Posts Tagged ‘Mathematics’

About Understanding Mathematics

Thursday, July 1st, 2010

When I was a student I made some money by helping young people to understand Mathematics. I Listened to the way they tried to Solve the Puzzles their Teachers gave them and tried to find out their Personal Way of Reasoning. 

When I found their reasoning problem I gave them a new Way to Think.

This approach was very effective. Sometimes I just needed one hour and the highly frustrated pupil transformed into a Lover of Mathematics. They saw that Mathematics is the Art of Beauty and Harmony.

The main problem most of these pupils had was the Why-Question. They wanted to know what was “behind” mathematics. In Mathematics there is no Why. Mathematics is “Just the Way it is“. It is a System of Rules you have to Apply.

When you are a Highly Creative Person Mathematics is a Highly Frustrating Science.

Highly Creative Persons are Highly Associative.  They See Links between Every-Thing. They Build Bridges between Islands almost nobody knows they exist.

Mathematics is about creating Abstractions.

Highly Creative Persons Think with their Imagination. They Jump from Images to Image.

The Images of the Mathematicians are Abstract Symbols and most of the time the Mathematical Symbols are chosen without any relationship to the Situation they want to represent.

If Creative, Associative, Persons are not able to See what Mathematics is trying to represent they are Lost in Space.

When we go back in History the Imagination (and not Thinking/Reasoning) was the most important “Thinking-Tool“. The meaning of the word “Think” originally meant “to See“. 

The Art of Reasoning was based on detecting Correspondences.

The Ancient Scientists observed Nature and found out that certain situations “looked alike“. They used and linked Visual Metaphors to explain what they observed. 

Abstract Concepts were always represented by something others could See.

The interesting point is that New Scientists are founding out what the Old Scientists already knew. Our Basic Reasoning System is based on Images.

When we move to the Abstract Domain we use Images (called Prototypes) to Reason. Abstract terms like Furniture are always represented by a prototype we have Seen.

This explains why most of the People are not able to See Mathematics and why most of the People have a big problem Understanding Ancient Knowledge.   

They try to Map the Ancient Visual Landscape of Knowledge to the Modern Space of  Abstract Terms they don’t understand.

They are looking for something that is already there.

They are asking the Why-Question while the  Ancient Knowledge is Visible All Around Us.


About the Foundation of Mathematics

About Old Fashioned Thinking

About Topology, the Art of Seeing

About the Art of Creation

About Psychic Reading

Wednesday, December 12th, 2007

When you are a young child you don’t know that some people are gifted with a certain talent and others are not. When you are born with an unusual talent people in your environment don’t understand you.

Sometimes they even tell you that you are a “weird” person and you have to behave “normal”. When you are “abnormal” it is very difficult to behave normal. When you get older you find a way to hide your ‘strange” talent. You start to behave like “the others”.

When I was young I experienced that I could “read” people. At that time I did not know my talent was called “reading”. To me “reading” was “normal” and as a young innocent child I told people many things about their “inner life” that I could not know.I was gifted with more “unusual talents” like music and mathematics.

My talents were unusual because nobody in my family and my social context was “para-normal”, “highy analytical” or “musical”.

When you look at the scientific community “reading” is classified as “para-normal” and a huge part of the scientific community, the skeptics, are fighting paranormal abilities.

I never understood why they are fighting something some people are gifted with. They are certainly not fighting people who are talented in art or mathematics.

They don’t believe the talent of reading exists because they are unable to explain this talent. They are also not able to explain the talents in art or mathematics. To me they are “the same talent”.

They are all related to what I would call Intuition. When you are Intuitive you “just know” something but you are unable to explain to other peoople why “you know what you know”.

Some people even want to pay a lot of money when you are able to prove that you are “para-normal”. They arrange weird experimental environments and don’t understand that the talent of “reading” is highly context-dependent.

The talents of art and mathematics are also context-dependent. Doing mathematics in a crowded space is impossible.

I want to give you (and the skeptics) some idea how “reading (and mathematics)” works with me.

When you want to “read” you have to be in a certain mood. You have to be “grounded”, relaxed and “opened up”.

“Grounded” feels like having “a close connection to Earth”. You are “grounded” when you feel there is “something” streaming through your body.

This “something” creates the state of relaxation. The “something” is also the connector that generates the “opening up”. The “something” is called Prana, Chi or the “Inner Light”. I prefer the last term.

It is not necessary that the somebody you want to “read” is available in the space you are staying. It is also not necessary that the somebody you want to read is alive, You need some kind of clue to make the connection. Most of the time a name is sufficient.

When the connection is made you have to make a distinction between two sensory systems. You have to stop you’re own system. This is the most difficult task to perform because you’re system is always interfering.

If you are connected to the wrong system you are “biased”. Reading works very well when you don’t know the person you are reading.

I “know” or “feel” when I have disconnected from my own system. The feeling “looks like” “being in the observer-mode”. You are looking at the world from a distance.

When this state is accomplished a “voice” starts to talk and you “see images”. The reading always starts with “hints”. “Hints” are words and flashes. A few seconds later the words and images change into a “movie”.

In exceptional situations you also feel emotions or are completely taken over by “the other”. If this happens you are “channeling”. I don’t like this state because I really don’t know who or what is taking over.

About Meta Art

Wednesday, September 5th, 2007

marcel_duchampSince 1915, Marcel Duchamp occasionally bought simple objects in order to exhibit them as art objects. What he wanted to show is that “The Spectator Makes the Picture“. To many people the Art of Duchamp was the End of Art.

The end of art was also a new beginning. Many of the artists who rejected the traditional art object found new realms to explore, by moving to a new level of abstraction, Meta-Art.

The meta-artwork is a class of possibilities rather than an individual thing. It may take the form of an always changing pattern (Open Form), a collection of building blocks (Interactivity), a physical process (Process Art), a computer program (Algorithmic Art), or a mere idea (Concept Art).

What Meta-Art is trying to accomplish is to generate all the possibilities and “Let the Spectator Choose what he Likes“.

Producing beautiful art is not easy. Especially if you have to make a living out of it. Many artists would sell their soul to the Devil in exchange for a magical tool that would produce the perfect artwork, enchanting their patrons and producing fame and fortune for themselves. In every era artists searched for generators and libraries of beautiful components. It is well-known that geniuses like Bach and Mozart used music-generators.

The concept of an Art Generator was described in the book Ars Generalis Ultima of Ramon Llull (1232-1315). Lullus (his Latin name) got his idea from the ancient Astrologers, the Magi. Ars Generalis Ultima inspired Gottfried Leibniz who inspired Gilles Deleuze (“Le Pli“) and George Chatin (“The Limits of Reason“).

Interviewer: “Can you tell us something about your new opera?” Giuseppe Verdi: “It’s exactly the same notes as the previous one, I merely changed the order a little bit.”

Giving the spectator a choice can be done on the level of a picture (“Now I like it“) or on the level of the process itself. “What he likes” is permanently changing according to the moods of the spectator. If would be even better if the environment and the spectator were constantly in the Now, kept in “a Permanent state of Pure Beauty“.

mondriaanThis is what Mondriaan wanted to achieve “Our material environment can only posses a pure beauty (i.e., be healthy and satisfy utility in a truly direct way), if it no longer reflects the egoistic feelings of our small personality: it does not even have any lyrical expression any more, but is purely plastic.”

“For the present moment I see no possibility for arriving at a purely ‘plastic’ expression by only following the organism of what is to be built, focusing only on utility. Our intuition is not sufficiently developed for that, and too involved with the past. [. . .]

For instance, utility often requires repetition in the way of nature (in workers housing, for instance), and in that case the architect needs the concept of plastic expression and the power to go against what the practical goal seems to indicate. Because there are always possibilities for architectural solutions which satisfy the practical goal and the esthetic appearance.”

Mondriaan experimented with Metrical Repetition and Symmetry. He studied Improvization and Jazz to find the perfect pattern. At that time Mathematics and Computers were not helpful to him. Chaos-theory (Emergence), Fractals (Self Reference) and Super Symmetry (The Multi Dimensional String) were “invented” much later.

Mathematicians have been gifted with the Talent of Art. All of them love Music and many of them make music. To me Mathematics is about pure Beauty. It is not a coincedence that Mathematics is the leading force to create innovative Art.

Mathematics in combination with the Computer is capable of much more. It is capable of generating and controlling adaptive environments. Places where happenings take place that create new narratives. We are not far away to create the automated Chronotope, the Holodeck in the famous television series Star Trek.

buildingsI have been involved in many experiments in this area. I worked with Erik Vreedenburgh and Remko Scha  and Ad Luytwieler . The website of Artifical contains many briljant articles. I used them in this blog (Thanks).

All of them are able to create beautifull buildings for a budget that is a fraction of what we pay now. They even create adaptive buildings. Buildings that can be used by everybody in every state of his body and in every state of his life.

It is time to move ahead. The Computer, the Calculator, is not only capable of slaving the human. He is also able to serve and help us to calculate, to count, to tell us about Harmony and even pure Beauty.

A Human needs to be creative to Understand The Self.

Our Personal Art is a Mirror to See what We Are.


About Magic and the Memory Palace

About Color and Music

About Morphology