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 View – the 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
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Who are you 
