Parashat Aharei-Mot – Kedoshim 5770/ April 24, 2010
the weekly Torah reading by the faculty of
Choosing the Scapegoat
Prof. Eli Merzbach
Department of Mathematics
At the beginning of this week’s reading Aaron is commanded, “Place lots (goralot) upon the two goats, one marked for the Lord and the other marked for Azazel” (Lev. 16:8). Lots relate to the notion of randomness, which we shall examine below.
The Sages deduce that the two goats on whom the lots were cast had to be absolutely identical in appearance, size and shape, so that one could not tell them apart.  The Torah commands that the process of drawing lots be applied to them. This was an interesting process: two utterly equal lots were brought and placed in a box (also required by the Torah). The box was placed in the eastern part of the Sanctuary courtyard, and the two goats were stood facing west, their rears to the east. The High Priest would approach, with the Prefect on his right, the chief of the weekly guard on his left, and the two goats in front of him, one on the right and the other on the left. The High Priest would shake the box and draw out the lots, “so that he not deliberately take,” i.e., so that there be no planning or ordered human factor influencing the outcome. The choice of goat had to be utterly random. So important was this that tannaim and amoraim argued among themselves as to whether mis-drawing of the lots impeded further action or whether the process was but for the sake of performing a commandment. The Halakhah ruled that mis-drawing the lots constituted an impediment: the entire worship of the Day of Atonement would become invalid if the goats were not chosen by lot. The Zohar also stresses the importance of drawing lots and the obligation to perform this action to the Lord’s satisfaction.
The Sages drew important conclusions from the outcome of
the lots. For example, Tractate Yoma
(39b) recounts that during the forty years during when Simeon the Just served
as High Priest the lot “for the Lord” always fell on the goat to the right – a
sign that the people were following the ways of the Lord.
But after his death the lot sometimes fell on
the goat to the right, sometimes to the left, and during the last forty years
Simple statistical analysis shows that the Sages’ conclusions were well-founded. The chances of randomly obtaining the same result forty times in a row is 2-39, or approximately 10-12. To illustrate the minuteness of this number, suppose that every day is the Day of Atonement and the High Priest casts lots 1000 times each day. Then it would take about three million years to come up with the same result forty consecutive times. In statistical analysis, when one has a probability less than 0.05 (i.e., a degree of significance of 95%) it is customary to reject the assumption of absolute randomness and to conclude that a “directing hand” is at play. 
For the Sages, evidently, randomness has clear theological
significance. Randomness denotes the
hidden hand of G-d and reveals the Creator’s will to human beings or is
supposed to reveal to humans the way they should follow.
Thus randomness is the diametrical opposite
of uncertainty. Casting lots to choose the goats for the sacred service on the
Day of Atonement conveys a clear message that human beings must free themselves
of their evil inclination, of all the false ideologies that have insinuated
their way into their lives during the past year.
These are hinted at by the goat for Azazel,
from which we must free ourselves. Even
if both goats are seemingly identical, choosing the goat on the left by lot meant
acknowledging that one must cast off undesirable qualities and signified that
repentance and atonement, as befits the Day of Atonement, is possible.
Likewise, the other goat is to be sacrificed
to the Lord. If the lots determined that
goat to be the one on the right, then the people concluded that they were on
the correct path. Herein lay the great
importance of the two lots on the Day of Atonement; for the special
relationship between the Holy One, blessed be He, and the High Priest,
representing the people of
Randomness has several manifestations in the Bible, including: chance, lot, luck, divination, and magic. Lots are also denoted by numerous terms. For example, in Yalkut Shimoni (Parashat be-Shalah, par. 285), we read as follows:
Lots were called by four names:
halash, pur, goral, and hevel.
The descendants of Esau were smitten by all
of them; Amalek, by halash, as it is written, “And Joshua overwhelmed [va-yahalosh;
the people of Amalek]” (Ex. 17:13); and the fourth kingdom [to subjugate
A wide variety of verbs are associated with lots in the Bible, including hippil, hishlikh, yadah, yarah, hittil, alah, yatzah, and hayah. This abundance of verbs attests to the actively rich appearance of the element of lots or fate in all walks of human life. As a noun, the word goral (=fate/lot) in Scripture hints at control and unequivocal direction by the hand of G-d.
To this day there exists no unequivocal scientific definition of randomness. A random event is thought to be an unimportant occurrence of uncertain cause. In the modern world the sanctity has disappeared entirely from the notion of randomness. There is a branch of mathematics known as probability theory that deals with quantifying randomness, developing axioms (logical systems) and investigating concepts such as independent events, stochastic processes, and boundary cases. Despite the achievements of this theory, nothing has been said about the deep significance of chance. Computer science attempts to develop algorithms that generate pseudo-random numbers, but human creativity is incapable of creating true randomness. To create randomness one must have a higher degree of complexity than is known today.
The special approach of the Sages to random events is not restricted to the realms of thought and philosophy, rather it has considerable impact on daily life. This finds expression in the many rules of halakhah that concern casting lots. Given the influence of Western culture to which Judaism has been subject for decades, one can well surmise that these rules of halakhah are not widely known today.
The word goral in the Bible ostensibly has several meanings. It denotes objects used to resolve problems or obtain definitive answers in time of uncertainty (such as how the tribal inheritance would be divided). Another sense is the fate or destiny of a person or thing, as in the book of Daniel: “Arise to your destiny at the end of the days” (12:13). Both these senses of the word are clearly connected: just as one does not know the outcome of drawing lots, so too the fate or future of a person is unknown and unforeseeable. Whether a person’s future indeed cannot be foreseen is subject to debate, nevertheless the term fate implies, be it consciously or unconsciously, that factors hidden from our awareness affect the result.
It is generally thought today that humankind is subject not only to chance or fate, but that we are fate itself. This does not mean that we do not control or affect the course of our lives. Freedom always exists, but we must give the existential course of freedom a direction of our choice. In hindsight people do not view what happens to them as reflecting the hand of chance.
Randomness has deep significance in Judaism and serves the following five objectives:
These ideas are not mutually contradictory. Their practical realization finds expression in the concept of fate/lot and in the many rules of halakhah surrounding this concept.
It is said to be an art to turn the unexpected into the inevitable. To this I add that fate is “to turn the inevitable into the unexpected.”
 Sifra, Parashat Aharei-Mot, ch. 2; Tractate Yoma 82a.
 Cf. my article, “Tahalikhim Mikriyim le-fi Tefisat Hazal,” Higayon 1 (1989), pp. 31-38.
 Randomness as an overt force calls to mind the holiday of Purim. This connection between the Day of Atonement (Yom ha-Kippurim) and Purim is well-known.