The Programmer God hypothesis

if we assign geometrical objects to mass, space and time,
and then link them via a unit number relationship, 
we can build a physical universe from mathematical structures.

Could a Programmer God have used this approach?

The mathematical electron

This website introduces a mathematical universe model (MUH) in which our universe is a simulation programmed at the Planck scale by an external intelligence - the Programmer God.

The model is based on the structure of the electron as a mathematical particle into which are embedded the Planck units (mass, length, time, charge) as geometrical objects (MLTA).

There is a simple way to test this hypothesis. The speed of light c = 299792458 meters/second (m/s). The mass of the electron is measured in kilograms (kg), electric charge is measured in amperes (A). We cannot use the mass of the electron and the electric charge to derive the speed of light, and even if we could numerically, the units don't match.

However, there are anomalies (an apparent mathematical relationship) between these units (the SI units kg, m, s, A, K), which does permit us to exchange them with each other (mass can be interchanged with space and time or with length and charge ...), furthermore these anomalies cannot be explained by a physical universe. If these anomalies are statistically valid, then they can be construed as evidence that we are in a simulation, and also therefore as evidence of a non-human intelligence, the Programmer.

For those familiar with the dimensioned physical constants (G, h, c, e, me ...) and the SI units, this wiki site lists those anomalies.

Are these physical constant anomalies evidence we are in a simulation?
wiki: Physical constants (anomalies)


Are we in a simulation?

The simulation hypothesis posits that our reality is an artificial reality, such as generated in a computer simulation. The idea was popularized in the 1999 sci-fi film 'The Matrix'. The ancestor simulation proposes that an advanced civilization could simulate our universe to the degree that we can observe (as with VR helmets today). This version however presumes a base reality, the physical planet of the original programmers. Conversely, a deep-universe (Programmer God) simulation begins with the big bang and constructs the universe in its entirety, down to the smallest detail.

As the language of mathematics appears to be the language used by the universe, any simulation model that can construct a physical deep-universe has these constraints;

a: the model must be able to construct physical units (of mass, space, time) from dimensionless mathematical structures within the simulation (the simulation itself is simply data on a celestial hard disk and has no physical dimensions). 

b: the model cannot use dimensioned constants such as G, h, c, e ... as they are a measure of physical units (see a), and so are emergent properties (generated from within the simulation) and not fundamental (not embedded into the source code itself). 

c: the model must be independent of any system of units such as kg, m, s, A ... (see a, b) and of any (artificial) numbering system.

This (the mathematical electron) model describes how the above points are resolved.

Introduction to the deep-universe (Programmer God) hypothesis


The Programming God

As a deep-universe (see 'the Planck scale') simulation hypothesis model is programmed by an external intelligence (the Programmer God), we cannot presume a priori knowledge regarding the simulation source code, other than from this source code the laws of nature appear (and from which the laws of physics are derived). 

Furthermore, although the source code may use mathematical forms we are familiar with (as it would be the origin of these familiar forms), this code would have been developed by a non-human intelligence, and so we may have to develop new mathematical tools to decipher the underlying logic. 

By implication therefore, the presence of such a model that fits the above criteria could be considered as our first tangible evidence of an external intelligence (external to the universe).

We must also consider that mathematics may simply be a programming language (as with C or Basic or Java ...), and so therefore not an absolute concept in, and of, itself. Although mathematics is the language of physics, and by extension the universe, it may be amiss to assign to mathematics a greater significance.


The Planck Scale

The science vs. God debate exists primarily because God (the 'external' hand) does not appear in the formulas of physics. There is no E = God.c2 for example, and so science has no practical use for a God. As God has no measurable parameters, God is an untestable hypothesis.

Physics is principally divided into studies of the quantum world and the macro world (of planets and stars). These are separated by 2 successful yet incompatible theories; quantum mechanics and relativity. However there is a deeper world, a theoretical world** that is far below the quantum world, and this is called the Planck world*. The quantum scale is to the Planck scale as our planetary scale is to the quantum scale.

It is posited here that in a deep-universe simulation, the (fundamental) mathematical laws of nature would operate at this Planck scale, and so to understand both the quantum world and the macro world, we must first begin with the Planck world

We can note that science usually interprets the Planck scale using quantum theories, this would be a mistake if the quantum world itself emerges from the Planck scale (it would be equivalent to applying classical physics to describe quantum mechanics). 

* In this model, the Planck level is a discrete level with processes occurring at unit Planck time, a time dimension (frequency) is then added to form particles, this then becomes the quantum level. Particles such as electrons therefore do not exist at unit (Planck) time, but rather are events that occur over time, time as a dimension of particles. The analogy being a casino, throwing a single dice is a discrete (Planck) event (win or lose), the total sum of wins and losses at the end of the day gives us those probabilities characteristic of the quantum level.

** Physics has no tools that can investigate much below the quantum world (the testable laws of physics mostly end around the quantum level), and so this Planck scale remains a theoretical world.


Links - The Programmer God

An general introduction to the Programmer God as a thesis.

The model covers much of physics for I have tried to show that a Planck scale universe model is feasible, that it can explain subjects such as gravity, relativity ... The eBook is an attempt to give a non-mathematical overview of the complete model.


Physical units from Mathematical structures

The biggest problem with any mathematical universe approach is constructing a physical reality (the physical dimensions of mass, space and time) from mathematical structures. Our computer games may be able to simulate our physical world, but they are still simulations of a physical reality. The 1999 film The Matrix and the ancestor simulation both still begin with a physical level (a base reality), the planet earth. The following describes how the Programmer God approach may resolve this crucial problem.

It is proposed that the basic constructs of our universe; Mass M, length L, time T and charge A, could be geometrical objects at the Planck scale (i.e.: these objects do not simply represent these units, they are these units, the function; mass, length, time ... is built into the geometry itself).

Furthermore, these objects are not independent, for example, M exhibits mass-ness in conjunction with L length-ness and T time-ness. This arrangement means that, for example, the length object L can combine with the time object T to form a complex object V which is velocity (V = L/T), and so we can construct a universe Lego-style by combining simple geometrical objects to form more complex geometrical objects (such as electrons and planets).

This however necessitates that the object for length L be able to interact with the objects for time T and mass M and charge A ..., which infers that there must be some relationship between their respective geometries, and indeed we can find what appears to be a numerical relationship (kg equates to 15, s to -30 ... see table below). This relationship tells us how these MLTVA objects can combine, however it creates problems when we compare with mainstream physics as this relationship is incompatible with the fundamental physical constants.

This is because physics has a set of parameters used to define the universe; such as the speed of light, the strength of gravity etc (G, h, c, e ...), these are often referred to as fundamental constants as they cannot be reduced to more fundamental structures. These constants are measured using the units (kgmsA, ...) and so these units therefore must also be independent of each other. Indeed it is the very independence of these units which characterizes ours as a 'physical' universe (as opposed to a computer simulation).

Thus we can determine whether or not we are in a simulation, for evidence of such a relationship between these (kgmsA, ...) units (see unit number) would constitute evidence of a simulation, and this is, as we see below, is not difficult to test.

A dimensioned physical constant is measured in units (kg, m, s, A ...), for example the speed of light has the units m/s. The main dimensioned constants referenced here are the gravitation constant, Planck constant, speed of light, elementary charge, electron mass, Boltzmanns constant (G, h, c, e, me, kB).  

** note: pi = 3.14159... alpha = 137.03599... and Omega = 2.0071349... and so we can calculate numerical values for these objects. For example, M = 1, T =  3.14159, V = 2πΩ2 = 25.312 

*** the metric units (kg, m, s ...) are known as SI units (System International).



The numerical value of M = 1, the SI equivalent is Planck mass = 2.18 x10-8 kg. Therefore to convert from M to Planck mass we can use a scalar k = 2.18 x10-8 kg where M*k = Planck mass.
M * k = 1 * 2.18 x10-8 kg = 2.18 x10-8 kg
We can assign to each object a scalar; mass k, time t, length l, velocity v, ampere a. The scalars have both the numerical conversion factor (for k = 2.18 x10-8) and the units (for k = kg). 

The speed of light c = 299792458 m/s or c = 186200 miles/s ... i.e.: the numerical value of the speed of light depends on the units we use, kilometers or miles. Likewise, if we were to meet aliens, they would write the speed of light in terms of their units, according to their numbering system, and so the numbering system and units are simply measurement systems, light continues to travel at the same velocity regardless of how we, and the aliens, measure it.

It is proposed that these geometrical MLTVA objects are used by the universe itself, they are built into the simulation source code, and so are 'universal' and independent of any numbering system or units. As example, the reason we can use c = 299792458 m/s or  c = 186200 miles/s to measure the speed of light is because embedded within our c is this geometrical object V, which is the real speed of light. Because this V is the geometry of Omega, and Omega has a numerical solution, Omega = 2.007134949, we can assign a numerical value to V = 2πΩ= 25.312....

To this V, we then add scalar v;

v = 11843707.905 m/s such that 

c = V*v = 299792458 m/s

or scalar v = 7356.08 miles/s such that
c = V*v = 186200 miles/s.

Aliens will also have a value for the speed of light but in alien units, and so their scalar v will not resemble our v (in miles or meters). 

However the geometrical V term is the same for aliens and humans alike, it is galaxy independent, the scalar v is just a conversion factor that we (and aliens) can use. We need a conversion factor because objects such as L or T are too small for daily use, the units that we use, such as seconds or feet or meters, are much more practical than these MLTA units (i.e.: 1 meter, a human size unit, is 6200000000000000000000000000000000 units of length L). These scalars however, it turns out, are not just simple conversion factors, they also embed the evidence we are in a simulation. This in turn gives us a 'universal' language.


Can we use these objects to communicate with Aliens

Arrival is a 2016 American science fiction film in which extraterrestrials communicate using patterns.

Speed of light c = object * scalar v. Planck mass = object M * scalar k ... and so on. If we simply add scalars to each of our MLTA objects then we have achieved nothing of value. However each scalar is not just a numerical value, but also includes a unit (v has units m/s or miles/s), and so they follow that unit number relationship, i.e.: the scalar v unit number = 17, k unit number = 15 ...

Via this relationship, we can define each scalar in terms of other scalars, and then we find that we need only 2 scalars to define all other scalars. For example a == 3, l == -13 and t == -30, and so a3 x l3 = -30 == t, and so if I know the numerical values for a and l then I know the numerical value for t, and if I know t and l then I know the value for k etc (see Planck objects).

This also means that if we only need to use 2 scalars, then we can arrange combinations of our constants where the units and scalars cancel. We are then left with only those MLTVA objects.

And so solving those combinations of constants (where the scalars cancel) will return the same numerical value whether we are using terrestrial values or alien values, because of course, sans scalars, we are simply combining the MLTVA object equivalents, without scalars the MLTVA objects are the system of units we are using, and as MLTA objects can be solved using only alpha and Omega (α, Ω), we can solve combinations of (G, h, c, e, me, kB) using only α and Ω (see anomalies (α, Ω)).

However we may wish to solve individual constants, and for this we need the 2 scalars. The following calculator uses as inputs scalars for the speed of light v and Planck mass k; 2 fundamental units. It then solves the fundamental physical constants based on those 2 scalars. If we feed in the alien scalars for (v, k), then the calculator will return the alien values for those constants (see also anomalies scalars).


Do the physical constants embed evidence we are in a simulation?

In summary, at our macro-level, the dimensions of mass, length (distance), time and charge (amperes), represented by the units kg, m, s and A, are independent of each other (we cannot measure the distance from Tokyo to London using pounds or kilograms or amperes). The units appear to be distinct (mass cannot be confused with length or time), the independence of these units then becoming an inviolable rule, as every high school science student can attest (the units must always add up!). 

Indeed, what characterizes a physical universe as opposed to a simulated universe is the notion that there is a fundamental structure underneath, that in some sense mass is, time is and space is … thus we cannot write kg or s in terms of m. To do so would totally render our concepts of a physical mass, space and time meaningless. A simulation universe however is required (in sum total) to be unit-less (units = 1), for the simulated universe does not 'exist' in any physical sense outside of 'the computer'.

Evidence therefore that the units do overlap and in certain defined combinations cancel, rendering our sum universe unit-less (as described above in the section on scalars), could therefore be construed as evidence that we are in a deep-universe (Programmer God) simulation.

This is because, in a physical universe there cannot be such a unit number relationship, indeed, as noted above, it is for this very reason that these physical constants (G, h, e, me, kB) can be designated as fundamental.

Note: in this model these constants are derived, for example there is no natural gravitational constant G because at the Planck scale there is no gravitational force (see gravity section).

A complete list of anomalies is given at this site:

wiki: Physical constants (anomalies)

are these anomalies evidence we are in a simulation?
(they cannot be explained by a physical universe)

J. Barrow and J. Webb on the physical constants; 'Some things never change. Physicists call them the {constants of nature}. Such quantities as the velocity of light, c, Newton's constant of gravitation, G, and the mass of the electron, me are assumed to be the same at all places and times in the universe. They form the scaffolding around which theories of physics are erected, and they define the fabric of our universe. Physics has progressed by making ever more accurate measurements of their values. And yet, remarkably, no one has ever successfully predicted or explained any of the constants. Physicists have no idea why they take the special numerical values that they do. In SI units, c is 299,792,458; G is 6.673e-11; and me is 9.10938188e-31 -numbers that follow no discernible pattern. The only thread running through the values is that if many of them were even slightly different, complex atomic structures such as living beings would not be possible. The desire to explain the constants has been one of the driving forces behind efforts to develop a complete unified description of nature, or "theory of everything". Physicists have hoped that such a theory would show that each of the constants of nature could have only one logically possible value. It would reveal an underlying order to the seeming arbitrariness of nature.'
-J. Barrow, J. Webb, Scientific American 292, 56 - 63 (2005)


The electron that isn't

This model is based on a formula for the electron fe. This formula fe resembles the formula for the surface area of a 4-axis hyper-sphere or volume of a torus ... 4pi2r3, where the pi term embeds time object T (T = pi) and the radius r term embeds the objects AL (Ampere Length).

Note, the unit for AL is the ampere-meter, and this is the unit for the magnetic monopole, the quark of this model (note: physics is searching for, but has never found, a magnetic monopole, perhaps they are looking in the wrong places).


This formula therefore has the units (AL)3/T, but is unit-less (it also has no scalars - in the above I used scalars r, v but they cancel), and so the electron is a universal constant - having no scalars or units it will have the same numerical value whether measured by humans or aliens.

The electron therefore is a mathematical particle, not a physical particle.

This electron formula encodes the information that we associate with the electron; mass, wavelength, charge ... by forming an oscillating event; for 0.2389 x 1023 units of Planck time the electron is in the AL electric (magnetic-monopole quark) wave-state. Then for 1 unit of Planck time the AL units combine with time T ... they then cancel, exposing 1 unit of Planck mass (the electron is centered on a Planck black hole). This mass state has defined point-coordinates.

And so what we define as the electron is this electric AL wave-state (duration = electron frequency in Planck time units = 0.2389 x 1023) to mass M point-state (duration 1 Planck time) oscillation. This also means that for each wave-state (which can be measured as a unit of Planck constant h), we have 1 point-state (a unit of Planck mass), and so the energy formula E = hf = mc2. This f term refers to the frequency of occurence of this unit of h, yet c is fixed, therefore the mass m term refers to the frequency of occurence of this unit of Planck mass. In other words mass as we understand it is average mass. Mass is not a fixed property of the particle. I do not weigh 80kg, my sum mass is an average 80kg (80kg/s).

embedded within the electron formula are geometrical objects for mass, length, time, ampere ... and so we can measure electron mass, wavelength, frequency and charge ... but the electron itself has no units, instead it is a geometrical formula that dictates how these mass, space and time objects are arranged. It is these measurements that we observe, not the electron itself.

** In standard physics the electron is a subatomic particle ... but it is not clear to physics what a particle is, we find the following definitions;
a particle itself could be a collapsed wave function or a quantum excitation of a field or an irreducible representation of the Poincaré group or a vibrating string or a thing measured in a detector (-wiki).

*** In the vision of quantum mechanics (in the formulas physics use), the electron is considered as a point particle with no volume and no size (-google).

**** ChatGPT (AI chatbox): According to current scientific understanding, the electron is a point-like particle, meaning that it is a very small object that is effectively a point in space and has no size ... While it is possible to imagine such an object in a purely theoretical sense, there is no evidence to suggest that objects without size actually exist in the physical world ... it is possible that the electron could be considered a mathematical particle. This is because, if it is indeed a dimensionless point, then it would have no physical size or shape, and its properties and behavior would be described by mathematical equations rather than physical characteristics.

And so, although the parameters of the electron are well studied, the existence of the actual electron itself cannot be measured, or tested. Science cannot say what the electron itself is, and so it is inferred. For physics, the electron, like God, is a matter of faith.


Links - mass, space, time

Planck units from a mathematical electron



There are 3 modes of time.
1) Universe time, the simulation clock-rate. It is a dimensionless incrementing counter, in a computer program it is usually a loop. The clock-rate is a dimensionless number.
2) The second. For every increment to the universe clock, a dimensioned object T is generated. This T is analogous to 1 unit of Planck time and so can be measured in seconds. And so the universe clock (that dimensionless incrementing counter) numerically equates to, but is not the same as, the dimensioned Planck time (whose unit is the second).
3) Observer time. For the observer, time equates to a change in state, if life was a movie then the incrementing counter would be the number of frames, T would represent each physical frame, but we, as actors in this movie, would only be able to detect motion (a change of state). If the Gods pressed the pause button on our movie, our time would stand still, although we could not know this. If for several frames there was no movement (each frame was the same), then we would not register time passing. Only when the frames have different information can we register time.

wiki: Simulation time


Gravitational and atomic orbitals

Science can fairly precisely model the gravitational orbits of satellites around planets and planets around stars, but gravity works at all levels, although a sandstorm in the desert (i.e.: a constantly changing environment) may not noticeably affect our orbit around the sun, gravitationally every particle of sand affects, and is affected by, every other particle in that storm (and by every particle on the earth and in the sun), and this complexity would be exceedingly difficult for our models to simulate, especially in real time.

The approach here is not to use a gravitational force, but rather to connect every particle (in the universe simulation) with every other particle to form a universe wide network of rotating particle to particle orbital pairs. The degree of rotation then depends on the radius of the orbital. These rotations occur at the Planck level at Planck time, but when summed and averaged over time, we find satellites orbiting planets and planets orbiting stars.

As these orbitals are geometrical, dimensioned constants (such as the gravitation constant G) are not required, and as each individual orbital comprises only 2 particles there is no barycenter (and so there is also no object center of mass). Such properties (barycenter, center of mass, G) emerge as a natural consequence of these particle-particle orbital pairs summed over time. Gravity, as we understand it, does not occur at the Planck scale, in this context science cannot solve the mystery of gravity if there is no gravity to solve.

We can use the same orbital approach (and formulas) for atomic orbitals. In this model the orbital is not a region where we may find the electron, but rather it (the Bohr radius of the orbital) is a 'physical' entity analogous to the photon (albeit of inverse phase), and is the origin of orbital momentum. For electron transition between orbitals, the incoming photon strikes the orbital (orbital radius) and replaces it with a new orbital. The Bohr radius is the active component, the electron has a passive role.


The singularity and the celestial hard disk

A black-hole has a surface in 3-D space but no physical interior - this is defined as a singularity, it is where the laws of physics break down. This singularity is characterized by mass, a Planck size black-hole would therefore include a unit of Planck mass.

Characters in our computer games are simply 1's and 0's. They may be able to study the physics of their 1's and 0's world (which is the software that defines the game), but they would have no means to study the hard disk upon which their game resides, for that is an electro-magnetic device independent of their data world. A data address on that hard disk would be the interface - the region where their game world ends and the hard-disk begins.

If the particle oscillates between an electric wave-state to Planck mass point state then the particle has mass. A photon has only the wave-state and so no mass. The photon travels at the speed of light whereas the particle doesn't move (unless pushed). We could then propose that this mass point-state is the center of the particle, around which that wave-state revolves. Could this particle Planck mass point-state be a Planck black hole, its singularity then a single data address on the celestial 'hard disk' upon which our simulation universe resides, the interface between our mathematical 'data' simulation world with its laws of physics and the 'electro-magnetic hard disk' world of the Gods?


The geometry of particle half-life

Can particle half-life be explained by the particle geometry?


Relativity as the mathematics of perspective

The mathematics of perspective is a technique used to project a 3-D image onto a 2-D screen (i.e.: a photograph or a landscape painting), using the same approach here would implement a 4-axis expanding hypersphere super-structure within which 3-D space is the projection.

An expanding 4-axis hyper-sphere can be used to replace independent particle motion (momentum) with motion as a function of the expansion itself. As the universe expands, it pulls all particles along with it. This means that all particles and objects (including us) are travelling at, and only at, the speed of this expansion, which is the speed of light (in hyper-sphere co-ordinates). There is only velocity c.

As photons (the electromagnetic spectrum) have no mass state, they cannot be pulled along by the universe expansion (consequently they are date stamped, as it takes 8 minutes for a photon to travel from the sun, that photon is 8 minutes old when it reaches us), and so photons would be restricted to a lateral motion within the hyper-sphere.

As the electromagnetic spectrum is the principal source of information regarding the environment, a 3-D relative space would be observed (as a projected image from within the 4-axis hyper-sphere), the relativity formulas can then be used to translate between the hyper-sphere co-ordinates and 3-D space co-ordinates.


General notes on the physical constants

In the “Trialogue on the number of fundamental physical constants” was debated the number of fundamental dimension units required, noting that "There are two kinds of fundamental constants of Nature: dimensionless alpha and dimensionful (c, h, G). To clarify the discussion I suggest to refer to the former as fundamental parameters and the latter as fundamental (or basic) units. It is necessary and sufficient to have three basic units in order to reproduce in an experimentally meaningful way the dimensions of all physical quantities. Theoretical equations describing the physical world deal with dimensionless quantities and their solutions depend on dimensionless fundamental parameters. But experiments, from which these theories are extracted and by which they could be tested, involve measurements, i.e. comparisons with standard dimensionful scales. Without standard dimensionful units and hence without certain conventions physics is unthinkable".
-Michael J. Duff et al JHEP03(2002)023.

At present, there is no candidate theory of everything that is able to calculate the mass of the electron.
- (02/2016)

Planck units (m_P, l_p, t_p, ampere A_p, T_P) are a set of natural units of measurement defined exclusively in terms of five universal physical constants, in such a manner that these five constants take on the numerical value of G = hbar = c = 1/4pi epsilon_0 = k_B = 1 when expressed in terms of these units. These units are also known as natural units because the origin of their definition comes only from properties of nature and not from any human construct. Max Planck wrote of these units; "we get the possibility to establish units for length, mass, time and temperature which, being independent of specific bodies or substances, retain their meaning for all times and all cultures, even non-terrestrial and non-human ones and could therefore serve as natural units of measurements...".
-Uber irreversible Strahlungsforgange. Ann. d. Phys. (4), (1900) 1, S. 69-122

In 1963, Dirac noted regarding the fundamental constants; "The physics of the future, of course, cannot have the three quantities hbar, e, c all as fundamental quantities, {only two of them can be fundamental, and the third must be derived from those two}."
-Dirac, Paul; The Evolution of the Physicist's Picture of Nature, June 25, 2010

In the article "Surprises in numerical expressions of physical constants", Amir et al write ... In science, as in life, `surprises' can be adequately appreciated only in the presence of a null model, what we expect a priori. In physics, theories sometimes express the values of dimensionless physical constants as combinations of mathematical constants like pi or e. The inverse problem also arises, whereby the measured value of a physical constant admits a `surprisingly' simple approximation in terms of well-known mathematical constants. Can we estimate the probability for this to be a mere coincidence?
-Ariel Amir, Mikhail Lemeshko, Tadashi Tokieda; 26/02/2016, {Surprises in numerical expressions of physical constants} arXiv:1603.00299 [physics.pop-ph]

"The fundamental constants divide into two categories, units independent and units dependent, because only the constants in the former category have values that are not determined by the human convention of units and so are true fundamental constants in the sense that they are inherent properties of our universe. In comparison, constants in the latter category are not fundamental constants in the sense that their particular values are determined by the human convention of units".
-Leonardo Hsu, Jong-Ping Hsu; {The physical basis of natural units}; Eur. Phys. J. Plus (2012) 127:11

A charged rotating black hole is a black hole that possesses angular momentum and charge. In particular, it rotates about one of its axes of symmetry. In physics, there is a speculative notion that if there were a black hole with the same mass and charge as an electron, it would share many of the properties of the electron including the magnetic moment and Compton wavelength. This idea is substantiated within a series of papers published by Albert Einstein between 1927 and 1949. In them, he showed that if elementary particles were treated as singularities in spacetime, it was unnecessary to postulate geodesic motion as part of general relativity.
-Burinskii, A. (2005). {"The Dirac–Kerr electron"}. arXiv:hep-th/0507109

The Dirac Kerr–Newman black-hole electron was introduced by Burinskii using geometrical arguments. The Dirac wave function plays the role of an order parameter that signals a broken symmetry and the electron acquires an extended space-time structure. Although speculative, this idea was corroborated by a detailed analysis and calculation.

Mathematical Platonism is a metaphysical view that there are abstract mathematical objects whose existence is independent of us.
-Linnebo, Øystein, {"Platonism in the Philosophy of Mathematics"}, The Stanford Encyclopedia of Philosophy (Summer 2017 Edition), Edward N. Zalta (ed.),

Mathematical realism holds that mathematical entities exist independently of the human mind. Thus humans do not invent mathematics, but rather discover it. Triangles, for example, are real entities, not the creations of the human mind.
- (22, Oct 2017).