0 Introduction
Stephen Wolfram worked more dan 50 years on his Dream for a New Kind of Science.
In dit blog I try to find out what he really means.
This blog is structured into three parts 1. General Theory, 2 Wolfram’s theory, 3 Conclusion.
In part 1 I collect alll the data to understand what cohomology-type theory is about.
It is about a way to find out what is the Same in Science which makes it possible to prevent Reinventing the wheel.
Skip part 1 push here.
Move to Conclusion push here.
This blog contains a lot of information.
I gathered all of this information to understand what Stephen Wolfram was really saying.
Now I have finished this blog I think he is too fixed on the goal of his first book “A new Kind of Science and has forgotten to look around if there are “competitors” he can cooperate with.
I hope this blog helps to understand him better.
1 General Theory
Wolfram is the creator of Mathematica, a software-system that makes it possible to express Complex ideas in Computational form.
It is based on a layer above mathematics and is therefore also based on the Foundations of Mathematics.
What are the Foundations of Mathematics?
The foundations of Mathematics are very old. They go back to Pythagoras (“Logic“)and especially Euclid (“Geometry”).
Logic
Logic is based on the Square of of Opposition of Aristotle that contains four combinations of the truth or falsehood of S and P in which the Predicate is either Asserted or Denied of the Subject.
This results in True, False, True-And-False andTrue-or-False.
True and False is called a Contradiction.
True or False is a Possibility.
Cube of Opposition
The Square can be generalized to higher Dimensions k with a value 2**k The higher the number the more difficult it is to Name them.
Euclid’s Axiom’s were Wrong
The theory of Euclid is based on Logic and Axiom’s, a statement that is taken to be true.
The reasoning of Euclid resulted in a lot of discussions that showed that not all of the Axiom’s where true.
Parallel Lines cross at the horizon (because the earth is not flat.
This resulted in different geometries that are dependent on the curvature of space and the Shape of the object.
The new Foundations of Mathematics was created around 1913 by Bertrand Russell in the Principia Mathematica with the use of Set Theory.
Set theory resulted in Rusell’s Paradox that resulted in he creation of Type Theory, a theory without Axiom’s.
In Type theory Axioms are called a Judgement.
| terminology | author |
|---|---|
| judgement | Frege (1879) |
| assertion | Russell & Whitehead (1910) |
| proof | Church (1940) |
| validation | Kochen (1961) |
| judgement | Martin-Löf (1984, 1996) Hofmann (1995, 1997) |
Martin-Löf Type Theory
Transforming Shapes
Later a combination was made between Geometry and Algebra (Calculus) called Algebraic Topology.
It shows how you can Transform Shapes to other Shapes.
This is possible when the shape does not contain a Hole, a place where nothing is connected except the boundary..
Category Theory: Mapping Mathematical Theories
A mathematical theory looks like a function (“functor” that connects the Types of two theories that can be connected to other functors to create a Path in the Space of Mathematical theories.
Type Theory and Computer Science
Type theory is a really a Definition for a special Computer Language rhat can be used to Define and Proof mathematical Theories.
What is the Same?
Shapes are the same when you can fit them to each other.
This can be translated in the possibility to deform the shape without destroying the shape.
The only thing that cannot be deformed is an empty part of the shape, a hole. The hole is a point.
A point is a location in space.
It is possible to map theories to shapes by describing the Proces of the theory.
This proces is a Path and Paths can be connected.
Connected theories can be compressed to a point being a location in the Space of theories.
The central point in the universe is the zero, the middle of the middle.
Theory Management?
When you formalize all theories it is possible to put them into a database and support creating new theories but also prevent repeating the work of others.
Homotopy Type Theory
is the result of the work of Vladimir Voevodsky.
It is a combination of Martin-Löf,Type theory, Algebraic Topology and Computer Science implemented in a software program (CoQ) that is able to check mathematical Proof.
It makes it possible to find out what is the same.
Is Science a Collaborative Game?
The rules of doing Science are still not clear and there is no Referee to decide who is Right.
Scientists make a lot of Mistakes that are sometimes not detected or hundreds of years later.
Current Physics is the result of many miatakes that lead to Contradictions.
Science now is a contest where status determinates what is true.
Collaborative Learning
What is Space and Motion in Physics?
Space consists of Locations that are connected to other locations by Actions that create Locations.
Motion is the Change of a Location and can be correlated by an Observer to a rythm of a cycle that connect locations.
Octonions
Octionions are numbers based on the Imaginary numbers that represent Spirals in Space.
Fractal Space
Space is a process in which processes grow out of a center that produce processes that grow and connect other centers.
This give rise to a Fractal Neural-net-like -like structure that can be seen in space al around us.
Physics made a big and fatal mistake by interpretating the Michelson-Morressey-experiment as a proof for the constantcy of the Speed of light.
What is Seeing and what do we See?
Flickering Consciousness?
What is Seeing is called an Observer and it is believed that we see with our Senses.
We are always situated in a Context where we are attracted to a Scene in Action
The big problem is that the observer is made of what we see mostly called Matter.
Matter is made out of Light so Light is observing Light.
The continuity in observing could be called Consciousness.
Some people believe that Consciousness is independent of the matter we are made of.
Our consciousness is comparable to a movie where the images are projected with a certain Periodicity.
The big question is what happens in between the projections?
Language
consists of Syntax, Semantics and Pragmatics. comparable to the Rules of Languaging, the Meaning of the sentences we speak and and the study of the use of linguistic signs, words and sentences, in Actual situations.
You will see that the work of Wolfram is highly related to Languages.
How Unique is “our” Consciousness?
Are Humans the only consciousnessness on earth or are there others and are they communicating with us and how do they do that?.
What is Time?
Time connects Moments.
A moment is a period of awareness of an Observer.
The shortest moment is related to the shortest distance the Planck unit.
Buckhard Heim created a model of the Universe that was based on objects with a measure based on the Planck-distance.
Essence? Ruliad?
The theory of Wolfram is based on his toolset Mathematica that uses Hyper Graphs to connect the Moments.
the ruliad contains everything that is computationally possible.
Is the Possible the complement of the Impossible being the Empty Set.?
It all has to do with the fact that we are bounded observers, embedded within the ruliad. We never get to see the full ruliad.
What you will see is that he is trying to find a kernel he calls the Ruliad that could have a Deep Mystical Meaning like the TAO.
E8 & 8Tonions and Symmetry
The E8 is the most symmetrical 8 Dimensinal model in mathematics that possibly unites all the forces in Nature.
The Octonions are also 8 Dimensional and represent a Spiraling Spiral.
According to Peter Rowlands they also unite all the known forces in Nature. He has shown that the octonions can be seen als a program that is rewriting itself in reaction to a rule that the sum of all the data is zero, het calls nilpotency.
Symmetry
Context
The model below represents the 4 possible ways (,a rectangle) a Human, according to Carl Jung, observes a context.
Jonathan Gorard on Compositionality
Jonathan Gorard is one of the contributors of Stephen Wolfram in his new Physics project. He is creating a new center at the University of Cardiff.Centre for Applied Compositionality.
His companion Xerxes Arsiwalla talks about Consciousness and Compositionality:
Integrated Information theory
How can we prove that an Object is is Conscious?
2 Wolfram’s Theory
Video about Homotopy Type theory and Wolfram research. push here
Toolmaker
Wolfram used his own tools to make and test the models and was therefore able to approach his target step by step, finding the Simplest Algorythm that generates the most of Complexity.
Kolmogorov Complexity
Leibniz
It was the same target of Leibniz and later Turing, Kolmogorov and Chaitin, who showed that the smallest part had to be the most Unpredictable or the last algorythm that compresses the compressors.
Leibniz was one of the last Magi that returned in the beginning of the Renaissance to bring back the Gnosis.
Many of them were killed by the Inquisition of the Roman Catholic Empire.
Breathing
The Universe breaths by Compressing and Expanding to the limit where te String almost Breaks.
Now Wolfram is ready to take the next atep (expansion) by starting again with an intermediate step of verifying where we are or detecting a completely new path that opens up another universe that is not a mirror of our current universe.
Is the future completely incomprehensible and do we need automatic explainers that show that “it is alreday there but not visible with the current sense”.
We will see.
Meta-metaPhysics?
Wolfram is trying to explain what he sees (with his intuition) and therefore moving from meta-mathematics to Psychology just like Cael Jung and Wolfgang Pauli where doing when Pauli was hunted by his dreams and his paranormal abilities. He found Robert Flud.
Wofgang Pauli and Carl Jung building the Bridge between Mind and Matter
Conclusion
It took me a long time before I found a match between Wolfram’s theory and other theories.
When you read or listen to Stephen Wolfram it looks like he is repeating the same story all the time,
The theory of Reginald Cahill has a lot of affinity with the theory of Stephen Wolfram.
I don’t think he is aware of this.
I also believe he is not aware of he role of the Octonions and the theory of Peter Rowlands.
Peter’s theory explains the same with a different background.
Peter tried to find the essence by making current physics moere simple.
He found a pattern that looks like a self-Rewriting machine that uses a Nilpotent Constraint.
Stephen Wolfram saw a pattern and did not stop until he could match the pattern with current theory.
Perhaps he does not believe what Rowlands and Cahill are explaining, that current theory is wrong because it was made too complex and not testable.