# Abstract

Physical processes can be viewed as dynamic distributed processing of information performed by elementary analog processors transforming input data to output data, which can be simulated in dynamic distributed processing of digital information performed by elementary digital computational processors.

**For the last 300 or so years, the exact sciences have been dominated by what is really a good idea, which is the idea that one can describe the natural world using mathematical equations**. (Stephen Wolfram)

**For seven and a half million years, this stupendously powerful, office-block of a machine had whirred. When it came to announcing what it had discovered, crowds had quite understandably gathered. “You aren’t going to like it,” Deep Thought warned. “Forty-two,” it said, with infinite majesty and calm.**

(Douglas Adams in The Hitchhiker’s Guide to the Galaxy )

## Computational Simulation: Panta Rhei

Digital computational simulation of physical processes is today opening new fields of science and technology

including

- computational physics
- computational chemistry
- computational biology
- computational fluid mechanics
- computational solid mechanics
- computational electromagnetics
- computational meteorology
- computational global climate modeling.

Computational simulation can be viewed as a dynamic flow of digital information performed by processors transforming input data to output data according to some algorithm. Similarly physical processes can be seen as dynamic flows of information performed by elementary physical processes transforming analog input

to output. This is a dynamic ever-changing world in constant transformation described by Heraclitus

Heraclitus was opposed by Parmenides who claimed that change is only an illusion in a static world without change. Heraclitus and Parmenides are the pre-Socratic god-fathers of Western philosophy, with the static world of Parmenides connecting to religion, monarchy and aristocracy, and the dynamic world of Heraclitus to science and democracy.

The static world of Parmenides was revived in modern time in Einstein’s space-time of relativity theory, but the view of the world as a dynamic process is prevailing.

Life is dynamic change in time, death is static without change, see The Direction of Time.

## Is the Universe a Computer?

The idea of the Universe as a gigantic computer has attracted the attention by physicists coming to different conclusions:

- Everyone knows that electronic computers have enormously helped the work of science. Some scientists have had a grander vision of the importance of the computer. They expect that it will change our view of science itself, of what it is that scientific theories are supposed to accomplish, and of the kinds of theories that might achieve these goals. I have never shared this vision. (Nobel Laureate Steven Weinberg)
- The universe actually is a giant quantum computer. All interactions between particles in the universe, convey not only energy but also information – in other words, particles not only collide, they compute. The universe computes its own dynamical evolution. As the computation proceeds, reality unfolds. (Seth Lloyd in
*Programming the Universe)* - So the thing I realized rather gradually – I must say starting about 20 years ago now that we know about computers and things – there’s a possibility of a more general basis for rules to describe nature. (Stephen Wolfram in
*A New Kind of Science*)

We favor the view of Lloyd and Wolfram, based on our experience of computational simulation presented in a series of knols in particular including the major open problem of classical physics:

- turbulent flow of slightly viscous fluids such as air and water.

We have found that time-dependent turbulent flow can be accurately simulated by computational solution by time-stepping of the Navier-Stokes equations expressing conservation of mass, momentum and energy. The all-important aspect is that this is shown to be possible using millions of computational mesh points instead of the impossible septillions of water molecules in every mole of water. This reflects a plausible invariance on macroscales to the actual size the microscales, reflecting that turbulent flow of air and water can look the same macroscopically although air and water molecules are different, or that the macrocopic world would look the same with a twice as big Planck’s constant.

The mesh points act like a fictional fluid particles which interact through elementary forces described by the Navier-Stokes equations in a time-stepping process with each fictional particle reacting to forces from the surrounding particles. The computational process thus mimics real physical turbulent flow resulting from the interaction of many fluid particles, like the evolution in time of an economy resulting from the dynamics of a large number of transactions and decisions.

Or the other way around: Real turbulent flow can be seen as an analog representation of computed digital flow.

A computational form of quantum mechanics based on the dynamics of interacting electrons is described in Many-Minds Quantum Mechanics.

## Propagation of Light: Dynamic or Static

We illustrate the difference between a static and a dynamic description of propagation of light in a medium consisting of two layers with different speed of light such as air and water. The static description is in terns of light rays minimizing the total time of travel (left figure below) , while the dynamic description is based on propagation of electromagnetic waves (right figure below):

The dynamic description represents the true physics of light as dynamic wave propagation, while the static description represents fictional physics of fictional light rays equipped with a mysterious intelligence capable of minimizing travel time.

## Laws of Force Balance vs Criteria of Equilibrium

There are many similar examples in physics allowing both a dynamic and static description: Lagrange’s equations of motion in mechanics can be interpreted both as dynamic laws of force balance, or as minimization principles.

As in the case of refraction of light, the dynamic picture is richer and more informative because it involves the mechanisms of reaching balance, not just criteria for being in balance.

In mathematical terms the static description takes the form of an equation

A(X) = 0

to be solved in the unknown X with A(X) a given function of X, while the corresponding dynamic description can take the form of a time-dependent equation

dX/dt + A(X) = 0

which can be approximated by time-stepping as

dX = -A(X)dt

with dX an increment of X in time from one time level to the next with the time step dt. Reaching stationarity

with dX/dt = 0 in the dynamic process, produces a state X satisfying A(X) = 0. But the static equation A(X) gives no information about the dynamic equation dX/dt + A(X) = 0. The dynamic description is constructive

by suggesting an algorithm how to reach equilibrium, if there is one, while the the static is non-constructive.

The time stepping equation dX = A(X)dt can be solved step-by-step by a computer for the increment dX, because the unknown X appears on the right hand side, while the computer does not know how to directly

solve A(X) = 0. The dynamic equation can be solved constructively, while neither reality nor computer knows how to deal with the static equation.

In more general terms, a dynamic description can offer a constructive route to become rich or happy, while

the static only expresses a criteria of being rich or happy. We give another example:

## How to Get from A to B in Paris

We can compare the dynamic process of walking from point A to B in Paris step-by-step with the statics of simply taking the metro minimizing the travel time. The dynamic process of walking is understandable and can be realized using only two legs and very limited intelligence, while understanding the statics of minimal time by metro requires considerable intelligence. Light rays cannot possibly be intelligent and thus only the dynamic process represents real physics.

The static description of quantum mechanics presents ground states with minimal energy requiring intelligent electrons and kernels, while the dynamic description is in terms of a system of electrons with each electron

updating its own wave function by time-stepping with input from the wave functions of the other electrons.

Dynamical time-stepping computational processes based on interaction of elementary processes, thus can simulate real physical processes, while statical descriptions seem to be non-physical.