This comment is going to seem unrelated or only tangentially related to the post, at first. I promise that it’s quite relevant, but explaining the relevance up-front would make the comment longer and more awkward.
Open up an old-school Dungeons & Dragons rule book (like this this one), and one thing you’ll find a whole lot of is random tables.
The idea was simple: your characters would encounter some situation; the Dungeon Master (DM) would roll some dice; then he’d consult a table, which would tell him what the outcome of the situation was, given the result of the die rolls.
If a player character contracted a disease, or developed a disorder (which, itself, would’ve been determined by some other die rolls), the DM would roll three dice: one (a d100) to determine the afflicted part of the body; one (a d8) for whether the affliction was acute or chronic; and a third (another d8) to determine severity. The table above indicated which values on each die corresponded to which outcome.
Here’s a table for determining whether a previously undiscovered fortress or castle is inhabited, and by whom (or by what!)[2]:
Finally, here’s a table for determining what happens when two magical potions are mixed (or, when a character drinks them both)[3]:
Random tables fell out of favor, for a time.[4] But they’ve been making somewhat of a comeback (along with many other features of “old-school” D&D—the so-called “Old-School Renaissance”). One sees discussions of random tables, now and then, on blogs and web forums dedicated to tabletop role-playing games. Often, peopleput togethertheir ownrandomtables.
And—as with everything else—one sees arguments about them.
Arguments for: These usually involve the word ‘fun’. Randomness is fun, we are told, and surprises are fun; and a random table can inspire a Dungeon Master, and suggest possibilities.
Arguments against: Randomness, the critics say, does not make sense; and surprises are not fun. (Because—it is implied—they might be bad; or they are often bad; or they are usually bad.)
Both sides miss the point entirely. Very few people—even among those who love a good random table—understand the tables’ nature, and their purpose. Without understanding, when people today try to construct random tables for use in their D&D games, they often find that something is missing—some ineffable quality that makes these modern imitations of the work of Gygax fail to have quite the same satisfying and enriching effect on the game as did the random tables in the D&D rule books of old.
And that ‘something’ is that random tables are not about the mere fact of randomness.
Here is what random tables really are: they are representations of a probability distribution across a set of outcomes. As such, they encode two critical things: first, what outcomes are possible; second, those outcomes’ relative frequency.
And in consequence, here is something else that random tables are: they are models of the game world.
Look again at that first table I presented (with the diseases and disorders). A character is exposed to disease; the DM rolls d100[5]. On a roll of 1, 2, or 3, the character contracts an affliction of the blood; on a roll of 4, an illness of the bones; a roll of 5 signifies a nervous system disorder.
But another way to look at this, is that blood-related disorders are 3 times more likely—and thus 3 times more common—than bone-related disorders (at least, among adventurers!).
And the table has no entry for a disease of the lymphatic system. As a consequence, in this fictional world, no such illnesses exist (or, perhaps, they do not occur among the sorts of people that the player characters are).
Similarly, the second table (with the castles) tells us that among small-sized strongholds found in wilderness regions, 45% are deserted entirely, 15% are infested with monsters, and the remaining 40% are occupied by civilized folk.
When constructing, or choosing to use, a random table of outcomes, what you are doing is modeling the fictional world of the game. The relative frequency of the possible outcomes of the category of situation which is to be resolved by rolling on the table—and, no less importantly, which outcomes are present in the distribution at all, and which are not—are facts about that world.
Now consider two random tables, for the same situation—let us say, two versions of the disease & disorder table given above. The first is as presented, while the second has all the same rows, but the distribution is altered: on this latter table, only a single number each (out of 100, on the d100) will yield any result but ‘skin’—to which the remaining 85 out of 100 numbers are now allocated.
What are the consequences for using this latter table? Well, in a D&D game where the DM chooses to use it (in place of the original table), it is rare indeed for any character to fall ill with a disease of the respiratory system—but afflictions of the skin are terrifyingly commonplace. One hopes that the DM has a good explanation for this skew (perhaps the fictional world on which the action takes place lacks an ozone layer, resulting in a permanent epidemic of skin cancers); if not, the modeled world will fail to make much sense (one can only suspend disbelief so far, after all, and perhaps—even after we’ve accepted the existence of dragons and elves—being told that skin conditions are 85 times more common than the cold, the flu, bronchitis, and every other respiratory condition combined, is a bridge too far).
And, similarly, we may imagine yet another version of this same table—an expanded one, with many more rows than merely the 16 we see above (with the die roll result ranges—i.e., the probability mass—of the existing entries being compressed, to make room); and these additional rows are all mental or psychological disorders. In this setting, characters are just as much in danger of developing a debilitating phobia, or lapsing into psychosis, as developing a skin condition. This, too, will result in a very different game world—and a very different game—than the original table.
The point, in other words, is not simply the fact of using a random table. The point, rather, is: just what exactly is on that random table, and what is not on it; and what is the distribution of the listed things. Not all random tables are created equal; not all are equally ‘fun’. The details are everything.
And now consider the application of the same caveat—to random tables, not of outcomes in a game, but of outcomes of a method of divination.
Suppose that we accept the basic idea, that we wish to be prompted to take some perspective, or think along certain lines, chosen at random out of a pool of such. The question, however, is: what, specifically, is the set of perspectives or prompts from which we are selecting? What perspectives are on there? What will be the relative frequency of certain perspectives or prompts, if you draw from this distribution repeatedly? And what is not in there?
We may imagine, for instance, two versions of the same divinatory device. In both versions, you draw a card from a shuffled 52-card deck, then consult a booklet of prompts, where each card corresponds to one entry. But the booklets are different; they were written (and the sets of prompts compiled) by people with very different philosophies (a Buddhist and a Randian, perhaps; or a Christian and a Communist).
Would not your choice of which version of this device to use for your divinations, affect the long-term outcome of using it? Might not your actions be nudged in one direction, or another—systematically? Might there not be some prominent gaps, in one or both of the distributions—perspectives which are simply absent from the set of possible prompts? What would be the consequence of such a lack?
Generators of random outcomes can be extremely efficient ways to model complex systems, by abstracting away the details of causal interactions. But be careful that the outcome distribution of the generator is one which you actually endorse.
The popular sentiment, you see, was that things should happen for a reason, because the DM decided they should happen, rather than being quite so… random. Or, of course, perhaps the game’s publishers merely wanted to economize by reducing the rule books’ page count.
I quite liked this. I’m not 100% sure how to apply it – I think I roughly agree with your final claim, and don’t think it’s reasonable to expect a fleshed out answer of how different real divination practices varied in usefulness. But I’m curious about some made-up-but-plausible examples you can imagine that would result in different outcomes, esp. factoring in something of the “what worldmodel is being communicated” bit.
I can think of a few further purely speculative inferences. Clearly, somebody created the divination systems used in various cultures throughout the world. The Xunxi quote gives reason to believe that for some members of at least some cultures, systems of ritual, perhaps including divination, were perceived as something like a useful technology. With perhaps daily use by a number of practitioners, possibly engaging in ongoing intergenerational discussions about the efficacy of their divination system, it might have been subject to many optimizing tweaks.
The I Ching does appear to have different versions. From Wikipedia: “Various modern scholars suggest dates ranging between the 10th and 4th centuries BC for the assembly of the text in approximately its current form” (emphasis mine). It seems to me that anyone telling fortunes for a regular clientele will stay in business longer if their advice offers at least the appearance of utility. Royalty might have been more educated and more sophisticated consumers of divination; perhaps they knew exactly what they were buying. After all, if it’s possible for divination to offer both the mere appearance of utility and thereal thing, all else being equal we’d expect the latter to drive the former out of the market.
When I synthesize the posts of Vaniver and Said Achmiz, it seems to suggest that divination is useful both when random and when the answers have an optimal wording and frequency distribution.
Given that different societies will feature very different pressures and power structures, it seems unlikely to me that a system of divination optimized for one culture (or segment of that culture, such as royalty) will necessarily translate with perfect fidelity to other contexts. It may not even optimize the conscious goals of the individuals using it, or the survival of their societies as a whole.
I can think of two ways divination systems might be retained. One is through conquest. If they promote that activity successfully, it might lead to the spread of the divination system. Another is through promotion of individual flourishing. If a divination system helps people achieve their aims, they might continue to use it, teach it to their children, promote it among their friends, and be imitated by their enemies.
I’d expect a system that does both to be most successful, and my mind immediately jumps to the dual nature of many religions, which are by turns warlike and peaceful. Though the “doves” and “hawks” of each culture or religion often seem to despise each other, they may very well work synergistically to promote the spread of their shared culture. The “hawks” promote an attitude of conquest and hardline defensiveness, while the “doves” promote the benefits of a focus on peaceful individual flourishing. Both can be useful propaganda tools both within their own borders and to outsiders. In order to be convincing to others, they need to be utterly convinced themselves that they are rigid hawks or committed doves. A savvy leader would known how to make use of both.
This is getting a bit away from divination at this point, so I’ll leave it there. I do think that any account of the utility of a divination practice (or other cultural practice) needs to explain for whom it provides utility and the mechanism by which it does so. That’s the reason for digressing into my “hawks and doves are best friends” theory. My guess is that even when a religion doesn’t have an obvious divinatory practice, that it has other ways of accomplishing something similar.
I’m less familiar with Island and Judaism, but in Christianity, it seems to me that sermons, rotating selections of the Bible chosen for study, prayer, and calls to take these words and rituals to heart in ways that are personally meaningful for the congregation are somewhat “random”—or at least out of the hands of the congregation unless they’re willing to change churches—and optimized, as judged by the size and growth of the congregation, or the success of cultures that and their varied practices.
It would be interesting to speculate on how much the physical form of the randomization practice or any reference text/image plays in the efficacy of these practices. Can yarrow sticks be replaced with a random number generator, if we’re aware that’s all that’s happening? Or would that make it less effective? Perhaps there is some aspect of human neurology that makes divination done with certain physical implements more compelling than that done with others.
Cf The Dice Man (a good idea for a mediocre book), in which the protagonist decides to make all decisions large & small by rolling a die.
But (and I don’t recall if the book discusses this) much then comes down to what 6 options to choose from—a decision made entirely by the protagonist. Eg if you fall out with Fred, do you include ‘punch Fred’ or ‘kill Fred’, or merely ‘criticise/ignore/undermine/forgive Fred’? And what proportion of options should be nasty vs nice?
And perhaps that decision (deciding the options) is more instructive than just making a decision cold.
This comment is going to seem unrelated or only tangentially related to the post, at first. I promise that it’s quite relevant, but explaining the relevance up-front would make the comment longer and more awkward.
Open up an old-school Dungeons & Dragons rule book (like this this one), and one thing you’ll find a whole lot of is random tables.
The idea was simple: your characters would encounter some situation; the Dungeon Master (DM) would roll some dice; then he’d consult a table, which would tell him what the outcome of the situation was, given the result of the die rolls.
Here’s a table for diseases (or disorders)[1]:
If a player character contracted a disease, or developed a disorder (which, itself, would’ve been determined by some other die rolls), the DM would roll three dice: one (a d100) to determine the afflicted part of the body; one (a d8) for whether the affliction was acute or chronic; and a third (another d8) to determine severity. The table above indicated which values on each die corresponded to which outcome.
Here’s a table for determining whether a previously undiscovered fortress or castle is inhabited, and by whom (or by what!)[2]:
Finally, here’s a table for determining what happens when two magical potions are mixed (or, when a character drinks them both)[3]:
Random tables fell out of favor, for a time.[4] But they’ve been making somewhat of a comeback (along with many other features of “old-school” D&D—the so-called “Old-School Renaissance”). One sees discussions of random tables, now and then, on blogs and web forums dedicated to tabletop role-playing games. Often, people put together their own random tables.
And—as with everything else—one sees arguments about them.
Arguments for: These usually involve the word ‘fun’. Randomness is fun, we are told, and surprises are fun; and a random table can inspire a Dungeon Master, and suggest possibilities.
Arguments against: Randomness, the critics say, does not make sense; and surprises are not fun. (Because—it is implied—they might be bad; or they are often bad; or they are usually bad.)
Both sides miss the point entirely. Very few people—even among those who love a good random table—understand the tables’ nature, and their purpose. Without understanding, when people today try to construct random tables for use in their D&D games, they often find that something is missing—some ineffable quality that makes these modern imitations of the work of Gygax fail to have quite the same satisfying and enriching effect on the game as did the random tables in the D&D rule books of old.
And that ‘something’ is that random tables are not about the mere fact of randomness.
Here is what random tables really are: they are representations of a probability distribution across a set of outcomes. As such, they encode two critical things: first, what outcomes are possible; second, those outcomes’ relative frequency.
And in consequence, here is something else that random tables are: they are models of the game world.
Look again at that first table I presented (with the diseases and disorders). A character is exposed to disease; the DM rolls d100[5]. On a roll of 1, 2, or 3, the character contracts an affliction of the blood; on a roll of 4, an illness of the bones; a roll of 5 signifies a nervous system disorder.
But another way to look at this, is that blood-related disorders are 3 times more likely—and thus 3 times more common—than bone-related disorders (at least, among adventurers!).
And the table has no entry for a disease of the lymphatic system. As a consequence, in this fictional world, no such illnesses exist (or, perhaps, they do not occur among the sorts of people that the player characters are).
Similarly, the second table (with the castles) tells us that among small-sized strongholds found in wilderness regions, 45% are deserted entirely, 15% are infested with monsters, and the remaining 40% are occupied by civilized folk.
When constructing, or choosing to use, a random table of outcomes, what you are doing is modeling the fictional world of the game. The relative frequency of the possible outcomes of the category of situation which is to be resolved by rolling on the table—and, no less importantly, which outcomes are present in the distribution at all, and which are not—are facts about that world.
Now consider two random tables, for the same situation—let us say, two versions of the disease & disorder table given above. The first is as presented, while the second has all the same rows, but the distribution is altered: on this latter table, only a single number each (out of 100, on the d100) will yield any result but ‘skin’—to which the remaining 85 out of 100 numbers are now allocated.
What are the consequences for using this latter table? Well, in a D&D game where the DM chooses to use it (in place of the original table), it is rare indeed for any character to fall ill with a disease of the respiratory system—but afflictions of the skin are terrifyingly commonplace. One hopes that the DM has a good explanation for this skew (perhaps the fictional world on which the action takes place lacks an ozone layer, resulting in a permanent epidemic of skin cancers); if not, the modeled world will fail to make much sense (one can only suspend disbelief so far, after all, and perhaps—even after we’ve accepted the existence of dragons and elves—being told that skin conditions are 85 times more common than the cold, the flu, bronchitis, and every other respiratory condition combined, is a bridge too far).
And, similarly, we may imagine yet another version of this same table—an expanded one, with many more rows than merely the 16 we see above (with the die roll result ranges—i.e., the probability mass—of the existing entries being compressed, to make room); and these additional rows are all mental or psychological disorders. In this setting, characters are just as much in danger of developing a debilitating phobia, or lapsing into psychosis, as developing a skin condition. This, too, will result in a very different game world—and a very different game—than the original table.
The point, in other words, is not simply the fact of using a random table. The point, rather, is: just what exactly is on that random table, and what is not on it; and what is the distribution of the listed things. Not all random tables are created equal; not all are equally ‘fun’. The details are everything.
And now consider the application of the same caveat—to random tables, not of outcomes in a game, but of outcomes of a method of divination.
Suppose that we accept the basic idea, that we wish to be prompted to take some perspective, or think along certain lines, chosen at random out of a pool of such. The question, however, is: what, specifically, is the set of perspectives or prompts from which we are selecting? What perspectives are on there? What will be the relative frequency of certain perspectives or prompts, if you draw from this distribution repeatedly? And what is not in there?
We may imagine, for instance, two versions of the same divinatory device. In both versions, you draw a card from a shuffled 52-card deck, then consult a booklet of prompts, where each card corresponds to one entry. But the booklets are different; they were written (and the sets of prompts compiled) by people with very different philosophies (a Buddhist and a Randian, perhaps; or a Christian and a Communist).
Would not your choice of which version of this device to use for your divinations, affect the long-term outcome of using it? Might not your actions be nudged in one direction, or another—systematically? Might there not be some prominent gaps, in one or both of the distributions—perspectives which are simply absent from the set of possible prompts? What would be the consequence of such a lack?
Generators of random outcomes can be extremely efficient ways to model complex systems, by abstracting away the details of causal interactions. But be careful that the outcome distribution of the generator is one which you actually endorse.
Dungeon Master’s Guide for Advanced Dungeons & Dragons, 1st edition; p. 14.
Dungeon Master’s Guide for Advanced Dungeons & Dragons, 1st edition; p. 182.
Dungeon Master’s Guide for Advanced Dungeons & Dragons, 1st edition; p. 119.
The popular sentiment, you see, was that things should happen for a reason, because the DM decided they should happen, rather than being quite so… random. Or, of course, perhaps the game’s publishers merely wanted to economize by reducing the rule books’ page count.
That is, the DM generates an integer between 1 and 100 (inclusive), with the distribution across the possible values being uniform.
I quite liked this. I’m not 100% sure how to apply it – I think I roughly agree with your final claim, and don’t think it’s reasonable to expect a fleshed out answer of how different real divination practices varied in usefulness. But I’m curious about some made-up-but-plausible examples you can imagine that would result in different outcomes, esp. factoring in something of the “what worldmodel is being communicated” bit.
I can think of a few further purely speculative inferences. Clearly, somebody created the divination systems used in various cultures throughout the world. The Xunxi quote gives reason to believe that for some members of at least some cultures, systems of ritual, perhaps including divination, were perceived as something like a useful technology. With perhaps daily use by a number of practitioners, possibly engaging in ongoing intergenerational discussions about the efficacy of their divination system, it might have been subject to many optimizing tweaks.
The I Ching does appear to have different versions. From Wikipedia: “Various modern scholars suggest dates ranging between the 10th and 4th centuries BC for the assembly of the text in approximately its current form” (emphasis mine). It seems to me that anyone telling fortunes for a regular clientele will stay in business longer if their advice offers at least the appearance of utility. Royalty might have been more educated and more sophisticated consumers of divination; perhaps they knew exactly what they were buying. After all, if it’s possible for divination to offer both the mere appearance of utility and the real thing, all else being equal we’d expect the latter to drive the former out of the market.
When I synthesize the posts of Vaniver and Said Achmiz, it seems to suggest that divination is useful both when random and when the answers have an optimal wording and frequency distribution.
Given that different societies will feature very different pressures and power structures, it seems unlikely to me that a system of divination optimized for one culture (or segment of that culture, such as royalty) will necessarily translate with perfect fidelity to other contexts. It may not even optimize the conscious goals of the individuals using it, or the survival of their societies as a whole.
I can think of two ways divination systems might be retained. One is through conquest. If they promote that activity successfully, it might lead to the spread of the divination system. Another is through promotion of individual flourishing. If a divination system helps people achieve their aims, they might continue to use it, teach it to their children, promote it among their friends, and be imitated by their enemies.
I’d expect a system that does both to be most successful, and my mind immediately jumps to the dual nature of many religions, which are by turns warlike and peaceful. Though the “doves” and “hawks” of each culture or religion often seem to despise each other, they may very well work synergistically to promote the spread of their shared culture. The “hawks” promote an attitude of conquest and hardline defensiveness, while the “doves” promote the benefits of a focus on peaceful individual flourishing. Both can be useful propaganda tools both within their own borders and to outsiders. In order to be convincing to others, they need to be utterly convinced themselves that they are rigid hawks or committed doves. A savvy leader would known how to make use of both.
This is getting a bit away from divination at this point, so I’ll leave it there. I do think that any account of the utility of a divination practice (or other cultural practice) needs to explain for whom it provides utility and the mechanism by which it does so. That’s the reason for digressing into my “hawks and doves are best friends” theory. My guess is that even when a religion doesn’t have an obvious divinatory practice, that it has other ways of accomplishing something similar.
I’m less familiar with Island and Judaism, but in Christianity, it seems to me that sermons, rotating selections of the Bible chosen for study, prayer, and calls to take these words and rituals to heart in ways that are personally meaningful for the congregation are somewhat “random”—or at least out of the hands of the congregation unless they’re willing to change churches—and optimized, as judged by the size and growth of the congregation, or the success of cultures that and their varied practices.
It would be interesting to speculate on how much the physical form of the randomization practice or any reference text/image plays in the efficacy of these practices. Can yarrow sticks be replaced with a random number generator, if we’re aware that’s all that’s happening? Or would that make it less effective? Perhaps there is some aspect of human neurology that makes divination done with certain physical implements more compelling than that done with others.
Cf The Dice Man (a good idea for a mediocre book), in which the protagonist decides to make all decisions large & small by rolling a die.
But (and I don’t recall if the book discusses this) much then comes down to what 6 options to choose from—a decision made entirely by the protagonist. Eg if you fall out with Fred, do you include ‘punch Fred’ or ‘kill Fred’, or merely ‘criticise/ignore/undermine/forgive Fred’? And what proportion of options should be nasty vs nice?
And perhaps that decision (deciding the options) is more instructive than just making a decision cold.