God (programmer)

Philosophy of mathematics is that branch of philosophy which attempts to answer questions such as: ‘why is mathematics useful in describing nature?’, ‘in which sense, if any, do mathematical entities such as numbers exist?’ and ‘why and how are mathematical statements true?’ This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math. Mathematical realism holds that mathematical entities exist independently of the human mind. We do not invent mathematics, but rather discover it. Triangles, for example, are real entities that have an existence ^[7].

The mathematical universe refers to universe models whose underlying premise is that the physical universe has a mathematical origin, the physical (particle) universe is a construct of the mathematical universe, and as such physical reality is a perceived reality. It can be considered a form of Pythagoreanism or Platonism in that it proposes the existence of mathematical objects; and a form of mathematical monism in that it denies that anything exists except these mathematical objects.

Physicist Max Tegmark in his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality"^[8][9] proposed that Our external physical reality is a mathematical structure.^[10] That is, the physical universe is not merely described by mathematics, but is mathematics (specifically, a mathematical structure). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Any "self-aware substructures will subjectively perceive themselves as existing in a physically 'real' world".^[11]

The principle constraints to any mathematical universe simulation hypothesis are;

1. the computational resources required. The ancestor simulation can resolve this by adapting from the virtual reality approach where only the observable region is simulated and only to the degree required, and

2. that any 'self-aware structures' (humans for example) within the simulation must "subjectively perceive themselves as existing in a physically 'real' world".^[12]. Succinctly, our computer games may be able to simulate our physical world, but they are still only simulations of a physical reality (regardless of how realistic they may seem) ... we are not yet able to program actual physical dimensions of mass, space and time from mathematical structures, and indeed this may not be possible with a computer hard-ware architecture that can only process binary data.

As a deep-universe simulation is programmed by an external (external to the universe) intelligence (the Programmer God hypothesis), we cannot presume a priori knowledge regarding the simulation source code other than from this code the laws of nature emerged, and so any deep-universe simulation model we try to emulate must be universal, i.e.: independent of any system of units, of the dimensioned physical constants (G, h, c, e .. ), and of any numbering systems. Furthermore, although a deep-universe simulation source code may use mathematical forms (circles, spheres ...) we are familiar with (for ultimately the source code is the origin of these forms), it will 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, any theoretical basis for a source code that fits the above criteria (and from which the laws of nature will emerge), could be construed as our first tangible evidence of a non-human intelligence.

A physical universe is characterized by measurable quantities (size, mass, color, texture ...), and so a physical universe can be measured and defined. Contrast then becomes information, the statement this is a big apple requires a small apple against which big becomes a relative term. For analytical purposes we select a reference value, for example 0C or 32F, and measure all temperatures against this reference. The smaller the resolution of the measurements, the greater the information content (the file size of a 32 mega-pixel photo is larger than a 4 mega-pixel photo). A simulation universe may be presumed to also have a resolution dictating how much information the simulation can store and manipulate.

To measure the fundamental parameters of our universe physics uses physical constants. A physical constant is a physical quantity that is generally believed to be both universal in nature and have a constant value in time. These can be divided into

1) dimension-ed (measured using physical units kg, m, s, A ...) such as the speed of light c, gravitational constant G, Planck constant h ... as in the table

Physical constants

constant	symbol	SI units
Speed of light	c	${\displaystyle {\frac {m}{s}}}$
Planck constant	h	${\displaystyle {\frac {kg\;m^{2}}{s}}}$
Elementary charge	e	${\displaystyle C=As}$
Boltzmann constant	kB	${\displaystyle {\frac {kg\;m^{2}}{s^{2}\;K}}}$

Physicist Lev Okun noted "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 dimension-ful scales. Without standard dimension-ful units and hence without certain conventions physics is unthinkable ^[13].

2) dimension-less, such as the fine structure constant α. A dimension-less constant does not measure any physical quantity (it has no units; units = 1).

3) dimension-less mathematical constants, most notably pi = 3.14159265358979 and e = 2.718281828459. Although these are transcendental numbers, they can be constructed by integers in a series, and so for a universe expanding incrementally (see simulation time), these constants could be formed within the simulation. For example, at time t;

$${\displaystyle t=1;{\frac {\pi ^{2}}{6}}={\frac {1}{t^{2}}}}$$

$${\displaystyle t=2;{\frac {\pi ^{2}}{6}}={\frac {1}{1^{2}}}+{\frac {1}{t^{2}}}}$$

$${\displaystyle t=now:{\frac {\pi ^{2}}{6}}={\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{4^{2}}}+\cdots +{\frac {1}{t^{2}}}}$$

We may now define the fundamental physical constant as a parameter specifically chosen by the Programmer and is encoded into the simulation code directly, and so whilst it may be inferable, it is not derived from other constants (Richard Feynman on the fine structure constant). It should also be dimension-less otherwise the simulation itself becomes dimensioned (if the simulation is running on a celestial computer it is merely data, it has no physical size or shape or ...), and so the dimensioned constants (G, h, c, e...) must all be derivable (derived from within the simulation) via the (embedded in the source code) fundamental physical constants (of which the fine structure constant alpha may be an example). Although pi and e are dimensionless, they can be derived internally (from integers), and as they have application in the mathematical realm, they can be referred to as mathematical constants.

The laws of physics are our incomplete observations of the natural universe, and so evidence of a simulation may be found in ambiguities or anomalies within these laws. Furthermore, if complexity arises over time, then at unit time the 'handiwork' of the Programmer may be notable by a simplicity and elegance of the geometries employed ... for the Programmer by definition has God-level programming skills. Here is a notable example.

Mass, space and time from the number 1

The dimensions of mass, space and time are considered by science to be independent of each other, we cannot measure the distance from Tokyo to London using kilograms and amperes, or measure mass using space and time. 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', that time 'is' and space 'is' ... thus we cannot write kg in terms of m and s. To do so would render our concepts of a physical universe meaningless. The 26th General Conference on Weights and Measures (2019 redefinition of SI base units) assigned exact numerical values to 4 physical constants (h, c, e, k_B) independently of each other (and thereby confirming these as fundamental constants), and as they are measured in SI units (kg, m, s, A, K), these units must also be independent of each other (i.e.: these are fundamental units, for example if we could define m using A then the speed of light could be derived from, and so would depend upon, the value for the elementary charge e, and so the value for c could not be assigned independently from e).

Physical constants

constant	symbol	SI units
Speed of light	c	${\displaystyle {\frac {m}{s}}}$
Planck constant	h	${\displaystyle {\frac {kg\;m^{2}}{s}}}$
Elementary charge	e	${\displaystyle C=As}$
Boltzmann constant	kB	${\displaystyle {\frac {kg\;m^{2}}{s^{2}\;K}}}$

We are familiar with inverse properties; plus charge and minus charge, matter and anti-matter ... and we can observe how these may form and/or cancel each other. A simulation universe however is required to be dimensionless (in sum total), for the simulated universe does not 'exist' in any physical sense outside of the 'Computer' (it is simply data on a celestial hard-disk).

Our universe does not appear to have inverse properties such as anti-mass (-kg), anti-time (-s) or anti-space (anti-length -m), therefore the first problem the Programmer must solve is how to create the physical scaffolding (of mass, space and time). For example, the Programmer can start by selecting 2 dimensioned quantities, here are used r, v ^[15] such that

${\displaystyle kg={\frac {r^{4}}{v}},\;m={\frac {r^{9}}{v^{5}}},\;s={\frac {r^{9}}{v^{6}}},\;A={\frac {v^{3}}{r^{6}}}}$

Quantities r and v are chosen so that no unit (kg, m, s, A) can cancel another unit (i.e.: the kg cannot cancel the m or the s ...), and so we have 4 independent units (we still cannot define the kg using the m or the s ...), however if 3 (or more) units are combined together in a specific ratio, they can cancel (in a certain ratio our r and v become inverse properties and so cancel each other; units = 1).

${\displaystyle f_{X}={\frac {kg^{9}s^{11}}{m^{15}}}={\frac {({\frac {r^{4}}{v}})^{9}({\frac {r^{9}}{v^{6}}})^{11}}{({\frac {r^{9}}{v^{5}}})^{15}}}=1}$

This f_X, although embedded within are the dimensioned structures for mass, time and length (in the above ratio), would be a dimensionless mathematical structure, units = 1. Thus we may create as much mass, time and length as we wish, the only proviso being that they are created in f_X ratios, so that regardless of how massive, old and large our universe becomes, it is still in sum total dimensionless.

Defining the dimensioned quantities r, v in SI unit terms.

${\displaystyle r=({\frac {kg\;m}{s}})^{1/4}}$

${\displaystyle v={\frac {m}{s}}}$

Mass

${\displaystyle {\frac {r^{4}}{v}}=({\frac {kg\;m}{s}})\;({\frac {s}{m}})=kg}$

Length

${\displaystyle (r^{9})^{4}={\frac {kg^{9}\;m^{9}}{s^{9}}}}$

${\displaystyle ({\frac {1}{v^{5}}})^{4}={\frac {s^{20}}{m^{20}}}}$

${\displaystyle ({\frac {r^{9}}{v^{5}}})^{4}={\frac {kg^{9}s^{11}}{m^{11}}}=m^{4}{\frac {kg^{9}s^{11}}{m^{15}}}=m^{4}f_{X}=m^{4}}$

Time

${\displaystyle (r^{9})^{4}={\frac {kg^{9}\;m^{9}}{s^{9}}}}$

${\displaystyle ({\frac {1}{v^{6}}})^{4}={\frac {s^{24}}{m^{24}}}}$

${\displaystyle ({\frac {r^{9}}{v^{6}}})^{4}={\frac {kg^{9}s^{15}}{m^{15}}}=s^{4}{\frac {kg^{9}s^{11}}{m^{15}}}=s^{4}f_{X}=s^{4}}$

And so, although f_X is a dimensionless mathematical structure, we can embed within it the (mass, length, time ...) structures along with their dimensional attributes (kg, m, s, A ..). In the mathematical electron model (discussed below), the electron itself is an example of an f_X structure, it (f_electron) is a dimensionless geometrical object that embeds the physical electron parameters of wavelength, frequency, charge (note: A-m = ampere-meter are the units for a magnetic monopole).

${\displaystyle f_{electron}}$

${\displaystyle units={\frac {A^{3}m^{3}}{s}}={\frac {({\frac {v^{3}}{r^{6}}})^{3}({\frac {r^{9}}{v^{5}}})^{3}}{({\frac {r^{9}}{v^{6}}})}}=1}$

We may note that at the macro-level (of planets and stars) these f_X ratio are not found, and so this level is the domain of the observed physical universe, however at the quantum level, f_X ratio do appear, f_electron as an example, the mathematical and physical domains then blurring. This would also explain why physics can measure precisely the parameters of the electron (wavelength, mass ...), but has never found the electron itself.

The (dimensionless) simulation clock-rate would be defined as the minimum 'time variable' (age) increment to the simulation. Using a simple loop as analogy, at age = 1, the simulation begins (the big bang), certain processes occur, when these are completed age increments (age = 2, then 3, then 4 ... ) until age reaches the_end and the simulation stops.

 'begin simulation
 FOR age = 1 TO the_end                       'big bang = 1                 
         conduct certain processes ........ 
 NEXT age 
 'end simulation

Quantum spacetime and Quantum gravity models refer to Planck time as the smallest discrete unit of time and so the incrementing variable age could be used to generate units of Planck time (and other Planck units, the physical scaffolding of the universe). In a geometrical model, to these Planck units could be assigned geometrical objects, for example;

 Initialize_physical_constants;
 FOR age = 1 TO the_end                                                    
         generate 1 unit of (Planck) time;       '1 time 'object' T
         generate 1 unit of (Planck) mass;       '1 mass 'object' M
         generate 1 unit of (Planck) length;     '1 length 'object' L
         ........ 
 NEXT age 

The variable age is the simulation clock-rate, it is simply a counter (1, 2, 3 ...) and so is a dimensionless number, the object T is the geometrical Planck time object, it is dimensioned and is measured by us in seconds. If age is the origin of Planck time (1 increment to age generates 1 T object) then age = 10⁶², this is based on the present age of the universe, which, at 14 billion years, equates to 10⁶² units of Planck time.

For each age, certain operations are performed, only after they are finished does age increment (there is no time interval between increments). As noted, age being dimensionless, is not the same as dimensioned Planck time which is the geometrical object T, and this T, being dimensioned, can only appear within the simulation. The analogy would be frames of a movie, each frame contains dimensioned information but there is no time interval between frames.

 FOR age = 1 TO the_end (of the movie)                                                   
         display frame{age}
 NEXT age 

Although operations (between increments to age) may be extensive, self-aware structures from within the simulation would have no means to determine this, they could only perceive themselves as being in a real-time (for them the smallest unit of time is 1T, just as the smallest unit of time in a movie is 1 frame). Their (those self-aware structures) dimension of time would then be a measure of relative motion (a change of state), and so although ultimately deriving from the variable age, their time would not be the same as age. If there was no motion, if all particles and photons were still (no change of state), then their time dimension could not update (if every frame in a movie was the same then actors within that movie could not register a change in time), age however would continue to increment.

Thus we have 3 time structures; 1) the dimension-less simulation clock-rate variable age, 2) the dimensioned time unit (object T), and 3) time as change of state (the observers time). Observer time requires a memory of past events against which a change of state can be perceived.

The forward increment to age would constitute the arrow of time. Reversing this would reverse the arrow of time, the universe would likewise shrink in size and mass accordingly (just as a white hole is the (time) reversal of a black hole).

 FOR age = the_end TO 1 STEP -1                                 
         delete 1 unit of Planck time;
         delete 1 unit of Planck mass;
         delete 1 unit of Planck length;
         ........ 
 NEXT age 

Adding mass, length and time objects per increment to age would force the universe expansion (in size and mass), and as such an anti-gravitational dark energy would not be required, however these objects are dimensioned and so are generated within the simulation. This means that they must somehow combine in a specific ratio whereby they (the units for mass length, time, charge; kg, m, s, A) in sum total cancel each other, leaving the sum universe (the simulation itself) residing on that celestial hard-disk.

We may introduce a theoretical dimensionless (f_X) geometrical object denoted as f_Planck within which are embedded the dimensioned objects MLTA (mass, length, time, charge), and from which they may be extracted.

 FOR age = 1 TO the_end                                                    
         add 1 fPlanck                     'dimensionless geometrical 'object'
         {
               extract 1 unit of (Planck) time;       '1 time 'object' T
               extract 1 unit of (Planck) mass;       '1 mass 'object' M
               extract 1 unit of (Planck) length;     '1 length 'object' L
         }
         ........ 
 NEXT age 

This then means that the simulation, in order to create time T, must also create mass M and space L (become larger and more massive). Thus no matter how small or large the physical universe is (when seen internally), in sum total (when seen externally), there is no universe - it is merely data without physical form.

As the universe expands outwards (through the constant addition of units of mass and length via f_Planck), and if this expansion pulls particles with it (if it is the origin of motion), then now (the present) would reside on the surface of the (constantly expanding at the speed of light; c = 1 Planck length / 1 Planck time) universe, and so the 'past' could be retained, for the past cannot be over-written by the present in an expanding universe (if now is always on the surface). As this expansion occurs at the Planck scale, information even below quantum states, down to the Planck scale, can be retained, the analogy would be the storing of every keystroke, a Planck scale version of the Akashic records ... for if our deeds (the past) are both stored and cannot be over-written (by the present), then we have a candidate for the 'karmic heavens' (Matthew 6:19 But lay up for yourselves treasures in 'heaven', where neither moth nor rust doth corrupt, and where thieves do not break through nor steal).

This also forms a universe time-line against which previous information can be compared with new information (a 'memory' of events), without which we could not link cause with effect.

In a simulation, the data (software) requires a storage device that is ultimately hardware (RAM, HD ...). In a data world of 1's and 0's such as a computer game, characters within that game may analyze other parts of their 1's and 0's game, but they have no means to analyze the hard disk upon which they (and their game) are stored, for the hard disk is an electro-mechanical device, it is not part of their 1's and 0's world, it is a part of the 'real world', the world of their Programmer. Furthermore the rules programmed into their game would constitute for them the laws of physics (the laws by which their game operates), but these may or may not resemble the laws that operate in the 'real world' (the world of their Programmer). Thus any region where the laws of physics (the laws of their game world) break down would be significant. A singularity inside a black hole is such a region ^[17].

For the black-hole electron, its black-hole center would then be analogous to a storage address on a hard disk, the interface between the simulation world and the real world. A massive (galactic) black-hole could be as an entire data sector.

The surface of the black-hole would then be of the simulation world, the size of the black hole surface reflecting the stored information, the interior of the black-hole however would be the interface between the data world and the 'hard disk' of the real world, and so would not exist in any 'physical' terms. It is external to the simulation. As analogy, we may discuss the 3-D surface area of a black-hole but not its volume (interior).

The scientific method is built upon testable hypothesis and reproducible results. Water always boils (in defined conditions), at 100°C. In a geometrical universe particles will behave according to geometrical imperatives, the geometry of the electron and proton ensuring that electrons will orbit nuclei in repeating and predictable patterns. The laws of physics would then be a set of mathematical formulas that describe these repeating patterns, the more complex the orbits, the more complex the formulas required to describe them and so forth. However if there is a source code from which these geometrical conditions were programmed, then there may also be non-repeating events, back-doors built into the code (a common practice by terrestrial programmers), these by definition would lie outside the laws of physics and so be labelled as miracles, yet they would be no less valid.

Particles form more complex structures such as atoms and molecules via a system of orbitals; nuclear, atomic and gravitational. The 3-body problem is the problem of taking the initial positions and velocities (or momenta |momentum|momenta) of three or more point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation.^[19]. Simply put, this means that although a simulation using gravitational orbitals of similar mass may have a pre-determined outcome, it seems that for gods and men alike the only way to know what that outcome will be is to run the simulation itself.