Archive for the ‘Computer and Communication Technology’ Category

About the Next Wave of the Kondratiev Cycle

Thursday, April 17th, 2014

The Future Center Smart Systems will be launched, 23-4-2014 in the Hague.

To prepare for the interactive part of the meeting this document has been written to provide some Food for Thought.

What is a Future Center?

A Future Center is a place to connect and innovate. We want to create an environment that facilitates interaction and stimulates collaborative action. We want to support cross-innovation and make it possible to make new combinations. Last but not least we want you to challenge Science to produce valuable insights at the right time and the right place.

A Future Center is a Smart System. At this moment it is an interaction system that helps Humans to innovate. In the Future we could automate the Future Center and automate the innovation-process itself.

What is a Smart System?

A Smart System looks like a human being. It is equipped with a Sensory-Motor-System, a Mind, Imagination and Emotions.

Smart Systems senses the outside (and his inside) world with much more sensors-types than the five sensors of his human look-a-like.

A Smart System is able to react very fast with its predefined processes on a event that is detected by its sensors.

A Smart System is an adaptable system. It is able to analyze and improve its behavior, communicate with a human being and other Smart Systems in an understandable way.

Smart Systems are there to compensate the human biases. Smart Systems are able to transform and optimize everything that contains some kind of structure.

Smart Systems  can optimize software, data and content using software/data/text-mining, analyze patterns, predict the short and sometimes the long term.

Smart Systems are perfectly suited to provide the knowledge needed and answer the questions humans ask. They are able to train humans in an almost real situation using simulators.

Smart Systems can be fun to play with.

About Cycles

In 1931 the US Department of Commerce assigned Edward Dewey the task of discovering the cause and underlying dynamics of the Great Depression. Dewey created a special institute called the Foundation for the Study of Cycles that is still in existence.

The most interesting observation of Dewey is that Cycles restore themselves all the time and are connected by a Harmonic (“Musical”) Pattern. Dewey discovered that we cannot control the Cycles.  Ups and downs are a fact of life.

The most researched Cycle in history by far is the Kondratiev-Cycle named after the Soviet economist Nikolai Kondratiev. The Kondratiev Cycle has a periodicity of 52 years.

The Kondratiev arises from the combination of basic innovations that launch technological revolutions that in turn create leading industrial or commercial sectors.

In the year 2000 the Kondratiev was at his top and is now in a decline that will take 26 years.

Currently we are in  the Kondratiev Spring Phase. It is the time of what Schumpeter, a big fan of Kondratiev, called Creative Destruction.

The old structures are dying and the new structures that will start the new upward wave are created.  It is a time of tremendous disruptions.

About the Software Factory

The last wave that started around 1950 was dominated by the rise of the centralized computer.

This computer was based on the factory-model of Henry Ford and Frederick Winslow Taylor of the previous wave.

Between 1950-2000 isolated creative programmers united in big software factories that are controlled by unified standardized methods and processes. Between 1950-2000 the programmers automated their own processes.

The methods are now transformed into standardized (BPML-)process-models that are abstracted into standardized (VDML-) business models that are filled with Industry-Models. An example is the ARTS-model that covers Retail.

Creative programmers are now replaced by creative business-modelers.

About the Next Wave, The Network of the Human Mind

On Christmas 1990 Tim Berners-Lee working at CERN published the first version of The World Wide Web. He launched the theme for the next wave, The Network.

From 1950 until 2000 the causal linear manual processes were automated but now the next level, the network of the human mind is at stake.

At the end of this wave around 2040 or much earlier as some people predict, the machines will imitate and surpass the human because they will unite in a global brain that can be connected to our Brains if we want that to happen.

At this moment we are creating the memory-banks of the Global Brain by producing billions of connected parts that contain complete human life’s, theories, music, movies, measurements and much more that we are now unable to imagine.

A Short Scenario for the Next Forty Years

It is clear that the Business-Domain-Models will speed up the process of value-chain-integration and value-chain-reversal.

This means that the customer will be in control of the value-chain en there will be direct contact between customer and producer. Value-chain-integration will in the end remove all the intermediaries in the value chain.

Value chains will finally converge into one standardized value chain. Best-practices of separate value-chains will become leaders in the new value-chain. Cross-innovation, combining the best of all worlds, is the way to move on.

To give customers control of the value-chain producers have to simplify their products and make it possible for the customers to create their own version of the product they want.

Products have to become configurations of simple building blocks that can be split into variable parts and infrastructure.  Product-configurators will connect to other configurators. This makes it possible to create completely new combinations.

In the next step the data that is produced by the systems will be analyzed and processes will not be controlled by human made models but by models that are created by statistical pattern recognition tools. The systems will understand humans and predict human behavior and adapt themselves to the human needs.

In the last stage the software will produce an image that reduces the complexity of its whole. It will create a virtual human world that gives us the illusion that we are still in control.

At that time most people will play and not work.

Challenges

The most important question you have to ask yourself is if your company is part of the “old world” that will finally be destructed by creativity or is already part of the new wave.

The big problem is change management,  how to move from the current state to a for most companies and institutions unknown future. Companies and people have to transform their collaboration patterns,  their software and data and their expertise.

The change process is accelerating. A lot of companies are stuck in their installed base of software and their organization structure that is not created to respond fast to the challenges that come from the outside word.

LINKS

About Smart Systems

Launch Future Center Smart Systems

Thursday, February 27th, 2014

Wednesday the 23th of April 2014 13:00 – 17:00 we want to launch the Future Center Smart Systems.

The meeting will take place in the Living Lab of the The Hague Centre for Innovation, 2nd floor Campus Den Haag, Schouwburgstraat 2, 2511 VA Den Haag.

The Future Center is an initiative of LIACS, Leiden Institute of Advanced Computer Science and Constable Research BV.

A Future Center is a place of dialogue and innovation.

Scientific research needs complicated real-life problems to solve to improve their theories. R&D wants to use proven solutions to improve or innovate their products or services.

R&D and Science can easily work together if the long-term strategy of Science matches with the short-term needs of Industry and Government. That is why we need to have a permanent dialogue.

We want to start a dialogue about Smart Systems between Scientific Research and the R&D of big and small companies and government agencies.

Smart Systems are and will be everywhere. Smart Systems control the car you (still) drive and the planes you fly. Smart Systems trade on the stock market, diagnose your illness and design sustainable buildings.

Smart Systems will manage courts & lawyers, cities, logistics and food safety. Smart Systems will entertain you and will stimulate your imagination. Smart Systems will even help you to innovate.

They are a combination of Analytics (Big Data), Artificial Intelligence, Expert Systems, Process/Case-Managers, Robots, Sensors (The Internet of Things), Simulators, Games, Intelligent User-Interaction (Augmented & Virtual Reality) and Social Networks.

The Smart Systems Future Center aims to help you find out what is happening with new technologies and its applications, what is already possible and what will be possible in the future.

We also want to discuss the big impact Smart Systems will have on our society. Many experts believe Smart Systems will lead to a huge increase of unemployment not only on the level of the not educated people but also on the level of the highly educated.

Others believe that the Smart Systems (“the machines, the robots”) will take over the World. They believe that this moment called the Singularity is near.  It is certain that Smart Systems will disrupt almost every company in the world. 

To prepare you for the future we want to connect people, companies and government agencies. We want to participate in projects and start the development of new research, new services or companies. We can also help with the funding of these projects.

In the first meeting representatives of other Future Centers in the Netherlands (ABN AMRO, Tax Office, Ministry of Infrastucture) will share their experiences, we want to tell you about the state of the art in Big Data and have an interactive discussion about our future plans and priorities and how you want to be part of this dialogue.

The amount of people of the first meeting is limited. After the first meeting we will organize many other meetings in which we will discuss a specialized subject. We will announce these meetings in the Linkedin group Smart Technology Network. If you join this closed network you will be always up-to-date.

If you are interested to come to the meeting or want to be informed by email about what we are doing please send an email to hans.konstapel@gmail.com. If you know people who could be interested to join our Future Center please forward this link to them.

About Number and Magnitude

Monday, January 9th, 2012

We have lost the relationship between Number and Form or Number and Magnitude as the Ancient Greeks called their Forms.

A few years ago a Revolution in Mathematics and Physics has started. This revolution is caused by Geometric Algebra.

In Geometric Algebra the Ancient Theories of Euclid and Pythagoras are reevaluated.

Numbers are Scalar (Quantum) Movements of Geometric Patterns and not Static Symbols of Abstractions that have nothing to do with our Reality.

Movements and not Forces are the Essence of Physics.

The basic rule Movement = Space/Time (v=s/t) shows that  Time and Space are two Reciprocal 3D-Spaces. Our Senses Experience Space and not Time.

The Simple Rule N/N=1/1=1 balances the Duals of Space and Time. One Unit Step in Space is always Compensated by One Unit Step in Time.

Geometric Algebra has a strange relationship with Pascals Triangle. This Triangle, also called the Binomial Expansion, contains all the Possible Combinations of two Independent Variables. Our Universe is a Combination of Combinations exploring Every Possibility.

The last and perhaps most important Discovery in Mathematics called Bott Periodicity shows itself in Pascals Triangle.

Bott Periodicity proves that we live in a Cyclic Fractal Universe, the Wheel of Fortune, that is Rotating around the Void, the Empty Set. The Empty Set contains Every Thing that is Impossible in our Universe.

This blog is not a Scientific Article. I have tried to connect the Old Sciences and the New Sciences in my own Way.

It contains many links to Scientific Articles and even Courses in Geometric Algebra.

So if you want to Dig Deeper Nothing will Stop You.

About the One and the Dirac Delta Function

Every Thing was created out of  No Thing, the Empty Set, ɸ, the Void, the Tao. The Empty Set contains 0 objects.

The Empty Set is not Empty. It contains Infinite (∞) Possibilities that are Impossible.

Every impossibility has a probability of 0 but the sum of all possibilities (1/∞=0) is always 1. In the beginning ∞/∞ =1  or ∞x0=1.

This relationship is represented by the Dirac Delta Function. It is used to simulate a Point Source of Energy (a Spike, an Explosion) in Physics.

The Delta is reprented by the Symbol Δ, a Triangle. The Delta is called Dalet in the Phoenican and Hebrew Alphabet. Daleth is the number 4 and means Door.

The original symbol of the Delta/Daleth contains two lines with a 90 Degree Angle. Two orthogonal lines create a Square or Plane.

The Dirac Delta Function is defined as a Square  with an Area of 1,  a Width of 1/n and a Height of n where n->∞.

The Dirac Delta Function is a Line with an Area of 1.

In the Beginning a Huge Explosion took place that created the Universe.

The Dirac Delta Function δ (x) has interesting properties: δ (x) = δ (-x), δ (x) = δ (1/x). It has two Symmetries related to the Negative Numbers and the Rational Numbers.

When we move from 2D to 1D, the Number Line, the Delta Function becomes the Set of the Numbers N/N =1.

The Tetraktys of Pythagoras

The Monad (1) of the Tetraktys of Pythagoras, the Top of the Triangle, was created by Dividing the One (1) by Itself without Diminishing itself. The Monad (1/1=1)  is part of  the 1D Delta Function.

Creation is an Expansion of the 1/1 into the N/N, adding 1/1 all the time,  until ∞/∞ is reached. At that moment every Impossibility has been realized.

File:Dirac function approximation.gif

The Dirac Delta Pulse

To move Back to the Void and restore the Eternal Balance of  the One,  Dividing (Compression) has to be compensated by Multiplication (Expansion).

At the End of Time N/M and M/N have to find Balance in the N/N,  move Back to  1/1, Unite in the 0 and become The Void (ɸ) again.

About the Strange Behavior of Numbers

The big problem of the Numbers is that they sometimes behave very differently from what we Expect them to do.

This Strange Behavior happens when we try to Reverse what we are doing.

It looks like the Expansion of the Universe of Numbers is Easy but the Contraction creates many Obstacles.

It all starts with the Natural Numbers (1,2,3,).

When we Reverse an Addition (Subtract) and move over the Line of the Void Negative Numbers appear. Together with the Natural Numbers they are called the Integers.

The same happens when we Reverse a Division and the Fractions (the Rational Numbers) (1/3, 7/9) suddenly pop up.

An Integer N is a Rational Number divided by 1 (N/1).

The Integers are the Multiples of 1, the Fractions are its Parts.

Numbers behave even stranger when we want to Reverse a Repeating Repeating Addition (Irrational Numbers) and want to calculate a Rational Power (2**1/2).

The Complex Numbers (or Imaginary Numbers), based on the Square Root of -1 called i, are a combination of the Negative Numbers and the Irrational Numbers.

Irrational Numbers ( the Pythagorean Theorem), Fractions (a Piece of the Cake) and Negative Numbers (a Debt) are part of our Reality but the Strange Number i represents something we cannot Imagine.

About the Duality and the Expansion of Space

In the beginning the only One who was in existence was the 1.

When the One divide itself again the number -1, the Complement of 1, came into existence.

1 and -1 are voided in the No Thing, the Empty Set, 0:  -1 + 1 = 0.

The Two, the Duality, both started to Expand in Two Opposite Directions (<– and +->) both meeting in the  ∞/∞. This expansion is what we call Space.

Space is a Combination of the Strings S(1,1,1,1,1,…) and -S = (-1,-,1,-,1,-1,…) where S+S=(0,0,0,0,0,0,…).

The Expansion pattern of Space is a Recursive Function S: S(N)=S(N-1)+1 in which + means concatenate (or add) the String “,1″.

An Addition X + Y is a concatenation of S(X) and S(Y). A Substraction X-Y is a concatenation of S(X) and -S(Y). In the last case all the corresponding combinations of 1 and -1 are voided. (1,1,1,1)-(1,1,1)=(0,0,0,1)=(1).

Multiplication XxY is Adding String S(Y) every time a “1″ of S(X ) is encountered: 111 x 11 = 11  11  11. Dividing X/Y is Subtracting S(X) every time a “1″ of S(Y) is encountered:.111  111  1/111=11 1/111. In the last example a Fraction 1/111 appears.

This Number System is called the Unary Number System.

About the Trinity and the Compression of Space called Time

The Strange Behavior of Numbers is caused by the Limitations of our Memory System. We are unable to remember long strings that contain the same Number.

To make things easy for us we Divide Space into small Parts so we were able to Re-Member (Re-Combine the Parts).

When we want to Re-member, Move Back in Time, we have to Compress Expanding Space.

Compressed Space is Time.

Time and Space have a Reciprocal Relationship called Movement (Velocity = Space/Time).

There are  many ways ( (1,1,1), (1,1,1),..) or ((1,1),(1,1))) to Compress a String in Repeating Sub-Patterns.

In the blog About the Trinity I showed that the most Efficient Way to group the One’s is to make use of a Fractal Pattern (a Self Reference) and Groups of Three Ones.

The Trinity applied to the Trinity ( A Fractal) is a Rotating Binary Tree. Binary Trees represent the Choices we make in Life.

The rotating Expanding Binary Trees generate the Platonic Solids (see linked video!) when the (number)-parts of the Binary Tree Connect.

The Ternairy Number System is represented by the Binary Tree

When we connect Three Ones (1,1,1) by Three Lines (1-1,1-1,1-1) a 2 Dimensional Triangle Δ is Created.

If we take the Δ as a new Unity we are able to rewrite the patterns of 1′s and -1′s into a much Shorter Pattern of Δ’s and 1′s: (1,1,1),(1,1,1),(1,1,1), 1,1 becomes Δ,Δ,Δ,1,1.

We can repeat this approach when there is still a Trinity left: Δ,Δ,Δ,1,1 becomes ΔxΔ,1,1.

This Number System is called the Ternary Number System.

About Ratio’s and Magnitudes

According to EuclidA Ratio is a sort of relation in respect of size between two magnitudes of the same kind“.

A Magnitude is a Size: a property by which it can be compared as Larger or Smaller than other objects of the Same Kind. A Line has a Length, a Plane has an Area (Length x Width), a Solid a Volume (Length xWitdth x Height).

For the Greeks, the Numbers (Arithmoi) were the Positive Integers. The objects of Geometry: Points, Lines, Planes , were referred to as “Magnitudes” (Forms). They were not numbers, and had no numbers attached.

Ratio, was a Relationship between Forms and a Proportion was a relationship between the Part and the Whole (the Monad) of a Form.

Newton turned the Greek conception of Number completely on its head: “By Number we understand, not so much a Multitude of Unities, as the abstracted Ratio of any Quantity, to another Quantity of the same Kind, which we take for Unity”.

We now think of a Ratio as a Number obtained from other numbers by Division. A Proportion, for us, is a statement of equality between two “Ratio‐Numbers”.

This was not the thought pattern of the ancient Greeks. When Euclid states that the ratio of A to B is the same as the ratio of C to D, the letters A, B, C and D do not refer to numbers at all, but to segments or polygonal regions or some such magnitudes.

The Ratio of two geometric structures  was determinated  by fitting the Unit Parts of the first geometric Stucture into the Other.

The Perfect Triangle of the Tetraktys contains 9 = 3x3 Triangels. A Triangle contains 3 Lines and 3 Points.

An Example:  The Tetraktys is a Triangle (A Monad) and contains 9 Triangles (a Monad). The 1x1x1-Triangle Δ, a Part of the Tetraktys,  is Proportional to the Whole of the Tetraktys (T) and has a Ratio T/Δ = 3= Δ -> T = Δ (3)  x Δ (3) = 9.

The Mathematics of Euclid is not a Mathematics of Numbers, but a Mathematics of Forms.

The symbols, relationships and manipulations have Physical or Geometric Objects as their referents.

You cannot work on this Mathematics without Knowing (and Seeing) the Objects that you are Working with.

About Hermann Grassman, David Hestenes and the Moving Line called Vector

Hermann Grasmann lived between 1809 and and 1877 in Stettin (Germany). Grassmann was a genius and invented Geometric Algebra a 100 years before it was invented.

In his time the most important mathematicians did not understand what he was talking about although many of them copied parts of his ideas and created their own restricted version. None of them saw the whole Grassmann was seeing.

When he was convinced nobody would believe him he became a linguist. He wrote books on German grammar, collected folk songs, and learned Sanskrit. His dictionary and his translation of the Rigveda were recognized among philologists.

Grassmann took over the heritage of Euclid and added, Motion, something Euclid was aware of but could not handle properly.

angle between vectors in 2 dimentions

A Displacement or Bivector

Grassmann became aware of the fact your hand is moving when you draw a 2D Geometric Structure. He called the Moving Lines, that connect the Points, Displacements (“Strecke”).

screw theory 2

A Displacement and a Rotation of a Vector

In our current terminology we would call the Displacements “Vectors”.

blades

Vector algebra is simpler, but specific to Euclidean 3-space, while Geometric Algebra works in all dimensions. In this case Vectors become Bi/Tri or Multi-Vectors (Blades).

The Trick of Grassmann was that he could transform every transformation on any geometrical structure into a very simple Algebra. Multi-Dimensional Geometric Structures could be Added, Multiplied and Divided.

The Greek Theory of Ratio and Proportion is now incorporated in the properties of Scalar and Vector multiplication.

add-bivectors

Combining (Adding) Bivectors creates a Trivector

About a 100 years later David Hestenes improved the Theory of Grassmann by incorporating the Imaginary Numbers. In this way he united many until now highly disconnected fields of Mathematics that were created by the many mathematicians who copied parts of Grassmanns Heritage.

About Complex Numbers, Octions, Quaternions, Clifford Algebra and Rotations in Infinite Space

Grassmann did not pay much attention to the Complex Numbers until he heard of a young mathematician called William Kingdon Clifford (1845-1879).

Complex numbers are ,just like the Rationals (a/b), 2D-Numbers. A Complex number Z = a  + ib where  i**2=-1. Complex Numbers can be represented in Polar Coordinates: Z = R (cos(x) + i sin(x)) where R = SQRT(a**2 + b**2).  R is the Radius, the Distance to the Center (0,0).

When you have defined a 2D-complex Number it is easy to define a 4-D-Complex Number called a Quaternion:  Z = a + ib + jc + kd or a 8-D Complex Number called an Octonion.

William Rowan Hamilton, the inventor of the Quaternions, had big problems to find an interpretation of all the combinations i, j and k until he realized that i**2 =j**2 = k**2 = ijk=-1.

What Hamilton did not realize at that time was that he just like Grassmann had invented Vector Algebra and Geometric Algebra.

Quaternions are rotations in 4D-space

This all changed when William Kingdon Clifford united everything in his new Algebra.  Clifford’s algebra is composed of elements which are Combinations of Grassman’s Multivectors.

The Clifford Algebra that represents 3D Euclidean Geometry has 8 = 2**3 components instead of 3: 1 number (Point), 3 vectors (Length), 3 bivectors (Area) and 1 trivector (Volume).

It turns out if you use combinations of these elements to describe your geometric objects you can do the same things you did before (you still have 3 vector components).

In addition, you can have additional data in those other components that let you find distances and intersections (and a lot of other useful information) using simple and (computationally) cheap numerical operations.

The most important Insight of William Kingdom Clifford was that the Complex Numbers are not Numbers all.

They are Rotations in higher Dimensional Spaces.

About Pascal’s Triangle and Mount Meru

The String 1,3,3,1 of Clifford’s 3D Geometry is related to the 4th Level of Pascal’s Triangle. Level N of Pascal’s Triangle represents N-1-Dimensional Geometries.

The Sum of every level N of the Triangle is 2**N. This Number expresses the Number of Directions of the Geometric Structure of a Space with Dimension N.

A Point has 0 Direction, while a Line has 2 Directions, relative to its Center point, a Plane has 4 Directions, relative to its Center Point, and a Cube has 8 directions, relative to its Center point.

Pascal’s Triangle is also called the Binomial Expansion. This Expansion shows all the Combinations of two letters A and B in the function (A+B)**N. Level 1 of the Triangle is (A+B)**0 = 1  and level 2 is A x A + 2 A x B + B x B -> 1,2,1.

The Binomial Expansion converges to the Bell-Shaped Normal Distribution when N-> ∞.

The Diagonals of Pascal’s Triangle contain the Geometric Number Systems (Triangular Numbers, Pyramid Numbers, Pentatonal Numbers, ..) and the Golden Spiral of the Fibonacci Numbers.

Pascal’s Triangle is a Repository of all the Possible Magnitudes and their Components.

The Normal Distribution shows that the first level of the Triangle (the Tetraktys) is much more probable than the last levels.

The Hexagonal Numbers

The first four Levels of the Triangle of Pascal contain the Tetraktys of Pythagoras.

The Tetraktys  is an Ancient Vedic Mathematical Structure called the  Sri Yantra, Meru Prastara or Mount Meru.

Mount Meru

About Numbers, Operations and the Klein Bottle

The Complex Numbers are not “Numbers” (Scalars) at all.

They are “Operations” (Movements) that can be applied to Magnitudes (Geometries) and Magnitudes are Combinations of the Simple Building Blocks of the Tetraktys, Points and Lines.

The Tao of Ancient China was not for nothing represented by a Flow of Water. According to the Ancient Chinese Mathematicians Every Thing Moves.  In the Beginning there was only Movement.

In the Beginning only the One was Moved but when the Duality was created the Two moved around each other never getting into contact to Avoid the Void.

When we look at the Numbers we now can see that they are the result of the Movements of  the first Diagonal of Pascals Triangle,  the 1′s (Points) or better the Powers of  the One: 1 **N (where N is a Dimension).

Even in the most simple Number System, the Unary Number System, Concatenation is an Operation, An Algorithm.

The Mathematician John Conway recently invented a new Number System called the Surreal Numbers that contains Every Number you can Imagine.

The Surreal Numbers are created out of the Void (ɸ)  by a simple Algorithm (Conway calls an Algorithm a Game) that describes Movements (Choices of Direction: Up, Down, Left, Right, ..)  that help you to Navigate in the N-Dimensional Number Space.

The Ancient Chinese Mathematicians played the same Game with the Numbers.

Algorithms were already known for a very long time by the Ancient Vedic Mathematicians. They called them Yantra’s.

SriYantra

Sri Yantra

Geometry is concerned with the Static Forms of Lines and Points but there are many other more “Curved” forms that are the result of  Rotating Expansion and Compression. These forms are researched by the modern version of Geometry called Topology.

The most interesting 4D Topological Structure is the Klein Bottle.  The Klein Bottle is  a combination of two Moebius Rings. It represents a Structure that is Closed in Itself.

It can be constructed by gluing both pairs of opposite edges of a Rectangle together giving one pair a Half-Twist. The Klein Bottle is highly related to the Ancient Art of Alchemy.

The movement of the Duality around the Void can be represented by a Moebius Ring the Symbol of Infinity ∞.

Later in this Blog we will see why the Number 8 is a Rotation of ∞ and the symbol of Number 8 is a combination of the symbol of the number 3 and its mirror.

First we will have a look at the Reciprocal Relation between Space and Time.

The Klein Bottle, The Universe Closed in Itself, the Basic Structure behind Alchemy.

The Klein Bottle, The Universe Closed in Itself, the Basic Structure behind Alchemy.

About Dewey B. Larson, Velocity and Time

Dewey B. Larson (1898 – 1990) was an American Engineer who developed the Reciprocal System of Physical Theory (RST).

Larson believed that the failure to recognize that Motion is the most basic physical constituent of the universe has handicapped the progress of the traditional study of physics, which focuses on Forces.

The definition of Motion stems from the Equation of Velocity, v = ds/dt.

Instead of depending upon the change of the location of an object to define an arbitrary “quantum” of space per “quantum” of time, such as miles per hour, or meters per second, the RST assumes that the observed universal passage, or progression, of time is one aspect of a universal motion that necessarily must be accompanied by a universal “passage,” or progression, of space.

The Units of Time fill up the Units of Space. Space and Time are Duals.

Space is not-Time and Time is not-Space. Time is Non-Local, Cyclic and represented by the Rotating Imaginary Numbers. Space is Local, Linear and Represented by the Scalar Numbers. Space is the Vacuum and the Nothing and Time is the non-vacuum, the Every Thing, the Solids represented by the Cube of Space.

The Cube of Space is the structure behind the Tetraktys but also behind the Book of Genesis.

Our Reality contains two Reciprocal 3D-structures related to Space and Time. Space and Time are related by the Simple Formula N/N=1/1=1, the Formula of Diracs Delta Function.

We are able to perceive the Real 3D-Structure of Space. The 3D-Structure of Time is Imaginary. It is situated in the Imaginary Number Space of i.

LarsonsScalarCube.jpg

Larson’s Cube, the Geometric Representation of the Octonion.

Larson, a Self Thought Genius like Grassmann, developed Geometric Algebra without knowing anything about Geometric Algebra but he also invented String Theory long before String Theory was invented.  The Mathematics of Larson is also the Mathematics of the Tetraktys of Pythagoras without even knowing anything about it.

wom_image3.jpg

The Periodic System of Larson

Larson was able to Calculate all the important Physical Numbers without any problem and was also able to Calculate Chemical Structures and Reactions.

About the Bott Periodicity

The fourth line of Pascals Triangle and the Tetraktys contains 8 Directions in the Four Geometric Dimensions: 0, 1, 2, and 3.

Mathematicians are intrigued with this number 8, because they find it popping up unexpectedly in advanced mathematics.

In fact, expanding the Binomial Expansion to 8 dimensions just creates an inverse copy of these first Four Dimensions, and then the pattern just repeats itself with a half-twist and back from there, ad infinitum.

This is called Bott Periodicity discovered by the mathematician Raoul Bott (1923-2005).

The mathematician John Baez wrote an article in which he relates this 8-fold Periodicity to the Scalars (1), the Complex Numbers (2), the Quaternions (2×2), and the Octonions (2x2x2 = 2**3).

Bott Periodicity

The Universe of Numbers and Magnitudes  is Cyclic and Fractal.

Our own Reality, symbolized by the Tetraktys,  repeats itself in Higher Dimensions until Infinity.

The Tetrad, represents Completion, because it contains all its Previous Numbers, the 1, 2, 3, and itself, 4, in One Number, 10 = (The One) +  9 (= 3 (Trinity)x 3 (Trinity) = Tetraktys).

As you can see in the Picture above the Fractal Pattern of 8 contains two kinds of Trinities/Triangles, an Upside and a Downside (Rotated by 180 Degrees) Triangle. When you Rotate by 180 Degrees the 1 becomes -1 and 1 + -1 =0 is the Void.

The Square is a combination of two Triangels. It is represented by the Of Star of David, the Symbol of the Heart Chakra.

The Star of David, the Symbol of Human Center, the Heart Chakra.

The Multi Dimensional Rotations of the Octonions always Come Back to Square 1/1=1, the One and keep Rotating around the Center, the Nothing,   Until Infinity.

LINKS

About the Tetraktys (1)

About the Tetraktys (2)

About Triangular Numbers and Pascal’s Triangle

About the Empty Set

About the Relationship Between Geometry and Music

About the Trinity

About the Game of the Surreal Numbers

About Larson and the Unification of Mathematics

The Collected Works of Dewey B Larson

About Number and Magnitude

About Ratio and Proportion

About Ratio and Proportion by Euclid

A book of Augustus deMorgan about “The Connection between Number and Magnitude”

The text of the Fifth Book of Euclid

An Educational You Tube Channel called Insights in Mathematics

About the History of Geometric Algebra

About the Sri Yantra

About Geometric Algebra

Free Software to use Geometric Algebra

About Clifford Algebra

About Yantra’s

About Movement

About Topology

About the Digital Root Patterns

About the Heart Chakra

A Video that shows how the Platonic Solids are created out of the Trinity Numbers

All you want to know about Geometric Patterns

About the Sum of Things

Thursday, September 22nd, 2011

The Lo Shu is a Chinese Model for Time and was used to design Cities, Temples, Cycles and Calendars.

lo-shu-color

The Lo Shu is a 3×3 Magic Square created by Fu Xi, the Founder of Chinese Civilization. Fu Xi lived around the time of the Great Flood.

The Magic Square was carried by a Turtle. The Turtle is the symbol of the Constellation Orion. Many Ancient Cultures claim that our Ancestors came from this constellation. The Square of Lo Shu is also referred to as the Magic Square of Saturn or Chronos (Time).

The Chinese Pollen Path

The Duality of Fu Xi and his Sister, The Snake of the Kundalini contains 3.5 (7/2) Twists. 2x3.5 = 7. 7 = (-1,-2,-3,0,1,2,3).

According to Chinese Creation Myth  the world started with 無極 (wuji: nothingness), the Tao. Out of the Tao, the Egg of the Zero (0) and the Supreme Pure One (1) emerged. In the next step the Trinity (3), the Three Pure Ones, was created.

The Tao produced One; One produced Two; Two produced Three; Three produced All things (Lao Tsu, Tao Te Ching, 42).

SriYantra

The Sri Yantra contains 43 Triangels and is generated by the Bronze Mean.

The Trinity is represented by a Triangle. A combination of Two Triangels is a Square. The combination of Two (2) Triangels is also the Symbol of the Heart Chakra, the merge of Heaven, the Upper Triangel and Earth, the Lower Triangel.

The most complex Yantra (“machine”), the Sri Yantra, contains 43 Triangels. The Sri Yantra is determinated by the Bronze Mean. The Bronze Mean is a generalization of the Sequence of Fibonacci based on the Trinity. The Bronze Mean generates Quasi-Crystals and Penrose Tilings.

The Square is a combination of two Triangels. It is represented by the Of Star of David, the Symbol of the Heart Chakra.

The Square is a combination of two Triangels. It is represented by the Star of David, the Symbol of the Heart Chakra.

The Lo Shu Magic Square not only shows the Connection between the Four Forces that came out of the Two Forces, Expansion and Compression, it also shows the connection between Heaven and Earth.

In the Magic Square of Lu Shu the Even Numbers (2,4,6,8 = 2 x (1,2,3,4 = 2×2)) are Black(Yang, Male). The Odd Numbers (1,3,5,7,9 = 3×3) are White (Yin, Female). The Sum of all the Numbers is 15 (3×5).

The Even Numbers are situated at the Corners of the Square.

When the numbers of each row are multiplied (8x1x6; 3x5x7; 4x9x2) they together total to 225 ((3×5)x(3×5)) — as do those of the columns (8x3x4; 1x5x9; 6x7x2).

The Magic Square is dominated by two numbers (2**1, 2**2, 2**3)  and (3, 2×3, 3**2), It contains four Prime Numbers (1,3,5,7). It also contains the first Perfect Number 6 (1+2+3 =1x2x3). 6 is also a Harmonic Divisor Number and has a Harmonic Divisor 2. The Sixth Day in the week is the day of Saturn, the God of Time.

The sequence 1,2,4,8, 1, 3,6,9, 27 is called the Tetrad of the Pythagorians and was, according to Plato, used by the Demiurg, the Creator of our Universe, to create the Soul. The Soul is a mixture of the Same (1), the Different (2), and Existence (3). The Tetrad was used to define the Harmony of the Spheres.

When you connect the numbers of the Lo Shu a pattern appears that is called the Seal of Saturn or the Dance of Yu.

The Seal of Saturn or the Dance of Yu

The Sum of Magic Squares is a Magic Square and the product of a Magic Square M with a number a is again a Magic Square aM. Both Rules can be used to construct a Magic Square out of simple Binary Squares called Magic Carpets. One of these Magic Carpets is the Identity Matrix with One on the Diagonal.

Every Magic Square is related by Rotation and Mirroring to Eight other Magic Squares. This means that the central Lo Shu Magic Square with the Five in the Middle is related to Eight other Magic Squares with the other Numbers in the Middle. One of them contains the Nine and is called the Well.

The Lo Shu and the Well

The Sum of numbers of the Well is 18 (2×9) and the sum of all opposites across the 8 Spoke Wheel = 9 (9+0, 8+1, 7+2, 6+3, 5+4). 2×9 means that there are Two Complementary Magic Squares. One Magic Square is Rotating with the Clock and the other Against the Clock.

The Well is an Expansion and Contraction Cycle based on Powers of 2.

The Nine is de most important Number in the Magic Square. The Nine come back in many ancient mythologies like the Egyptian Pesedjet and the Greek Ennead.

When you add the separate numbers of a number (54 = 5+ 4 = 9) the result is the Remainder when you divide the number by 9.  This number is called the Modulo 9 number.

The Powers of 2 (= Expansion) Mod 9 creates a pattern (1,2,4,8,(16)7,(32)5,(64)1,(128)2,…). This pattern is reversed when we divide by 2 (=Compression) (1/2 (0,5 =5), 1/4 (0,25 = 7), 1/8 (0,125 =8), 1/16 (0,625 = 4), 2,1).

The Expansion and Compression Pattern shows that the same pattern repeats itself when the Magic Square is expanded or compressed Six (6) Times. The 7th Step is the Same as the First Step.

After 2**6=64 (8×8) divisons of the cell a Specialized Cell is created, the stem cell. The same happens in Music.  The Game of Chess (Chiu King in China) with its 8×8 = 64 = 2**6 Playing Board contains every possible situation of the Game of Life.

The Two-Pattern does not contain the numbers 3,6 and 9. The number 9 is repeated every time when the pattern is expanded and compressed which means that Nine is the same as the Identity, the One (1+9 = 1). 3 and 6 Oscillate (1x2x3=6 and 1+2+3 =6) and  therefore represent the Duality (3+6 = 9, = the One).

If we combine the Expansion and Compression patterns a Torus (a Rotating Circle, The Wheel of Time) appears. The Zero (the Void) is in the Center and Contains the Vortex. The Vortex represents another Cycle (Black/White Hole, 3,6,9, the Wheel of Order) in which every structure/pattern is destroyed to start All Over Again.

Lo Shu Torus

If we subtract the numbers in the Square by the number of the Center, 5, a highly Symmetric Pattern emerges. This pattern shows that there are Two Mirror Universes both containing four Forces.

When we transform this pattern from Modulus 9 to Modulus 3 (the Trinity) we see that the number 4 equals 1 and represents a new beginning of the Cycle.

4

9

2

-5

-1

4

-3

3

5

7

-5

-2

0

2

8

1

6

-5

3

-4

1

The Magic Square with the Zero in the Middle is surrounded by two Sequences of 123(4) with different Signs. The Signs are arranged in a Cyclic Pattern (- -, + -, + +, – +) that contains the Four Permutations of – and +. The Sum of the ++ and the — is -3 and +3, the Trinity. The Sum of +- en -+ is the One.

The Cyclic Pattern of + and – represents the Prisoners Dilemma that is solved by the Strategy of Tit for Tat. This strategy is applied by the Trickster, the God of Paradox, a concept of God in which God creates games that create games.

When you use the basic Addition and Multiplcation Rules of the Magic Square many important numbers and patterns  appear that are related to Ancient CalendersSymbols and Cycles.

About the Sum of Things

The Lo Shu Magic Square appeared a few years ago when I wanted to know more about Acupuncture.  Acupuncture is related to the Sheng Cycle and the Sheng Cycle is related to the Lo Shu. A Magic Square is the perfect way to visualize the Constraints that control the Four Forces in our Universe.

Soon after this discovery I found out the Lo Shu is related to the Trinity and the Bronze Mean which is an abstraction of the Fibonacci Sequence. The Bronze Mean generates the Sri Yantra and so called Quasi Crystals. Quasi Crystals explain Acupuncture.

A few weeks ago I started a discussion with Kim Veltman. Kim Veltman is the director of the Maastricht McLuhan Institute. He is researching Ancient Architecture and wrote a very interesting document called “Alphabets, Elements and Cosmologies”.

Ancient Alphabets are related to Numbers and Tones so Ancient Texts also represent  Numerical Patterns and Music. You want be surprised to read that the Lo Shu showed itself in every Text Kim Veltman has analysed.

His document started a new inquiry into the pattern of the Lo Shu. During this research I detected the book “the Sum of Things” by Paul Martyn-Smith. Paul Martin-Smith worked together with Lee Burton.

This blog contains just a litte bit of the tremendous amount of information Paul Martin-Smith & Lee Burton have found about the essence of the I Tjing which is contained in just one simple 3×3 Magic Square.

If you want to know more the only thing you can do is to buy this book and start reading.

LINKS

About the Book “the Sum of Things”

About the I Tjing

The Calculations  behind the Number of Things

The Relationship between the Lo Shu and the I Tjing

About the Lo Shu Torus

About Saturn, the Son of the Sun

About the Trickster

How to construct Magic Squares out of Binary Squares (Magic Carpets)

The Sistine Chapel (Rome) and the Seal of Saturn

About the Relationship between the Lo Shu and Music

About the History of the Lo Shu

About the Wheel of Eternal Order and the Wheel of Time

About the Relationship between the Lo Shu and Chinese Alchemy

About the Great Flood

About the Orion Myth

About Plato, Pythagoras and the Lo Shu

About the Nothingness

About the Trinity

About the Heart Chakra

About the Sri Yantra

About the Lo Shu Magic Square and the Chinese Domino Game

About the Mirror Universe

About Acupuncture

About Tit for Tat

About the Prisoners Dilemma

About the Bronze Mean

About the Sheng Cycle

Everything You want to Know about Sacred Geometry

About the Influence of the Lo Shu on Recent Art

The Lo Shu Square with Imaginary Numbers

About Smart Systems

Wednesday, June 16th, 2010

global brainWhen a Search Engine crawls the web and indexes information so that you can access it quickly, the search engine is doing Proactive Computation.

Servers don’t wait for you to execute a search query to start crawling the web; they are being proactive because it takes Too Much Time to find and index what you want.

The Sensory Motor System of Our Body is constantly performing Proactive Computing because it has to be Ready to Act, when something happens that is fatal to the Body.

In a State of Arousal  the Sensory Motor System Reacts with predefined Scripts (Impulses).  The Sensory System fails completely when there is too much data available (Overload, Panic).

The Sensory Motor Computer is not able to calculate exactly what the Body really needs because it does not have the time and the capacity to calculate every possibility. Therefore the Human Body sometimes makes terrible mistakes, called a Gognitive Bias, when it is Highly Stressed.

The Rational System, the Human Predictor of the Future, the Expectation,  is able to override the Sensory Motor System when there is enough Relaxation, Time and Capacity available. This State of Mind is called Reflection.

To Reflect the System needs enough Data, Provided by the Senses and our Memory, and a Model, a Believe System, that describes the Context we want to Evaluate.  Most of the time we are unable to collect the Facts or to define a suitable Model. We See what our Believe System guided by our Experiences in the Past wants Us to See.

The Imagination creates the images we See. Sometimes the Images are made by the Senses. We see Reality as it Really is. Most of the Time the Imagination projects the Images of the Reflection System. We See what our Believe System wants us to See.

The most interesting part of the Imagination is related to the Dream World, the Unconsciousness. The Dream World projects the Images we Have to See. They contain a “hidden meaning“, something we have to know but are unable to Express.

Making a Choice is one of the most difficult things to do. The Emotional System, the Oldest System in our Body, acts on the basis of Feelings. It wants to move to a situation where there is enough Certainty to Survive (Food, Shelter, Love,….) and avoids situations that are threatening to the Existence of the Body.

The Reflective System transforms Human Feelings into Values, Preferences and Selection Criteria.

The big problem is that the Emotions (the Movers, Our Moti-vation) change all the time because they are influenced by Situations (the Context), Others (Status) and all kinds of Fields in the Environment (Gravity (Moon), the Electro Magnetic Field).

The fifth human system, the Consciousness, monitors the four “organs” (the Senses, the Expectation, the Emotions and the Imagination) to make sure they stay in the right balance.

What is Happening?

The Computer is a Cold Rational Calculator without any Emotions. The Computer is therefore perfectly suited to Support, Complement and Replace the Heavely Biased Impulsive Unconscious Emotional Human Being.

According to Forrester Research ,a big Advisory Bureau, we are moving into a New Wave of Computing called Smart Computing. Big IT-Companies like IBM (“Smart Planet“), Oracle and of course Google (“Implementing the Singularity of Kurzweil“) are now completely redefining their strategy to be able to Move with the New Wave.

The Amount of Available Computer Memory, the Capacity to Calculate in Real-Time and the Intelligence of the Pro-Active Algorithms and Reaction Scripts is increasing by the day and the Costs of  Computing are going down fast.

Smart Computing extends existing technologies by adding new real-time Situation Awareness based on Sensor Technology and Automated Analysis to help firms and people solve smarter and more complex problems.

Smart Computing integrates the Physical World of the Senses and the Body with Automatic Process Optimization via a Four Step Cycle: Awareness (Sense), (Statistical) Analysis (Reflect), (Generate) Alternatives (Feel, Evaluate, Select & Choose) and Act -> Sense.

What has Happened?

Until recently IT-Technology was only able to Replace the Repetitive, Predictable, Processes on a Very Small Scale. Most of the Humans soon get Bored by these processes. They need a little bit of Exitement (Arousal, Challenge, Change) to feel the Joy of Living.

The Repetitive processes are part of the Human Motor System, the Muscles. Until 1970 IT-Technology was only able to automate Manual Processes. Before that time many People made their living from these processes. At this moment Process Management (Workflow) and Case Management, have reached the level of maturity.

The introduction of the Internet Protocol, the Increase of the Capacity of the Infrastructure (Broadband, Glass Fiber, Optical Switches) and the Standards defined by the World Wide Web Consortium (W3C) have widened the Scale of the Automation of the Manual Processes until the World Level was reached.

One of the most exiting new standards of W3C are related to the Semantic Web. The Semantic Web will make it possible to Reason with the Data that is available on the Internet.

The Semantic Web will generate a Revolution in the Educational System (“Just in Time Learning“) because everybody will be able to Ask every Question that is possible. The Experts will not be needed anymore.

All kinds of processes in all kinds of Industries are now connected and are constantly redefined until every “useless” intermediary proces is removed. This trend is called Value Chain Integration.

The introduction of the PC and the Intelligent User-Interface opened up the Market to the Consumer and started a new wave of Value Chain Integration. Direct contact between Producer and Consumer is now possible. This development is called Supply Chain Reversal. Chain Reversal gives the customer the control of the complete supply chain.

Because of their Software Legacy most of the Companies have not opened up their Private Old Fashioned Infrastructures to their Customers and their Producers. If every company would do this many companies would disappear.

This is the main reason why these companies are not transforming their business. Most people (and companies) are Afraid to Reflect about their own Death. They wait until the Last Moment. At that time it is too Late to make a change.

The Removal of “Useless Manual Processes” (and “Useless Employees“) is now highly stimulated by the Economic Crisis, the Energy Crisis and the Climate Crisis.

The User-Interface made it possible to make a  Connection with the Organ of Imagination. This started a Creative Phase in IT. Humans are now able to create their own Books, Music, Art and are able to Play Collective Games and use Simulators to Explore Alternatives in an almost Real Life Environment. The Creative Wave has almost destroyed the Old Fashioned Amusement Industry.

At this moment the Social Media (Facebook, Linked in, Twitter,..) are exploding. They are mostly used to have a dialogue (Chat, Forums,…) between people in a Network. The Social Media make it possible to make a Connection with the Organ of the Emotions (the Opinions) of large groups of people all over the World.

The Social Networks give us the Opportunity to Feel what is Happening and make it possible to Influence (and Manipulate) the Masses.

What is Smart Computing?

The next wave,  Smart Computing,  adds two things, new Senses that are able to Sense much more than the Human is capable of and Artificial Intelligence (AI, Big Data, Reflection), the possibility to Detect and generate Scripts that are much more advanced than any pattern that is available in the Human Being.

AI can be used to analyze data (data mining), text (text mining), software (software mining) and processes (process mining).

One of the most important “Sensors” a this moment  is the Mobile Phone. Many people fail to understand the significant sensor innovations that are being designed into smartphones. Today’s smartphones contain microphones, cameras, motion sensors, proximity sensors, and location sensors.

New internet-connected GPS applications also have built-in feedback loops, reporting your speed and using it to estimate arrival time in real time.

Don’t underestimate the “other Sensors” like the Social Networks, Smart Energy Meters, Global Satellite Monitor Systems, Earth-Based Integrated Camera Systems and Medical Sensors that are able to detect all kinds of Physical Changes in Your Body.

In the next step Smart Sensors will be incorporated in the Clothes you Wear and of course your Body (if you allow that!).

Soon the Collective Technical Infrastructure, the Global Brain, will be able to Alert, Control, Manipulate and Support the many people that live on Earth. When this happens the Role of the Humans in the System will be the same as the Cells in the Body.

To make sure that one of the “Organs” will not  Dominate the Global Brain we have to incorporate a Monitor, a Global Conscioussness.

What can we do with Smart Computing?

When the Sensors are everywhere you are able to measure everything you want with a High Precision and a Fast Sample Time (Frequency).

The Sample Measurements can be Added Anytime you want (Real Time) and transformed into Transactions with a Flexible Price.

This Price is calculated by Adding the Real Time Transactions that are related to the Components You Buy subtracted by the Real Time Information of the Costs you are making.  Smart Computing makes it possible to create a complete Autonomous Real Time Company.

You can measure human transport (movement), chemicals, temperature, pressure on every location and react to the these measurements on a real-time basis based on a highly advanced prediction system based on neural nets.  In this way you can prevent traffic jams, calamaties and every other event that is predictable.

You can create highly sustainable processes in Food and Energy and Educate people Just-in-Time about Everything they want.

Software will be able to read billions of documents real-time and use the knowledge to diagnose every problem you want. With the help of this software (called Semantic Analytics) IBM’s Doctor Watson project will soon deliver an automatic Doctor that will know more than all the Doctors in the World.

It will also be possible to Design and Simulate every Structure you want and generate the Structure when you are satisfied.

Designing a House or a complete City will look like a Collaborative Game and Building can be done by everybody including Robots because “the System” will tell you what to do.

The Banking System will return to its ancient roots and will keep the Transaction-System in Short and Long Term Balance.

Will it be possible to incorporate the Human Emotions in a Machine?

Some Scientists  think that the Universe is already an Emotional Machine, a Quantum Computer Creating Itself. The Emotions are a Random Quantum Fluctuation, a Wheel of Fortune, to make it possible that the Universes Explore Every Possible Path. The Unpredictable Human Emotions are the Source of Creation.

Predictable Automated Emotions are not Creative because they lack the ability to make Mistakes. Making Mistakes and Learning from Mistakes are the Motor of the Proces of Innovation.

Machines without Emotions are more Reliable than Machines with Emotions but the Machines will stay the Same until their Emotional Human Creator has Invented a new Type or a new Theory.

At this moment the Robots are Instruments but it will not take long until we give the Instruments the Freedom to Act because they are more Reliable (less Emotional) and much more Cheaper than a Human Being.

If this happens many people will be Out of Work. The only thing that will be left over for us is the Act of Creation and of course the Care for Others.

If we are able to Incorporate the Emotions into the Machines we, the Humans, will be Completely Out of Work.

The Machines will be able to Create new Types of Sensors, Robots, Systems and Theories until Eternity. The Machines will take Care of Themselves and of course You.

The Programmed Robot Nurse, the Robotic Pilot, the Robotic Money Market Trader, the Robot Soldier, the Robotic Surgeon and the Robot Barber are already there.

They wait Patiently until their Human Creator will give them a Soul.

LINKS

The Forrester Report about Smart Computing

About Smart Cities

About Autarkic Systems

About Just-in-Time-Learning

About the Smart Planet of IBM

About the Smart Strategy of Google

About Semantic Analytics and Dr. Watson

About the Next Wave of Artificial Intelligence

Why the Universe is a Quantum Computer Creating Itself

Why the Robots will take over every job there is

Why the Human sometimes makes terrible mistakes

About the Automatic Need Machine

About the Global Consciousness

About the Care Industry

About Just in Time Learning

About Erving Goffmann and the Games People Play

How to Incorporate Mistakes in Programming Languages

About the Global Brain

Why we will soon be completely Out of Work

About the Sensory Motor System

About the Emotions

About Morphology or How Alan Turing Made the Dream of Goethe Come True

Tuesday, November 17th, 2009

The Ancient Greeks believed that the images of waking life and dreams came from the same source, Morpheus (Μορφέας, Μορφεύς), “He who Shapes“.

The Science of the Shapes, Morphology, was created and named by Goethe in his botanical writings (“Zur Morphologie“, 1817).

Goethe used comparative anatomical methods, to discover a primal plant form that would contain all the others-the Urpflanze. Goethe being a Romantic Idealist hoped that Morphology would Unify Science and Art.

The Uhrplant shows itself also in the Lungs and Riversystems

The Uhrplant shows itself also in the Lungs and Riversystems

“The Primal Plant is going to be the strangest creature in the world, which Nature herself shall envy me. With this model and the key to it, it will be possible to go on forever inventing plants and know that their existence is logical”. Nature always plays, and from which she produces her great variety. Had I the time in this brief span of life I am confident I could extend it to all the realms of Nature – the whole realm“.

Goethe (wikipedia)

Goethe (wikipedia)

Hundred years later in the 1920s Goethe’s dream came true. Morphology moved outside Biology to other parts of Science due to the works of D’Arcy Thompson’s On Growth and Form, Oswald Spengler Morphology of History, Carol O. Sauer Morphology of Landscape, Vladimir Propp, Morphology of the Folktale and Alfred North Whitehead Process and Reality.

Goethe observed nature and reflected on similar structures. He believed that there was something behind this similarity, an archetypal plant.

According to Goethe the archetypal plant was the leaf (“While walking in the Public Gardens of Palermo it came to me in a flash that in the organ of the plant which we are accustomed to call the leaf lies the true Proteus who can hide or reveal himself in all vegetal forms. From first to last the plant is nothing but leaf“).

At this moment scientists know the reason why the leaf is the most important structure of the plant. It is a solar collector full of photosynthetic cells.

The energy of the sun provides the energy to transform water from the roots gathered by the leafs and carbon dioxide out of the air also gathered by the leafs, into sugar and oxygen. Plants are structures with many leaves. These leafs shield other leafs from collecting sunlight and water.

To solve this problem a plant has to optimize its structure to collect enough Sunlight and Water. The process of Optimization is not a Central Coordinated action. Every leaf tries to find the best place in the Sun on its own. This place determinates the growth of the next level of branches and leafs.

Goethe observed a pattern and deduced a structure, the leaf, the Uhrplanze. What Goethe really observed was not a Static Uhrplant but the Dynamic Process of the Branching of all kinds of leaves in all kinds of plants (Morpho-Genesis).

The leafs of the plants are not the main target of the morphogenesis of the plant. The visible External and the invisible Internal Forms or Organs are one of the many solutions of an equation with many variables and constraints. The optimal solution is reached by experimenting (“Nature always plays”).

Many solutions fail but some survive (Evolution of the Fittest). When a solution survives it is used as a Foundation to find new rules for more specific problems (Specialization). When the environment, the context, changes old rules have to be replaced by new rules (a Paradigm Shift).

The Fractal Geometry of Nature

The Fractal Geometry of Nature

New mathematical paradigms in the field of the Machines and Languages (Alan Turing, The Chemical Basis of Morphogenesis) and the Self-Referencial Geometry of Nature (Benoît Mandelbrot, The Fractal Geometry of Nature) have stimulated further investigation in the Field of Morphology.

In 1931, in a monograph entitled On Formally Undecidable Propositions of Principia Mathematica and Related Systems Gödel proved that it is impossible to define a theory that is both Self-Consistent and Complete. The paper of Gödel destroyed the ambitions of the Mathematicians at that time to define one theory that explains everything.

In 1936 Alan Turing produced a paper entitled On Computable Numbers. In this paper Alan Turing defined a Universal Machine now called a Turing Machine. A Turing machine contains an infinite tape that can move backwards and forwards and a reading/writing device that changes the tape. The Turing Machine represents every Theory we can Imagine.

Turing proved that the kinds of questions the machine can not solve are about its own Performance. The machine is Unable to Reflect about Itself. It needs another independent machine, an Observer or Monitor to do this.

It can be proved that Turing proved the so called Incompleteness Theorem and the Undecidability Theorem of Gödel in a very simple way.

eniac

The Eniac

In 1943 Turing designed and realized a Real Turing Machine, the Eniac. It was used to Crack the Codes of the Germans in the Second World War.

At that time it was very difficult to Program a Computer. This problem was solved when Noam Chomsky defined the Theory of Formal Grammars in 1955 (The Logical Structure of Linguistic Theory).

When you want to define a Language you need two things, an Alphabet of symbols and Rules. The symbols are the End-Nodes (Terminals) of the Network of Possibilities that is produced when the Rules (Non-Terminals) are Applied. The Alphabet and the (Production- or Rewriting) rules are called a Formal Grammar.

If the Alphabet contains an “a” and a “p” the rules S→AAP, A→”a” and P→”p” produce the result “aap”. Of course this system can be replaced by the simple rule S→”aap”. The output becomes an infinite string when one of the rules contains a Self-Reference. The rules A→a and S→AS produce an Infinity String of “a’-s (“aaaaaaaaaaaaaaaaaa….”).

The system becomes more complicated when we put terminals and rules (non-terminals) on the Left Side. The System S→aBSc, S→abc, Ba→aB and Bb→bb produces strings like, “abc”, “aabbcc” and “aaabbbccc”. In fact it produces all the strings a**n/b**n/c**n with n>0.

The inventor of the theory of Formal Grammar, Chomsky, defined a Hierarchy of Languages. The most complex languages in his hierarchy are called Context-Dependent and Unrestricted. They represent complex networks of nodes.

A language where the left-hand side of each production rule consists of only a single nonterminal symbol is called a Context Free language. Context Free Languages are used to define Computer Languages. Context Free Languages are defined by a hierarchical structure of nodes. Human Languages are dependent on the context of the words that are spoken.

It is therefore impossible to describe a Human Language, Organisms, Organisations and Life Itself with a Context Free Computer Language.

Context Free Systems with very simple rule-systems produce natural and mathematical structures. The System A → AB, B → A models the Growth of Algae and the Fibonacci Numbers.

A Recognizer or Parser determinates if the output of a formal grammar is produced by the grammar. Parsers are used to check and translate a Program written in a Formal (Context Free) Language to the level of the Operating System of the Computer.

grammarRegular and Context Free Grammars are easily recognized because the process of parsing is linear (causal, step by step). The stucture of the language is a hierarchy.

The recognizer (now called a Push-Down Machine) needs a small memory to keep the books.

Context Dependent (L-systems) and Unrestricted Grammars are difficult to recognize or are not recognizable in practice because the parser needs a huge sometimes Infinite Memory or Infinite Time to complete its task.

To find the Context the Recognizer has to jump backwards and forwards through the infinite string to detect the pattern.

If the network loops the recognizer will Never Stop (“The Halting Problem“).

Turing proved that the Halting Problem is Undecidable. We will Never Know for Sure if an Unrestricted Grammar contains Loops.

The Rules and the Output of Unrestricted Grammars Change and never stop Changing. Our Reality is certainly Context Dependent and perhaps Unrestricted.

Parsing or Recognizing looks like (is similar with) the process of Scientific Discovery. A theory, a Grammar of a Context-Free Systems (“aaaaaaaaaaa…”) is recognizable (testable) in Finite Time with a Finite Memory. Theories that are Context Dependent or Unrestricted cannot be proved although the Output of the Theory generates Our Observation of Nature. In this case we have to trust Practice and not Theory.

cellular automata

A 3D Cellular Automaton

In 2002 the Mathematician Stephen Wolfram wrote the book A New Kind of Science.

In this book he tells about his long term Experiments with his own Mathematical Program Mathematica. Wolfram defined a System to Generate and Experiment with Cellular Automata.

Wolfram believes that the Science of the Future will be based on Trial and Error using Theory Generators (Genetic Algorithms). The big problem with Genetic Algorithms is that they generate patterns we are unable to understand. We cannot  find Metaphors and Words to describe the Patterns in our Language System.

This problem was adressed by the famous Mathematician Leibniz who called this the Principle of Sufficient Reason.

Leibniz believed that our Universe was based on Simple Understandable Rules that are capable of generating Highly Complex Systems.

It is now very clear that the Self-Referencial Structures, the Fractals, of Mandelbrot are the solution of this problem.

The Scientific Quest at this moment is to find the most simple Fractal Structure that is capable of explaining the Complexity of our Universe. It looks like this fractal has a lot to do with the Number 3.

It is sometimes impossible to define a structured process to recognize (to prove) a Grammar. Therefore it is impossible to detect the rules of Mother Nature by a Structured process. The rules of Mother Nature are detected by Chance just like Goethe discovered the Uhrplanze. Science looks a lot like (is similar with) Mother Nature Herself.

When a Grammar is detected it is possible to use this grammar as a Foundation to find new solutions for more specific problems (Specialization, Add More Rules) or when the system is not able to respond to its environment it has to Change the Rules (a Paradigm Shift). All the time the result of the System has to be compared with Mother Nature herself (Recognizing, Testing, Verification).

Turing proved that if Nature is equivalent to a Turing machine we, as parts of this machine, can not generate a complete description of its functioning.

In other words, a Turing machine, A Scientific Theory, can be a very useful tool to help humans design another, improved Turing Machine, A new Theory, but it is not capable of doing so on its own – A Scientific Theory, A System, can not answer Questions about Itself.

The solution to this problem is to Cooperate. Two or more (Human) Machines, A Group, are able to Reflect on the Other. When the new solution is found the members of the Group have to Adopt to the new solution to move on to a New Level of Understanding and drop their own Egoistic Theory.

Each of the individuals has to alter its Own Self and Adapt it to that of the Group. It is proved that Bacteria use this Strategy and are therefore unbeatable by our tactics to destroy them.

Turing proved that Intelligence requires Learning, which in turn requires the Human Machine to have sufficient Flexibility, including Self Alteration capabilities. It is further implied that the (Human) Machine should have the Freedom to make Mistakes.

Perfect Human Machines will never Detect the Patterns of Nature because they get Stuck in their Own Theory of Life.

The Patterns of Turing

The Patterns of Turing

The Only ONE who is able to Reflect on the Morphogenesis of Mother Nature is the Creator of the Creator of Mother Nature, The Void.

Gregory Chaitin used the theory of Chomsky and proved that we will never be able to understand  The Void.

The Void is beyond our Limits of Reason. Therefore the first step in Creation will always be  a Mystery.

At the end of his life (he commited suicide) Alan Turing started to investigate Morphology.

As you can see the Patterns of Alan Turing are created by combining many Triangels. The Triangel is called the Trinity in Ancient Sciences.

According to the Tao Tse King, “The Tao produced One; One produced Two; Two produced Three; Three produced All things”, which means that the Trinity is the Basic Fractal Pattern of the Universe.

In modern Science this pattern is called the Bronze Mean.

It generates so called Quasi Crystals and the Famous Penrose Tilings.

The Bronze Mean is represented by the Ancient Structure of the Sri Yantra (“Devine Machine”).

Goethe was not the real discoverer of Morphology. The knowledge was already there 8000 years ago.

LINKS

About the Observer and Second Order Cybernetics

A PDF About the Morphology of Music.

The origins of life and context-dependent languages

A Website About the Morphology of Botanic Systems

A Website About the Morphology of Architectural Systems

A Plant Simulator using Morphology

About Intelligent Design

The Mathematical Proof of Gödel of the Existence of God

About Bacteria 

About the Bronze Mean

About the Trinity

About Enterprise 2.0 and the New World of Work

Sunday, May 17th, 2009

At this moment there is a lot of discussion going on about the New World of Work. In the New World of Work the new developments of the Internet 2.0 (Social Networks, Blogging, Twittering, etc) are used to Speed up the Work of the Knowlegde Worker. The infrastructure to make this possible is called Enterprise 2.0.

Enterprise 2.0 is : A System of Web (2.0)-Based Technologies that provide rapid and agile Collaboration, Information Sharing, emergence and integration capabilities in the Extended Enterprise. An Extended Enterprise is a Supply or Value Chain.

The definition of Enterprise 2.0 is constantly changing because Enterprise 2.0 is still a Concept. Many people are now struggeling to move from the concept/idea-stage to the realization-phase.

The main issue behind de term “Web 2.0” is the move from a Sender/Receiver-model, the One-Sided Website, to a more Collaborative use of the Internet (Discussions, Social Networks). According to the Inventors of the term Web 2.0 the “new web”, is a Collaborative Web.

For some reason they have forgotten that the World Wide Web (WWW) software of Tim Berners Lee was part of a Collaborative Platform to support the scientists that Participated in a Network called DARPANET. This network was created by DARPA, the Technological Think-Tank of the American Army in 1957!.

What is the definition of the term “Collaboration”?

The word “collaborate” comes from the Latin “Collaboratus” meaning “Work (Labore) together (Col)”. The term “to-gather” comes from the term “gadurojan” which means “in good fellowship” or “United“. When you Collaborate you are not working Alone but with Others United in Good Fellowship.

The Potential to Collaborate is an Aspect of the Personality.

The Personality Types of the Human Being can be described with two variables Agency and Communion. Comm-Union is the capability to Col-Laborate, to accomplish a Union. The variable Agency describes your relationship between the Self and the Other.

When you are High in Communion and Low in Agency you are suffering from a Dependent Personality Disorder. This disorder is characterized by a pervasive psychological dependence on other people. You always want to Collaborate and are very Emotional.

When you are High in Communion and High in Agency you are suffering from a Histrionic Personality Disorder. People with a Histrionic Personality Disorder have good social skills, but they tend to use these skills to manipulate other people to become the Center of Attention. They are very Imaginative.

According to Interpersonal Theory a “normal” person is able to Combine Two or More Interpersonal Faculties.

There are two Disorders left called Paranoid (High Agency, Low Communion) and Schizophrenic (Low Agency, Low Communion). Paranoid people have a big problem with their Expectation. They want to control the Future and Every Person in their Context. Schizophrenic people are completely influenced by their mostly Visual Senses. They See what they Want to See.

If you combine the Four Interpersonal Faculties (Emotions, Imagination, Expectations and Senses) Twelve Interpersonal, Collaborative, Patterns emerge. A good example is the Master(Paranoid)/Slave(Dependent)-Relationship (Expectation/Emotions). Some People Love to be Dominated by the Other.

Interpersonal Faculties can be combined into Collaborative Work Patterns.

In my blog about Vocation I showed that work is an Expression of the Personality. If you believe this is True and you believe Interpersonal Theory is True you have to admit there are Twelve Types of Work.

When you are highly Imaginative and Sensitive (You Believe Your Own Eyes, You are Realistic, Factual) you are an Entrepreneur, You want to bring An Idea into Reality. To Find the Facts you need an Information System to Investigate what is Happening. The Internet with all its Sources of Information is a beautiful tool to use.

To bring an Idea into Practice you have to Realize the Idea. In this case you need a Designer (Transform Ideas into Models) and a Maker (Bring Models into Reality). A Maker is not a Collaborative person (Low Communion). Makers want to work Alone.

When you create a Team of Makers to Realize your Idea the Team will fail. To avoid Competition the Designer has to define a Model (An Architecture and a Project Plan) in which all the Lonesome Workers are able to do their Specialized Job.

I hope you believe we are able to define a complete (meta)-Architecture and a (meta)-Plan to move around in the (meta)-Work-Space.

What is the Relationship between the Work Patterns and Enterprise 2.0?

An Enterprise is a combination of many people with many Collaborative Work-patterns. We could Specialize an Enterprise to perform one kind of Pattern. If we Specialize an Enterprise we have to combine many Enterprises in an Extended Enterprise to do Everything we Want to Do.

We need a Designer Company, A Sales Company, Visionairs, Entrepeneurs and other Roles to cover the Complete Spectrum of Work. If We want to Produce we always need the Makers. The Makers need a well defined Structure (A Hierarchy), a Plan and an Architecture, to operate in.

At this moment Enterprise 2.0 is nothing but a Concept. Somebody of High Agency and High Communion (A Creator) has gotten the Idea that the new 2.0 Internet is able to support an Enterprise.

 He hopes that the new tools will break down the Hierarchical Structure of the Organization of the Makers. Creators don’t like Hierarchies. They love Networks. If Creators are One-Sided, Histrionic, they want to Stay in the Center of Attention of the Network.

What Creators don’t realize is that Makers, the Majority of the Human Beings,  don’t want to use Collaborative Tools. They want to work Alone in their own Specialized Compartment of the Beehive.

Enterprise 2.0 is a Concept to support Innovation. Someday the Innovation has to be Stabilized. If we want to do that we still need Enterprise 1.0, The Factory until we find another Solution (The Robots?).

Don’t forget the Worker Bees. They Bring in the Honey.

About (Software) Quality

Tuesday, January 20th, 2009

When I attended the University of Leiden Software-Development was in its infancy. In 1969 just a few people were programming for the simple reason that the amount of computers was very low. It took a lot of time (many weeks), intelligence and perseverance to create a small working software-program.

At that time the effect of a software-program on other people was very low. Software-programs were used by the programmers themselves to solve their own problems.

When User-Interfaces, Databases and Telecommunication appeared it became possible to create software for Many Non-Programmers, Users. The software-systems got bigger and programmers had to cooperate with other programmers.

When the step from One-to-Many was made in the process of software-development and exploitation, Software-Quality became on very important issue.

What is Software?

A Software-program is a sequence of sentences written in a computer-language. When you speak and write you use a natural language. When you write a computer program you use an artificial, designed, language.

The difference between natural and artificial languages is small. Esperanto is a constructed language that became a natural language. Perhaps all the natural languages were constructed in the past.

Software programs are very detailed prescriptions of something a computer has to do. The specifications of a software-program are written in a natural language (Pseudo-Code, Use-Case).

To create Software we have to transform Natural Language into Structured Language. The big problem is that Natural Language is a Rich Language. It not only contains Structural components but is also contains Emotional (Values), Imaginative ((Visual) Metaphors) and Sensual Components (Facts). The most expressive human language is Speech.

In this case the Tonality of the Voice and the Body Language also contains a lot of information about the Sender. When you want to create Software you have to remove the Emotional, Imaginative and Sensual components out of Human Language.

What is Quality?

According to the International Standards Organization (ISO), Quality is “the degree to which a set of inherent characteristics fulfills requirements“. According to the ISO the quality of a software-program is the degree in which the software-coding is in agreement with its specification.

Because a specification is written in natural language, Quality has to do with the precision of the transformation of one language (the natural) to another language (the constructed).

According to Six Sigma Quality is the number of defects of an implementation of the specification of the software.

Another view on Quality is called Fitness for Use. It is this case Quality is “what the Customer wants” or “What the Customer is willing to pay for“.

If you look carefully at all the Views on Quality, the Four World Views of Will McWhinney appear.

Six Sigma is the Sensory View on Quality (Facts), ISO is the Unity View on Software (Procedures, Laws, Rules) and Fitness for Use is the Social View on Quality (Stakeholders).

The last worldview of McWhinney, the Mythic, the View of the Artist, is represented by the Aesthetical view on Quality. Something is of high quality when it is Beautiful.

The Four Perspectives of McWhinney look at something we name “Quality”. We can specify the concept “Quality” by combining the Four definitions or we can try to find out what is behind “the Four Views on Quality”.

The Architect Christopher Alexander wrote many books about Quality. Interesting enough he named the “Quality” behind the Four Perspectives the “Quality without a Name“. Later in his life he defined this Quality, the “Force of Life“.

What Happened?

In the beginning of software-development the Artists, the Mythics, created software. Creating high quality software was a craft and a real challenge. To create, a programmer had to overcome a high resistance.

The “creative” programmers solved many problems and shared their solutions. Software-development changed from an Art into a Practice. The Many Different Practices were Standardized and United into one Method. The Method made it possible for many people to “learn the trade of programming”.

When an Art turns into a Method, the Aesthetic, the Quality that Has No Name, Life Itself, disappears. The Controller, Quality Management (ISO), has tried to solve this problem and has given many names to the Quality without a Name. Many Aspects of Software Quality are now standardized and programmed into software.

But…

It is impossible to Program the Social Emotions and the Mythic Imagination.

So…………

Software developers don’t use Methods and Standards because deep within they are Artists. The big difference is that they don’t solve their own problems anymore. They solve the problems of the users that are interviewed by the designers.

And…..

The Users don’t want the Designers to tell the Programmers to create something they want to create themselves (the Not-Invented Here Syndrome). They also don’t know what the programmers, instructed by the designers will create, so they wait until the programmers are finished and tell them that they want something else.

What Went Wrong?

The first Computer, the Analytical Engine of Charles Babbage, contained four parts called the Mill (the Central Processing Unit, the Operating System), the Store (the database), the Reader, and the Printer. The Analytical Engine and his successors were based on the Concept of the Factory. In a Factory the Users, the Workers, The Slaves, have to do what the Masters, the Programmers, tell them to do.

A part of the Analytic Engine of Charles Babbage

The Scientists modeled successful programmers but they forgot to model one thing, the Context. At the time the old fashioned programming artists were active, software was made to support the programmer himself. The programmer was the User of his Own software-program.

At this moment the Factory is an “old-fashioned” concept. In the Fifties the Slaves started to transform into Individuals but the Factory-Computer and the Practices of the Old Fashioned Programmers were not abandoned.

To cope with the rising power of the Individual the old methods were adopted but the old paradigm of the Slave was not removed. The Slave became a Stakeholder but his main role is to act Emotionally. He has the power to “Like or to Dislike” or “To Buy or not to Buy”.

The big Mistake was to believe that it is possible to program Individuals.

What To Do?

The Four Worldviews of Quality Move Around Life Itself.

According to Mikhail Bakhtin Life Itself is destroyed by the Process of Coding (“A code is a deliberately established, killed context“).

When you want to make software you have to keep Life Alive.

The Paradigm-Shift you have to make is not very difficult. Individual Programmers want to make Software for Themselves so Individual Users want to Do the Same!

At this moment the Computer is not a tool to manage a factory anymore. It has become a Personal tool.

It is not very difficult to give individuals that Play the Role of Employee tools to Solve their own Problems.

When they have solved their own problems they will Share the Solutions with other users.

If this happens their activities will change from an Individual Act of Creation into a Shared Practice.

If People Share their Problems and Solutions, their Joy and their Sorrow, they Experience the Spirit,  the Force of Life, the Quality that has no Name.

LINKS

How to Analyze a Context

About the Human Measure

About the Autistic Computer

About the Worldviews of Will McWhinney

About Christopher Alexander

About Computer Languages

About Mikhail Bahtin

About Ontologies

About Model Driven Software Development

About the Illusion of Cooperation

About the Analytic Engine of Charles Babbage

About the Analytic Engine of Thomas Fowler

About Human Scale Tools

About Old-Fashioned Programming