Tag Archives: infinity

Carla Drift – Looking back at my innocence


Before we started the quest for “Who are you”, I told Narrator in a few words about my youth – the years of my innocence.

“There was once a girl that was so clever that everywhere she was an outlier. She surpassed all the knowledge of her environment. This girl was so wise to show this special gift to nobody. Very soon she discovered that this gift completely confused her environment. Now and then she showed a glimpse whereof she thought.

In elementary school children learned to add, multiply and divide. This girl already calculated in the infinite or in the uncountable as she called it. Countable was all that fitted within a box of the “knowable”. Hereby she thought about the matchbox in which she formerly had caught a grasshopper.

[1]

When the class learned to count until ten, the content of the Matchbox was ten for her. For the class innumerable was at that time “ten plus one”. When the class learned to count until one hundred, from then on countable was one hundred; “hundred and one” was innumerable and so on as far as the classmates could count.

The countable and therefore the knowable grew along with the knowledge of the classroom and the innumerable became bigger and bigger. This girl learned that the countable – so the content of the matchbox “L” – changed along the changes of the environment. The uncountable was then still “L+1”. This girl started to add the countable, so when for the class L was equal to ten, the girl decided to place ten matchboxes in a row: for her “10 times L” was equal to one hundred; infinite was then ten matchboxes plus 1. She placed hundred matchboxes in a row and “hundred times 10” or “1000” was countable and infinite was “hundred boxes plus 1”. She did the same with boxes that were getting smaller like Russian dolls. Infinitesimal was one size smaller than the smallest knowable.

[2]

And zero was an empty table without any box or doll. She wrote this as “O”. This was very easy for her.

For simplicity, this girl decided to write the infinite as “L + 1”; This was equal to the largest box plus one or the greatest number of knowable boxes plus 1.

Now this girl was so far that she saw infinitely – or L + 1 – as a matchbox of all knowable plus one. She began in the first class of primary school to calculate with the infinite, which was also an outlier that fell outside the knowable. For infinite the same rules applied, but it the infinite was still outside the knowable of the others: in this way she remained in touch with arithmetic lessons of her classmates. The ordinary multiplication tables were applicable for the infinite and normal division rules applied to the division of the infinite – a piece of cake. Increases the knowable and the infinite is just slightly larger; decrease the smallest knowable and the infinitesimal small is just slightly smaller.

According to her the infinite or L + 1 was the evidence for the existence of God on the Catholic primary school. God could adopt all dimensions depending on the circumstances required, but God himself was larger than the knowable so he remained all encompassing. If the changes increased rapidly, God also increased quickly and vice versa. And because God was all encompassing or L + 1, God took the required form immediately. In this way the girl derived and integrated in the second class of elementary school. The most beautiful thing was that God was no foreigner, he was also an outlier just like her. God made woman and man (as knowable) like his image – also the outliers like her were created like his image. She made the knowable slightly larger because she was an outlier. Later she adjusted her view on God.

In the second class of elementary school she read in a book from the library – that was smuggled through her father – about primes. she decided to look at primes as matchboxes for calculation purposes. According to her new calculation method the core numbers were L, 2L, 3l, 5l, 7l, 11l, 13L, 17L, 19L and so on as primes. With these primes all known matchboxes could be created [3].

In the fourth grade of elementary school she saw in the library at the Department of mathematics a book on Gödel. In this book she read Gödel’s two incompleteness theorems [4]. She borrowed this book via her father. By naming L + 1 she already knew the first incompleteness theorem and with her new calculation method – whereby she used the core numbers L, 2 L, 3 l, 5 l, 7 l, 17 l, 11L, 13L, 19L according to the sequence of primes – she saw immediately the second incompleteness theorem; we can never prove the whole arithmetic L because there will be always a L + 1. This evidence is a piece of cake.

She purposely made a few mistakes in long divisions [5] in order to appear normal.

In the fifth and sixth class of primary school a new schoolmaster let her read the book “Cosmic View, The Universe in 40 Jumps” by Kees Boeke. With her father she studied astronomy and microscopy. She calculated the Kepler orbits on her own. In a course mechanics within theoretical physics [6] at the University of Technology in Delft, she saw these calculations again. One of the two authors was an outlier [7] in the field of mathematics and physics.”

[8]

After this brief description of my years of innocence in elementary school, Narrator and I decided to start the quest “Who are you” together. During the preparations we invited Man Leben – after the death of his second life companion – to go along. He accepted the invitation “With hope and consolation”.


[1] Source image: http://en.wikipedia.org/wiki/Match

[2] Source image: http://fr.wikipedia.org/wiki/Fichier:Floral_matryoshka_set_1.JPG

[3] See also: http://en.wikipedia.org/wiki/Prime_number

[4] See: http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

[5] See also: http://en.wikipedia.org/wiki/Long_division

[6] See: http://en.wikipedia.org/wiki/Course_of_Theoretical_Physics

[7] See also: http://en.wikipedia.org/wiki/Lev_Landau

[8] Source image: http://en.wikipedia.org/wiki/Course_of_Theoretical_Physics

Carla Drift – Years of Flourishing 3


My study at the University of Technology in Delft progressed smoothly. The mathematics was still addition and subtraction – sometimes in a slightly different manner than counting at the primary school. I was fascinated by infinite times [1] addition and subtraction of very small numbers. Depending on the properties of a certain tiny number, the outcome of infinite times adding of this tiny number may be:

  • Infinite tiny;
  • a specific number
  • extremely slowly moving to infinity
  • very fast moving to infinity.

Especially the point where the additions changed from a huge number to infinity, captivated me.

Infinity is quite funny, because it is beyond our comprehension. If a monkey types at random on a typewriter, than after a long time this monkey will produce the full Ulysses by James Joyce [1]. Infinity is so huge that this monkey also will produce it a number of times in succession – it will take an extreme long time before this may happen.

[3]

This addition – with positive, negative or imaginary numbers – could take place over a certain distance on a line, on a surface or in a given space. The distance across the line, the surface or the certain space can vary from tiny to infinity, depending on where is looked at.

The way these additions behave across a line, on a surface or in space – from different points of view –, can be examined with vector-analysis [4]. This analysis examines the direction in which the addition increases the fastest – gradient. Also can be examined how much the increase or decrease is at a given point – divergent – for example: how much heat is radiating from a point or how much heat is taken from the environment at this point. Also can be examined if at a given point the closest neighbours change faster – curl.

Sometimes there are irregularities in the additions. This is the case if at a certain place one divides by nearly zero. If above the line the number also is nearing zero, then the outcome can range from very small to infinity. Around this particular place the outcome can change from minus infinity to plus infinity, depending on the direction in which this given point is accessed.

In my second year of studies, the results of investigations into behaviours of the weather by Benoît Mandelbrot became known. To do this, he used rather simple equations. The results of these equations showed after many repetitions fascinating images. Black are the places that will fit neatly within the equations. The blue colours fall outside. The edges are extremely complex and interesting: zooming in shows an ever greater complexity.

[5]

To zoom in further into the transition between black and blue, increasingly complex images are shown until the computer can no longer handle the calculations.

[6]

The equations of the Julia-set show a same complex and familiar image:

[7]

The results of the equations for the behaviour of the weather on Earth show, that tiny differences in the initial value in critical areas can – within a few days – influence the weather over the entire earth. E.g.: the flight of a butterfly in the Amazon region can directly affect the weather in Europe a few days later and the other way around [8].

In that time I tried to establish a link between the results of the pioneering work by Benoît Mandelbrot and the content of Kees Boeke’s “We in the universe, a universe in ourselves” [9]. Each scale left a universe with a very intriguing and complex environment that was determined by relative simple equations.

The equations for the (sub) atomic physics were relatively simple. The results were complex where particles can have a wave and a particle nature. The particle was with great chance in one place or may be in a few places, but there was also an extremely tiny chance that the particle could be anywhere and nowhere. I had seen the microcosm in her wealth through a microscope. Anyone can see our world. A glimpse of the splendour of the macrocosm I had seen through a telescope.

In the third year of my studies I was planning to study an universal field theory with equations that were as simple as the equations of Manderbrot-sets [10]. These equations promised in a similar manner at critical places to show large differences in outcome with very minor differences of the initial condition. The equations also promised to provide a coherent wholeness when viewed from all separate points within the field. Most shifts from this point of view were smooth and predictable, but some shifts showed big jumps that occasionally could be infinite. An explanation for the big bang [11] may be possible, because a small part of all local energy may conglomerate in one place simultaneously and then this nearly? infinite energy could distribute in a big bang. According to this proposed universal field theory, a big bang may occur anywhere, but the chances are extremely small.

Hereto remains the question of the total energy in the infinite universe:

  • zero – than there may be one or more “mirrored” universes with mirrored energy
  • a fixed number – than the question for the explanation of this number arises
  • infinite – hereto the question arises whether there exist infinitely many other universes resembling our universe, and/or there exists a layering in universe where one infinite universe is a part of many other infinite universes; a solution may be the “powers of ten” whereby every scale meets the equations for this universal vector field

This idea [12] was very ambitious. The elaboration of this idea exceeded my possibilities within three or six years of study; it had to be studied in a group. The University of Technology could not offer the necessary support. The idea did not fit within the existing research programme of the University.

In the second half of my third year in Delft I was empty-handed in my study and empty hands in love. Now I noticed the disadvantage of being the oldest in the real world: I could not control everything that happened around me [12]. I was forced to say goodbye to my great love and to my ambitions in my technical study.

After discussions with many people I decided to continue my study at a University in Amsterdam in humanities. Fortunately I could – with a recommendation of tutors at the University of Technology – get a post at the University of Amsterdam in mathematics in humanities.


[1] See also: http://en.wikipedia.org/wiki/Infinity

[2] See also: http://en.wikipedia.org/wiki/Infinite_monkey_theorem

[3] Source image: http://en.wikipedia.org/wiki/File:Monkey-typing.jpg

[4] See also: http://en.wikipedia.org/wiki/Vector_calculus

[5] Source image: http://nl.wikipedia.org/wiki/Mandelbrotverzameling

[6] Source image: http://nl.wikipedia.org/wiki/Mandelbrotverzameling

[7] Source image: http://nl.wikipedia.org/wiki/Juliaverzameling

[8] See also: http://en.wikipedia.org/wiki/Chaos_theory

[9] See: Boeke, Kees, Wij in het heelal, een heelal in ons – Twee tochten: door macrokosmos en microkosmos. Amsterdam: J.M. Meulenhoff, 1959. This book has been published in English as “Cosmic Viewthe Universe in 40 Jumps”

[10] See also: http://en.wikipedia.org/wiki/Mandelbrot_set

[11] See also: http://en.wikipedia.org/wiki/Big_Bang

[12] The described idea is fictional. The author has not checked all implications of the idea on sense and nonsense.

[13] See also: Brown, Eleanor, The weird Sisters. HarperCollins p. 121