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Randomness and God’s Governance, Part 1

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May 7, 2012 Tags: Divine Action & Purpose
Randomness and God’s Governance, Part 1

Today's entry was written by Randall Pruim. Please note the views expressed here are those of the author, not necessarily of BioLogos. You can read more about what we believe here.

Note: This essay is Part 1 of a three-part series from Randall Pruim’s chapter in the book Delight in Creation: Scientists Share Their Work with the Church, edited by Deborah Haarsma & Scott Hoezee. Other essays from the book appear at The Ministry Theorem.

Today's post explains what scientists and mathematicians mean when they speak of something being “random.” Building on this concept, the other two parts of Pruim's essay will address God's use of apparent randomness in creation.

I’ve enjoyed playing games as long as I can remember. Among my earliest memories are playing Candy Land, Chutes and Ladders, Don’t Break the Ice, and Don’t Spill the Beans. When I was a child, whenever someone did not know what to get me for a birthday or Christmas present, a game was always a good choice. Today, in the back room of our house, we have a closet filled with games that my children and I have accumulated over the years. The rest of our games are either in a closet upstairs or in one of several large boxes in the attic. Periodically we rotate the location of the games for variety.

Many of the games I enjoyed playing involve a combination of strategy and randomness: card games of various sorts, backgammon, and board games like Monopoly and Parcheesi. Some games that rely exclusively on chance (like War and Candy Land) or too heavily on chance (like Sorry) quickly became uninteresting to me. In fact, for Sorry, War, and several other games, I introduced additional rules to change the balance of strategy and luck—for example, by allowing each player to hold a hand of cards rather than merely flip a card and follow its bidding.

When my children were young, I played many games with them, especially those involving some amount of chance. I always play to win, so games of pure strategy like chess gave me too great an advantage—at least when they were still young. I still remember the first time I played the German game Mitternachtspartie with my children and some of their cousins. The game uses a die on which the number 5 has been replaced with the image of Hugo the ghost. Each player rolls the die and moves one of his figures the specified number of squares, unless Hugo is rolled, in which case Hugo moves instead.

I quickly worked out the expected distance Hugo would move for each of my turns and the expected number of squares I would get to move my own figures each turn. Using that information, I could strategically place my figures in the opening portion of the game. I fully expected to win this first game, since my young children were going to have to learn from experience what I already knew by the mathematics of probability. I lost—badly. As it turned out, the die had two Hugos on it. So compared to my expectations, Hugo moved twice as often, and my figures moved slightly less far. That combination turned the carefully calculated positioning of my figures into a disaster.

From Fun and Games to Science

I still enjoy playing games, including games that involve chance. But these days I encounter randomness even more often in my profession. I was trained as a mathematician and now work at the intersection of mathematics, statistics, and computer science. Like many scientists, I use randomness on a daily basis as part of our toolkit for modeling and investigating all sorts of phenomena. Models known as stochastic models, which explicitly incorporate random components, often via simulation in computer software, are used to model everything from diffusion to genetics to quantum mechanics. Insurance companies and financial institutions use stochastic models to manage risk. If we include all the applications of statistics, then almost no area of science is untouched by the use of randomness.

Most of the time, scientists and game players alike don’t devote much thought to just what makes randomness tick. But they both know that the better they understand the probabilities, the more successful they are. Nevertheless, if you ask many of them what it means for something to be random, they may struggle to put it into words. I won’t try to give a precise definition either, but it is important that we have some idea what we are talking about, so let’s consider one of the prototypical examples of randomness: the tossing of a fair coin.

If I flip a coin, the result could be heads or tails. Until I flip the coin, I don’t know which it will be. In this sense, the coin toss is unpredictable. If the coin is fair, each result is equally likely, so while I cannot say in advance whether a particular result will be heads or tails, I can say something about a large number of flips: approximately half should be heads and the other half tails.

A little mathematics even allows me to determine a range around 50% in which the percentage will almost surely lie. For example, if I flip a fair coin 1,000 times, the percentage of heads will most likely be between 45% and 55% (where “most likely” means a 99% chance). If the percentage of heads lies outside this range—especially if it is quite far outside this range—I am going to be suspicious that the coin flipping process is not fair. That’s one of the key ideas in statistics: not only can we calculate the frequency with which an event occurs, but we can compare data to a stochastic model to see if they are compatible or incompatible.

There are several interesting things we can learn by considering a coin toss. First, probability calculations rely on assumptions. If the assumptions are incorrect, then the probability calculations will also be incorrect. For example, if the coin is biased (such as one that is heads 60% of the time), but we assume it is fair, then the probability calculations given above will be wrong. Of course, if the assumptions are not too far from correct, the results may still be sufficiently accurate for scientific conclusions. If we have an appropriate way to collect data, then we can test our assumptions by comparing data to projections made based on the assumptions.

Second, “random” does not imply “equally likely.” A fair coin should have equal probabilities of heads or tails, but a biased coin is no less random. It’s just different. It is not as simple to handle arithmetically as a situation in which all outcomes are equally likely, but it is not otherwise special. It is a common mistake to assume random events are equally likely when they are not (or when that assumption is not justified).

Third, randomness is about the process. It is a fun experiment to flip a penny 100 times, then spin a penny 100 times and record the side that is showing when it finally tips over, then to stand the penny on end (this takes a steady hand and a little practice) and record which side is showing after pounding the table. These are three different processes, and they do not yield the same results.

Fourth, random processes produce patterns. I sometimes ask my students to mentally flip a coin and record the results as a sequence of letters (e.g., “HTTHHTHT”). Then I have them actually flip a coin and record the results. If the sequences are long enough, I can almost always tell them which is which. The sequences imagined by the students tend to have too few runs of consecutive heads or tails. The sequences based on real coin flips usually include several heads in a row. People not familiar with randomness are often surprised at the patterns that result and assume that the process must not have been random when they perceive a pattern. Our eyes and minds are drawn to similarities and patterns—even those that are produced purely randomly. This can lead us to draw false conclusions from coincidences of all sorts.

Consider the image in Figure 1. It was constructed using a computer to randomly throw 300 darts at a square board. Every position on the board was equally likely to be hit by a dart. This does not, however, mean that the dots are evenly spaced. There are 100 smaller squares. The average is three dots per square. But your eye is likely drawn to some clusters and voids. My eye also catches a graceful downward swoop in the lower part of the upper left quarter. All of this is exactly what we should expect from this random process. If we repeated this experiment, we should expect similar results. Several of the smaller squares would be empty and some others would have two or three times the average number of dots, but these clusters and voids would appear in different places.

Finally, randomness can be used to produce patterns intentionally. Consider the two pictures in Figure 2. You may think the two pictures are identical, but they are not. However, they were each constructed using the same random process:

  1. Start at the lower left corner of the big triangle.
  2. Randomly choose one of the three corners of the big triangle.
  3. Move half way to that corner, placing a dot at the new location.
  4. Repeat steps 2 and 3, 50,000 times.

The first few steps of this process for each image are illustrated in Figure 3. Although the final images look very similar, the route taken to get there is very different. In fact, the only point the two images have in common is the starting point. As the creator of the program that generated these images, I knew full well that the result would resemble a fractal image known to mathematicians as Sierpinski’s Triangle, even though I did not know or exercise any control over how the individual points would be selected.

Despite our familiarity with children’s games and the importance of stochastic models throughout the sciences, many Christians have a reaction to randomness that falls somewhere between uneasy and antagonistic. And yet, those same Christians may well watch the evening news to learn about public opinion polls forecasting upcoming elections, take prescription drugs approved by the FDA based on statistics found in clinical trials, obtain electrical power from a nuclear power plant that uses random fission reactions, and insure their cars with companies that rely on stochastic models to set the rates. The foundation of each of these activities is a thorough understanding of randomness that begins with the simple description above.

So where does the uneasiness come from? Likely it comes from the feeling that taking randomness seriously means not taking God seriously. Or put more strongly, it comes from a fear that believing in randomness means not believing in God. Next week we’ll address that problem by asking the question, “Could God use randomness to achieve his purposes?”

Randall Pruim is Professor of Mathematics and Statistics at Calvin College in Grand Rapids, Michigan. His research interests include biostatistics, statistical genetics, and the relationships among statistics, philosophy, and religion.

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Merv - #69734

May 7th 2012

Thanks for sharing your thoughts, Dr. Pruim.  I hope you don’t mind if I also share some that I’ve had on the subject of randomness.

One exercise I would like to do with my high school math students but haven’t yet is to premake several placards on which I mark where ten rain drops actually hit  (by leaving them out briefly as it is just starting to rain, and then covering it after about ten fair sized drops have landed on it, and permanently marking those locations.  Then, if I asked students to artificially make their own placard and try to “fake it” by being as random as they could; would another party be able to distinguish between the real rain drop landings and the constructed ones?  I suspect that we in our zeal to appear random would do an artificially thorough job of making our locations too evenly spread out whereas the real boards would probably end up with unseemly clusters of drops.  I know there are well studied laws about randomness (not used enough by me to remember the names here) that can help distinguish between, say, a real accounting ledger, and one that has been cooked with artificial numbers.  A person filling in their own numbers will choose distributions more artificially even over all digits than real distributions would typically be.

When our family plays “settlers of Katan” we loudly complain when our own favored dice rolls don’t occur as much as they were “supposed to”  (e.g.  when rolling two dice, getting a six or an eight is more likely than, say, a ten or eleven).  But the dice don’t always cooperate leaving us feeling cheated out of our calculated probabilities.  But of course those probabilities take larger numbers of instances before their relative occurences come more sharply into focus.  When we “zoom in” to small numbers of occurrences, unpredictability carries the day and we see no clear view of any probabilistic curves. 

I wonder if that could also apply to our view of events in general.  If we could “zoom out” to God’s view, a grand plan may come into focus, but from where we stand in our corner of time and space, we see a lot of apparent “randomness”.


sy - #69739

May 7th 2012

I think you have hit the nail on the head, Merv. In fact, in order to come up with most laws of science, we need to zoom out from single molecules, atoms or particles to a large enough statistical mass, so that we can regularity. Billions of gas molecules follow Boyle’s law, but a single gas molecule does not. I think the same can be said of natural laws in economics and social science governing human behavior. We can predict what a mass of people will do, but not what one person will do. A single electron follows a whole different, (and pretty crazy) set of quantum laws, and individual people follow their own will.

I dont know how, but I think God is involved in both of these examples. God’s laws govern the group, but the hand of God Himself can be seen in the apparently random acts of the individual.  

Merv - #69741

May 7th 2012

Sy wrote:  “I dont know how, but I think God is involved in both of these examples. God’s laws govern the group, but the hand of God Himself can be seen in the apparently random acts of the individual. “

I think Scriptures confirm your conjecture, Sy when they speak of God being attentive to the hairs of our head as well as to the little sparrow that alights.  I don’t think a person escapes God on either direction of the logarithmic scale —-zoomed out or zoomed in.

I like your example of Boyle’s law applying only to billions of molecules.  I’ll have to use that in chemistry.


Roger A. Sawtelle - #69760

May 8th 2012

My biggest problem with “random” is that it has so many meanings, thus it is difficult to determine what meaning is meant it its use without any clear context. 

Thus a set where the choice is between heads or tails is considered “random,” just as a set where the choice is any number between one and ten, or 1 and 1000, or 1 and 1,000,000. I am old fashioned to think that random without qualification means any number without qualification.

Of course the other problem with randomness is the misunderstanding that evolution is a random process, which is not.  Variation is a random process within certain limits, however Natural Selection is not random.  Neither Darwin or Dawkins makes the claim that it is random.  What makes it seem random or indeterminate is that they say that the basis for selection is indeterminate.  This is not true because it is clear in most instances that the ability to adapt to the environment is the key to success or failure of phenotypes.  

The process of evolution could be compared to the mining of stones from a quarry.  You have a machine to separate rocks from the earth, and then another machine to break the rocks up into stones.  This second machine produces Variation, or stones of various grades and sizes.  However before the stones can be used, they must be sorted by size and grade so they can be selected for the proper use and job.  The sorting is like Selection.  A particular stone is selected for particular use according the the criteria for the job.  There is nothing random about this. 

The problem is not with Natural Selection as an idea or a process, but be the concept that because nature cannot think, it has no plan or purpose, even though for Darwin it did and all around us birds and squirrels are making nests for shelter, ants and bees are highly organized, birds learn flight plans to migrate the summer homes, and much other purposeful behavior can be observed.    

jamie.semple - #69871

May 10th 2012

This is something I’ve spent a bit of time considering. Laplace was convinced of a God-killing determinism based on Newtonian laws, but the advent of quantum mechanics really put a stopper in that; the idea of God working in the world today would (I assume) require a mechanism of sort, and the inherent uncertainty that dominates the quantum world allows for things to happen that would be classically impossible.

There are a number of mentions in the Bible of people that rely on the ‘casting of lots’ to determine God’s will (Jonah 1:7, Acts 1:24-26). Whilst I have not the insight to delve into that further, it makes for an interesting consideration.

(On further reading, this is referred to as cleromancy, and there are about six explicit references to it in the Bible. I’m going to put my hands up and say I’m very unlikely to base a major decision, such as throwing someone off a boat, on the outcome of a game of chance. Oh me of little faith?)

Jon Garvey - #69953

May 15th 2012

George Whitefield pleaded with John Wesley not to base a major decision on the casting of lots. The fact that it was used by God in the Bible isn’t a justifciation for us to do so. In fact, though, it was more than 6 occasions, in that the urim and thummnin used by priests who discern God’s will was, in effect the use of lots.

What it  does show, though, is that in the case of casting lots, chance is not chance to God. Which has great implications for our understanding of his world. Try this translation of Proverbs 16.33 for example:

The stochastic mutation is cast into the gene, but its every decision is from the Lord.

liberale - #69908

May 11th 2012

This is also my problem with the “God” model.  The ubiquity of randomness speaks strongly against the existence of “God’s providence.”  If “God’s providence” work via randomness, why need the concept of “God’s providence” at all?  Why not just stop at randomness and refrain from speculating beyond it?  Anybody can say anything “works via randomness.”  For example, “Flying Spaghetti Monster (FSM)‘s providence works via randomness.”  When asked “why FSM?” an often encountered answer is that “I have faith in FSM; faith, precisely because It cannot be seen.”  In my opinion, “faith” is just a pleasing name for speculation.  Yes, I am unable to disprove the existence of an unobservable (“spirit”) FSM, but there is no good reason to speculate its existence either.

Merv - #69929

May 12th 2012

For example, “Flying Spaghetti Monster (FSM)‘s providence works via randomness.”

Well, or it would if the FSM really existed.  Someone may say they have faith in the FSM,  but they don’t really because they don’t even believe it exists and just use it as a rhetorical device.  The sincere Christian however really does believe (and has plenty of reason to believe) that God exists and is active.  She has a “cloud of witnesses” both present and past as well as authors, martyrs, apostles whose lives were transformed and who spread the good news.  FSM has got exactly zilch.  When the day comes when we have FSM hospitals, orphanages, faithful devotees giving their lives to sharing the good news of how FSM transformed their lives ... maybe then we can reconsider, but until then…

Still, the point you bring up about randomness is a good one.  Why call it providence at all?  Part of the answer could lie in whether or not it is as “ubiquitous” as you imagine, or for that matter what do you mean by “ubiquity”?  We already know that defining “random” is not a trivial task and it carries a lot of ideological freight.  If I scatter grass seed do I do it randomly?  Yes and no.  Yes, I don’t pay attention to where every little seed goes and I count on the randomness of a spreader to do a good job spreading it.  But no, I’m not just putting grass seed everywhere on driveways, sidewalks, etc.  And one hopes that they don’t get over abundant clumps of seed in some spots and no seed in other spots.  (This very example makes an interesting parallel to the parable of the sower, who Jesus has spreading the seed in a more extreme random way—making it seem in comparison that God is even freer with ‘randomness’ than you or I would tend to be—but of course, that was not a parable about ‘randomness’ so we probably shouldn’t draw much from that.)   But a planter may actually be counting on randomness to get a uniform distribution.  That is an obvious way that an intelligent agent uses randomness to achieve a result that is not random –at least not completely.  It has constraints.


GJDS - #69941

May 13th 2012

“I won’t try to give a precise definition either, but it is important that we have some idea what we are talking about,” 

1)      The discussion on randomness has shown that this is dealt with mathematically – stochastic approaches are widely used. I wonder if random is not interchanged by some with haphazard, or lacking any comprehensibility in terms of non-related events?

2)      If we can reason on random events, this implies they are grounded on reasonable matters, and it is our comprehension (or lack of it) that is communicated in discussions on the accidental and unpredictable. Thus are we confusing random with lack of predictability, or perhaps, lack of understanding, which accompanies confusion?

3)       Even patterns that may have appeared haphazard and unintelligible have been analysed and rendered comprehensible (e.g. fractal geometry).

What of randomness and God? We are told an Apostle was selected by casting lots (Acts 1:26); this was after a ‘selection’ had been made and instead of people choosing the best, it was acknowledged that both were suitable, and it was taken as an act of faith to indicate which one may have been chosen by God. 

“Or put more strongly, it comes from a fear that believing in randomness means not believing in God.”

I think this comes from a view that if something is random, it lacks purpose, and is the result of some inconceivable accident. It would be instructive to consider the dynamics of any system, including that of the planet earth (and despite the magnitude, even the Universe); some (or many) events may be presented to human reason as random (or more likely insufficiently understood), yet this does not obviate a conclusion that it is accidental, in the sense that we often understand this term.

We may delve into sub-atomic events and consider the uncertainty principle, which ultimately means we as human beings cannot obtain complete information on these particles/events. This also confers uncertainty to ourselves within the Universe.

I think we need to consider our capacity to comprehend the world of objects and energy, and the inherent uncertainty of this as within ourselves, rather than conclude that the Universe (before we could discuss God) is random in some sense. Our ignorance and uncertainty may ultimately mean we are using God’s name for a venture into vanity.

Roger A. Sawtelle - #69959

May 15th 2012


I think you make some excellent points.  Everything does have a cause as far as we know, so it is impossible to say anything is truly random. 

Quantum events may be an exception, but they are so small that it seems unlikely that they  affect the non-quantum world and also we know so little about the quantum world that we really can’t say how it works.  I will repeat my understanding based on Stanford Enclycopedia of Philosophy that the quantum world is relational and thus knowable rather than random.  

George Bernard Murphy - #69946

May 13th 2012

I think Alan Turing was a mathematician who struggled with this same subject matter.

 You might want to google him.

 He was also gay and suffered mightily for it.

GJDS - #69965

May 15th 2012


The point I wish to emphasise is our inability to know, and perhaps how we deal with information we derive from studies of nature (i.e. the exact sciences). The quantum events are such that we are unable to derive ALL of the information we feel is needed for us to know what the thing is. But we can approximate and mathematics and theoretical physics have constructed some powerful tools; stochastic methods are just some of these tools. 

On the question of causes and purpose, when we discuss God, my view is that it is our ignirance and uncertainty that is the issue, not if God does this or that. Thus it is our purpose in what we do and how we do it that is relevant. However, there has been a very long tradition of seeking to make statements about what God may do, and I guess these discussions continue today. Such matters are profound; my take is that science and scientists are in a position to provide knowledge of nature AND our very significant limitations in such knowledge. It is something that is not acknowledged all that often.

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