“The Big Bang Theory”

Stephanie : So, how was your day?
Leonard   : Y'know, I'm a [theoretical] physicist - 
            I thought about stuff.
Stephanie : That's it?
Leonard   : I wrote some of it down.

“The physics is theoretical but the fun is real”

MODELS & THEORIES

(1) simplified representation of elements of reality

(2) simplified representation of the effects of elements of reality

(3) non-representational

Stephen Hawking

"It's meaningless to ask what is real, only what agrees with observation."

“it depends on what the meaning of the word “is”, is” (4 sec.)

SystemOpen["https://www.youtube.com/watch?v=j4XT-l-_3y0"]

METHODOLOGIES

(1) equations

(2) computer simulations

(3) simple programs

Aphorism

“LAW OF THE INSTRUMENT”

“Give a small boy a hammer, and he will find that everything he encounters needs pounding.”

Feynman’s final backboard

create => write an equation and solve it
   
create => write a program and run it

EQUATIONS

“not knowing mathematics is a severe limitation in understanding the world” (1 min. 27 sec.)

SystemOpen["https://www.youtube.com/watch?v=tF7jUnYbBIc"]

John von Neumann

“The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work.”

ELASTICITY & VISCOELASTICITY OF A POLYMER NETWORK

cross-linked component

entangled component

chain hedged in by other chains

Statics

Dynamics

COMPUTER SIMULATIONS

David Deutsch

“The universality of computation entails that everything that the laws of physics require a physical object to do can, in principle, be emulated in arbitrarily fine detail by some program on a general - purpose computer, provided it is given enough time and memory.”

SIMPLE PROGRAMS

The study of simple programs is a new scientific discipline which systematically explores computational systems using experimental methods in order to understand and characterize the computational universe.

”why computer science isn’t a science” (1 min. 25 sec.)

SystemOpen["https://www.youtube.com/watch?v=lL4wg6ZAFIM"]

For a program to qualify as simple, there are several requirements:

It can be implemented in a computer language using just a few lines of code.

The number of its possible variations is small enough so that all of them can be computed.

Its operation can be visualized by a graphical illustration.

Simple programs can be seen as a minimal example of emergence. Making simple programs more complicated seems to have little effect on their overall complexity which is evidence that simple programs are enough to capture the essence of almost any complex system.

Because the details of the program's rules have little direct relationship to its behavior, then it is difficult to directly engineer a simple program to perform a specific behavior. An alternative approach is to create a simple overall computational framework, then do a brute force search through all of the possible computational outcomes Then specific fields and behaviors can choose among these discoveries for those that best match.
		
Some simple programs are capable of producing great complexity.
Where does the complexity come from? Simple programs can be seen as a minimal example of emergence. An alternative approach is to try to engineer a simple overall computational framework, and then do a brute-force search through all of the possible components for the

Wolfram advocates using models whose variations are enumerable and whose consequences are straightforward to compute and analyze.

Intrinsic randomness generation - the idea that natural systems can generate their own randomness implies that computational models do not need to include explicit randomness.

Wolfram introduces abstract systems small enough and simple enough that we can enumerate all the rules or programs that might possibly govern their behavior. If the rules are kept simple enough to stay below the threshold, the outcome is always rather dull. But once the rules get just a little more intricate, passing a threshold of complexity, all four categories of behavior appear and once the system has crossed the threshold, further embellishments of the rules have little effect. New details may appear, but all the patterns can still be assigned to the same four basic categories.

Programs or algorithms are the best way of expressing ideas in the sciences. In particular, explicit rules of evolution are preferable to equations, which merely state the constraints that a system must satisfy without necessarily showing how to satisfy them.

GAME OF LIFE

CellularAutomaton[{224, {2, {{2, 2, 2}, {2, 1, 2}, {2, 2, 2}}}, {1, 1}}, startconfiguration, timesteps]

[:+/(3 4=/[:+/(,/,"0/~i:1)|.])*.1,:]

AGENT-BASED MODELS

methodological individualism

* Not all cellular automata are simple programs. *

BIG DATA / DATA ‘SCIENCE’

correlation ≠ causation

GRAPHICS

Wolfram’s Views on Physics

The Second Law

The content of the Second Law is that if one repeats the same meaurements at different times, then the entropy deduced from them will tend to increase with time.

There is, I believe, no choice but to conclude that for practical purposes rule 37R simply does not obey the Second Law.

Albert Einstein

“[Classical thermodynamics] is the only physical theory of universal content concerning which I am convinced that within the framework of the applicability of its basic concepts, it will never be overthrown.”

James Clerk Maxwell

“Thermodynamics [...] is deduced entirely from the first and second law without speculation as to the molecular constitution.”

Definition of Entropy

Entropy is defined as the amount of information about a system that is still unknown after one has made a certain set of measurements on the system.

Richard P. Feynman

“Entropy is the logarithm of the number of ways that the insides can be arranged so that from the outside it looks the same.”

Claude Shannon

“My greatest concern was what to call [the measure of uncertainty in my information theory]. I thought of calling it ‘information’,but the word was overly used, so I decided to call it ‘uncertainty’. When I discussed it with John von Neumann,he had a better idea. Von Neumann told me, ‘You should call it entropy,for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, nobody knows what entropy really is,so in a debate you will always have the advantage.”

Structure of the Universe

from “The World According to Wolfram” by Brian Hayes in American Scientist, 90(4), July/August 2002, pp. 308-310.

There is no continuum, and particles are a mere epiphenomenon; indeed, motion and geometry are also little more than illusions. In this cosmology, space and time are both assumed to be discrete (digital) [...] and the only things that move are signals passing from cell to cell.

The most obvious way of implementing this idea would be to partition space into tiny cubical volumes, creating a cellular automaton on a three-dimensional grid.

However, this simplest solution is unacceptable because it imposes a particular geometry on space and also requires some kind of master clock to synchronize the updating of all the cells throughout the grid.

An alternative is a model where the cells are nodes of a free-form network that has a well- defined topology but no specific geometry. In other words, the connections between nodes are all determined beforehand, but the spatial coordinates of the nodes are left unspecified. Concepts such as shape and position have no meaning at this level: The geometry of space emerges from the model rather than being built into it. Specifically, the world is perceived as being three-dimensional because each node of the network has three incoming links from other nodes and three outgoing links, creating the same connectivity as a three-dimensional lattice. Another feature of the model is that updating the cells requires no synchronizing master clock; updating events propagate along the links of the network itself. Making each link a one-way conduit defines a direction for time and causality; the whole structure is called a causal net.

Miscellaneous

The Principle of Computational Equivalence (PCE) - almost all processes that are not obviously simple are of equivalent sophistication.

Computational Irreducibility - some computations are not amenable to short-cuts and cannot be “reduced” so there are fundamentally no laws (or equations) that allow one to work out the behavior more directly and the only way to determine how the system will behave is essentially to perform the computation.

This is the ultimate origin of free will in a nominally deterministic universe.