Tag Archives: organised chaos

Five common realities – facts and logic 7


Carla, Man and Narrator have visited the inside of the Baptisterium San Giovanni and they are now standing outside for the closed Eastern door of the Baptisterium.

“This is according to Michelangelo the “Porta del Paradiso” or the gateway to paradise. On the top panel in the left door, “Adam and Eve in paradise”, “the fall” and “the expulsion from paradise” are shown. Paradise and the fall are beautiful metaphors for the human illusion of the paradisiacal possibility to an all-encompassing knowledge of the organised chaos. After Gödel had eaten from the apple of wisdom with the proof of the two incompleteness theorems – whereafter the illusion of omniscience of “facts and logic” was basically unreachable forever – the scientific world knew that humanity has forever no access to the paradise of omniscience.

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It is absolutely right that the “Porta del Paradiso” is closed and there is a fence before this gate”, says Carla.

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“I have read in my city guide that both doors are copies of the original doors that were severely damaged by the ravages of time and the flood of the river Arno [3] on November 6, 1966. Because of this flood, several panels were torn from the Porta del Paradiso [4]. I think the flood of the river Arno was also a manifestation of organized chaos”, says Man.

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“Certainly. The river has exceeded the banks to a nearly equal height in 1333 and in 1557 AD. Perhaps this is the reason that the living quarters in the Florentine palaces are located on the first floor.

[6]

OLYMPUS DIGITAL CAMERA[7]

This flood is an outstanding example of the organised chaos. Within reasonable certainty it can be stated, that once every few hundred years a similar flood can occur in Florence, like – within certain limits – all other water levels in the river can manifest themselves at any given time with a certain probability – this is the ordered nature of the organised chaos. But no one can predict on which day in the future a similar flood as in 1333, 1557 and 1966 AD will happen – this is the chaotic nature of the organised chaos”, says Carla.

“Good example. Yesterday I was looking for more information about Gödel. I read Gödel’s ontological proof of God. I have a copy of this proof for you”, says Narrator.

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“I can rarely accept a first definition without questioning. During my study at Delft University of Technology I had always asked my teachers where the first definition was based on. Initially teachers could give a limited answer to my question, but by asking further questions the answer always came down to the platitude: “We must start somewhere“. This answer remained unsatisfactory for me, I was actually always asking for an answer to “Why” while at best teachers could give an answer to “How – within a certain context”. Looking back, my change from my study of Applied Physics to the subject Humanities can be traced to the fact that Applied Physics has no answers available to why facts and logic manifest itself in a certain manner to us. Coming back to the first definition in Gödel’s ontological argument: why has God-like only positive properties and no negative characteristics or imaginary properties – as imaginary numbers in electrical engineering [9]? Based on the lack of an answer to my last question and based on Gödel’s first incompleteness theorem, Gödel’s ontological proof cannot contain a complete system – or a complete description of God-like. In the case Gödel’s ontological proof would contain an all-encompassing system – which is not the case in my opinion  – the consistency of the axioms cannot be proven from within its own system according to Gödel’s second incompleteness theorem. For completeness, I must say that my statements are based on scientific logic – and not on religious principles [10]. I think Gödel’s ontological proof is only a first exercise of Gödel in the field of religion and no more”, says Carla.

“I think you’re right”, says Narrator.

“Sounds convincing. During lunch I would like to hear your opinion about facts and logic of the look on God as described by Abraham Joshua Heschel in “God in Search of Man” [11] and the two aspects of “One” in the “Commentary on the Awakening of Faith” by Fa-Tsang [12], says Man.

“This fits nicely with Gödel’s ontological proof. My introduction to the mind of the warrior can wait for a while. Shall we look for a place for our lunch? ”, says Carla.

“I know a nice place in the Piazza di Santa Croche”, says Narrator.


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

[2] Source image: http://nl.wikipedia.org/wiki/Baptisterium_(Florence)

[3] See also: http://en.wikipedia.org/wiki/1966_Flood_of_the_Arno_River and http://it.wikipedia.org/wiki/Alluvione_di_Firenze_del_4_novembre_1966

[4] Source image: http://nl.wikipedia.org/wiki/Baptisterium_(Florence)

[5] Source image:http://it.wikipedia.org/wiki/Alluvione_di_Firenze_del_4_novembre_1966

[6] Source image: http://de.wikipedia.org/wiki/%C3%9Cberschwemmung_in_Florenz_1966

[7] Source image: http://en.wikipedia.org/wiki/1966_Flood_of_the_Arno_River

[8] Source image/text: http://en.wikipedia.org/wiki/G%C3%B6del’s_ontological_proof

[9] Calculations of electronic circuits are considerably simplified by use of imaginary numbers with a real value equal to zero. See also: http://en.wikipedia.org/wiki/Imaginary_number

[10] See also the statement made by Prof. Dr. W. Luijpen on the scope of science in relation to religion referred to in the post “Five common realities – facts and logic 6”

[11] See also: Heschel, Abraham Joshua, God in Search of Man: A Philosophy of Judaism. New York: Farrar, Straus and Giroux, 1976 (Reprint – original published in 1955).

[12] See also: Vorenkamp, Dirck, An English Translation of Fa-Tsang’s Commentary on the Awakening of Faith. New York: The Edwin Mellen Press. 2004

Five common realities – facts and logic 6


The next morning Carla, Man and Narrator drink a cup of coffee on a terrace in front of the Baptisterium San Giovanni [1] opposite the Basilica di Santa Maria del Fiore in Florence.

801px-Baptistry_Florence_Apr_2008[2]

“This morning I have thought about your introduction to the development of science. It is an impressive summary in brevity and in depth. At one point I would wish to make an addition; in my opinion human science had started much earlier than the moment people started giving meaning and perceiving meaning within rituals to increase survival. I think human science had started at the first conscious creative act during giving meaning and taking meaning to sound, to feeling, during love and raising children. Do you agree?”, Narrator asks Carla.

“Fully. Besides I have also ignored the difference between atomism [3] – wherein all facts are based on the smallest possible basic elements, particularism [4] – wherein facts and logic serve to promote our own interests above (and, if necessary, at the expense of) the interests of others, pluralism [5] – wherein different systems of facts and logic co-exist within a certain balance, and holism [6] – wherein facts and logic form a coherent whole. I hope to be able to include particularism in an introduction on the mind-set of the warrior. Also, I have ignored the many wrong representations of facts and the fallacies to serve a certain interest. Shall I now proceed with the orderly chaos – both fragmented and universal?”, says Carla.

“I am curious about your remark “both fragmented and universal”. Last night I had read in a different context a chapter on the coherence of both subject”, says Man.

“Please add information where you see fit. Actually from the beginning of science, people have usually tried to create an order out of chaos by looking at reality as an ideal. Facts that didn’t fit within the ideal frame of mind – such as friction, air resistance and unwelcome religions and cultures – were neglected as being irrelevant, or were fiercely contested during religious wars. By the end of the third scientific revolution, scientists thought that only a few obstacles within the basic elements of scientific knowledge had to be overcome, such as knowledge about the transfer of the gravity and the nature of light, before the paradise of the omniscience could be accessed within which everything would be known and may be explained by the application of the basic elements. The East doors of the Baptistry – or Porta del Paradiso [7] – are a beautiful metaphor for this way of thinking.

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With knowledge of these panels and of the interrelationship between these panels, scientists had thought to obtain the doors the heavenly omniscience.

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The organised chaos – fragmented and universal – prevented access to the paradisiacal omniscience with unambiguous repeatable predictability of facts in our world.

With “organised chaos” I mean that within certain limits every possible fact has a certain chance to manifest itself at a certain moment. As example I take a grazing cow in a delimited field with just enough food for the cow: the cow will graze within certain limits (the field and the edge that the cow can just reach with her mouth); each clump of grass in the field has a certain chance to be eaten at a certain moment; a butterfly – flying-by – can change the grazing of the cow after which the cow wil use another grazing pattern; this other grazing pattern has no influence on overall grazing of the total field in the long run, but it makes a huge difference for the life of several clumps of grass in the proximity of the cow [10].

With “fragmented and universal” I try to explain that the fragmented organised chaos manifests itself within a particular environment – such as the delimited field for the cow and such as the grasshopper in a matchbox [11] – and that the universal organised chaos takes place within the overall universe. “Fragmented and universal” relate to each other as the clouds, waves and ocean to the universal organised interplay and chaos within the total universe. The clouds, waves and the ocean are manifestations of the universal organised chaos, such as the weather – in the short term with a good predictability up to 4 days, and with good predictability over the long term – is also a manifestation of the universal organised chaos in space.

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With “unambiguous repeatable predictability of facts” I mean that the course of facts has the same outcome at identical starting positions. In everyday life, there is rarely an identical starting position, so a “uniform repeatable predictability of facts” arises rarely. Well there are many starting positions with similar characteristics: these situations often show a similar predictability of facts, but with minor differences in the starting positions the progress of the facts can show an organised chaotic behaviour in specific situations.

Under ideal conditions the constant of Heisenberg [13] limits accuracy of the determination of the starting position and of observations within the quantum mechanics [14].

In 1931 Gödel has published [15] the formal proof of the two incompleteness theorems [16]:

  • If a system – for example, a system (or grasshopper) in a matchbox – is consistent, then the system cannot be complete.
  • The consistency of the axioms cannot be proven from within the own system.

The combination of the “organized chaos”, the “limitation of observation within quantum mechanics” and “observations that – within the theory of relativity – depend on the way of observing” limit the “unambiguous repeatable predictability of facts”. The consistency of logic is seriously limited by the Gödel’s second incompleteness theorem.

By both restrictions, the ambition of the third revolution in science to unambiguously know and describe our world, was basically stalled. Part of the logic took distance from the organised chaos of daily life: this intuitionistic [17] logic only focused itself on symbol. Another part of the logic connected symbols with assumptions of reality as an extension of the intuitionistic logic – this extension was also called superintuitionistic logic. Classical logic was regarded in the superintuitionistic logic as the most strongly coherent system, which was seen as an intermediary – or intermediate [18] – between classical and intuitionistic logic. In a detour within another framework – symbols instead of rituals – the impact of the first revolution in the scientific development of mankind is demonstrated once again.

This is my introduction to the organised chaos; I hope you were able to follow me”, says Carla.

“Impressive in all respects. If I understand you correctly, then according to Gödel’s second incompleteness theorem the cohesion within a holistic system cannot be proven from its own system. This means that the cohesion of the “All-encompassing One” cannot be shown within itself”, says Man.

“That’s right within the conceptual framework of Gödel. I should add that Gödel proved his incompleteness theorems in a mathematical manner, using symbols that do not necessarily have an interpretation within our daily life. Some technical scientists only recognise symbols and ideal conditions as pure science. In the late 1970s, Prof. Dr. W. Luijpen – professor of philosophy of science at Delft University of Technology – had made the following statement during his lecturers: “Solely recognising symbols and ideal scientific conditions as the only scientific reality is a religious statement. Religion is not the area of expertise of technical scientists: this recognition is, until now, no scientific statement“. In line with Popper and Kuhn I do not rule out that outside mathematics – with its world of symbols – the two incompleteness theorem of Gödel may not be applicable under certain circumstances”, says Carla.

“Fascinating thoughts. Let us visit the Baptisterium San Giovanni. I suggest to come back to your introduction later on”, says Narrator.

“That’s good”, say Carla and Man.


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

[2] Source image: http://en.wikipedia.org/wiki/Florence_Baptistery

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

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

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

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

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

[8] Source image: http://nl.wikipedia.org/wiki/Baptisterium_(Florence)

[9] Source image: http://nl.wikipedia.org/wiki/Baptisterium_(Florence)

[10] Source metaphor: Stewart, Ian, Does God Play Dice? London: Penguin Books, 1992², p. 132

[11] See also: Nārāyana, Narrator, Carla Drift – An Outlier, A Biography. Omnia – Amsterdam Publisher, 2012, p. 15 en p. 151 – 156

[12] Source image: http://en.wikipedia.org/wiki/Ocean

[13] See also: http://en.wikipedia.org/wiki/Heisenberg_uncertainty_principle

[14] See also: http://en.wikipedia.org/wiki/Quantum_mechanics

[15] Zie ook: http://en.wikipedia.org/wiki/Kurt_G%C3%B6del

[16] Zie ook: Nārāyana, Narrator, Carla Drift – An Outlier, A Biography. Omnia – Amsterdam Publisher, 2012, p. 154

[17] Zie ook: http://en.wikipedia.org/wiki/Intuitionism and http://en.wikipedia.org/wiki/Intermediate_logic

[18] Zie ook: http://en.wikipedia.org/wiki/Intermediate_logic