Random thoughts on chance

One: the email

Some time ago, a colleague called Henk of me sent me an email, with the request to write a text on whether such a thing as chance exists. He wrote (my translation):
Please a text on: Does "chance" exist? ("Bestaat toeval?") Was it the meteor that made the dinosaurs extinct, or was it an 'act of God'? How to tell the difference?

Concerning the meteor, that is quite some different discussion. As far as I know, the meteor is not a scientific proven fact, also not among evolutionists. But that is a different story, and I won't go into it here. (So, if you want random thoughts on the meteor: send me an email...)

Telling whether chance exists, is actually not a simple thing.

Sometimes, we think something is chance, and it actually isn't, and who knows if the reverse also happens? An answer to the question involves arguments that deal with logic, with hidden variables, with modeling ignorance, of course with religion, and I think that a valid discussion on this issue cannot ignore quantum mechanics.

Ignorance, that what we do not know, is also something that plays a role when we talk about chance. In my case, in two ways. One, see below. The other: I am a computer scientist, whose work mostly involves deterministic algorithms. That makes me perhaps not the most qualified person to give definitive answers to the question at hand, (which is an understatement). So what you get are just a few random thoughts (after quite some time of thinking, Henk, sorry about all the delay), for what they are worth.

Lets call the viewpoint that chance exists non-determinism, and the viewpoint that chance does not exist determinism. For both, there exist different versions, e.g., depending on religion, like atheistic and theistic determinism. (Theism: the belief in the existence of God.)

Two: the discussion

One of my colleagues, a professor in computer science, had the following discussion with a woman of the Islam religion.

Computer Scientist: If I throw a die, the chance that I throw a six is 1/6.
Woman: No. Allah decides everything, so also what you throw.

This very short discussion is actually a rather interesting food for thoughts. Who is right? Or would it be possible that both, or neither of the two participant in this discussion are correct?

Three: fair dice do not exist

At one hand, the statement of my colleague is imprecise. In my collection of board games, there are several dice that do not even have a 6 on one of the sides, but have other numbers. (E.g., The Starship of Catan has a a die, with 2 times a 1, 2 times a 2, and 2 times a 3.) But also, a six-sided die with numbers 1 to 6 is always a little unfair, and the probabilities (if we can speak about these...) will be almost 1/6 but not precisely, due to inaccuracies in the design, the fact that some parts are just slightly heavier than others. If I throw a fair die, than indeed the chance that I throw a six is 1/6, but then, fair dice do not really exist in the real world. Fair dice are just mathematicians models of reality, but are not reality. So, when I say that the chance throwing a six is 1/6 (and I have made such statements also in my classes myself), this refers to a mathematical model of reality, but not necessarily to reality itself. (There is also the issue of the hidden cause, which I will discuss later.)

Still, the statement if I throw a fair die, the chance throwing a 6 is 1/6 is rather useful. Probability theory has very important applications. (You certainly would not be reading this, if there was no probability theory.) So, as the model is sufficiently close to reality, it becomes a good tool. But, we should not think it is reality. It is easy to confuse a model of reality with reality itself. (A mistake, for instance made by some scientists that do not understand how one can accept the evolution theory and be a Christian at the same time, but that is another discussion.)

What does this show? In any case, it shows that we cannot conclude that chance exists, because we have probability theory.

Four: what if God decides the die

At the other hand, suppose God indeed decides the outcome of a die, when I throw it. I.e., suppose we assume a theistic deterministic viewpoint. Even in this case, the statement the chance that I throw a 6 is 1/6 has meaning, as we do not know what God will decide.

In fact, there is little difference between atheistic and theistic determinism: in both cases, probability theory still is a useful model of reality. What it actually does in this case is to model our ignorance.

Five: pseudo-randomness

Many programs use something called pseudo-randomness. This is true for simulations, scientific computations, but also for about all computer games. Say, in your computer game, there is some random event, e.g., the number of points that your warrior loses when he is struck by an arrow. There is usually some routine, called a random generator, that decides how much this is, or whether the event happens at all or not. This random generator is not a real random generator, but a deterministic function, whose behavior looks enough like random, to make it useful for this purpose.

Suppose we would play Colonists of Catan, but instead of using dice, we would look to the decimals of the root of 7, starting at the 1000000 decimal, skipping the decimals that are 0, 7, 8 or 9. This is still a fair game, except when one of the players has a hidden computer where he can consult the outcomes beforehand, or has learned these decimals by heart. But, if none of the players knows the decimals, it is still a fair game. Also, we can still use probability theory here to guide our play...

Six: modeling ignorance

So, even when the process is totally deterministic, probability theory can be used to model and predict. The essential thing is that we do not know something - there is ignorance.

This is also when we throw a die. Ignoring quantum-mechanic effects, the outcome depends on the position the die had in our hand when we have thrown it, the movement of our muscles, and perhaps some other, totally deterministic facts like some imprecisions of the table on which the die rolls. Given all these factors, the outcome is deterministic. However, we do not know the factors, and thus probability theory can be used to make statements - and thus we model our ignorance with help of probabilities.

What we know affects chances. For instance, we learn that the chance that we throw six with two fair dice is 5/36, but it will be 1/6 when we know that the first of the two dice gives a 1. But even more, what we know may affect whether we say something is luck or not. We can say that it is chance when someone throws a dice behind a cup, and we correctly tell what is the thrown number. However, if the cup is made of glass, we won't say this is chance.

Seven: is there a hidden cause

So, probability theory can be used to model just our ignorance, so the existence of probability does not really help us to find a viewpoint in the determinism versus non-determinism question.

So, what can be the causes of events? Determinism means that we assume that everything is caused by

In this case, things that appear as random still have a cause, which perhaps is hidden to us, but still is there.

Non-determinism means that possibly also events, caused by

For instance, if there is something like free will, then not everything will be caused by the current state, but humans can make decisions that change events in the future. Below, I'll give my viewpoints for non-determinism, but before that, I like to point out that often, some things that look like random events, are not random.

Eight: God and miracles

I believe that some things that look like random, are actually acts of God. It happens often that after praying, something happened, that could be random, but given the praying, it appears that this is the work of God. Let me give two examples, of things that happened during the time, I was working on this text.

Recently, I was feeling somewhat desperate when I was at work. I prayed to God - a short prayer, saying not much more than: God help me. Less than half an hour later, I received a phone call from my oldest daughter: she was in the neighborhood, and she came to my office, and we chatted and drank some coffee. It may seem a simple example, but Christians that live with God experience more such events. God is at work in our lives, and helps us to go through difficult times, and often, he uses the natural, seemingly random events.

Another example that happened recently to a friend of my wife: She was studying a literature study. This went very well, except for one course: the computer literacy exam, which was very hard for her. When she was praying about this when biking, a few minutes later she met an old friend, which she had not met in years. She told the friend the problem, and the friend offered to help her. (The results were excellent.) Was it a coincidence that she met this friend just a few minutes after the prayer, or was it the work of God? I believe the latter.

Similar to what we discussed before, it depends on what we know whether something is chance or not. Things that may be chance when we do not know that God exists, are explained (and thus we know the Cause) when we know God.

Evolution is another example: when atheistic evolutionists sometimes talk about a magnificent accident: the fact that the human species appeared on earth - in their view as the result as a rather lucky event, theists can see the hand of God in the creation of man. Regardless if God used evolution, intelligent design, or a six-day creation, for the theist, God wanted us and thus made that humans came into being.

So, I believe that many things that we think are chance, actually are the work of God.

How can God influence the things that happen? I think he can as well sometimes bend the laws of physics, but also use them, e.g., I believe he can decide if he wants, the outcome of quantum-mechanic "chance" events.

In one of the games, we play at home, some events are decided by the throw of a dice. There is a card, and when this card is played, the player does not need to throw the dice, but can state the number that is used as outcome. This is of course speculation, but it may be that God can affect quantum-mechanic events in the same way.

Nine: A quote from Einstein

After having said the above, I believe that not everything is deterministic. For what I wrote above, it is clear that religious viewpoints are important for this question. Let us first look at deterministic atheism.

Deterministic atheists have a problem: they should have an answer to the modern outcomes of physics. The determinism versus non-determinism discussion was already debated heavily by famous physicists in the 20th century. Einstein believed in a deterministic universe. He stated this in his very famous quote:

God does not throw dice.
In this quote, Einstein means to refer to nature when he talks about God; he is assumed not to believe in a personal God (like Christians or Muslims). He assumed that there is some hidden cause; some hidden variables by which the seemingly random events of quantum mechanics are caused. The modern insights in quantum theory indicate that Einstein was wrong: they indeed state that there really is non-determinism in the universe.

What does this show? In any case, for any deterministic atheistic viewpoint, one should have a good answer to the recent insights in quantum mechanics.

Ten: and what about theistic determinism?

But then, I believe that atheism is in itself mistaken. I know God exists, and have experienced his love, his power, his presence, his guidance in my life.

If you believe in God, then you can also believe that He still decides the outcomes of all quantum mechanic processes. So, quantum mechanics does not really help to sift between deterministic and non-deterministic theism.

So, here we should look to what the religion itself tells us. There thus will be a different outcome of the debate, depending on your religion. I will try to give my viewpoints here, based upon my Christian belief.

Christian determinists exist; this theological viewpoint is often known as predetermination. God decides everything, so also what we want and what we do, and there is no room for a free will. That viewpoint is contrary to the God I know: God loves us, and wants a relationship with us. You cannot have a relationship with puppets or robots.

Eleven: free will

Indeed, I believe that God loves us so much, that he has given us a free will. He has given us the ability to choose between good and evil, we can choose for Him or against Him, and we can choose if we want Jesus as our Saviour and Lord in or lives or not. Indeed, God has made us real people, not robots. This is also what the Bible tells us: it tells us we can make these choices; it gives directions and guidances in life: do not steal, do not murder, trust God, etc.

No, the Bible is not a book to push badly programmed robots to work a little better. The Bible tells us that men were created to the image of God; it is to help us to live a life, as it was meant to be.

Indeed, I see no room for determinism: God gave us the gift of a free will - thank Him. Let's use it in a good way!

Twelve: all is well that ends well

Is there a place for our free will? Maybe it has to do with small quantum mechanic processes that affect the firing of neurons in our brain - who knows?

The probability that we throw twelve with two dice is one divided by thirty-six, isn't it? Perhaps, but in any case, I hope to have made clear that the future is not completely determined by the present - and indeed, you are important, and what you do, think, pray, and say is relevant and can make a change!

I hope you, the reader (and Henk - thank you for your question), are satisfied enough with these random thoughts. In any case, thank you that you were willing to read through this text.

Hans Bodlaender, 2006/2007