How does mind come into matter– and does it have a meaning?

Prof. Dr. F. JarreDepartment of Mathematics

Heinrich-Heine University Dusseldorf, GermanyMarch 13. 2018

The physical world:How can it be explained that consciousness – a system that reflects on itself –came into being in nature out of nothing? To resolve this paradox, an approachthat dates back to Russell [18] shall be recalled: Russells contributions to theaxiomatic basis of mathematics as it is being taught today were essential. Thecomplex numbers as we know them can be described in full by a handful ofvery simple axioms (annotated in [1] below) – “in full” in the sense that thereis nothing that humans would know and that cannot be derived from theseaxioms. And based on these axioms, very complicated fractal sets such as theMandelbrot set can be defined with a single simple iterative rule [2]. A setwhose pictures likely have been encountered not only by most mathematiciansbut also by most laymen at some point in time. A fascinating set of literallyinfinite variety; permanently new buds sprouting out of buds, each very similarand yet each of them always a bit different.

Detail of the Mandelbrot set [3].

This continues on and on, from the hundredth to the thousandth. There isa multitude of mathematical laws that would describe these similarities – theyjust have never been written down; for the one since no-one would be interested,and for the other since the basic law for generating this set is known and easilyunderstandable.

Sets such as the Mandelbrot set could also be defined in higher dimensions orin a 4-dimensional space-time-model and would then yield even more fascinatingstructures but which could not be visualized so easily such that a layman could

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admire them. And also in 2 dimensions they would still be fascinating andcomplicated if the iteration was not carried out to infinity but stopped after afinite number of steps – in the end all pictures that have been published aboutthe Mandelbrot set so far always have been the result of a finite termination ofthe iteration.

The real world of physics is running similar to the Mandelbrot set but stillconsiderably more complicated: While the Mandelbrot set can be defined bythe temporal progression of a single particle – the starting point of the iterationsequence, in the real world of physics an incredibly large number of elementaryparticles are interacting with each other according to simple laws, laws that arecurrently just being deciphered more or less completely by humans. While forthe Mandelbrot set the iteration sequence defined by the starting point is deter-ministic, in the real world of physics there is a multitude of factors determiningthe chronological progression that are categorically not predictable accordingto current physical understanding, due to Heisenberg’s uncertainty principle ordue to the uncertainty of the radioactive decay of a single particle – here weonly know a statistical mean, the half time. Finally, in the definition of theMandelbrot set, the time proceeds in discrete time steps and thus correspondsto a quantized time axis, while we imagine the time axis in the real world ofphysics as a continuous axis. (But in the end we don’t know whether time reallyruns continuously or in very short time steps.)But in spite of all these differences, also very fascinating structures arise outof these simple laws of physics – galaxy clusters, pulsars, quasars, black holes,neutron stars, stars and planets,

Crab Nebula, Result of a supernova in the year 1054 [4].

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on which a complicated sub-structure such as life could evolve. Large parts ofthe development of life could be traced by evolutionary biologists starting withfirst organic structures that may have evolved for example at black smokersin the deep sea, [12] over the development of first elementary organics sensorsthat could register temperature for example or light, over neuronal develop-ments that could process such sensory information, up to a memory “there wasfood recently” or “carnivores had recently lurked around here” that entailed anevolutionary advantage in the daily struggle for survival.

MindOrganisms learned to flee in face of danger, to develop a feeling of fear or hunger,they learned to protect their offspring, first instinctively, and from such instinctsfeelings of solicitude evolved. Such developments often occurred in parallel indifferent animal species. The eye evolved several times in very different mannerin the animal kingdom, with the octopus quite unlike from (and better than) themammals and again different from than the compound eyes of insects, see e.g.[13, 15]. Also forethought and planning can be observed with corvids, parrots,and other animals, and for humans this has evolved further to a reflection aboutnature and one self, see also [6]. This development of consciousness starting fromlifeless elementary particles is a very long process similarly as the computationof the Mandelbrot set starting from the axioms of the real or complex numbersalso is a very long process.

The question “How can matter produce mind?” spans a long stretch. In itsfull length a single person can hardly grasp this stretch. He or she cannot capturethe overall development in all detail and thus the formation of consciousnessmanifests itself as a miracle, but a miracle that can be traced nearly step bystep, such as also the magnificent structure of the Mandelbrot set can be tracedstep by step. In that sense the miracle of formation of consciousness is a miracleof the complexity that can evolve from simple rules and this miracle repeats itselfin the development of each human, humans that are alike on the one side, sameas the buds of the Mandelbrot set resemble each other, and that differ on theother side, as also the buds of the Mandelbrot set are always different from eachother (up to certain symmetries). In contrast to the Mandelbrot set, the basicunderstanding of the physical world is still missing and will always be missing– a human as part of the system “world” can never understand this system as awhole, not even with the help of computers, no matter how powerful they maybe. A simple contradiction by self-reference similarly as Godel had used it toprove the incompleteness theorem – i.e. the incompleteness of our knowledgeabout the natural numbers [9].

On the other hand, in spite of Godels incompleteness theorem, sooner orlater man will probably puzzle out more and more of the facts about the naturalnumbers that are of relevance to him, and many of the remaining open questionssuch as maybe the question “Do there exist infinitely many prime twins?” willsimply remain without relevance for most people. It can be anticipated andhoped for that also in physics and biology, many of the decisive open questionswill be solved. As far as the formation of consciousness is concerned, veryessential parts of this puzzle seem to be known already. In full detail this puzzlewill likely never be tractable.

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Even if the single steps in the development of consciousness may be tractable,this does not really satisfactorily answer the basic question “How can matterproduce mind?”.

Naive overall questions such as this one always harbor the risk of misun-derstandings: How can man build a car? A single man can’t do this! Theconstruction of a car is possible only when thousands of humans interact, mineores, smelt them, cast and mill them, when other humans produce oil, and againothers process synthetics from it, in factories that have been designed and builtagain from other people, say if literally a whole army of humans work together.This army of humans generates a product whose complexity likely cannot begrasped in full by any of them; the material properties of the synthetics usedhave been optimized by chemists, the steering has been designed by engineers,the transmission by other engineers, etc.; there is such a multitude of specialdevelopments in a single car that a single human cannot understand all of them.And yet we know that the car was made by humans. Humans as a species cangenerate complex products that a single human could never make. This veryarticle is the result of many peoples work, a single human could never figure outall scientific interconnections that were explicitly or implicitly used and thatform the basis of this work.

Mind also is a very complex phenomenon linked to matter, and not a singleparticle of matter could ever produce it. The surprizing complexity of sub-structures that result from a large number of repetitions of simple rules hasalready been addressed for the Mandelbrot set or for the emergence of life.It is to be observed though that not every arbitrary collection of axioms issuitable to generate phenomena such as the Mandelbrot set; the rules used herefollow a certain internal logic, both, the axioms of mathematics upon which theMandelbrot set is built, as well as the laws of physics from which our real wordemerges. We assume for example, that the axioms of mathematics are free ofcontradictions and that they are made up in a way such that (following Galilei)the laws of physics can be written in the language of mathematics. Only thisinternal logic of the axioms of mathematics generates the infinitely fine structureof the Mandelbrot set.

Whether those events in the real world that we consider as random, i.e. asfundamentally unpredictable for humans, whether these events also follow aninternal concept, this is something we cannot know – if we knew then theseevents would no longer be fundamentally unpredictable. But if there is aninternal concept for the random events then, on the one hand, this conceptis much more complicated than for the axioms of the real numbers – else onemight find it after all, and on the other hand it will manifest itself in specificproperties of the real world, properties that must be of relevance also for thedevelopment of consciousness but that are out of reach for human understanding.Thus, the development of consciousness can be observed in retrospect, becausein retrospect, the randomness is resolved, while we are not able to explain it inadvance. But the possibility remains that the development of consciousness canbe viewed as the consequence of a possibly given but for humans fundamentallyunpredictable inner concept of randomness, and whether we view this conceptas an “absolutely incomprehensible, illimitable” god as the Catholic theologianKarl Rahner tries to describe god in [16], or as Weltgeist (“world spirit”) in the

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sense of Hegel, or as whatsoever, this is subject to our personal preferences.

MeaningIn many situations we can directly understand the purpose of an act; if a fellowhuman presses the button at a pedestrian light then typically he or she wantsto pass the street. The meaning and purpose of pushing the button is clear. Bygaining individual consciousness, man transfers the question for a meaning; hestarts the extended search for a meaning, a meaning in this world, a meaning ofhis individual life. Humans who reflect and ask themselves learn that they areunable to understand the world and its meaning. Already in the book of Job inthe Old Testament man has posed the question of the meaningfulness of onesexistence in face of catastrophes in this world. (For Job see [10]).

As a tiny part of this world they cannot understand the world in full, and inthe end nobody can give a transferable answer to the question of the meaningwithout having understood the world in the first place. Here, a transferableanswer means that the answer is right not only for oneself but also for everybodyelse. Someone who believes in Jesus may have found a meaning for himself inthis belief, a meaning that might also be a meaning to some other fellow humansbut for still others maybe not. In this respect Christianity is not transferable toeverybody else. And in the course of rapid progress of scientific, archaeological,and historical knowledge that complements each other among the different fields,the basic facts of the old religions that gave support and confidence to man – butalso triggered murder and war – and that were passed down from long beforethe times of Galilei, Newton, Darwin, or Einstein, these basic facts are subjectto doubts for more and more people. In particular, many American churchesaim for a conflict with the natural sciences, a conflict that the Catholic churchand also the German Protestant church have long left behind. The protestanttheologians Theißen and Merz for example give a historically and scientificallyquite plausible account of the life of Jesus in [17]. But also for a pastor inGermany, how difficult it must be for him to really question the belief in theresurrection of Christ – how can he as an insignificant tiny human being dare toquestion the Almighty? What kind of guilty feelings will he have to go throughfor this? And if he listens to the inner doubts as did Drewermann, Kung, orLudemann [7, 11], if he makes these doubts public, then he can no longer besustained by the church. Professional drawbacks and possible unemploymentmay be the consequence, an emotional and existential challenge. And criticsfrom Muslim background must fear even more severe consequences should theymake their doubts public [5]. A scientific – meaning open-ended – research isbarely possible within the theology of the old religions. This is regrettable, giventhat the question about god is the central question that conscious humans posethemselves.

Atheists, agnostics, doubting, questioning, or searching men must pass crisesof meaning. In that course, such a searching man naturally does not like toaccept that Christians or followers of other religions might have a Darwiniancompetitive advantage over him, simply because (according to his conviction)they believe in objectively incorrect facts, a belief which gives them a meaningand power to live. A searching man therefore cannot limit himself to search forfactual errors in individual religions or to point to such errors; he must find analternative meaning, an own goal in life.

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The established religions generally offer an answer to the question of mean-ing; Judaism, Christianity, and Islam promise eternal life and have thus raisedexpectations of life very high. For an Atheist something comparable to eternallife typically is not in sight. He may recognize that from an objective point ofview eternal life is equally likely or equally unlikely for Christians and Muslimsas it is for him, but this cognition does not offer any support and is thus unsat-isfactory. In the end he faces the question, what makes life worth living? Thisis always a personal question, whose answer can be transferred to all others justas little as the individual religions.

Even if the atheist is left to a large extent on his own with this question somepossible answers shall be exemplified. For those who have family or friends animportant meaning can lie with these fellow humans, with the good and thepainful memories with them. The meaning consists in both, the highs andthe lows of the feelings experienced with them, and by which man grows andbecomes who he is. Such memories shape everybody somewhat differently. Onecan decide that one wants life as it happens to be, or one can decide that one doesnot like this, and in this case it won’t be fun, and nagging questions will remain.This decision is nothing that is scientifically or mathematically provable, itis a decision of the will, and even with a positive decision there will still besufficiently many problems ahead, but also sufficiently many beautiful moments.And it turns out: Whether one perceives a given situation as frustrating or asagreeable, this does not only depend on the situation itself but also to a largeextent on ones own attitude – deeply impressively accounted in Viktor Franklsbook “Man’s Search for Meaning” [8], a book where the author was able toanswer the question of a meaning of life in a positive form for himself in spite ofhis detention as a Jew in German concentration camps, and after his mother, hisbrother and his pregnant wife were murdered, and without recourse to religiousfaith. Also under less severe circumstances one may quarrel with life — or onemay find satisfaction to endure hardships in everyday life. It is the attitude thatcan carry someone through life and that makes life worth living in the end.

When setting as a goal to help preserving this world that we all live in, orto engage for justice in this world, one may find a personal purpose herein andwhen orienting ones goal about the own self, one might also find a meaningherein. The worldwide observable sense of humans that often feel much morefulfilled and happy when following altruistic goals than when following egoisticgoals, this may be due to “the genes”, genes whose development, as indicatedabove, was also guided by unfathomable i.e. fundamentally unpredictable events.When believing in an inner concept in this randomness one can therefore viewthe development of these genes as an indirect consequence of this higher principlewhich – next to many problematic developments in the human existence – inthe end also conveyed “in these genes” an intuition for the essential things inthis world. Hence, if someones feeling says, not everything is given when onlyseeing the world as we can grasp it; there must be more, then he or she can livewith this personal hope and without contradiction to natural sciences, see also[14].

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Finisterre, a tiny fraction of the universeand the end of the world in the European middle ages. (Own recording).

Final RemarkKnowledge has at least two aspects. On the one side, if I hear something and

can say “yes that was known to me”, then I knew it. But this is not the sameas being conscious of this knowledge, and able to use it, and to establish linksfrom it. To this end it may be necessary to read some things several times orto write them down (or to underline them). In this sense there may be nothingnew in the above text, but nevertheless it might help to bring to ones mind someof the links between the different natural sciences and human sciences listed inthis text.

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The first 2 images are taken from Wikipedia; their resolution was compressedfor this text.

References and Remarks

[1] Essentially, the axioms of mathematics referred to in the text consist of theelementary rules that we learn in school, such as the commutative propertyor the associative property. These rules appear to describe our intuitiveexpectation regarding counting and numbers. The commutative propertystates for example that it does not matter whether I first put 3 apples on atable and then 4 more apples afterwards or the other way round. In the endthere is the same number of apples on the table. This rule is considered asmeaningful and is postulated as an axiom, but it is not proved. However,if these simple rules do hold true, then everything else that is known inmathematics about the real or complex numbers can be derived from this.These axioms are the basis for everything we know about the real numbers.

[2] The iteration referred to in the text can be described by a sequence ofnumbers x0, x1, x2, . . ., where the elements of the sequence are not realnubers but complex numbers and can be represented by points in a 2-dimensional plane. One first chooses a complex number c and starts withx0 = 0. Given an element xk of the sequence, the next element xk+1 of thesequence is then computed as: xk+1 = x2

k + c. And if the elements of theresulting sequence x0, x1, x2, . . . remain bounded, i.e. if they do not “driftoff to infinity”, then the number c is colored in black color. If this processis repeated for every single point c in the plane, one obtains a “tattered”set of black points with an infinitely complicated boundary; the image [3]shows a tiny section of this set, and also in this section the boundary isbranched in infnitely many tiny twigs. For purely aesthetic reasons, aftercomputing the set of black points, one may compute which force would beexerted on an electron located at one of the points that are not colored inblack if the black set was charged with an electric charge, and then onecould apply some color scale to visualize this force. This process generatesimages such as the one in [3].

[3] Partial view of the Mandelbrot set. Step 7 of a zoom sequence. Created byWolfgang Beyer with the program Ultra Fractal 3.

Permission is granted to copy, distribute and/or modify this document un-der the terms of the GNU Free Documentation License, Version 1.2 or anylater version published by the Free Software Foundation; with no InvariantSections, no Front-Cover Texts, and no Back-Cover Texts. A copy of thelicense is included in the section entitled GNU Free Documentation License.

[4] This is a mosaic image, one of the largest ever taken by NASA’s HubbleSpace Telescope of the Crab Nebula, a six-light-year-wide expanding rem-nant of a star’s supernova explosion. Japanese and Chinese astronomersrecorded this violent event nearly 1,000 years ago in 1054, as did, almostcertainly, Native Americans. The orange filaments are the tattered remainsof the star and consist mostly of hydrogen. The rapidly spinning neutron

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star embedded in the center of the nebula is the dynamo powering the neb-ula’s eerie interior bluish glow. The blue light comes from electrons whirlingat nearly the speed of light around magnetic field lines from the neutronstar. The neutron star, like a lighthouse, ejects twin beams of radiation thatappear to pulse 30 times a second due to the neutron star’s rotation. A neu-tron star is the crushed ultra-dense core of the exploded star. The CrabNebula derived its name from its appearance in a drawing made by Irishastronomer Lord Rosse in 1844, using a 36-inch telescope. When viewed byHubble, as well as by large ground-based telescopes such as the EuropeanSouthern Observatory’s Very Large Telescope, the Crab Nebula takes on amore detailed appearance that yields clues into the spectacular demise ofa star, 6,500 light-years away. The newly composed image was assembledfrom 24 individual Wide Field and Planetary Camera 2 exposures taken inOctober 1999, January 2000, and December 2000. The colors in the imageindicate the different elements that were expelled during the explosion. Bluein the filaments in the outer part of the nebula represents neutral oxygen,green is singly-ionized sulfur, and red indicates doubly-ionized oxygen.

Permission details: Material credited to STScI on this site was created,authored, and/or prepared for NASA under Contract NAS5-26555. Unlessotherwise specifically stated, no claim to copyright is being asserted bySTScI and it may be freely used as in the public domain in accordancewith NASA’s contract. However, it is requested that in any subsequentuse of this work NASA and STScI be given appropriate acknowledgement.STScI further requests voluntary reporting of all use, derivative creation,and other alteration of this work. Such reporting should be sent to copy-right@stsci.edu.

[5] Reza Aslan: “No god but God: The Origins, Evolution, and Future ofIslam”, Random House, 2005.

[6] Frans de Waal: Our Inner Ape, Riverhead Books New York, 2005.

[7] Eugen Drewermann: Den eigenen Weg gehen, Piper, 1995.

[8] Viktor Frankl: Trotzdem Ja zum Leben sagen, DTV, 1998. (related Englishtitle: Man’s Search for Meaning, Beacon Press, 2006)

[9] Kurt Godel: Uber formal unentscheidbare Satze der Principia mathematicaund verwandter Systeme, Monatshefte fur Mathematik und Physik Nr. 38,Akademische Verlagsgesellschaft, Leipzig 1931, 173–198.

[10] Job: The book Job in the Old Testament describes an upright and exem-plary godly man Job. God makes a bet with the devil that Job will remaingodly even when the devil takes away from him everything he has, his for-tune, his health, his kids. And thus Job learns about one blow of fate afterthe other, and he bemoans his fate very much. His friends try to supporthim with their advice but they disappoint him on top of his poor fate. Inthe end God gives him back wealth, health, new kids and a blessed life.The first kids remain the victims of the silly bet with the devil.

This story has been written in several stages over a longer period of time andis based on an originally Sumerian reference. What this story exactly means

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to say this is left up to the interpretation of the reader. It is conceivable thatthe only thing that really counts is the eternal life with God in the hereafter.There, all hardships of earthly life will be resolved, and in retrospect theearthly life is just an insignificant step whose only goal is the qualificationfor eternal life. Against this background God knew that Job will qualifyin spite of all blows of fate and that he will be a role model for all otherhumans in his sufferings. In the hereafter Job will also be thankful that inhis earthly life he could be an example for the irrevocable loyalty of Godand that he could thus be a tool for Gods good will. Together will all hischildren he will have part in Gods glory.

[11] Hans Kung: My Struggle for Freedom: Memoirs, New York, London: Con-tinuum, 2003.

[12] William F. Martin (2017): “Going back in genes”, The Biologist Vol. 64,20–23.

[13] Lynn Margulis, Dorion Sagan: What is Life? Simon and Schuster, NewYork 1995.

[14] K.R. Miller: Finding Darwin’s God. A scientists search for common groundbetween God and evolution, Harper Collins New York, 1999.

[15] Simon Conway Morris: Life’s Solution. Inevitable Humans in a LonelyUniverse, Cambridge University Press, New York 2003.

[16] Karl Rahner: Foundations of Christian Faith: An Introduction to the Ideaof Christianity, The Crossroad Publishing Company, 1982.

[17] Gerd Theißen, Annette Merz: Historical Jesus: A Comprehensive Guide,Fortress Press, 1998.

[18] A.N. Whitehead and B. Russell: “Principia mathematica 1-3”, Cambridge:Cambridge University Press (1910–1913).

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