Posts Tagged ‘bertrand russell’

Why Numbers are Waves

Wednesday, September 3rd, 2008

Pythagoras, the inventor of the Music of the Spheres, thought that the principles governing Number are the principles of all things.There are many principles behind the Numbers. The most intriguing is called the Riemann Hypothesis. It defines a spiraling relationship between the Prime numbers.

What is a Number?

A Number is a Symbol that represents an Object we use to Count and to Measure. The Number-Object 1 is often represented by the symbol “1″ and the sound “One”.

When we Count we are able to Tell How Many Objects are available in a certain Set. In mathematical terms the Amount of Objects in a Set is called the Cardinality.

To define a Set we have to define “What the Objects Are”. If we don’t do this we are not able to See, to Observe, the Objects. To Count we have Define “What we are Counting“.

To define what we are counting we have to Classify and to Describe. To Classify we have to Name. The name “Sheep” is connected to a Mental Picture of something that “looks like a” Sheep.

There are Names who are not represented by a Mental Picture. An example is the name “number”. This Class of Objects contains Abstractions of Real, Visible, Objects or of Actions that are Performed on Visible Objects. Abstract Objects/Actions are related to, Mapped, to Visible Objects/Actions by Metaphors. One Apple “is representing” the Number One.

There is no fundamental law that Tells us How to Classify. Classifications are highly Culture and Time Dependent. The effect is that different people will count different amounts of objects when they don’t agree about “What they are Counting“.

When we have Counted a Set of Sheep we are able to Add when we have counted another Set of Sheep at another Place. We are only able to Add when the Sheep at both places are “the Same“.

It is impossible to add Sheeps and Cows unless we define a more abstract Set called Animals. Again the problem of classification arises.

When we want to Count Every Thing we have to find the Cardinality of The Set of All Sets. The Cardinality of this Set is “not knowable“. Most scientists would say that the cardinality of this set is infinite (“not bounded“). Mathematicians would say that this Set maps to the Set of Numbers or to a Sub-set of the Set of Numbers. The paradox of Russell shows that the Set of all Sets “does not exist“.

It does not matter in what order we Add Numbers. A+B = B+A. This is called the Commutative Quality of the Numbers. Remember that this Quality only applies when we are counting the Same Objects

Another Quality of Addition is called Associativity. It does not matter in what order we add a sequence of numbers. 1+(2+5)+3 = (1+2) + (5+3). Remember that this Quality only applies when we are counting the Same Objects.

 When we are Counting Sets of Sheep that contain the Same Amount of Sheep we are able to create a new operator “*” called Multiplication. Multiplication is a Repetition of the Same Amounts (another word for Cardinality) of Counting.

When we Multiply the same Qualities of Addition are applicable. Multiplication is Commutative and Associative. 6*7=7*6 and 6*(7*8)=(6*7)*8.

 What is a Prime?

We have finally reached the Primes. A Prime is a Number that can only be divided by 1 and Itself OR Every Number can be written as a Multiplication of One or more Primes.

Mathematicians Think that the Set of Prime Numbers is the Foundation of the Set of Numbers.

Nobody thought that this Foundation contains another Foundation until Riemann formulated his famous hypothesis. Riemann observed that the frequency of prime numbers is very closely related to the behavior of the so called Riemann Zeta function, ζ(s) = 1 + ½**s + 1/3**s + ¼**s + . The hypothesis is still not proven but is verified by computer programs that generate very big numbers (1,500,000,000) and until now it still holds.

The operator “**” is called Power or Exponent. It represents a Repetition (s) of the multiplication of the same number. 2**2 = 2*2=4. The operator “/” represents the operator Division. Division is the “opposite” of Multiplication.

A Foundation is something that is used to build on. It is the “lowest” layer of all the layers. If a Foundation contains a Foundation many theories that were formulated using the old foundation are at stake. One of the most important theories is the theory about the Numbers themselves. If the Numbers are not what they are thought of new mappings, new metaphors, are possible. In this blog I will try to explain that Numbers are not Distinct Isolated Objects. Numbers are not Parts.

Numbers are Waves.

The Primes are the Foundation of the Number System if we Accept that:

  • A Number is something we use to Count Objects
  • We are Counting the Same Object
  • Multiplication is Repetitive Counting
  • the Quality of Commutativity in Multiplication and Addition Applies

We are not Counting the Same Object at All.

We are always Counting Cows and Sheeps because every Object is Unique. If we make a Picture of one Sheep we see a Lot of Detail. We ignore these details because we are not interested in them when we are Counting Sheep. The Sheep are treated as Objects.

When we want to Articulate the Details of One Sheep we Run Out of Words to describe all the details. We are unable to define all the attributes to classify all the details.

When we are Counting, Every Thing has to be treated as an Object because Counting implies the Perspective of the Object.

The Quality of Commutativity in Multiplication and Addition does not Apply.

If we want to treat Every Thing As It Is, the Commutative Law is not applicable: A+B is not equal to B+A. When we want to treat Every Thing As It Is, Every Thing is One. If we Map every Unique Object on the Number Line every Number is representing a Unique Object. A Number is a Unique Key, An Identifier.

If we are not able to Add we are not able to Multiply. If we are not able to Multiply the Primes are non-existent. If we accept that Every Thing is Unique we are not able to Talk about Anything. We have be Silent and Observe. We could also accept that Language is a Funny Game We Play (Wittgenstein) or Accept that a Picture Paints a Thousand Words.

When we want to Quantify or Qualify we are always Equalizing.

When we want to Count we have to accept that we have to make Some Things the Same when they are really not the Same. If we want to Quantify we have to accept that we are making Mistakes all the Time.

If we want to Qualify we have to accept that Numbers are not usable. If we want to Qualify we have to accept that Classifications are not usable. If we want to Qualify we have to Accept that somewhere we are using the Numbers and are Quantifying.

When we use Language to Qualify somewhere we introduce concepts like High and Low and are forcing an Order on Reality. The only thing that is left is to use the Emotions to do this. We could Say that Every Thing is Beautifull and produce a Sound (“Ahhhhhhhhhhh” or “Wauw“).

When we want to Quantify or Qualify we have make sure we are not equalizing something that is really unique. We have to Make a Choice and think about the Consequences. If we define a Selection Criterium or Define an Attribute of a Unique Object or Define a Filter, we have to be aware that the Attribute simply defines a new Object. This Object is always an Abstraction. When we define the Attribute or Quality of Race we Divide Reality in Races.

Language always Divides The Whole in Parts.

Multiplication is Repetitive Counting.

When we Multiply we make use of two Types of Numbers. We are using a “repetition factor” and we use a “counting factor“. These types of Numbers are not the same. When they are not the same the Commutative Law is not applicable. 7*6 is different from 6*7. The first statement is about 7 times a Set of Sheep with Cardinality 6. The other is about 6 times a Set of Sheep with a Cardinality of 7.

Primes are Frequencies.

A Repetition Factor could be defined as a Frequency. If we move from the domain of the Rectangular frame, Cubes, to the Circular frame of Mathematics, Waves, the Riemann Hypothesis changes into a statement about the Musical or Harmonic Behavior of the Primes. The primes have Music in them. You can even Listen to this Music. Pythagoras was Right.

If Primes are Frequencies What are Numbers?

If every Number is a combination of one or more Prime Numbers, every Number contains one or more repetition factors. If we move to the Circular Domain, Multiplication changes into Addition. A Number is the Sum of Waves. A Mapping from the Rectangular to the Circular Domain is called a Fourier Transformation.

If Numbers are Waves what are Objects?

Objects are also Waves.

If Objects are Waves is there a Boundary between Objects?

No. They are All One. In a Circular World there is no Beginning and there is no End. In a Spiraling Spiral World Everything is Closed in Itself. We are an Enfolding of the One that is Closed in Itself. The One is Aware. It is Consciouss. Every Thing Contains a Conscioussness, A Spark of the One.

What is Behind Every Thing?

0. It all starts with the Primal Void, 0.

1. Out of the Primal Void the One is Created. The One is The Mover that Moves Itself, The Center. It Enfolds in Itself.

2. The One is Observing Itself so there are Two. The One becomes Conscious.

3. The Two Expand and Compress so there are Three, the Trinity. The Two are named Control and Desire. The One, Conscioussness, stays in the Center. The One Voids the Two (-1 + 1 = 0).

4. The Two are split in Two so there are Four Forces or World Views. Control and Desire are “compensated” by Spirit and Soul.

5. The One, Consciousness, is always in the Middle. Now there are Five, the Pentagle. The Five are called the Hu-Man. It contains Control, Desire, Spirit (Creativity), Soul (Love, Emotion) and Conscioussness. The last part connects the Human to the One. A Human is a Dynamic Instability where the Four Forces are constantly trying to find Harmony. The Conscioussness Observes and Reflects. It helps the Forces to find Balance.

6. The Four Forces combine. There are Six or Twelve combinations. This depends on the way the combinations are made. Four independent Forces generate 1*2*3 combinations when the Combinations, the Relationships or the Mappings, are considered Unique. When a Relationship is a Two-Way Connection (A Dialoque), the amount of combinations is 2* (1*2*3) =12. Six is the first Perfect Number. The Sum and the Product of its Divisors is Equal. 1+2+3 = 1*2*3.

7. The One is always in the Middle so there are 6 + 1 = 7 Relationships. There are Seven Chakra’s. The Chakra in the Middle, The Heart, is related to the Centre, The One (-3,-2,-1, 0, 1, 2, 3).

9. This is a Pattern where the Four Forces are connected in a Circular Pattern. One Pattern moves with the clock and the other counter the clock. The complete pattern looks like a Moebius Ring

10. This is the Lowest Level in the Sephirot, The Tree of Life. It is called Malchut, the Kingdom of God. It exists outside the Pattern of the Nine.

12. See 6. The four Forces are now in their Dialogic State. 12 is a Highly Composite Number (HCN). A HCN is a Social Number. It contains Many Divisors. HCN’s are used in situations where many divisions are needed like Clocks and Calenders. HCN are used to avoid conflicts. Other HCN’s are 24 (hours), 60 (seconds) and 360 (degrees).

There are twelve signs of the Zodiac, twelve Tribes of Israel, twelve Apostles of Jesus and twelve Houses in Astrology. Every number is a Relationship between Two Powers of the Four Powers and can be interpreted as such. The Four Powers are the cornerstones. Examples are the Apostles John (Spirit, Eagle), Marc (Control, Laws. Lion), Luc (Desire, Bull, Ox) and Matthew (Soul, Human/Angel).

13-24. With the Thirteen a new Cycle on Another Level Starts. The 13th Card of the Major Arcana of the Tarot is called Death, a New Beginning. The Soul has travelled in the UpperWorld (Earth, 1-12, Our Material Reality) and moves to the Under World (Heaven, The World of Souls, 13-24) to Clean itself and to start a new Cycle as the Fool (0).

The Tarot spelled as TARO-T is a Cyclic Structure that operates on Three Levels. In every level the four Forces (T, A, R and O) are combined in different ways. The Highest Level is called the Major Arcana and contains 24 (1*2*3*4) Cards. The last card indicates the End of the Cycle of the TARO. Every card in the Higher Arcana is named with a Permuation (without Repetition) of the letters T,A,R and O.

25-36. The Second Level contains 12 Cards (3*4). The King, Queen, Knight and Page represent the four Forces.

37-76. The Third Level (40 Cards) contains the Ace (1) and the numbers 2-10. The four Forces are called Sword (Mind, Control), Cups (Soul, Emotions), Wands (Spirit, Creativity) and Pentacles (Senses, Desire).

 The One Enfolds into a Spiraling Spiral.

New Numbers and New Levels are Created.

We are One AND we are Many. We are The Same AND we are not The Same. We are Music AND we are Producing Music. We are Repetitons AND we are Creating Repetitons. We are Primes AND we are not Primes.

LINKS

Chaitin, About the Russell Paradox and other Controversies concerning the Foundations of Mathematics

Listen to The Music of the Primes

About Noncommutative Geometry

About the Same and not the Same

A Book about The Music of the Primes

Explaning the Riemann Hypothesis

Every Thing You want to know about The Riemann Hypothesis

How the Proof of the Pudding is Really in the Eating

Monday, August 25th, 2008

When you want to know the truth you are looking for facts. This seems very evident but Philosophy and especially the field of Epistemology has spend a lot of time to find out if this Statement about Truth is really True.

The first step is to look up the definition of the word “fact“. We use Wordnet to do this. WordNet is a semantic lexicon for the English Language. The database contains about 150,000 words.

Fact: A piece of information about circumstances that exist or events that have occurred.
Fact: A statement or assertion of verified information about something that is the case or has happened.
Fact: An event known to have happened or something known to have existed.
Fact: A concept whose truth can be proved.

The meaning of words changes in history. If you want to know how the meaning is changed you have to look up the Etymology of the word.

Fact: 1539, “action” especially “evil deed,” from L. factum “event, occurrence,” lit. “thing done,” from neut. pp. of facere “to do”. Usual modern sense of “thing known to be true” appeared 1632, from notion of “something that has actually occurred.”

When we combine the result of both dictionaries we see that the original meaning of the word “Fact” is-related to the word “Event”. Later around 1632 it changed into a concept “whose truth can be proved”.

To find more about the meaning of the word Event we can look for all the occurrences of this word in the sentences of English language. One of the scientists who spend a lot of time researching the meaning of the word “Event” is George Lakoff. He defined The Event Structure Metaphor.

A Metaphor Is-A Mapping. A Mapping Is-A Relation between two Domains, the Source and the Target.

The Event Structure Metaphor is one of the most widespread of all the conceptual metaphors in the world. It maps from the source domain of Space to the target domain of Events, and leads to the following concepts:

A State Is-A Location (a bounded region in space).
A Change Is-A Movement (into or out of bounded region).
A Cause Is-A Force.
An Action Is-A Self-Propelled Movement.
A Purpose Is-A Destination.
A Mean Is-A Path to destinations.
A Difficulty Is-A Blockage.
Expected Progress Is-A Travel Schedule.
A Schedule Is-A Virtual Traveler, who reaches pre-arranged destinations at pre-arranged times.
An External Event Is-A Large Moving Object.
A Long-term, purposeful activity Is-A Journey
.

An Event Is-A Blockage that prevents us to Move from One Destination to an other Destination in the Journey called Life. To Move from one Destination to an other Destination we are Propelling our Self. Sometimes we are propelled By something else, An External Event. If this Happens it feels like we are hit by a Large Moving Object.

When we are Hit by an External Event “things get out of hand” or “we are not able to keep a tight rein on the situation” or “we are not going with the flow” or “things take a turn for the worse“.

A Fact is an Event that Causes the Emotion of Frustration (Anger, Irritation, Sadness, Worry,..). An Event Forces us to Move Away from our Original Route, the Path that leads us to the Destination that we wanted to Reach in Life. We have to take a Detour.

What happened around 1632?

Around 1632 Francis Bacon advocated a new method for achieving knowledge, based on careful observation and eliminative induction. Bacon warned that effective reasoning must be freed from the “idolatrous” influence of human nature (Emotions & Imagination).

Francis Bacon started The Age of Enlightenment. The Enlightenment advocated reason as a means to establishing an authoritative philosophical system which would allow human beings to obtain objective truth about the whole of reality. Much later Emmual Kant dedicated his Critique of Pure Reason to Francis Bacon.

What happened?

Facts were moved from the Emotions (Judgement, Opinion) to the Level of the Mind (Truth). With the help of Logic it would be possible to Prove Everything.

According to Aristotle there are four types of truth: universal affirmatives take the form: All S are P, universal negations take the form: No S are P, particular affirmatives take the form: Some S are P, particular negations take the form: Some S are not P. Later so called contingent truths were added. They are dependent on the situation/context.

The Quest for the Eternal Logical Truth is still going on. Many very bright minds have tried to find a solution but the terrible thing is that the Truth of a logical proposition is entirely dependent on the Truth of the Facts that are put into the Proposition. We are again in a State of Infinite Regress.

One of these bright minds was Frank Plumpton Ramsey (1903-1930). Ramsey lived and worked in Cambridge and was befriended with Bertrand Russell, G. E. Moore, J. M. Keynes and Ludwig Wittgenstein. Ramsey created a theory called Pragmatism.

In his paper ‘Truth and Probability’, written in 1926, Ramsey shows that if people in their behaviour obey a set of axioms or rules, the measure of our ‘degrees of belief’ will satisfy the laws of probability. The Truth is highly related to Judgment and “if we have analysed judgment we have solved the problem of truth“.

“..it is, for instance, possible to say that a chicken believes a certain sort of caterpillar to be poisonous, and mean by that merely that it abstains from eating such caterpillars on account of unpleasant experiences connected with them. … An exact analysis of this relation would be very difficult, but it might well be held that in regard to this kind of belief the pragmatist view was correct, i.e. that the relation between the chicken’s behaviour and the objective factors was that the actions were such as to be useful if, and only if, the caterpillars were actually poisonous. Thus any set of actions for whose utility p is a necessary and sufficient condition might be called a belief that p, and so would be true if p, i.e., if they are useful“.

What Ramsey is telling is that “the proof of the pudding is in the eating“.

What happened?

We are finally back to square one! After about 400 years of Enlightment we have to admit that the only way to find the Truth is to find out if what we Think is true is really True. We don’t have to use very complicated reasoning to prove what we are already experiencing in the Real World.

LINKS

About the Age of Reason

About Pragmatism and Ramsay

About Truth

About the War of Words

Monday, May 12th, 2008

The amount of people that are confused or are creating confusion is growing. It all has to do with Language. New words are created. Languages and Cultures are mixing. New Inventions and Theories are Created and Destroyed. We are in a highly creative phase, the End Game of Time Wave Zero. Is it possible to find the pattern behind this pattern?

The Encyclopedia Britannica is the oldest English-language encyclopedia still in print. It was first published between 1768 and 1771 in Edinburgh and quickly grew in popularity and size. The Brittanica expanded from 3 volumes in 1768 to 32 volumes today.

In France Diderot created the first French encyclopedia in 1745. It started as a translation of the English Cyclopedia of Ephraim Chambers. When he and his co-editor, mathematician Jean d’Alembert, were finished, they created a new work, the ‘Encyclopedie’. At that time it contained everything that was necessary to known about the Western World.

Its aim was “to collect all the knowledge that now lies scattered over the face of the earth, to make known its general structure to the men among we live, and to transmit it to those who will come after us,” to make men not only wiser” but also “more virtuous and more happy“.

Denis Diderot was one of the originators and interpreters of the Age of Enlightenment. This 18th-century movement was based on the belief that Reason could find True Knowledge.

During the Enlightment many scientists hoped that it would be possible to find the Eternal Truth, The Simple set of Rules that would Explain Every Thing. It was just a Matter of Time.

What they did not realize was that Truth is Highly Context Dependent. It is dependent on the Spirit of the Time, the Knowledge and Interpretation of the Writer of the Context, The Status of the Writer and the Genesis of Science.

Not only Knowledge changes but also Words change their meaning all the time. Everything Changes and the only thing that is left is to accept this Fact of Life.

The awareness of the problem of the Eternal Truth has created Cynicism. Scientists especially in the Social Sciences (Post-Modernism, Deconstruction) don’t believe it will be possible to find any objective general accepted pattern or explanation. They are fighting the goals of the highly rational Enlightment with very complicated rational arguments of their own.

When the exponential rise of Novelty predicted by Time Wave Zero (and other comparable models) reaches the Point Omega we will be literally lost in Space. Innovations that took centuries to happen in history will happen in a few days.

It is really true that there are no general Explanations possible? Is Everything Context Dependent?

The problem that the Eternal Change of our primary communication vehicle, Language, is creating is analyzed by many great minds in history. Perhaps the greatest genius was Wittgenstein. At the end of his life his students put all his Observations (he did not believe in Theory) in something called The Blue and Brown Books. In these books he is teaching the Art of Clarification.

Wittgenstein invented a new way of looking at the world called a Family Resemblance. If we gather together members of the same Family, they probably Look Alike, although there is no Distinctive Feature that they all share in Common. A brother and a sister might have the same dark eyes, while that sister and her father share a slightly turned-up nose.

They share a group of features, some of which are more distinctly present in some members of the family, while some features are not present at all. Wittgenstein argues that the different uses of one word and rules share the same Family Resemblance.

A Family is a Vague Set of Relationships that have something in Common but the parts of the set are Different. A Family is a unique set of permutations of distinctive features.

The only way to recognize a Family is to meet the members and create an intuition, a feeling. To do this we have to leave our study room and walk around in Reality. We have to move into the Context instead of floating above The Context.

Floating above the Context is called Imagining. There is nothing wrong with imagining. The imagination (Spirit) is the Mother of Art. Changing Art into a Science Destroys the Beauty of the Work of Art. Just like a Family a Piece of Art shows a pattern but is also shows exceptions of the pattern. The exceptions show a pattern but this pattern also contains a pattern. The world is a self-reference, a Fractal.

Scientists don’t realize that they are creating Fiction. When they would realize that they are producing Fiction they would certainly improve their Style. Scientific Fiction (a Genre) is mostly unreadable for other Scientists and especially for “Normal” people like me.

There are Many Families and there are even Families of Families. Some people have been born with a Talent to Observe one Family. Others are aware of completely different Families. All of them share features but it will never be possible to find The Set of all Sets of features. Finding the set of sets created a huge problem in Mathematics. It was the main reason why Wittgenstein changed his “theory”. He left the field of Mathematics, spend years in complete isolation (he was a teacher) until the people of Cambridge begged him to come back.

It does not help to spend a lot of time to discuss a joint Family. It only creates a War of the Words or a nicer term of Wittgenstein, A Language Game. A major part of Scientific Fiction is about the Quest to find the general Definitions of the set of all sets, The Holy Grail of Science… When we spend too much time to Fight we will never See.

The quest of Objectivity shows itself in the Use of Statistics. Scientists are unable to find the right Context (a Family) but they are also unaware of the Fractal Structure of the Universe. They are also completely unaware about the boundaries of Statistics. They accept the General Truth of Statistics without any awareness of the background.

What is the solution to all these problems?

The fist step is to accept the Spiraling Spiral and Self-Reference as the fundamental Fractal of the Universe. It is really a simple clarifying explanation.

The next step is to determine the Level and the Phase of the Spiral You are in (Style, Chronotope, Family, Network, Field of Reference, Bias). It determines what You are able to See and Do. It defines the Place in Time/Space you are Watching. If You want to move to another Level or State change the State of Your Awareness.

The last step is to feel the Movement of the Force of Life, The Tao,  and connect to this Movement. If you have accomplished this all the Clarifications you are looking for are given to you by the Great Force of Creation, Inspiration.

About the Foundations of Mathematics

Friday, August 3rd, 2007
Bertrand Russell

Bertrand Russell

In the beginning of the 20th century the mathematicians Bertrand Russell and Alfred North Whitehead wanted to define the eternal foundation of Mathematics.

To build a foundation Mathematicians always start with defining what they “mean”. They use a symbolic language called Logic to do this.

In Logic “=” means Being the Same“. If we would use the mathematical “=” in human languages we would say things like “a House is a House“.

These statements are without any meaning. We believe them but they are not adding something to our knowledge of the world we live in. “=” is called a Tautology in Logic. It is the only statement that is always true.

Mathematics is about changing the left hand and the right hand of the tautology without changing the truth. Mathematicians are always proving that the left and the right in what they mean are the same (=).

To speed up the process of proving, Mathematicians define new symbols that are “based on” other symbols. They use the foundation of “lower” symbols to define higher symbols. This process of mapping is called Abstraction (going UP). A Number is abstracted into the symbol A, called a variable.

Human languages are different from Logic. Depending on the language, the context and the person, terms have a different meaning. Mathematicians don’t like that.

The term Foundation is a Latin term (fundus). In the English language “Foundation” means “stable layer“. In the Dutch language “Foundation” is translated into the term “grond-slag“. “grond-slag” means “hitting” (slag) a pole (paal) into the Earth to build a house on. A foundation is something that is connecting a foundation (Poles) to another foundation (Earth). In human language the right and the left are equal AND not equal. They have something “in common“.

When we talk about a foundation most of us See a House. When we communicate we share this picture unconsciously. If we have not lived in a context where houses are build we are not able to share meaning. When a Dutch person “wants to fund” he has “to hit the pole“. In other places “Laying a Foundation” is a much more gentle process.

Human languages differ from Logic in many ways. The left and the right have something in common but are also different. The symbols (words) in human languages are connected to real pictures. A very important difference is the principle of truth. In mathematics we want to be certain. Mathematical truth is binary, Yes or NO. In human languages we have to believe and believing is an Emotion.

Believing is Seeing and Feeling. We have abstracted a thing that is Seeing and Feeling. It I situated in our body. We call it Mind. Mind is a Latin word (“mental“) and it means Spirit and Soul.

Spirit is connected to the Imagination and Soul is connected to the Emotions. We Feel with our Soul and we See with our Spirit (Inspiration, Inspire). Our Soul moves to something it likes and it moves away from something it dis-likes. Our Spirit takes us away. Suddenly we get a Flash of In-Sight and we Have to Move. Soul is gentle. Spirit hits us, like we hit a pole.

Russell used a “Thing called a Set” to create the eternal basis of Mathematics. He defined many operations on the Set. In the end he believed he had succeeded.

Suddenly a nasty problem arose. The set of all sets created a paradox (The Russell Paradox). It contained itself and it did not contain itself. To solve this paradox he defined a new rule (an axiom) that a set had to contain itself. Later others proved that this was not helping him at all. The foundation of Russell proved to be completely unstable.

The reason he failed was related to the boundary of the set. The boundary is not nothing. It can be open or closed to its environment (other sets). An open boundary looks-like your skin. A closed boundary looks-like an armor. Somewhere the set of sets (of sets of ..) had to close itself but the Set of the Whole could not be found.

Ludwig Wittgenstein

Ludwig Wittgenstein

One of the companions of Russell, Ludwig Wittgenstein, totally changed its views about mathematics. He did not believe in logic and a foundation any more.

He showed that we are playing games with language. Language is context-dependent. It’s meaning changes all the time.

He also showed that many sciences are simply impossible because they belong to the domain of the emotions. Examples are Ethics and Esthetics. Formalizing emotions is impossible. We all know what is right and wrong and beauty is a personal experiences. Nobody is able to tell you what you have-to-like.

Later the Dutch Mathematician Brouwer proved that everything we cannot imagine always leads to a paradox.

Later Gödel created a new problem. Gödel proved that an abstraction (a higher layer) is unable to explain every part of a lower layer. If we go UP we always loose meaning. The Set of Sets of … cannot contain all sets.

Later Lakoff and Nunez proved that the language of Mathematics acts in the same way as human languages. Mathematical Truth is not only connected to Seeing (Brouwer) but also to Feeling. The emotion of believing is necessary to believe mathematics.

Lakoff showed also that in human languages the process of abstraction has an end. It ends when we are unable to imagine what we are talking about (see Brouwer). When we use highly abstract words like “relation” or “furniture” we reason with a part of the set (a prototype) we are using. We use a chair or a table when we use “furniture“. Abstraction without visibility again creates confusion (a paradox).

Now I want to apply the flashes of insight of all the people to show you something about the abstraction called Mind.

(1) Russell: If you think your Mind is a closed environment you’re wrong. You are using the concept of the Set. Your mind is open to other Minds.

(2) Brouwer: If you cannot imagine a Mind it does not exist. Many people see the Brain when they imagine the Mind. The Brain is controlling everything in our body. If we use (1) we have to find a way of explaining how the mind is communicating with other minds. Scientists found the solution. The mind is producing words (speaking).

(3) Wittgenstein showed that speaking is not a reliable tool of communication. Behind words we are exchanging pictures and emotions. Wittgenstein showed that it is impossible to reason about emotions. We cannot reason about the emotional part of the Mind (Soul).

(4) Gödel: Your mind is an abstraction and therefore Your mind is unable to explain everything You Are.

(5) Lakoff: Mind is an abstraction without an image. When you reason about your mind you use a visual (!) sub-set of the Mind. The visual subset we use is “Actor”. Your Cold Analytical Mind (An Actor) controls Your Warm Body. You are a Walking Thinking Mind that is desperatly trying to manage the Instable Fluctuating Emotions (now called Desire) and the Imagination (now called Fantasy). We are back to You again.

The best thing to do is to skip the whole concept of Mind and start to look for something else.

George Lakoff has a theory that is able to give you some insight.

When we are born we come out of a Body and we become a new Body. The Body has to learn to crawl. Crawling gives us the feeling  that we were moving-away (Mother) and moving to-something (Mother?). Crawling is an emotion.

Our most difficult learning process is to learn to stand-”up” and to “keep balance“. In all cultures “Up” is more important than “Down“. Management is always on the upper floor and God is Up  in the heavens and the Devil is Down in hell.

The feeling of “Up” is basically a bias. We are so dominated by our difficult childhood learning process that we Evaluate many things with our “Up-feeling“. Thinking with the “Up” is getting you Down. It kills self-confidence. We believe that we think Up with our head (Brain) and the Brain (Mind) is the manager.

Let’s get back to what You are. You are your Body and your Body is open to its environment.

Lakoff found that the sentences we speak contain metaphors. Many metaphors are connected to the body. We use our organs to define the types of truth. We feel with our heart (com-passion). We feel with our bellies (In-tuition, inner teaching). We also feel with our stomach. Our stomach tells us that we want to express something. Funny enough these places in the Body (the Chakra’s) are independent of Culture. The reason is that every human shares the same body.

When you believe something you will feel this with your heart. You will feel excitement. The rythm of your heartbeat will change. When somebody is explaining something and you don’t see the picture with your inner eye (your imagination) don’t believe him. Ask somebody to draw what he is trying to explain. If your stomach protests ask a question. If you want to do something with what you believe you will feel it in your solar plexus (Navel). Don’t hesitate Act.

Now I want to come back to the foundation Russell was looking for. When you use your body the basic level to reason with is Earth. What we See on Earth is what is and what is does not need an explanation. Trees grow without any theory. The clouds move without any theory.

If you want to develop a theory start to look with attention (Focus). Be aware and watch what is happening on Earth. What is happening on Earth is always Cyclic. The Earth moves around the Sun. The Moon moves around the Earth. The Planets move around the Sun. Seeds turn into flowers and produces seeds again.

When we try to predict these movements we find patterns. These patterns are stages in a cyclic process of enfolding. The patterns are waves and waves are strongly related to Music (Pythagoras). The patterns in Music create overtones. They interfere. Short term Cycles are part of long term cycles. You’re body is a Standing Wave and it resonates with other Standing Waves with the same wavelength.

Out of the analyses of these patterns mathematics was created. Mathematics is about Music and Beauty. A mathematical theory has to be beautiful. If it is not beautiful it is not correct. This is simple. You have to feel enlightened when you understand mathematics. If you don’t get this feeling your teacher does not understand what he is explaining.

The problem of the Set of Sets can now be solved easily. The Whole is part of itself. The Whole is One but also Two. It is OBSERVING itself. It is conscious.

Perhaps now you understand why the Ears are the place in the Body that controls your Balance. Close your Eyes and Listen to the Rhythms in your Body and Nature. Erase your non-existing Mind. Get back to the level of You, Your Body. Observe your Self. Become conscious. Feel the warmth of your skin. Let the images come and observe them without touching them. Feel your gentle Soul move in and out when you breathe. Concentrate on your Belly (the level of In-tuition). Suddenly you get an Insight. Spirit has hit you. You feel full of Joy about the beauty of the Whole. You found the foundation Russell was looking for. Its You.

LINKS

About the Axiomatic Foundations of mathematics

A video interview with Bertrand Russell