Chance and providence

Yahtze is an entertaining family dice game. The highest scoring throw is all five dice the same, for which you get 50 points, and 100 bonus points if you throw another in the same game. I think the odds of a Yahtze are 6^4, or 1:1296. The odds of throwing two Yahtzes are that number squared. Correct my maths if it’s wrong – but by any calculation it’s not a highly probable outcome. We used to play it when camping with the kids, since it used less skill than other games and so caused less tantrums. There’s nothing worse than mums and dads throwing tantrums. At times, though, It used to give me some parental qualms.

Maybe my conscience was oversensitive, but it was at the time the National Lottery began, and I was a little concerned at encouraging the children in games of chance. Partly this was for fear of their growing up to gamble their money away, but theologically my logic was that, since the Bible says every decision of the dice is from the Lord, a Christian in need of money is better advised to ask his Father for it than putting him to the test for it. One evening my son, then aged about twelve, threw five (honest) Yahtzes in one game, and said, “I’m scared – I don’t want to play this any more.” Somehow it seemed to confirm my scruples. He still does the Lottery sometimes, though. Kids nowadays…

Some time later I was intrigued to read that a similar episode cured the great Puritan Richard Baxter of gaming. He was living at Ludlow Castle at the age of seventeen (that would be in 1632), and decided to learn the art for lack of any other entertainment. The best gambler in the place undertook to show him the ropes. On the first or second game, Baxter was in such a hole that the bystanders were laughing and telling him to jack it in. But on the naive basis that it ain’t over until it’s over he ignored their advice, and let his opponent lay down ten shillings to his sixpence on the result:

As soon as the money was down, whereas he told me there was no possibility of my game but by one cast often, I had every cast the same as I wished, and he every one according to my desire, so that by the time one could go four or five times round the room his game was gone, which put him in such great admiration that I took the hint, and believed that the devil had the ruling of the dice, and did it to entice me on to be a gamester. And so I gave him his ten shillings again, and resolved I would never more play at tables whilst I lived.

Now, do statistics negate his sense of the significance of this? On average even over his game, if not during the last few throws, the dice favoured each roughly equally. And no doubt a bored statistician in Ludlow Castle counting all the die-casts over a month would find a pretty random distribution of results. But the fact remains that Baxter became renowned as a Puritan preacher and writer rather than lost in obscurity as a gamester because of a statistically unusual pattern within the greater distribution. Just as my son’s brief 1:1296^5 run happened to coincide with my theological musings rather curiously.

What happened in Baxter’s experience? Does the devil really get to control randomness? Well, in Job’s case he did, but only under the the permission of God. A more nuanced view of Baxter’s experience, then, would be that God used the devil’s enticement knowing that it would cure, rather than corrupt, him. Or maybe God doesn’t delegate natural phenomena to Satan, and acted directly to the same beneficial effect.

In Mike Gene’s model, God chose to create the very universe in which, at that particular locus, random chance had been forseen to produce that effect. OK, but it seems rather a sledgehammer to crack a nut that directly tweaking a few variables like muscle potentials and so on would achieve more easily.

Does Baxter’s interpretation, or these variants on it, violate science? Forget Elliott Sober’s philosophical concessions. In this example, “random” does not mean intrinisically undetermined, but unconsciously determined. We can probably assume that every throw of the dice was actually determined by the voluntary muscular activity of the two players, the only other factors being fixed values like friction. But those muscle potentials were regulated blind. One could imagine a machine so accurate that it could calculate every movement of a die from picking it up to thowing it unerringly to a predicted score – the ultimate determinist gambler. But since there was (and is) no such machine, merely the incalculably complex and highly inconsistent activity of two independent humans, invoking deterministic law is simply whistling in the wind. Science has nothing useful to say about why the dice fell precisely as they did, and can only comment on the large scale statistical pattern. Any claim that a “lucky streak” is undirected is without evidence. Baxter’s precise game-winning sequence of throws conformed, we may conjecture, to statistical norms but can still, to any Christian, be plausibly attributed to God’s (and/or the devil’s) influence.

So why is the situation any different in organic evolution on the Neodarwinian model? The non-involvement of humans, especially Puritan divines, hardly seems a rigorous criterion for distinguishing the situations. God willed a result (a spooky gambling victory) and used one of the proverbial examples of randomness (a specific sequence of dice throws) to achieve it. So what if he should will to create Homo sapiens sapiens (and every other species too) by the apparently stochastic nature of DNA mutations? What, indeed, if he should want to create Richard Baxter of Eaton Constantine (an idyllic hamlet, by the way) by a rather longer sequence involving the contingency of human reproduction, and indeed of every event in history up until then? What conceivable right has a scientist to proclaim that it was actually an undirected process, and that the result was in the slightest way fortuitous?

The sceptic could, of course, assert that Baxter was completely mistaken in attributing his dramatic win to anything more than superstition. But all Baxter would need to do in reply would be to assert the opposite. Bare assertions don’t carry much weight as evidence, especially when the contrary assertion helps explain the course of a uniquely useful life. And in the biological realm too, what is to be explained is not just one useful life, but an entire useful world. The matter still reduces to two competing assertions of undirected chance and directed providence.

Perhaps we should toss for it?

Avatar photo

About Jon Garvey

Training in medicine (which was my career), social psychology and theology. Interests in most things, but especially the science-faith interface. The rest of my time, though, is spent writing, playing and recording music.
This entry was posted in Creation, Science, Theology. Bookmark the permalink.

4 Responses to Chance and providence

  1. Gregory says:

    As I remember from playing Yahtze a considerable # times, one can score a Yahtze by collecting 5 dice of the same number in 3 throws, not just in the first throw. One may choose to ‘go for it’ if they think they are close or near the end of the scorecard. One can also score for 3 or 4 of-a-kind on their tally if they fail to reach their Yahtze.

    If your son threw 5 Yahtzes all on the first throw, that would be impressive. I must admit I’ve only seen it done 3 or perhaps 4 times on the first throw in a single game. From memory, I’ve done it at least 2, maybe 3 times myself.

    “a bored statistician in Ludlow Castle counting all the die-casts over a month” – Jon

    Yeah, this is a description of some advocates of intelligent design/Intelligent Design, who are caught up in the ideology of ‘statisticism.’ This is indeed a very significant ideological cloud hanging over IDM-ID. Can’t count the number of times IDers have resorted to coin flips to try to prove their point to non-IDers!

    “Science has nothing useful to say about why the dice fell precisely as they did, and can only comment on the large scale statistical pattern.”

    Exactly. That’s why passing a course and examination in statistics is so very important in western Phd programs, right?

    “undirected chance and directed providence” is simply the wrong language for biologists to use, whether they are neo-Darwinian or not. Category error obvious and up-front. Openly declared theological (or religious) biology courses would of course require a different approach. But why would e.g. ‘Christian biology’ make sense to teach in schools and universities today?

    Biology (as a self-limited realm) in the context of (natural and social) science, philosophy, religion dialogue; now that’s a different story!

  2. Avatar photo Jon Garvey says:

    Ah your memory of the game is better than mine, Gregory. I’ve obviously purged my mind of all that devil’s business! In that case No 1 son will have thrown in 5 consecutive games: reduced odds by an order of magnitude or so – but the point is essentially unchanged, I hope.

    I disagree about boring statistics, speaking as one who worked assiduously to undertand the stats lectures at Uni, and not grasping it at all, only to find my lazy colleague who’d stayed in bed for the lectures hailing my notes as the clearest explanation he’d seen!

    Counting die-casts yields a normal distribution. Boring. But doing probabilities for first self-replicating molecule or DNA synthesis yields far more interesting figures. I’ve been fascinated with that since I heard about the 1966 Wistar conference back in 1986.

    But though statistics have a vital place in science, they can be blind to important individual events. In UK medicine that was exemplified by prescribing limitations: Drug A has 75% success rate, Drug B only 5% and is expensive. Drug B is taken off the formulary. But I’m not treating 75% of people – just Mrs Smith, who only responds to B. In biology it’s often amongst the statistical outliers where interesting stuff occurs.

  3. Cal says:

    The “dicey” (pun intended) thing about providence is that Christians many times don’t use it consistently.

    Spooky dice rolls or a sunny day, God’s providential helping hand. Terrible storm or flesh eating virus, natural evil.

    I do agree that I don’t want to say “God killed X people with a Hurricane”, though certainly His hand was somewhere on the statistical likeliness that a storm accumulated X strength at Y for Z duration ending with Q deaths. Maybe like the Tower of Siloam, it doesn’t mean anything about the people who died, all it means is: repent, the time is short.

    A bit of a derail, but you got me thinking on providence and the “natural evil” is what drives a lot of people into odd “creational liberty” heterodoxies. ‘It wasn’t God’s fault, it’s just silly old nature’ kind of attitude. Perhaps the “chance” is driven by what I call active-permission.

    The Lord doesn’t stop all gamblers but perhaps in Baxter’s attempt at playing, this certain event, as it occurred, was woven into His guiding Hand in moving Baxter into abandoning a destructive habit. Or maybe he was just superstitious about dice 🙂 .

  4. Avatar photo Jon Garvey says:

    ‘The “dicey” (pun intended) thing about providence is that Christians many times don’t use it consistently.’

    Another modern aberration, Cal – the older, more realistic assessment was in the hymn:

    Judge not the Lord by feeble sense,
    But trust Him for His grace;
    Behind a frowning providence
    He hides a smiling face.

    William Cowper, who had his share of adverse providence.

Leave a Reply