The Ultimate Space-Saver
This article originally appeared in the Jewish Free Press, Calgary

The Ultimate Space-Saver*

Modern technology has devised many ingenious ways to make more efficient use of space and to miniaturize objects so that they perform their functions without leaving large footprints. Nonetheless, to the best of my knowledge, we have not yet reached the stage where we can produce structures that literally occupy no space at all.

It would appear that Jewish lore ascribed such impressive qualities to architectural masterpieces of the past, especially to the holy Temple of Jerusalem.

Take for example the passage in the Mishnah Avot that relates the experiences of the throngs of pilgrims who assembled for the major festivals. “They would be constricted when standing, but had adequate space to prostrate themselves.” Rashi explained that this was a truly miraculous occurrence—a twofold miracle, in fact. Not only would the bodies of the worshippers be elevated above the ground to prevent their intruding on each other’s individual space, but the area would actually expand to separate them, in order to insure privacy when they were reciting their personal confessions.

However, not all the commentators were willing to interpret the passage in blatantly supernatural terms. Rabbi Menahem Meiri wrote more prosaically that the worshippers were forced to stand on their tiptoes to keep from trampling on their neighbours’ toes. According to Maimonides, the Mishnah was merely describing the subjective feelings of the worshippers who became oblivious to the crowding because they were overwhelmed by feelings of intense reverence for the holy place.

In other talmudic passages, the rabbis read various biblical texts as implying that hundreds of thousands of Israelites were squeezed together in the doorway or courtyard of the Tabernacle for the dedication ceremonies; or atop the small rock that produced water for the congregation in the wilderness.

In a similar vein, the talmudic sages claimed regarding Solomon's Temple, that “the ark was not included in the measurement” of the twenty cubits of the sanctuary’s length. The simple sense of this statement is probably that the area contained by the ark was not included in the calculation of the ten cubits separating each of its sides from the wall of the inner sanctuary. However, in the Babylonian Talmud the statement was construed as proof that the ark “was standing miraculously.” Rashi explained this to mean that the ark “did not occupy any space at all that would diminish from the dimensions of the space of the room”!

Rashi's interpretation follows logically from the analogy that the Talmud drew between the case of the ark and a similar phenomenon involving the dimensions of the cherubs and their wings. The third-century sage Samuel calculated that it is impossible to fit the two cherubs into the twenty cubits of the sanctuary’s length, since the length of each of their wings was five cubits; so if they were allowed to spread to their full capacity, the four wings would span twenty cubits, and would not leave any room for the parts of cherubs’ bodies that were not coextensive with the wings. This led Samuel to the conclusion that the cherubs and their wings did not occupy any measurable physical space in the sanctuary. The fact that the Talmud equated the cases of the ark and of the cherubs demonstrates that, in their opinion, the essence of the miracle lay in the premise that neither object occupied any space in the sanctuary.

The miracles in question were evidently characterized by violations of the laws of geometry: if we were to measure from either edge of the ark until the Sanctuary wall, we would come up with a distance of ten full cubits, even though the ark itself was two and a half cubits wide and the total length of the Sanctuary was exactly twenty cubits.

In most of the Greek and Roman philosophical schools that were contemporary with the talmudic rabbis, it was widely assumed that even God is subject to the fundamental laws of logic and mathematics. On these grounds, several philosophers ridiculed religious beliefs that defied basic logic, such as the doctrine that the universe was created out of nothing.

The famed physician and philosopher Galen (129 – c. 200) chided the Torah for believing that there are no limits to what God can do. “We however do not hold this; we say that certain things are inherently impossible and that God does not even attempt such things at all.”

In the twelfth century, the Jewish physician Maimonides was aware of Galen’s position and of his accusations about the Torah’s irrationality. Maimonides refuted those charges, insisting that they were based on a misrepresentation of Jewish teachings. “Moses’ real opinion is that the power to do impossible things cannot be ascribed to God.” While there may be room for legitimate philosophical debate over which things are inherently impossible (such as the doctrine of creation out of nothing), this does not alter the basic axiom that even God acts within the principles of rationality, which include the laws of mathematics.

It would appear that the traditions that spoke literally of the ark or cherubs not occupying any space in the sanctuary would have been treated by Maimonides as no different from a claim that two and two equal five. People who believe in miracles of this sort are not enhancing the Almighty’s greatness—quite the contrary, this kind of primitive credulity is characteristic of “those who are ignorant of mathematics and …know only the words in isolation but do not comprehend their true meanings.”

In the end, Maimonides determined that the tradition about pilgrims standing crowded but bowing spaciously, if taken literally, misrepresented the capabilities of the omnipotent deity, notwithstanding the whimsical embellishments of the rabbis.

In spite of Maimonides’ defense of Judaism’s intellectual sophistication, a survey of rabbinic texts would seem to bear out some of the allegations that were directed by Galen and others against the uncritical Jewish acceptance of impossible miracles. The sages of the Talmud and the Midrash remained largely unaffected by the philosophical views that were prevalent in their Greek-thinking environment. This strikes us as all the more astonishing when we bear in mind that, at about the same time, the question of God’s power to violate logical rules was the topic of vehement debates between the philosophers and the representatives of revealed religious traditions, and that the uncritical Jewish belief in miracles had provided ammunition for assaults on the intellectual cogency of Judaism (and of Christianity).

Come to think of it, in our brave new world of quantum mechanics, wormholes, non-Euclidian geometry and nanotechnology, the notion of zero-space objects need no longer be dismissed as absurdly illogical. Indeed, it might offer renewed hope for us commuters who have to squeeze ourselves into packed trains or overloaded urban parking lots.


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My email address is: eliezer.segal@ucalgary.ca

[*]
  • First Publication:
    • The Jewish Free Press, Calgary, February 5, 2016, p. 11.
  • For further reading:
    • Dienstag, Jacob Israel. “Introduction: The Relationship of Maimonides to His Non-Jewish Predecessors; an Alphabetical Survey.” In Studies in Maimonides and St. Thomas Aquinas, xxxvii – xxxix. Bibliotheca Maimonidica 1. New York: Ktav, 1975.
    • Goldin, Judah. “A Philosophical Session in a Tannaite Academy.” In Essays in Greco-Roman and Related Talmudic Literature, 366–86. New York: Ktav, 1977.
    • Guttmann, Julius. The Philosophy of Judaism: The History of Jewish Philosophy from Biblical Times to Franz Rosenzweig. Northvale, NJ: J. Aronson, 1988.
    • Harvey, Warren Zev. “Rabbinic Attitudes Toward Philosophy.” In “Open Thou Mine Eyes ...”: Essays on Aggadah and Judaica Presented to Rabbi William G Braude on His Eightieth Birthday and Dedicated to His Memory, 83–101. Hoboken, NJ: Ktav, 1992.
    • Husik, Isaac. A History of Mediaeval Jewish Philosophy. Mineola, NY: Dover Publications, 2002.
    • Rabinovitch, N. L. “The Concept of Possibility in Maimonides.” Tarbiz 44, no. 1 (1975): 159–71.
    • Rokeah, David. Jews, Pagans and Christians in Conflict. Leiden and Jerusalem: E J Brill and Magnes Press, 1982.
    • Schacht, J., and Max Meyerrhof. “Maimonides against Galen, on Philosophy and Cosmogeny.” Bulletin of the Faculty of Arts of the University of Cairo 5, no. 1 (1937): 53–88.
    • Segal, Eliezer. “‘The Few Contained the Many’: Rabbinic Perspectives on the Miraculous and the Impossible.” Journal of Jewish Studies 54, no. 2 (2003): 273–82.
    • Stern, Menahem. Greek and Latin Authors on Jews and Judaism. Fontes Ad Res Judaicas Spectantes. Jerusalem: Israel Academy of Sciences and Humanities, 1974.
    • Walzer, Richard. Galen on Jews and Christians [microform. Oxford Classical and Philosophical Monographs. London: Oxford University Press, 1949.