"The universe is a computer simulation" (Konrad Zuse).
"The universe is literally a computer that is being used by someone or something to solve a problem."(Edward Fredkin)
"The universe is a gigantic quantum computer" (Seth Lloyd).
The Digital
The term "digital" −from Latin "digitus" (finger)− refers to the discrete, the opposite of the continuous or analog. Discrete or digital quantities are expressed by integers.
The concept of digital has experienced an enormous boom with the irruption of the so-called "digital computers", with important properties:
A digital computer has a finite number of instructions with which it is possible to express any algorithm.
The digital computer has meant a new paradigm, a new way of looking at reality and a new way (the digital or discrete) of modeling physical phenomena, as opposed to the traditional mathematical models based mainly on differential equations, which are of a continuous nature.
In computers, digital has been simplified to reduce it to the concept of "bit" (acronym of "binary digit"). The bit is the unit of information, which has two possible states, usually represented as binary digits (0 and 1). With bits, integers can be represented and also allow the (binary) logic of digital computers to be modeled.
In the development of digital computers has played a key role the simplicity of the representation of information and the simplicity of logical operations, both themes based on binary digits (0 and 1).
The computational model of the mind
With the appearance of the digital computer −a realization of the human mind−, at once arose the metaphor "the mind is a digital computer", the computational theory of mind (or computationalism). In fact, digital computers are referred to as "electronic brains". This metaphor was very justified, as there are many analogies between the computer and the mind:
Hardware. It corresponds physically to the brain.
Instructions. Correspond to the basic or elementary principles that connect brain and mind.
Software. The mind is the software of the brain. Software is flexible, capable of creating all kinds of mental content.
Memory. Computer memory corresponds to human memory.
Processing. Data or information processing corresponds to mental processes (thoughts).
Logic. The Boolean logic used by the computer is that which is the logic of human reasoning.
Input/Output. They correspond, respectively, to the sensory organs (input) and to the responses (output) to the outside.
Cellular automata
Another important milestone in the move toward digital (or "digitalism") has been the invention of cellular automata. A cellular automaton is:
A grid-like structure, where each cell has one state among a finite set of possible states (e.g., black or white). The simplest grid is one-dimensional and with only two states (0 and 1). In 2D, the grid can be composed of triangular, square or hexagonal cells. The grid can also be n-dimensional, with an arbitrary number of dimensions in Cartesian space.
A finite set of rules governing the evolution of the structure at successive discrete times. The rules act locally (according to the state of neighboring cells): the state of each cell at time t+1 is a function of the state at time t of neighboring cells. The rules are applied iteratively.
From a set of simple rules a wide variety of dynamics is produced, with unexpected (emergent) behaviors. John Conway's game of life is an example of a digital system based on a simple cellular automaton, with emergent properties.
Cellular automata were invented by Stanislaw Ulam in the 1940s. John von Neumann (at Ulam's suggestion) used them to study the mechanisms of self-replication. For von Neumann, the most important cellular automaton is what he called the "universal constructor," a cellular automaton that reproduces itself [von Neumann, 1996].
Ulam and von Neumann showed that cellular automata were capable of performing all kinds of computation in the Turing sense.
Just as a universal Turing machine is capable of emulating a particular Turing machine, a universal cellular automaton is one that is capable of emulating the behavior of any particular cellular automaton. Von Neumann showed that it was possible to construct a universal cellular automaton with cells with 4 orthogonal neighbors, 29 possible states per cell and about 200,000 cells [Gardner, 1985]. Bill Gosber showed that Conway's set of life is a universal cellular automaton [Dewdney, 1985].
Stephen Wolfram has investigated cellular automata in depth. His developments are reflected in his work "A New Kind of Science" [2002]. According to Wolfram, cellular automata constitute a universal scientific paradigm. Wolfram's one-dimensional cellular automaton Rule 110 is equivalent to a Turing machine (or is Turing-complete), i.e., it is capable of universal computation. This was discovered by a Wolfram student named Matthew Cook [2004].
The Digital Philosophy
From the convergence of all these ideas was born the so-called "digital philosophy", a universalist philosophy, a universal paradigm or a "theory of everything", a monistic type of philosophy based on information and information processing (computation). This philosophy was applied mainly to physics, thus emerging digital physics, advocated by several mathematicians and theoretical physicists such as Konrad Zuse, Edward Fredkin, Stephen Wolfram and Seth Lloyd.
According to digital physics, the universe is describable by information and is therefore computable. Digital physics is a bridging field between physics and computer science. In this context, the concept of cellular automata has strongly emerged as a standard model, comparable to the field concept in physics.
Computational physics is not the same as digital physics. Computational physics is a branch of theoretical physics that focuses on computational modeling of physical phenomena. It can be considered as an intermediate discipline between theoretical and experimental physics. In contrast, digital physics is a physics based solely on information and information processes.
The principles of digital philosophy are as follows:
Information theory.
Physical science and cognitive science are based on the common concept of information. Information theory is the universal theory. Reality, at its most fundamental level, is information and not matter or energy.
Nature is discrete.
Reality is digital. Everything is quantized. Nature does not harbor the continuum or infinity or infinitesimals or random variables. All quantities in nature are finite and discrete (including space and time), and can be represented exactly by an integer.
"We must find a way to free ourselves completely from the continuum" (Einstein).
"I consider it entirely possible that physics cannot be based on the field concept, i.e. on continuous structures" (Einstein).
Some examples of discrete elements in physics are: 1) in an atom there are always an integer number of nucleons (protons and neutrons) and electrons; 2) there are 3 spatial dimensions; 3) there are two types of particles (according to spin): fermions and bosons; 4) there are two electric charges (positive and negative); 5) there are 3 types of color charges (R, G, B); etc.
Examples in biology are 1) Mendel's laws involving small integers (such as 0 and 1, male/female, true/false) and ratios such as 1/4 and 1/2; 2) the genetic code of DNA governing growth and inheritance.
All processes are computations.
External (physical) processes and internal (mental) processes are computations, informational processes. This is what is called "computational universality", i.e., behind every physical process there is an underlying computation.
A precursor of this principle was Leibniz −inventor of the differential/integral calculus and builder of the first mechanical multiplier in 1670− who claimed that "everything is computable," including human reasoning.
Pancomputationalism is the theory that every process (physical or psychic) is computation, including the universe, considered as a computational machine governed by the fundamental laws of physics.
The idea that computation and computer programs may be the foundation of the universe has its origins in pioneers Konrad Zuse and Edward Fredkin and, modernly, Stephen Wolfram.
Determinism.
Fundamental physical processes at the microscopic level are deterministic digital processes. Therefore, the Copenhagen interpretation of quantum physics is rejected as nondeterministic.
Discrete space-time.
Space-time is a grid of a cellular automaton in which in each cell there is a digital information, which is its state. The states are restricted to a fixed number of possible information. These cells do not exist in physical space. The space is relational between the states defined in the cells.
Exact modeling.
Modeling of physical processes is performed with full accuracy. Traditional modeling based on differential equations are only approximations. The fuzzy concepts of infinity, infinitesimal, continuum and differentiability are rejected.
Simplicity.
Maximum simplicity is achieved with the concept of bit, the unit of information, which is an entity with two possible values, usually represented as 0 and 1. A bit is an object with two states, with no other intrinsic structure. And computation is based on very simple concepts (the Turing machine).
Universe.
The universe is a deterministic computer or mathematically isomorphic to a computer. This computer is a gigantic cellular automaton.
"We now have a picture of the universe as a large computer program whose software consists of the laws of nature running on hardware composed of nature's elementary particles" (John Barrow) [2008].
The digital philosophy of Konrad Zuse
Konrad Zuse, engineer, inventor and pioneer of computer technology, is considered the "German Turing". He was the first to use the term "digital physics", later changed to "digital philosophy". He invented the first Turing-complete programmable digital computer, the Z3, in 1941. Zuse also invented, in 1945, Plankalkül, the first high-level programming language. Zuse was ahead of Turing in theory of computation and ahead of von Neumann in the idea of the program stored in memory (in turn, von Neumann was inspired by the idea of the Turing machine).
Zuse was the first to suggest (in 1967) that the universe is being computed by a gigantic digital computer: a cellular automaton or other discrete computing device. He did so in his work "Rechnender Raum", which was translated into English as "Calculating Space". This work was the first work on digital physics.
All physical processes and laws of nature can be considered discrete computations.
The universe is a computer. More precisely, the universe is the result of a discrete computational process running on a giant cellular automaton of deterministic type.
Entropy cannot increase in this type of deterministic computational systems because the information contained in these systems cannot increase.
We do not know the concrete algorithm that computes our universe.
Edward Fredkin's digital philosophy
Fredkin is one of the pioneers of digital philosophy. His digital philosophy is a type of computationalism, and is based on: 1) All processes in nature are forms of computation or information processing at the most fundamental level of reality; 2) Biology reduces to chemistry, chemistry to physics, physics to computation, and computation to information.
Fredkin's main ideas are:
NF (finite nature) hypothesis.
It is the hypothesis that assumes that space, time and the other physical quantities are discrete and finite.
Physical states and processes.
They are represented in binary format. Digital processes evolve digital states. The most basic laws of physics are computationally universal. Computational universality is a physical property.
Digital information cannot be changed, created or destroyed. The only way to change it is through a digital process.
Space-time.
Space-time is a fixed, digital reference frame. It has a lattice structure. There are rules that establish the transitions from one state at instant t and the next instant (t+1).
If space and time are discrete, there must be some kind of "motion atom". The simplest process of digital motion is one that preserves information and is reversible: two spatial neighbors exchanging their positions.
Digital mechanics.
Digital processes are realized in a reversible finite cell automaton (RUCA). The idea is to replace mathematical models of physical processes, mainly based on differential equations, with digital mechanics. If the NF hypothesis is true, the digital modeling is performed with full accuracy.
Fredkin uses the values +1 and −1 for the one-bit states, instead of the traditional values 0 and 1.
The bits of digital mechanics are located in digital space-time by 4 integers (their space-time coordinates). Properties such as charge, energy, momentum and spin are configurations of bits in digital space-time.
Law of conservation of information.
For example, in the trajectory of a particle, information is conserved at all times. The conservation of information is a direct consequence of reversibility (the laws of nature are reversible at the microscopic and local level).
Random events are impossible and there is no room for indeterminism. The Copenhagen interpretation is not correct.
The "Other" machine.
Digital computations are performed on a machine that exists somewhere that he calls "Other". OOther does not have the restrictive laws of our universe. In it there are an arbitrary number of spatial dimensions and it has all kinds of connectivity. Nor do conservation laws of any kind apply.
The universe.
The universe is a computation. The universe, with its finite resources is busy computing its future as fast as it can. All the past or future can be calculated exactly from another higher universe.
Stephen Wolfram's digital philosophy
Stephen Wolfram claims that current mathematics (the one limited by Gödel's theorem) is not at all the most adequate framework for understanding the physical world, as science has had great difficulty modeling many phenomena with differential equations, such as fluid mechanics. In his work "A New Kind of Science" [2002] he proposes to give up mathematics and turn to computer science, and in particular cellular automata, to model the physical world by means of a rule-based programming language. This he justifies:
Very simple computer programs can produce extraordinarily complex results.
The universe itself could be generated by a computer program simple enough to be expressed in a few lines of code. "If the laws are simple enough, and we find the right way, we will see them."
Computer science provides a new vision of phenomena, with more practical, simple techniques and immediate results. "The algorithm is more powerful than the equation."
Seth Lloyd's digital philosophy
According to Seth Lloyd [1967], physicists have focused their attention on the large collection of particles and fields in the physical world, and have ignored the most fundamental: the universe as a majestic computer, whose output is reality itself. In this computational process, information plays an essential role:
The information of the universe is continuously increasing. Each physical event increases the information of the universe.
In 1865, Rudolf Clausius coined the term "entropy" to refer to the degree of disorder of a system. According to the second principle of thermodynamics, the entropy in any closed system increases, i.e., its disorder increases. There is an inexorable and irreversible tendency towards disorder.
For Lloyd, entropy and information go hand in hand: they are parallel concepts. Both increase over time. Entropy is an information phenomenon rather than a thermodynamic phenomenon. Information is the connecting thread between the past and the future.
Information always generates information. It is for this reason that the universe is constantly increasing in complexity. From the initial simplicity of the Big Bang to ever increasing complexity. The laws of physics are simple. The initial state of the universe was simple. The universe is simple in the deep and complex in the shallow. This is justified because simple programs can generate complex structures after many iterations.
For Lloyd, the universe is a quantum computer:
A quantum computer makes it possible to model quantum phenomena such as superposition and entanglement.
In a quantum computer the information increases all the time and with it the complexity. As computation progresses, reality unfolds.
The language of the computer that computes the universe is the laws of physics.
Everything in the universe is information. Elementary particles are information based on superpositions of states such as spin. Collisions between particles are computations.
The universe is not deterministic. The microscopic and macroscopic worlds operate with the same model: the quantum computer.
The universe operates with qubits. The qubit (quantum bit) is the unit of quantum information consisting of the superposition of two states, |0⟩ and |1⟩: α|0⟩ + β|1⟩, affected by factors that add up to 1 between the two: α+β = 1.
John Wheeler's theory "it from bit" (reality is a manifestation of information) must be replaced by "it from qubit" (reality is a manifestation of quantum information).
The universe can be simulated with a quantum computer, but since we do not yet have a theory of quantum gravity, such a simulation is not yet possible.
Digital vs. MENTAL Philosophy
Digital philosophy is a new conception of Pythagorean and Galilean philosophy:
Pythagorean ontology: Everything is number.
Galilean Ontology: The book of nature is written in mathematical characters. God is a mathematician.
Digital philosophical ontology: The book of nature is digital software and is written in a programming language. God is a programmer.
With MENTAL we can add an even more universal conception:
Universal ontology-epistemology: The book of nature and mind are written in the simple universal language of the primary archetypes (or archetypes of consciousness). God is the supreme consciousness using the principle of economy (Occam's razor).
The principle of downward causality and MENTAL allow to clarify the digital philosophy:
At a deep level, reality is continuous. At the surface level, reality is discrete. Discrete reality is a manifestation of continuous reality.
Simplicity resides in the deep. The superficial is complex.
The superficial world is not real. True reality lies in the deep.
The problem of capturing the continuum is solved by the definition of infinitesimal: ε2 = 0, which is an imaginary expression.
There are analogies and differences between digital and MENTAL philosophy:
MENTAL is a universal language based on a finite set of primary archetypes, which are like the instructions of a theoretical or abstract computer. It is the code of the metaverse, that is, the code of possible universes. With this code physical phenomena can be modeled.
With MENTAL, finite expressions can be constructed and a finite or infinite number of expressions can be described by a finite expression.
In MENTAL, space and time are abstract and bound together. Space in MENTAL is relational: it is created by the relationships between expressions.
The universe is not a computer, but it is a system governed by the primary archetypes that manifest themselves in physical laws. These archetypes are, however, like the instructions of a theoretical computer.
Digital philosophy is founded on the simplest concept, which is the bit. But this foundation is "too simple". It does not fulfill Einstein's razor principle: "Everything should be done in the simplest possible way, but not simpler." Digital philosophy is perhaps the most representative example of what not to do: to go beyond reasonable conceptual simplicity. The bit is a concept that makes sense at the level of implementation, but not at the level of supreme conceptual abstraction.
Instead of the binary values proposed by Fredkin (+1 and −1), perhaps it would be more appropriate to consider 3 values: +1, −1 and 0. 0 represents the union or harmonization of opposites (−1 and +1), in a metaphorical and literal sense (since arithmetically, the sum of the opposites is zero). It also symbolizes or represents consciousness, totality and emptiness. We can also say that 0 manifests itself as a pair of opposites.
According to Fredkin's digital philosophy, there is a machine that computes the universe that has no restrictions and that he calls "Other". MENTAL can be considered the instruction set of "Other". The primary archetypes of MENTAL are of deep type and can be combined without restrictions.
The universe is not a cellular automaton (Zuse, Fredkin, Wolfram) because a cellular automaton cannot model quantum phenomena (such as entanglement and superposition). Nor is it a quantum computer (Lloyd) because it has limitations. The universe is the result of computations based on a theoretical and deep machine (MENTAL) whose instructions are the primary archetypes, which are capable of performing classical and quantum computations. Classical and quantum computations are particular cases of the universal theoretical machine (MENTAL). MENTAL is the foundation of the code of the universe and possible worlds.
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