What makes us trust God?

Truth and trust - a mathematician speaks of God

Arnold Neumaier

Revised version of a lecture at the University of Kaiserslautern
held on April 24, 1991


miniporta 7 student mission in Germany (SMD)

`` The Truth Will Set You Free ''

I come from Freiburg - Freiburg has an old university and an old college building. Outside the college building is a sentence above the portal that says `` The truth will set you free ''. The founders of the university considered this phrase to be the motto of science. But nowadays the statement made is no longer so self-evident. Science embodies truth for many, but at the same time many feel enslaved by this science in some respects. We have to run after things in order to put back in order what we have neglected and what we are to blame for in the application of the undesirable side effects and possibilities of abuse that science has produced.

Perhaps it is worth looking at the context from which the quote comes. It comes from the Bible, from the Gospel of John. Since the Bible has become largely foreign to many nowadays, I would like to read something from it here, and also quote some things afterwards. The context in question is a conversation between Jesus and the people. Then he says: '' 'When you will crucify the Son of Man, you will see that I am sent from above and do nothing of myself. But as the Father taught me, so I speak, and he who sent me is with me. He doesn't leave me alone, because I always do what he likes'. When he said that, many believed in him. Then Jesus said to the Jews who believed in him: 'If you will abide by my word, you will truly be my disciples, and you will know the truth, and the truth will set you free'. They answered him, `We are Abraham's children and have never been in bondage to anyone. Then how do you say 'you shall be set free'? Jesus answered them and said, 'Verily, verily, I say to you, whoever commits sin is the servant of sin. The servant does not stay in the house forever, the son stays forever. If the son sets you free, you are really free '' ' (John 8: 28-36).

I just want to leave it that way for now, and you can make your own thoughts about it. Just a note: Jesus says: 'God, the one who sent me, is with me; he doesn't leave me alone, because I always do what he likes'. That is also what a Christian wants, what he longs for, what he cares about, that he does what pleases God at all times. From this he draws joy and backbone in his life, the meaning to be able to shape his life and the peace that enables him to overcome and cope with the turns that life takes.


Truth and Faith in Science

This lecture is supposed to be about truth and trust. In the first half of my talk, I want to discuss what science has to do with truth and trust. The central thesis is that science is based on truth on the one hand, but also on trust on the other. As a mathematician, I am interested in definitions of terms; I will offer you the following definition as a starting point, which I will explain a little afterwards. I would like to describe truth as knowing what is certain, and trust as relying on what is reliable.
Science is based on
truthandtrust
Knowledge of the saferely on the reliable
2 + 2 = 4 tau_Neutron = 898 + -16s
E = mc ^ 2 Delta x Delta p> = hquer
proof rating
Truth values Probabilities, areas of confidence
security risk
exact information Mean values
Logic, analysis Probability theory, statistics

We can see the difference between the two terms if you look at the two columns in the table here: on the one hand the proverbial truth, `` Two plus two is four, which is obvious to everyone here, and on the other hand '' tau-neutron equals 898 plus / minus 16 seconds ": something that you know pretty well, but not so exactly - and where you then specify the degree of reliability using plus and minus; in this specific case, the lifetime of neutrons that I copied from the physics book.

Now there are not just mathematical truths; there are also physical truths. There is one on the left that you probably all know, that is Einstein's famous `` E equals m-c-square '' relationship between energy and mass. On the right-hand side we have something correspondingly important, but perhaps not that well-known, that is Heisenberg's uncertainty principle: `` Delta-x times Delta-p is greater than or equal to h-across ''. This says something very fundamental about the nature of physical truth, namely the following: Although science tries to be precise, it has limits which it cannot exceed. In the present case, the inaccuracies Delta-x in the position measurement and the inaccuracies Delta-p in the pulse measurement cannot be made arbitrarily small by measuring increasingly precisely. Rather, the laws of nature draw fundamental limits for the product of inaccuracies with Planck's quantum of action h-across. So with what you can find out about nature you have to withdraw to less certain things, to statistics and so on. In this way, the knowledge of what is secure becomes a limitation to what still seems reliable.


Proof and evaluation

On a more theoretical level, truth is characterized by being able to prove true statements, while trust is characterized by evaluating statements and viewing them as more or less reliable, as the case may be. On the mathematical level, on the one hand, this corresponds to the truth values ​​zero and one, so one can say that one is true (one), the other is false (zero). Instead, at the level of trust, one only has probabilities which then lead to areas of trust, such as the one given above for the lifetime of the neutron. You can state that I think it is likely or unlikely that the service life will be one way or the other, and in between there is a certain limit area that indicates in which area one is just still satisfied if the alleged fact so far agrees with reality . Correspondingly, one has security and mathematical accuracy on the truth side; on the trust side you have risk and mean values. This difference in the choice of words is characteristic and indicates two completely different attitudes. In fact, very different tools are required if one tries to grasp the two worlds scientifically: the world of truth and certainty is mathematically captured by logic and analysis, the world of trust and risk by probability theory and statistics.

Axioms

In both cases, whether it is truth or trust, one must make assumptions about reality. These assumptions about reality, formulated mathematically, are on the truth side the axioms, principles that are assumed to be valid. On the trust side, if one wants to be mathematically precise, one must define probability distributions as a basis, which are also assumed to be valid. So you assume you know what is most likely, what is less likely, and what is fairly unlikely. Both are assumptions about reality that someone trying to describe reality simply makes; which he selects with the intention of matching reality as well as possible, but which in principle are not proven. If you have studied mathematics, you will know that, for example, the axioms for real numbers in most books are just presented, with some motivation, but no proof. The books that prove the rules for real numbers assume that the axioms for natural numbers are correct without proof. In a sense, the axioms fall from heaven - the famous mathematician Kronecker once said at the beginning of the 20th century: “God made natural numbers, everything else is the work of man.” We simply start from the axioms; if you don't like that, you can't do math.

But of course it is not that the axioms for the real numbers were simply invented; rather, they have developed in historical processes and have proven to be very useful and reliable. This is exactly what is happening everywhere in science as it progresses. Mathematical axioms, but also the probability distributions that a physicist uses to describe the radiation background from space and to bring it into harmony with his theories, both have to prove themselves in order to be trustworthy. And they have to be trustworthy in order to survive - otherwise new, better theories will emerge which are then more likely to be accepted and the old ones to be discarded.


falsification

From a philosophical point of view, there is the principle of falsification, according to which additional confirmations of assertions do not count very much, refutations of assertions are even more important. The philosopher Popper even makes this the decisive criterion for real science, whether a theory leads to assertions in previously unchecked areas that appear risky a priori - i.e. before the theory is examined - but still prove themselves on subsequent verification. Others, according to the science historian Kuhn, have shown that real science does not quite meet this ideal criterion, since many theories are useful even though it is known that they do not make correct predictions everywhere. What remains universally valid about Popper's principle, however, is that a theory that repeatedly fails to prove itself will no longer be pursued as soon as a more reliable one appears on the horizon.

Standards

The question still remains, where do the assumptions that one makes as axioms come from. I have already briefly touched on an answer to this and would like to go into it again in more detail. I would like to address four sources. The first is tradition - you trust in what the teachers or parents have always trusted. Next up is intuition - you have a feeling for the thing, put your feeling into thought, and hope that intuition carries through. Then the relevance - there are differences, more important things and less important things; by basing everything on what explains and connects what is important, one often finds the crux of the matter. Finally, there is elegance - some things are more beautiful, easier to convey or rather inspire the listener, other things not so; and what arouses enthusiasm is more likely to be adopted by others.

Further criteria that decide what assumptions are made are based on personal or cultural developments. Things that you come across again and again are seen as conspicuous and more important, especially when you have to plan ahead, i.e. to foresee the future. And if you have to rely on making decisions - good decisions that, in an uncertain environment, rely on being able to make predictions that are as reliable as possible - then, in this context, probation and success are a crucial assessment criterion.


quality

If one looks at what all these headwords have in common, one sees that the quality of the axioms determines which judgment one makes about the acceptance of axioms. Quality is of course something subjective and controversial, and such things are usually not discussed in a scientific lecture, but are somewhere in the background. They are in the background precisely because they are subjective and controversial because everyone thinks differently about them. It is more effective and safer if you limit yourself to what you can reliably pass on - and those are the purely factual things, these are the results of the theory.

But for the life of the individual who has a future ahead of him that he must plan and who wants to think about making the best possible use of the world and his life - such questions play one role for the life of the individual bigger role, and it is a pity that they are often neglected in the standardized world of studies.

It is therefore interesting to see that the subjective and the controversy, namely the problem of quality, is to be found in the very center of the objective world of science. On the borderline between subjective and objective - that on the one hand science is experienced as objective, and on the other hand that science in its foundations is often based on subjective and sometimes even questionable assumptions - on this borderline all the central philosophical questions play out, which makes physics interesting even for laypeople, for example, because one can speculate: What is actually the cause of the world? Why are the laws of nature just like that and not different? How much can you actually learn about the world? Is everything random or determined? Why is there so much regularity and beauty in the world, and so close by is disorder and chaos? What actually is life, an atom, a crystal?


interpretation

In any case, in order to step between science and reality, it is necessary to make an interpretation, to apply what one learns to reality. You can do this on two levels, on the one hand theoretically and on the other hand experimentally. The theorist studies the axioms, which in mathematics are more or less arbitrarily - but on closer inspection mostly well motivated - chosen axioms, and in physics proven natural laws. He doesn't usually question them, but says: that's the way it is. For example, he can say that quantum theory is the theory of reality. He knows that there are still problems somewhere, but that is not so important to him at first. This is an axiom for his investigations, and based on it he draws his conclusions, these are the predictions of the theory.

What can still be done very well in physics becomes problematic in other areas. Let us take a look at economics, for example: If one is supposed to make predictions about which political means are most effective in combating unemployment, for example, then the predictions are much more questionable. Usually because the axioms on which the prediction is based are correspondingly questionable.

On the other hand, there are the experimentalists, who take whatever models the theoreticians provide and check whether these are useful in situations that are of interest in practice. Both theory and experiment play together and combine science and reality.


prejudices

Now I dare to call the axioms and the laws of nature prejudices that a human being - or rather humanity - has. But by prejudice I don't mean anything negative at first, but what it literally means - a prejudice, i.e. a judgment before you yourself observed. Much of what you learn in your studies is things that you take over from other people. You take on these things before you are confronted with reality, namely with the application, which only begins afterwards - during an internship, with your thesis or at work. In this respect, it is a preliminary judgment, something that you have formed before you can use it. And the question is not so much whether or not you are prejudiced because everyone is prejudiced. Almost everything a person does is based on prejudice, because only with a small fraction of them does he have the opportunity to really test it for reliability in his life.

But what matters is that one does not take up the prejudices that one has arbitrarily, but that one examines them and adjusts them to reality. That happens in the scientific tradition - it is done everywhere, and you do it even where the theories don't quite fit with reality: then you start to change the interpretation a little. In a certain sense you are playing with marked cards, you are practicing '' data massage '' in the sense of moving the data back and forth until it roughly corresponds to what you want. This can be a very questionable business, but it can also make a lot of sense. Because the aim of every theory is to say something about reality with it. Above all, it depends on whether you want to cheat with the data or whether you want to capture reality with the data - and that then decides how you `` massage '' the data.

In any case, the axioms and the interpretation often decide what we consider reality. Reality is somehow, and every person finds a certain approximation to reality, a personal view of the world. Such a worldview is more or less in line with reality: in questions in which it is particularly important to one personally and in which one has already had many bad experiences, it usually corresponds better because one has paid dearly for one's mistakes; in areas where someone has hardly any personal experience, the ideas are usually only roughly correct, and sometimes hair-raising wrong.


Axioms shape reality

It has been the same in the history of science. The axioms decided what to consider as reality. I would like to highlight a few major steps here. In antiquity, the exact science of geometry was essentially as it was built up by Euclid - synthetic geometry. Reality has been interpreted in the light of what one could think. Points, straight lines and circles were considered to be the perfect and therefore fundamental shapes, and the Greeks made the geocentric view of the world out of date, but very successful at the time. This was recognized as reality because it could not be imagined otherwise, because the chosen axioms (of the perfect figures) no longer allowed any other choice. The name of Ptolemy stands for this system because he adapted it to the increasing demands of astronomers for accuracy through increasingly complex corrections.

Later, in the 17th century, with Descartes, analytic geometry emerged, and with it mathematical aids that allow one to deal with geometric shapes more precisely. Shortly before, Kepler had discovered that the planets move in ellipses rather than in increasingly corrected circles. Because analytic geometry made a much greater variety of forms of calculation accessible, one soon saw nothing particularly perfect in the circle; the ellipse described the reality of the planets better and was therefore quickly accepted. The resulting freedom in the formulation of axioms was used again and again in the following years to adapt the worldview to new possibilities of expression by reformulating the fundamentals.

theoryreality
synthetic geometry (EUKLID, PTOLEMÄUS) Points, straight lines, circles
analytical geometry (KEPLER, DESCARTES) versatile geometric shapes
Analysis (NEWTON) Solutions of differential equations
non-Euclidean geometry (RIEMANN, EINSTEIN) curved space, big bang
Stochastics (BOLTZMANN, HEISENBERG, PRIGOGINE) Coincidence, self-organization

Fifty years later, Newton, who was a mathematician and physicist at the same time, developed analysis. Analysis offers possibilities of previously unimagined variety and precision to describe continuous events and to model movement processes. Since then, movements have been represented mathematically by solving differential equations. Because Newton saw reality in the light of his new axioms and methods, he found the law of gravitation and the basic equations of mechanics - which have proven themselves for centuries and still prove themselves today in many applications.

Later there were mathematicians who invented so-called non-Euclidean geometry, initially as a toy or as an answer to an old philosophical question that I do not want to explain further here. Einstein then used this to bring physics a little closer to reality by postulating that space is curved. One of the consequences we draw from this today is that it is commonly believed that the world came into being with a great explosion.

The last revolution in the basic assumptions of physics came with the introduction of stochastic methods, methods of chance, which I want to associate with names like Boltzmann, Heisenberg and Prigogine. The point is to still get a grip on what is random, what you don't have in your hand. As long as the coincidental was only that about which nothing could be said, there was no point in building any theories on it. But because chance has become mathematically comprehensible, one could - despite chance - gain knowledge from it. This has led to notions of self-organization that are still very relevant today, and where the exact consequences of the ideas based on it are still being worked out, by many people around the world. It is one of the most interesting areas of development in physics, chemistry and biology today.


Limits of Theory

So one system of axioms replaces the other, and you see: depending on which ideas and assumptions you base the world on, you get a different idea of ​​reality. Such changes in theory are usually based on the fact that one realizes that a theory has limits and that one cannot explain everything so well after all. If then, as I said before, the attempt to bring theory into harmony with reality is less and less successful, the data massage becomes more and more implausible, and the contradictions can no longer be swept under the carpet of interpretation - then at some point you notice one that the previous theory resembles a Procrustes bed.

In case you can't do anything with the Procrustes bed, I would like to remind you of an old story. Procrustes was a giant from Greek mythology, a highwayman who invited the people he met to stay in his cave. He had a short and a long bed; He put the tall people in the short bed and chopped off their legs, the short people he put in the long bed and tore their bones apart so that they would both fit into the bed. That is exactly what you try to do in practice with a theory that doesn't really fit. You want - in the picture - to adapt the bed and the person to one another, and if you exercise such violence as Procrustes, then it just goes wrong. Sooner or later you will no longer have confidence in such beds; you want to have matching beds. This then leads to what the philosophers of science call a paradigm shift, that someone becomes creative enough to present a new idea of ​​the world that is better adapted.


Complexity and uniqueness

Then there is a second limit to the theory: besides the theories that turn out to be poorly compatible with reality, there are also aspects of reality that are so poorly compatible with any theory because they are so complicated that you can no longer be precise can say. Instead of still searching for the exact truth, one must increasingly replace knowledge of the truth with trust in the reliable, and the theories take on a completely probable character.

And then there are such complex systems that you can say very little about because everything you observe is unique, or at least the most interesting aspects are unique. The human being is one of these complex systems. When one has to do with the unique, the trust is no longer even statistically measurable, but then the only thing that can still be done is the attempt to recognize a qualitative regularity in all the unique. That's exactly what we all do when we meet other people. We try to find out what he or she is like, and we find out that there are certain regular traits that then make up a person's character. From what is regular about a person, we deduce whether he deserves trust and how much trust he deserves. That’s all that is left of predictive power.

So find - from the level of mathematics, in which you can determine everything exactly, to physics, in which you can perhaps say a lot more precisely, to biology, in which the abundance of phenomena almost exceeds the ability to organize, right down to humans - an increasing shift from the left side of truth to the right side of trust is taking place. Human togetherness is primarily characterized by the degree of trust or mistrust that one shows in one another.


Does God still have a place in a world shaped by science?

Now I would like to ask the question whether there is still room for God in a world shaped by science. This question is often answered in the negative; it is often thoughtlessly negated, by some in spite of many thoughts. It is affirmed by me; but the fact that one can have different opinions suggests that what matters is which axioms we recognize, namely what we base our assumptions about the world on. Now every person is free to base his view of the world on any assumption. But when he makes bad assumptions, he suffers from not getting a grip on reality, and therefore everyone looks for good assumptions. On the scientific side, you have control options through repeatable experiments. On the personal side, this doesn't work so well because of the uniqueness of personalities; therefore the variety of assumptions that are made in the world of man and in the world of faith is much greater than in the realm of science.

Now, as in science, we do not want to ask about the proof of the axioms, because - as I said - that is not possible. Rather, we ask how the axioms, once selected, prove themselves in practice. If they work well, one can be satisfied; if they do badly, one is dissatisfied and tries to change the axioms.

`` Test everything and keep what is good (1 Thessalonians 5:21) This recommendation of the Apostle Paul is the characteristic attitude with which all successful science proceeds. This attitude is fruitful and beneficial not only for science, but also in the personal life of every person, which Paul writes in a letter to friends in Thessalonica - today Salonika - in Greece - which has been passed down from the Bible. It's a maxim that I found interesting even before reading Paul, and I've tried to apply it in my life. After a long search, I found the Bible to be a reliable basis for knowledge of God, but that was not always the case. I was an atheist for many years; a thoughtful atheist who has given a lot of thought to what the world might be like and what the role of humans is, and I hadn't seen any place in it for God. I thought God was an invention of man - certainly a successful invention, since it gives support to many people, as I had observed - but something that was not really appropriate for a scientist. Only in the course of time did I experience God differently. It was really a surprise to me to find out who he really is! That is why I would like to put the second half of my lecture under the heading: 'God is different from what we think'.


God is different from what we think

Anyone who has not had a personal experience with God carries around an image of God that is shaped by what he has heard and what he has experienced in people who more or less distort God. He may have known Christians who were anything but an example to him and then concluded that God had to be like that too. But whoever gets to know God better then realizes that he has been mistaken. It's a lot like getting to know people. If you don't know or have only seen a couple of times, you judge by superficial impressions, by how he appears in the crowd, what you hear him say, what others talk about him. When you get to know someone personally and win his or her friendship, you see them in a different light. Then the talk of the others and the anonymous mask become irrelevant, and one recognizes the actual worth or worthlessness of the person. In the case of God, it turned out to be very valuable to me to get to know him.

I would now like to single out a number of points where God is different from what we might think.


God is unique

Since God is unique, he cannot be scientifically grasped. For, as we have seen, the unique eludes the scientific method; In order to be able to check anything at all, this needs regularity. On the other hand, he is always the same, and you can experience that - and that is why he is trustworthy, just like us people who are constant and prudent in all their uniqueness and unpredictability, appear trustworthy.

God is like a person

When you hear and see how the Bible speaks of God and how people who know God speak of him, then in many ways he is like one person. He acts, he thinks, he judges, he plans, he is happy, he suffers, he has likes, he dislikes, he loves and hates, he does this and does that like a person. Whether God is actually a person is beyond our grasp; he is much more than a person in other ways. But it is a very good comparison to take God as a person; and since when we talk about God we have to use a language that is accessible to us, the view of God as a person is the most fruitful. There are also other ideas about God, God as an abstract principle. But if one takes such ideas as a basis, then God remains inaccessible, hollow and empty, and he does not affect one's personal life. For people with such a concept of God, God becomes worthless, it no longer matters to them whether they deal with God or not, and then at some point they let it stay. But the Bible doesn't talk about God like that. Rather, with the qualification I mentioned earlier, God is a person for the authors of the Bible.

God is powerful

God created the world that we experience and in which we live, and He maintains it to this day. And I believe, in accordance with the Bible, that he takes care of all the necessary details within the framework of the laws of nature, and thus rules the universe. How far this goes, I would like to demonstrate with a quote from Psalm 139, where it says of him: `` For you prepared my kidneys and formed me in the womb. I thank you for being wonderfully made; your works are wonderful. My soul knows this '' (Psalm 139: 13-14). This is best seen by biologists. If you are a biologist - but also otherwise - you know that man is a very wonderful creature. Whether you blame God for that, or chance, or self-organization or evolution, that is another question. But nobody can evade the wonderful thing about people who consciously perceives how everything works in healthy people and harmonizes with a whole. And according to the Bible, it is God who takes care of it, who creates our being before we are born, so that we become what he imagines. In view of what man knows and can do today, one wonders how God can act in the world at all. Is there room for it in our scientific worldview?

God is the master of chance

I am convinced that the essential thing is that God intervenes in the world where chance is decisive for the future. Coincidence is often irrelevant and then it is no longer relevant to bother about it. But sometimes it makes a big difference how the coincidence turns out to be.

Mathematicians talk about the exponential gain of fluctuations. A fluctuation is something random, something small, a slight deviation. An exponential gain, which means that something doubles in equal periods of time, so that what is only one at the beginning is two after a unit of time, 1000 after 10 units of time and an astronomical amount after 100 units of time. And therefore, no matter how tiny the cause was at the beginning, it is obvious in the end. Jesus speaks of the kingdom of God in this way: `` With what do we want to compare the kingdom of God, and by what parable do we want to depict it? It is like a mustard seed: when it is sown in the country, it is the smallest of all the seeds on earth. And when it is sown, it rises and grows larger than all herbs and branches large branches so that the birds can dwell under the sky under its shadow '' (Mark 4: 31-32).

On another level, mathematicians speak of bifurcations in the context of so-called catastrophe theory. (I don't know how many mathematicians there are; you do that in higher analysis when you consider dynamic systems.) The essential thing for us is that sometimes the continuity of nature suddenly breaks, something discontinuous happens. For example, if I bend this rod here, it can be bent.But if I bend further and further - which I don't want to go too far, but you can imagine it - at some point something really happens that is out of the ordinary, namely that the rod breaks. This can be expressed mathematically on the dynamic level by bifurcations, and on the static level by the first eigenvalue of some differential equations. (If you don't understand that, it doesn't matter much: you can understand God without math - but some insights he has reserved for mathematicians.) But if you look closely at what's happening, there's a tiny difference between whether the stick is still holds or whether it breaks. And this is exactly where God intervenes.

Further points in biology are the fertilization process. This is a process in which chance plays a big role, and where very minor changes can have big consequences. Random mutations in individual genes can have a very drastic effect on what has been developed. Or, if you try to think about how the spiritual is related to the material, then there are famous people like Popper and Eccles who ascribe the will in the brain a certain possibility of influencing statistical differences. So it happens that here, too, only minor, hardly measurable changes are necessary in order to achieve great things. That God has all these things in hand is a crucial axiom of the Bible.

By controlling chance, God creates the new and the unexpected. Not so long ago we saw a drastic example of this in public: how the wall in the GDR was opened. Chance played a not insignificant role in this. Because Schabowski accidentally read the document that was to be announced 8 or 9 hours too early on television, the border guards were not prepared and therefore gave everything free rein. If everything had had its socialist order, everything would probably have turned out very differently. By a small coincidence, God opens the floodgate to the unforeseen.

There are several places in the Bible where this is also the case. I would like to read a small excerpt from the story of Gideon from the Book of Judges. Gideon is an insignificant man, but God has chosen to deliver the people of Israel from their oppressors. Gideon doesn't know God well, he wants to trust him and yet has doubts whether he can rely on him. God expects unheard of things from him, he should rebel against traditional things and entrenched situations. As a test of whether he can really rely on God, he makes a deal with God and says:

`` If you want to save Israel by my hand, as you promised, I will put shorn wool on the threshing floor. If the dew is alone on the wool and the whole ground is dry, I will know by it that you will save Israel by my hand, as you have promised. ' And so it happened. And when he got up early the next morning, he pressed the dew out of the wool, a bowl full of water! And Gideon said to God: Your anger will not be kindled against me if I speak again. I just want to try again with the wool. It was dry on the wool alone, and dew on the whole floor. '' (Judges 6: 36-39) - So just the other way around as before. Apparently Gideon was a scientist who backed up his experiments with control experiments. He had thought to himself that I want to make sure that this is not something unknown but lawful going on where God's special activity would not be necessary, and so he put God's abilities to the test. `` And God made it so in the same night that it was dry only on the wool and dew all over the ground. '' (Judges 6:40)


How the unbelievable can become understandable

Of course, all of this seems very incredible to us - and there are more stories in the Bible that seem incredible. Some stories become more understandable over time, as you broaden your own horizons and learn more. Other things remain as incredible as they are. As before, it is again the question of how much trust one has, this time in the tradition, whether things are presented correctly or not. In this particular case, however, I can tell you something specific that amazed me extremely. I often have to take the minor examination in mathematics from graduate physicists; The diploma theses are always included with the examination papers, and I have made it a habit to read them through to see if there is anything interesting in them to broaden my horizons. Now one of the physicists (by chance) did a diploma thesis on concentration phenomena, and there he discovered a phenomenon that explains exactly the first case, namely that under certain atmospheric conditions it can be that the grass remains dry and the wool becomes moist because the dew is focused on the wool. This is because wool and grass have a different physical structure. In a limit area, when the temperature is at a certain threshold under certain humidity conditions, the wool already attracts the water and the grass does not yet. So God only had to manipulate the local temperature and humidity to be (coincidentally) correct in order to satisfy Gideon's request. Mathematicians and physicists know how sensitively - chaotically - the weather can react to small causes - it is not for nothing that weather forecasts are still rather uncertain, even despite the massive use of weather satellites and computers. (Perhaps someday someone will find an explanation for the second, opposite case.)

So we see that things that are inexplicable to us are often inexplicable to us only because we do not know the mechanisms. Sometimes they are inexplicable to us because things are just wrong and someone has told them exaggerated, or someone has taken them from others in good faith, or out of misunderstanding. It is often difficult to decide what is causing what and if something is trustworthy, and one has to weigh things up. Some things turn out to be trustworthy, what we initially judge as unreliable based on what we have experienced ourselves, and with some we are downright carelessly gullible, where it only later turns out that we were mistaken.


God directs human culture

By mastering chance, God not only creates the new and the unexpected, but he also creates the gradual and in this way guides the cultural development of humanity. This is very clearly anchored in the German language: Our creative activities will come from such idioms as '' Einfall '' or '' I get an idea '', or '' I see the light '', '' to me good thoughts''. These are all things where we ourselves are passive, something comes up, we get the idea, something dawns on us, the thoughts come - we are not actively involved at all. We have prepared the creative act when we have taken care of a favorable atmosphere or where we have tried to understand something. But then, all of a sudden, it happens. If you describe things like this mathematically - there are experiments like this in computer science, where it has a lot to do with pattern recognition and similar things - then chance again plays a major role. The crucial point is this: wherever incomprehension turns into understanding, there is only a small threshold, and it is precisely at this point that God intervenes. We are '' creative '' because we draw from what God gives us.

What I wanted to show: One can certainly argue on a scientific level how God intervenes in the world, with decisive effects on us humans, without having to violate the laws of nature. God, who keeps the whole world in harmony, created the laws of nature so that they support what he does and not that they put him in chains.


God acts optimally

To keep the fate of the world under control, God works extremely economically. He not only works so economically that he moves things where they can be moved with minimal effort: If you want to shape people, a lot more work is required to shape a full-grown person than to make small corrections in the chromosomes, which are necessary to let one person become one way and another person different. In this way, God achieves an inexhaustible diversity in an economic way in biology.

Physics, too, testifies to such effectiveness principles of God. God is an ideal engineer who does not waste a bit of energy: there is the law of conservation of energy. God is out for optimal effect, as the operating principles in mechanics show. The second law of thermodynamics shows that God has made sure that the inner diversity (entropy) of the world always increases. And the law of minimum entropy production shows that God also handles the available information optimally.


Miracles reveal repairs

Then there are exceptional cases that can best be understood by comparing the world with a computer. A computer needs occasional maintenance; or a repair is due; or a program is changed - and then in a computer where the routine things happen, unusual things happen that no one would have expected who has sat down and statistically analyzes what is going on in the processors and in the memory memories during normal operation goes. Extraordinary things just happen at extraordinary times that do not conform to the rule. When we do research, we catch the rule, but we don't catch the exceptions; therefore they remain inaccessible to scientific research.

This comparison of our world with a computer creates the possibility the To understand miracles that go beyond the scientific framework. I say nothing about which miracles actually happened, and which only became miracles through careless tradition, even though they originally had a perfectly natural explanation. Since the judgment about it depends on personal assumptions about what is still accepted as real, there are very different views about it even among Christians. The Bible is written by men and therefore also afflicted with human imperfections; but God has made sure that even through these shortcomings, His Word will be empowered to express in the Bible and provide us with guidance, advice, comfort, and hope. The hope that God can make the hopeless into reality and sometimes does it is one of God's great gifts to us, and has already saved many from despair.


God loves us humans

The love of God is literally in the talk of the `` dear God '' - but this expression has become an empty phrase and deceives the true nature of God. God unites love with sovereignty, lordship and righteousness. God loves us human beings as those he created, `` in his own image '' so that he has partners who have something of his own kind. As our Creator, God knows what is best for us and cares for us to act accordingly. If we adhere to his will, the natural consequence is a fulfilled life, a life that fills us in his alternation between rest and demand, in the security of God. If we neglect his will and go our own ways not paved by God, then we forego his blessing.

Life without god

The natural consequence of this is initially excessive demands on ethical decisions. In the book of Genesis, the book of Moses, this is beautifully expressed in the story of the Fall. Adam and Eve's disobedience fulfills part of the serpent's promise: `` You will know what is good and what is bad. '' But as is the case with the devil's promises: they are tempting, but they have a diabolical one Hook, and he won't tell us; it is his gain that we fall for it. In the case of Adam and Eve, they now know what is good and what is bad, but they are completely overwhelmed when trying to do what is good. The devil cannot help us with this, and he is not interested in it at all. His aim is to make evil seductive and to blind us to the evil side effects in our good intentions. Our world suffers from this to this day, and our science with it: In the frenzy of progress, the associated threat and destruction is downplayed.

The next stage of deviating from God's way is alienation; As a result of the fall of man, we are told: “You will nourish yourself with hardship all your life.” As many of us know, work can be extremely fun, but it can also be an unheard of frustration. I believe that the original quality of the work was the beautiful, the fulfilling. Not necessarily the easy thing, but something that is fun despite all the difficulty. The alienated, boring, agonizing work that we often experience today is one of the consequences of our not behaving as God wants us to.

When the alienation has progressed enough, a sense of futility arises. Ultimately, annihilation occurs, which in some people leads to physical annihilation by committing suicide. With other people it leads to a psychological annihilation in that they feel as nothing and become nothing. And if you have a materialistic view of the world, then in the end all that remains of being human is the accidental non-being, a speck of being in the infinite universe.


Jesus Christ - Center of Truth and Trust

While the Old Testament paints a picture of God for us, who is often distant from us because our fault separates us from him, God in the New Testament has become humanly close, accessible and understandable to us through Jesus Christ. According to the testimony of the Bible, Jesus is the guarantee that we can get out of confused situations again by being forgiven. He enables us to start afresh through his spirit. He shows us how to act lovingly and not to let the circumstances make us bitter. According to the Bible, Jesus is the center of truth and trust.

I would like to read two passages from the Gospel of John. One is in John 14: '' I am the way and the truth and the life. Nobody comes to the father except through me '' (John 14: 6). Through Jesus the truth gains a personal quality. If we Christians try and strive to become more like him, then that is a striving for truthfulness, which on the personal level is similar to what a scientist also has on the factual level, to which his striving for truthfulness in the cognition of material reality realize addiction.

And another quote from John 11: ''I am the resurrection and the life''says Jesus, '' Whoever trusts me will live, even if he dies, and whoever lives and trusts me will never die '' (John 11: 25-26). This promise of eternal life is one of the central statements of Christianity. It allows us to be different from many people. We don't need to feel bound by practical constraints because we have eternal life. It doesn't matter that tomorrow or the day after tomorrow or next week or at the next election we will have achieved this or that. With this we can avoid the practical constraints because we live according to God's standards. God is an eternal God; he promises us eternal life. This gives us the opportunity to see beyond our own horizons, to meet the world with different eyes, and to act with love and care where, on the surface, practical constraints force us to make bad compromises.


God gives us freedom to choose what is good

God has given us the freedom of will that we can do what we want. But at the same time he has reminded us again and again that it does not make sense to simply do what we can think of, but that we should choose life.

Freedom serves to enable us to act with love: a robot cannot adapt to unique situations; a loving person can and does it. And love only thrives in freedom. I would like to read something from Deuteronomy, the Deuteronomy, about this. The book from which this section is taken consists largely of Moses' farewell speech, where he resigns as leader of the people of Israel and hands over his office to Joshua. In his report he takes stock of what he has done and wanted during the entire time he has led the people. At the point I read he is speaking in the name of God:

`` See, I have presented you today with life and good, death and evil, '' - you, that means the whole people, each individual, - `` I take heaven and earth to witness over you today; I have presented you with life and death, blessings and curse, so that you may choose life and stay alive, you and your descendants, loving the Lord your God and his Voice obeys and trusts him. Because for you that means that you live and grow old and stay in your country '' (Deuteronomy 30:15, 19-20). It is for our own benefit to choose life. If you later work as a scientist, then you have the possibility of researching and acting on behalf of life or on behalf of death; it is important to always be aware that one is choosing life.


God - resting point and challenge

God is there for everyone. He is not a God for individuals, not just God for Christians. He is not only a god for people with high moral ideas or for people with special protection needs, but he is there for everyone.

For the strong it is a challenge. Most of you will know the Sermon on the Mount in whole or in part, where Jesus makes an unprecedented claim on us humans, where he finally goes so far that he says: `` You shall be perfect just as my Heavenly Father is perfect. '' God's perfection can be seen in many things in nature. For me as a physics-related mathematician, the perfection of God as expressed in physics is extremely impressive. God wants us to be as perfect as he is - as a goal.

Those who are strong, who are looking for a challenge in life, after all of their efforts for a task that is worthwhile - they find it in being a Christian. From where you are, you can always go much further in terms of perfection. In some areas you may become almost perfect; in other areas one notices that despite serious efforts one can hardly cross the threshold to the beginning.

On the other hand, God is a resting point for those who are overwhelmed by life, for the weak and disappointed. In the Old Testament, the prophet Isaiah says: `` He gives strength to the tired, and strength enough to the inept. Men get tired and weary, and young men stumble and fall, but those who wait for the Lord get new strength, so that they soar up with wings like eagles, that they run and don't get weary, that they walk and don't get tired '' (Isaiah 40: 29-31). When we are weak, God is a source of strength for us whenever we deal with him. And in the New Testament, Jesus takes that and says: `` Come to me, all of you who are troublesome and burdened, I will refresh you. Take my yoke upon yourselves and learn from me, for I am gentle and humble in heart. In this way you will find rest for your life. Because my yoke is gentle and my burden is light '' (Matthew 11: 28-30). Lighter than the burden that the environment often tries to impose on us.


Invitation to fellowship with God

I have mentioned many points, and that are still inadequate, God is much more than that. But you can only experience who God really is if you are friendly with him. He invites us to make and cultivate friendship with him. And it's nice (if sometimes quite exhausting) to live with him. In conclusion, I would like to testify for myself what the Apostle Paul also testified in the Bible: `` But we know that those who love God, all things serve for the best '' (Romans 8:28). To serve for the best doesn't just mean doing well, but doing very well, and all things are really all things. These are the things that make us complain and the things that make us happy. These are the things that hurt us and the things that enrich us. These are the things that demand our strength and abilities, and those that overwhelm us. In living with God one experiences that even the most difficult aspects of life are beneficial for our personal development, and I hope that you will experience the same.

discussion

(Some of the questions are given in slightly abbreviated form.)

Question: You shared how to explain from a scientific perspective how God acts in the world. Now I wanted to ask you how do you explain the origin of suffering, pain and torment? I am also thinking, for example, of hunger in the third world.

Answer: I don't have a ready-made explanation for this, but I've given it some thought. Perhaps it is so that things look very different from the perspective of God than from the perspective of us humans. We humans think that life is the time we have from birth to death. God thinks forever; he has given us eternal life. I have the impression that our life - what we call life - is a school, a preparation for another world that God is preparing and of which Revelation speaks: a new world in which there is no suffering, there will be no more pain. It will be a world to which not all people have access, but people who can be prepared for it in our world, who accept God's challenges in this world. I see suffering from this perspective. Personally, I reckon that I will survive after my death, and that what I have learned here is not in vain, but that it will also be used in eternity; and that helps me to bear my own suffering. I'm not exactly sure this is correct, but that's one of the ideas I have about it.

Just like I imagine a student who can have a lot of suffering coping with lectures or exams, but who, by getting through and conquering everything, prepare him for a life in practice, where he is then matured and capable, completely to tackle other things. What you learn in your studies is not just knowledge; What is needed later in the job is often more different: that you have learned to overcome hurdles, to have a long breath, to be patient, to show perseverance, that you will not be discouraged by problems, etc. You can realize that these are the very problems that you are struggling with now, during your studies, that are worrying you now. Everything that comes your way during your studies is also a test of whether you are capable of tackling and getting through large projects. When you finish your studies, many of you will soon take on managerial positions in business, not necessarily at the highest levels, but some of you at the top and some at the bottom. Being able to lead means having a broad perspective; to know long in advance what to consider; not to be influenced by every changing situation; to understand the people to be led; and you can only learn that through your own painful experiences. Similarly, I assume that what God expects us to do prepares us for later. And I think that he causes a lot of suffering to many people, to very different degrees to the individual. He even let his Son Jesus Christ go through all human suffering on earth in preparation for the exercise of heavenly rulership after his resurrection, so that now, when he reigns, he understands us and can lead us wisely and lovingly.

Question: I believe that God does not want people's suffering, but that much suffering comes from our own fault, because we to miss something. I find it very dangerous to relate everything to eternity; I think much more that the kingdom of God should begin now, and we are contributing to it. If we see it that way, more will improve in the world too.

Answer: I also believe that we humans are to blame for a great deal of suffering ourselves. But I don't think that is a sufficient justification for all of the suffering in the world. The fact is that God shows us how we should treat one another so that we are well - and not just us as individuals, but us as a community. If we do not take this into account, then of course we will reap the consequences of our own unreasonable behavior. There are also other things that we hardly have in hand, and where the suffering of others - or even our own suffering - is a challenge for us to develop the good qualities God has inherited in us, and so the suffering of People diminish.

But much suffering has come into the world without our doing anything. We are of course fully responsible for suffering such as the Chernobyl reactor accident. But suffering that arises from the fact that there are diseases in the world was almost completely beyond human control until about 150 years ago, and it is still so today with diseases such as cancer. I would take care not to say that no one would get cancer if they behaved optimally; I just can't stand for that. And I don't think you could argue that with someone who actually has cancer.

Question: At the beginning you said, in a general sense, how I experience reality depends on how I choose my axioms. And then you said that one can only make subjective statements about reality or truth, which you have almost equated, depending on how one has chosen one's axioms. The statements you made about God afterwards, however, were of a very objective character. Doesn't one necessarily only have to state that subjectively?

Answer: I have named the basis on which I have made my statements about God, namely on the one hand the Bible, on the other hand what I have had in terms of experiences with God and the Bible. That was my starting point for what I said in the second half. This is a subjective starting point, but it tries to find the greatest possible correspondence with objective reality. I am not blind to reality, but have tried and continue to try to reconcile my understanding of the world with what I actually experience. That's the way Paul recommends - `` But test everything, and keep what is good, '' - and is also the kind that has helped natural science to achieve its success.

It is true that my assumptions are subjective and must be accounted for subjectively. But even if physics is based on fundamentals that have been accepted for the subjective motives I have mentioned, what it describes is nevertheless extremely reliable. Subjective does not mean unreliable, but rather: reliable to the extent that it has proven itself with careful examination. As I said, you can choose good or bad starting points; if the starting points are good, the truth is great, if the starting points are bad, the truth is low.

Question: If God is in control of nature, how can he allow man to destroy his environment, or even nature to destroy man?

Answer: The reason is the same as when a chemist who wants certain reaction products determines the reaction conditions in such a way that the desired result comes out in the end, even if things get very hot in the chemical reactor in between. For the duration of the process, it is sufficient if certain limits are not exceeded.

If you look at the world from our point of view - which we perceive only a very small part of a period of many thousands of years - then you cannot understand such a large-scale thing as the world. From God's point of view, our world is only designed for time, for wear and tear; one end is expressly provided. The world is also just a tool in the hands of God. The world is a reactor of God, created to allow people to mature. The prophet Isaiah, whom I have already quoted earlier, uses exactly this image - of course in a language that was appropriate for the culture of the time: he speaks of God as the potter who shapes us, the clay, and that God makes us purifies suffering in the crucible - the reactor of yesteryear - just as one cleans silver from the slag. And God has promised that he will bring us no more suffering than we can bear; like the chemist, he is interested in the good outcome and in between ensures that the limits are kept.

As I said, I believe that suffering plays a constructive role with God. The difficult thing is that suffering is hard to bear and painful; but we all know cases where we don't care about our pain because we have enough interest and motivation for something that cannot be achieved without pain. What matters is that our lives are so shaped by hope that we have little regard for the adversities of life in realizing what is good. And that's what God wants to make us capable of.

This view is also of great help to me. Things don't go smoothly in my life either; I have quite a problem in some areas. And it is a great help to me to know or to trust that these difficulties will also benefit me, as I said at the end of my lecture. What Paul writes there that “all things must serve us for the best”, I could not take fully at the beginning; that was something I had very much doubted when I started reading the Bible. But I learned to trust, and I made that statement an axiom in my life when I saw that I could do better with it.

Question: In the creation account there is also talk of God having entrusted the earth to man. Then God should also have given man the insight how he should deal with the earth so that he does not destroy his environment, as he is currently doing. He is on the mend, but nevertheless he is permanently destroying the environment. If man - or indirectly then God - does not put a stop to this soon, then at some point the earth will be broken, and that cannot be in God's way.

Answer: As I said before, God planned an end of the world, so your last statement is not entirely correct. On the other: The Evangelist John quotes Jesus with the words: `` Verily, verily, I say to you, whoever believes in me will also do the works that I do, and will do greater things; because I'm going to the father '' (John 14:12). This is what Jesus said to his disciples. I believe that his prediction has come true, for the natural science that arose on the breeding ground of Christianity has produced many beneficial works. Even if science has largely broken away from Christianity today, that is still the fulfillment.

Jesus healed individuals, not particularly many. We are healing people on a large scale today, and we have eradicated many diseases that used to bring much suffering to people. How many things has science achieved that 2000 years ago - during Jesus' lifetime - should have been considered unimaginable miracles! It just becomes pointless to call something a miracle that happens every day - not least because of this, there are fewer and fewer miracles in the world.

The problem is, however, that half of Jesus' word was no longer heeded in the course of time. It is called namely '' who believes in me '', i.e. who trusts me, and what this means is specified elsewhere: It means, among other things, that one adheres to what advice and goals God has given us. Then the effect will also be as it was with Jesus, namely beneficial.

But when the experience we have gained becomes independent and detaches itself from God's values, it is like holding a sharp knife in one hand: the effect depends on whether the hand belongs to a surgeon or a criminal good or bad.

The abilities of mankind have been enormously increased through the sciences, but - and I have already quoted Moses earlier - according to God's will it really comes down to choosing life! That's an activity that we have to do; if we don't, then - as our capabilities grow - we are threatening the world.

At the beginning I quoted Jesus: `` If you will abide by my word, then the truth will set you free. '' To become free from the destructive side of science, we need to immerse ourselves in God's word so that we can recognize his will and live according to it.


Believe as a mathematician
Thoughts on living as a Christian
My Views on the Christian Way of Life
Science and Faith
On Christianity
my home page (http://www.mat.univie.ac.at/~neum) Arnold Neumaier ([email protected])