck for the conclusion of the contest

Kind regards

Steven Andresen

Darwinian Universal Fundamental Origin

Christian,

Shame you're not engaging in the process and answering posts. I find much value from reading others essays. There are many but I invariably manage to read comment & score all those who read mine and I know others do to.

Very best

Peter