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Abstract. Poe divination, akin to multiple coin-flipping in form, is the commonest sort of everyday divination used in Taiwan. This paper explores the statistical properties of poe as they are used by Hokkien-speakers in Taiwan, and suggests that these qualities are known and deliberately manipulated by Taiwanese when they use poe, even though they simultaneously believe the fall of the poe to be governed by divine will.
A simple man believes every word he hears; a clever
man understands the need for proof.
—Proverbs 13:15 (NEB)
In temples and occasionally at home, Taiwanese routinely perform simple divination by means of two half-moon-shaped wooden or bamboo blocks, each of which is flat on one side and rounded on the other. Held with the flat sides together, the pair looks rather like a small banana cut in half lengthwise. They are inevitably painted red, and in Taiwanese Hokkien they are called poe (pronounced "bwey," to rhyme with English "whey").
The poe are used by throwing them on the floor to see whether they land rounded-side-up or flat-side-up. We may envision the process as comparable to throwing a pair of coins. The most usual procedure is for the petitioner to pose a question, and then phrase an answer. He then throws a pair of poe to receive confirmation or disconfirmation of the answer. If the two poe fall identically (both flat-side-up or both rounded-side-up), then the formulation of the answer is disconfirmed and a new answer must be proposed. If they fall differently (one flat-side-up, the other rounded-side-up), this represents a positive response.
If the probability of a single poe falling rounded-side-up is the same as the probability of its falling flat-side-up (that is, if it is equivalent to a statistically "fair" coin), then the probabilities for positive and negative responses on one throw of a pair of poe are as shown in Table 1.
However, confirmation of the formulation normally requires a run of three positive responses (siūn-poe) in a row. Thus if a petitioner formulates his revelation, throws a pair of poe, and gets a negative response, he reformulates the revelation and tries again. If he gets a positive response, then he throws the poe a second time. If he gets a second positive response, he throws them a third time. The third positive response concludes the divination session on that question, since the formulation now gains the status of a confirmed revelation.
If the probability of a "different" toss (D) is the same as the probability of a "same" toss (S), that is if D = S = 50%, and if a confirmed formulation requires three successive D tosses, then the probability of confirming any particular formulation (C) is D3 or 0.125: one chance in eight.
| Table 1: Probabilities of Different Combinations of Tosses of a "Fair" Poe | ||||
|---|---|---|---|---|
| Name | First Poe | Second Poe | Probability | Positions |
| i. chhìo-poe 笑盃 |
flat side up | flat side up | 25% | Same |
| ii. im-poe 陰盃 |
rounded side up | rounded side up | 25% | Same |
| iii. siūn-poe 聖盃 |
rounded side up | flat side up | 25% | Different |
| iv. siūn-poe 聖盃 |
flat side up | rounded side up | 25% | Different |
Not surprisingly, most revelations must be reformulated several times before they are confirmed. The probability of a statement requiring N formulations to be confirmed is equal to the product of the probabilities of disconfirmation (1-C) on all previous trials times the probability of confirmation (C) on the Nth trial, or
This is a constantly declining number, that is to say, the probability of a revelation requiring two formulations is less than the probability of its requiring one, and the probability of requiring three formulations is less than requiring two, and so on. The result, as Table 2 shows, is an infinite series of declining probabilities, with some revelations requiring a very large number of reformulations indeed. Or, as any worshipper knows, it sometimes takes a long time before you can get a god to agree to something.
| Table 2: Probability OF Confirmation by Poe on the Nth Formulation | ||
|---|---|---|
| Formulation Number | Probability of Confirmation at N | % of Divinations with Confirmation (cumulative probability) |
| N=1 | 12.5% | 12.5 |
| N=2 | 10.9% | 23.4 |
| N=3 | 9.6% | 33.0 |
| N=4 | 8.4% | 41.4 |
| N=5 | 7.3% | 48.7 |
| N=6 | 6.4% | 55.1 |
| N=10 | 3.8% | 83.1 |
| N=20 | 1.0% | Nearly All |
| N=50 | 0.018% | Nearly All |
| N=100 | 0.0000002% | Nearly All |
Slightly fewer than half of all petitioners will receive a confirmed revelation within their first five formulations. The mean (M) number of formulations to confirmation, however, is much higher, since occasionally confirmation is not achieved for a long time. The mean number of formulations to confirmation is given by the formula:
The standard deviation (S) will be given by:
or in this case:
Statistically, poe divination is not dissimilar to flipping a pair of coins. Unlike the pair of coins, however, the fall of the poe is invested with religious meaning. Poe are the most general and simple device used to approximate the godly side of religious interaction in Táiwān. As fair coins are expected to be governed by the "laws" of chance, so poe are expected to be governed by divine intelligence and will.
However —and here we come to the crucial point for the present argument— the typical Chinese believer seems to have a simultaneous realization that the poe are subject to influences other than godly ones. Quite aside from the possibility of malign forces affecting them (which is believed to happen occasionally), there seems to be an understanding that "Thou shalt not tempt the Lord thy God" by asking that the poe perform statistically improbable feats. The poe must be dropped from a reasonable height, not merely a couple of centimeters off the floor, for example. Similarly one cannot "correctly" specify in an invocation that confirmation or denial will require a run of some very high number of "sames" or "differents" in a row rather than the usual three.
An eccentric elder in the village of Bao-an (Bǎo'ān 保安) in southern Táiwān tried to make such a specification. A certain village-wide ritual was due to come to an end when the gods finished partaking of ritual food. The elder was in charge of the divination that determined when they had had enough, but he also wanted the ritual to continue as long as possible (for reasons that need not concern us here). To prevent the ritual from ending, he kept wording prayers of inquiry so as to require a run of a very high number of "differents" in a row as an indication that the gods were done and that the rite could be stopped.
The evening wore on, and the gods never seemed to finish eating. Finally another elder removed his sacrifices in disgust on the grounds that "He is asking questions in such a way that he can't possibly get an affirmative answer" (Jordan, 1972: 63). Both elders clearly appreciated the statistical nature of the poe, and the second one easily enough recognized and described the misuse of them by his colleague.
Using the poe with the belief that they are divinely manipulated rather than controlled by chance requires a suspension of one's belief in their statistical characteristics. But at the same time the correct use of the poe requires action that takes account of those characteristics, and when action does not take account of them, the action may be condemned (very carefully) as "wrong." The believer using poe, unlike the statistician flipping coins, must appreciate the statistical nature of the instrument and act in terms of it while at the same time maintaining a belief that denies that same nature. This is similar to the petitioner engaging in prayer who must pray believing that his prayer will be answered, at the same time he resists asking for what he cannot reasonably expect to get in the natural course of things. To perform such intellectual juggling requires one of two intellectual devices if it is to remain viable:
Either a convention for solving the problem or a prohibition on discussing it represents a cultural response to it, however. "Somebody" has asked the questions, and "somewhere" it was decided what answer would be acceptable or what inquiries would be rejected.
Returning to the general point, poe divination depends upon slight of hand by the believers themselves, upon a kind of individual or collective self-deception. The devices by which this self-deception is sustained are a legitimate object of ethnographic inquiry because they are legitimate parameters of the system of religious practice and belief.