A Philosopher's Blog

Of Dice & Chance

Posted in Metaphysics, Philosophy, Uncategorized by Michael LaBossiere on August 9, 2017

d20Imagine, if you will, a twenty-sided die (or a d20 as it is known to gamers) being rolled. In the ideal the die has a 1 in 20 chance of rolling a 20 (or any particular number). It is natural to think of the die as being a sort of locus of chance, a random number generator whose roll cannot be predicted. While this is an appealing view of dice, there is a rather interesting question about what such random chance amounts to.

One way to look at the matter, using the example of a d20, is that if the die is rolled 20 times, then one of those rolls will be a 20. Obviously enough, this is not true—as any gamer will tell you, the number of 20s rolled while rolling 20 times varies a great deal. This can, of course, be explained by the fact that d20s are imperfect and hence tend to roll some numbers more than others. There are also the influences of the roller, the surface on which the d20 lands and so on. As such, a d20 will not be a perfect random number generator. But, imagine if there could be a perfect d20 rolled under perfect conditions. What would occur?

One possibility is that each number would come up within the 20 rolls, albeit at random. As such, every 20 rolls would guarantee a 20 (and only one 20), thus accounting for the 1 in 20 chance of rolling a 20. This, however, seems problematic. There is the obvious question of what would ensure that each of the twenty numbers were rolled once (and only once). Then again, that this would occur is only marginally weirder than the idea of chance itself.

It is, of course, well-established that a small number of random events (such as rolling a d20 only twenty times) will deviate from what probability dictates. It is also well-established that as the number of rolls increases, the closer the outcomes will match the expected results (assuming the d20 is not loaded). This general principle is known as the law of large numbers. As such, getting three 20s or no 20s in a series of 20 rolls would not be surprising, but as the number of rolls increases, the closer the results will be to the expected 1 in 20 outcome for each number. As such, the 1 in 20 odds of getting a 20 with a d20 does not mean that 20 rolls will ensure one and only one 20, it means that with enough rolls about 1 in 20 of all the rolls will be 20s. This, does not, of course, really say much about how chance works—beyond noting that chance seems to play out “properly” over large numbers.

One interesting way to look at this is to say that if there were an infinite number of d20 rolls, then 5% of the infinite number of rolls would be 20s. One might, of course, wonder what 5% of infinity would be—would it not be infinite as well? Since infinity is such a mess, a rather more manageable approach would be to use the largest finite number (which presumably has its own problems) and note that 5% of that number of d20 rolls would be 20s.

Another approach would be to say that the 1 in 20 chance means that if all 1 in 20 chance events were formed into sets of 20, sets could be made from all the events that would have one occurrence each of the 1 in 20 events. Using dice as the example, if all the d20 rolls in the universe were known and collected into sets of numbers, they could be dived up into sets of twenty with each number in each set. So, while my 20 rolls would not guarantee a 20, there would be one 20 out of every 20 rolls in the universe. There is still, of course, the question of how this would work. One possibility is that random events are not random and this ensures the proper distribution of events—in this case, dice rolls.

It could also be claimed that chance is a bare fact, that a perfect d20 rolled in perfect conditions would have a 1 in 20 chance of producing a specific number. On this view, the law of large numbers might fail—while unlikely, if chance were a real random thing, it would not be impossible for results to be radically different than predicted. That is, there could be an infinite number of rolls of a perfect d20 with no 20 being rolled. One could even imagine that since a 1 can be rolled on any roll, someone could roll an infinite number of consecutive 1s. Intuitively this seems impossible—it is natural to think that in an infinity every possibility must occur (and perhaps do so perfectly in accord with the probability). But, this would only be a necessity if chance worked a certain way, perhaps that for every 20 rolls in the universe there must be one of each result. Then again, infinity is a magical number, so perhaps this guarantee is part of the magic.

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Is God Compatible with Evolution?

Posted in Philosophy by Michael LaBossiere on September 18, 2007

 

While the theory of evolution is considered as a matter of established scientific fact, there is still very significant opposition to the theory from the religious community. The main concern is that the theory of evolution is a threat to faith and religious belief. Some thinkers content that religious belief is compatible with evolution-that a person can have science and God. It is to this matter that I know turn.

 

 

Addressing this matter requires being clear about what exactly is being debated. If the theory of evolution is taken to involve the claim that there is no God, then obviously God and the theory are not compatible. While this is a commonly held view, the theory does not actually explicitly deny the existence of God. What is does is postulate a mechanism of natural selection in place of an intelligent designer. So, rather than having an intelligent being design and create life forms, new life forms emerge through mutations and selection in terms of survival and reproduction. Mutations that survive and breed can eventually differ enough from the original species that they become a new species. As odd as it might seem, natural selection seems initially compatible with the existence of God.

 

 

God could have created the universe and put in place the method of natural selection as the means by which new life forms would arise from older ones. So, rather than designing each life form in hands on acts of creation, God would set the universe up so that a natural mechanism of selection did the work for Him. This sort of view is not without precedent. Many thinkers have argued that God created a world of laws and natural machinery that run without his direct intervention. The best known version of this view is deism.

 

Of course, there is the question of why God would use such a method and whether it is compatible with His other alleged traits.

 

 

God is, in Philosophy 101 terms, supposed to be all good, all powerful and all knowing. These attributes do seem to clash with using natural selection. First, if God is all powerful and all knowing, He could simply create the life forms He wants and not have to rely on a mechanism to do the work for him. An obvious reply to this is, however, to re-emphasis the view that God is the divine watchmaker who builds a world that can run on its own. Of course, many religious thinkers, such as Berkeley, regard this view as unacceptable. After all, if laws and mechanisms do all the work, what need is there for God? In any case, this does rekindle the old debate over the degree of God’s involvement in the world.

 

 

Second, if God is all good, then natural selection seems incompatible with God. This is so for two main reasons. The first reason is that natural selection seems to be terribly wasteful and brutal. It seems almost inconceivable that an all good being would allow so many species to simply perish. The second reason is that natural selection seems arbitrary. It is, after all, a chance driven mechanism. To leave survival up to chance hardly seems like the action of a perfectly good being.

 

Of course, this sort of problem is really nothing new-it is but the problem of evil with the twist of natural selection added in for a different flavor.

 

 

Thus, the logical conclusion seems to be that God is compatible with evolution, but serious problems arise with reconciling God with the nature of natural selection.