Tag Archives: Ian Stewart

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.

feiten en logica 62[8]

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

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Five common realities – facts and logic 5


Carla, Man and the Narrator are sitting in a restaurant for their dinner. They have received their drinks and menu map.

“Cheers, on the progress of our quest. Are you happy so far?”, says Man.

“Partly. The All-encompassing One – and also the binding between the other with the All-encompassing – are well discussed, but the “other” as entity remains underexposed. Maybe we can give more attention to the other”, says Narrator.

“I may have put too much emphasis on the “All-encompassing One” due too many forced separations during my life. The last years I gave much – maybe too much – attention to all kind of links between events in my life. What do you think, Carla?”, says Man.

“During my introduction to the ordered chaos I will pay attention to the other; this is necessary in an overview of the development in science in a nutshell. Please add information from your background and conceptual framework. Let us first order our meal”, says Carla.

Carla, Man and the Narrator make their choice from the menu and they ordering their diner.

“An overview of the development of science – which in our time accumulated in an ordered chaos – can be given in many ways . There are many books with excellent introductions to the origin of logic, mathematics, physics, astronomy and other sciences. My introduction is a personal one and is certainly susceptible to criticism; a characteristic of science according to Popper and Kuhn [1]. In my opinion science had started when people began to consciously pay attention to their living environment so that they could increase their survival by getting grip on conditions and tangible things [2]. Probably people had initially tried to give interpretation to their environment by means of rituals such as hunter-gatherers had identified with their prey via rituals [3], pastoralists via the cattle-cycle [4] and via worshipping the golden calf in the Old Testament to maintain and enhance their cattle, and farmers via timing with corresponding rituals to determine the moment for sowing and harvesting during the year. At the same time people have also given magical powers to rituals whereby rituals could accomplish the desired circumstances. This creative act of giving meaning and perceiving meaning [5] by rituals was a first revolution in the scientific development of people; remnants of this revolution we can still see today in current rituals within our society, for example at rituals during major changes in personal and public life and at the year celebrations.

feiten en logica 51[6]

The second revolution in the scientific development of mankind consisted of a shift of attention from obtaining desired conditions or tangible things through the provision of rituals to an understanding  – and research – of human life on earth; the self/Self became subject of research. In the Western world a temporary cohesive peak was achieved in the Medieval Scholasticism, in which its philosophy – at that time directly connected to the theology – completely stated (an gave interpretation to) the entire human environment; life was in service of God, his creation, and the afterlife (preferable in heaven or in hell after a bad life). In India around 600 BC, this attention resulted in the Upanishads with emphasis on “self/One” as oneness [7]; and life became subject of meditation.

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The third revolution in the scientific development of mankind consisted of the shift in attention from the central ”Self/One”– or God within the Medieval Scholasticism in which everything was directly connected with God in one way or another – to a self-awareness of the individual and to “the other” which consisted of the other people, the setting, the circumstances and the tangible things. In the Western world, science – and later philosophy – were separated from religion so scientific research could develop open-minded, (value) free from dogmas and focused on facts and logic. In the Renaissance, mankind initially depicted science like a clockwork in which the mutual movement of wheels and links had to be discovered, from which the living environment and the way things worked could be explained [9]. Thereafter scientists tried to find mathematical equations for everything [10]. The first developments were so impressive that mankind still uses the equations of the classical mechanics [11] to send spacecraft extremely precise through space.

feiten en logica 53[12]

After a while, the knowledge about solving mathematical equations became an inhibiting factor: a number of linear (differential) equations were relatively easy to solve. Science tried to describe the living environment under ideal conditions – without friction, headwind and all the unknown factors were summarized in constants – in linear equations whose solution was known, just like our world is only arranged as cultivated French gardens.

feiten en logica 54[13]

Until more than a hundred years ago the development of science was so promising that only a few small imperfections – like how gravity is transferred and whether light is composed of particles or of waves – need to be solved. The first cracks in this expectation arose after it became clear that light consists at the same time of particle and of light waves, that in quantum mechanics the speed and location of particles cannot be determined at the same time, and that results in the theory of relativity are dependent on the way of perceiving.

These cracks grew with the observation that our everyday environment largely consists of non-linear differential equations that cannot be solved and often only can be approximated. Furthermore, even simple models – like the three-body-problem [14] in space – are extremely complex and can only be solved in simple special circumstances. In addition simple models – such as a double rod pendulum [15] – showed chaotic characteristics where the outcome considerably differs over time with minor differences in the initial state. I see that our meal will be served. I’ll continue later”, says Carla.

“Upon hearing your introduction, it stikes me that the Mahābhārata caused a similar revolution compared to the Upanishads which focus on the One/All-encompassing. In the Mahābhārata, the attention shifted to the other/self in relation to the One/Self, wherein nothing can be understood independent of the rest. The Self is a being in relationship with itself and at the same time the Self is itself a being in respect to the other and herewith One’s/one’s own life is connected to the life of the other [16]. The way – in which attention is shifted in the Mahābhārata – is more focused on explaining and describing life and less focused on control and grip on the living environment”, says Narrator.

“During your introduction, I am reminded of the title of a collection of poems by Rutger Kopland:

Who finds something,

has badly sought. [17]

and of a statement of Prof. Dr. W. Luijpen during his lectures at Delft University of Technology:

“To prove” is compellingly letting know in order that the other has to kneel.

Maybe something to think about during the continuation of our quest”, says Man.

“Interesting thoughts; I will come back on “compellingly letting know” at the mind of the warrior, but first let us enjoy our meal”, says Carla.

“Enjoy your meal”, say Man and Narrator.


[1] See also: Nārāyana, Narrator, Carla Drift – An Outlier, A Biography. Omnia – Amsterdam Publisher, 2012, p. 34

[2] See also: Origo, Jan van, Who are you – A Survey into our existence – 1. Omnia – Amsterdam Publisher, 2012, p. 103. See also: Calvin, William H., The River That Runs Uphill: A Journey from the Big Bang to the Big Brain. New York: Macmillan, 1986

[3] See also: Eliade, Mircea, A History of Religious Ideas, Volume I, Chicago: The University of Chicago Press, 1982, p. 5 and Origo, Jan van, Who are you – A Survey into our existence – 1. Omnia – Amsterdam Publisher, 2012, p. 111 – 112

[4] Origo, Jan van, Who are you – A Survey into our existence – 1. Omnia – Amsterdam Publisher, 2012, p. 33 – 34 en 94 – 95

[5] See also for the creative act of giving meaning and perceiving meaning: Merleau-Ponty, Maurice, Phénoménologie de la perception. Paris: Gallimard, 1945

[6] Source image: http://nl.wikipedia.org/wiki/Gouden_kalf_(Hebreeuwse_Bijbel)

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

[8] Source image: http://nl.wikipedia.org/wiki/Scholastiek

[9] See also: Stewart, Ian, Does God Play Dice? London: Penguin Books, 1992², p. 5 – 8

[10] See also: Stewart, Ian, Does God Play Dice? London: Penguin Books, 1992², p. 18 – 33

[11] Zie ook: http://en.wikipedia.org/wiki/Classical_mechanics

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

[13] Source image: http://en.wikipedia.org/wiki/French_formal_garden

[14] See also: http://en.wikipedia.org/wiki/Three-body_problem

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

[16] See also: Badrinath, Chaturvedi, The Mahābhārata – An Inquiry in the human Condition. New Delhi: Orient Longman Private Limited, 2006, p. 530

[17] Source: Kopland, Rutger, Verzamelde gedichten. Amsterdam: Uitgeverij G.A. van Oorschot, 2010, p. 103