Superstition

Pesachim 109b ~ The Square Root of Two and the Danger of Pairs

The Mishnah established that a person must drink four cups of wine on the night of the Passover Seder. But this may pose a problem:

פסחים קט, ב

לֹא יִפְחֲתוּ לוֹ מֵאַרְבָּעָה. הֵיכִי מְתַקְּנִי רַבָּנַן מִידֵּי דְּאָתֵי בֵּהּ לִידֵי סַכָּנָה, וְהָתַנְיָא: לֹא יֹאכַל אָדָם תְּרֵי, וְלֹא יִשְׁתֶּה תְּרֵי, וְלֹא יְקַנַּח תְּרֵי, וְלֹא יַעֲשֶׂה צְרָכָיו תְּרֵי

Dice double 2.jpg

But wasn’t it taught in a baraita: A person should not eat pairs, i.e., an even number of food items; and he should not drink pairs of cups; and he should not wipe himself with pairs; and he should not attend to his sexual needs in pairs.

The rabbis were concerned that doing things in pairs exposes a person to sorcery or demons. Why then would the Mishnah require that an even number of cups be drunk? That would place a person in great danger! Rabbi Nachman provides some reassurance. No harm will come because the night of the Passover Seder is a special night.

פסחים קט, ב

אָמַר רַב נַחְמָן, אָמַר קְרָא: ״לֵיל שִׁמּוּרִים״ — לַיִל הַמְשׁוּמָּר וּבָא מִן הַמַּזִּיקִין

Rav Nachman said that the verse said: “It was a night of watching to the Lord” (Exodus 12:42), which indicates that Passover night is a night that remains guarded from demons and harmful spirits of all kinds. [Therefore, there is no cause for concern about this form of danger on this particular night.]

Additional, or perhaps alternative reasons for reassurance are provided by the great Babylonian sage Rava (c.280-352), and Ravina, who lived several generations later:

רָבָא אָמַר: כּוֹס שֶׁל בְּרָכָה מִצְטָרֵף לְטוֹבָה, וְאֵינוֹ מִצְטָרֵף לְרָעָה. רָבִינָא אָמַר: אַרְבָּעָה כָּסֵי תַּקִּינוּ רַבָּנַן דֶּרֶךְ חֵירוּת, כׇּל חַד וְחַד מִצְוָה בְּאַפֵּי נַפְשַׁהּ הוּא

Rava said: The cup of blessing for Grace after Meals on Passover night is used in the performance of an additional mitzva and is not simply an expression of freedom. Therefore, it combines with the other cups for the good, i.e., to fulfill the mitzva to drink four cups, and it does not combine for the bad. [With regard to the danger of drinking pairs of cups, it is as though one drinks only three cups.]

Ravina said: The Sages instituted four separate cups, each of which is consumed in a manner that demonstrates freedom. Therefore, each and every one is a distinct mitzva in its own right.[In other words, each cup is treated separately and one is not considered to be drinking in pairs.]

The Danger of Pairs

Over the next few pages of Talmud (Pesachim 109-111) the rabbis explain some of the issues around pairs.

פסחים קי, א

תָּנוּ רַבָּנַן: שׁוֹתֶה כִּפְלַיִם — דָּמוֹ בְּרֹאשׁוֹ. אָמַר רַב יְהוּדָה: אֵימָתַי — בִּזְמַן שֶׁלֹּא רָאָה פְּנֵי הַשּׁוּק, אֲבָל רָאָה פְּנֵי הַשּׁוּק — הָרְשׁוּת בְּיָדוֹ. אָמַר רַב אָשֵׁי: חֲזֵינָא לֵיהּ לְרַב חֲנַנְיָא בַּר בִּיבִי, דְּאַכֹּל כָּסָא הֲוָה נָפֵיק וְחָזֵי אַפֵּי שׁוּקָא. 

The Sages taught in another baraita: If one drinks in pairs his blood is upon his head [i.e., he bears responsibility for his own demise]. Rav Yehuda said: When is that the case? When one did not leave the house and view the market place between cups. However, if he saw the marketplace after the first cup, he has permission to drink another cup without concern. Likewise, Rav Ashi said: I saw Rav Chananya bar Beivai follow this policy: Upon drinking each cup, he would leave the house and view the marketplace.

The great Babylonian sage Abaye (d~337 CE.) was raised never to drink precisely two cups.

פסחים קי, א

וְאַבָּיֵי, כִּי שָׁתֵי חַד כָּסָא, מְנַקֵּיט לֵיהּ אִימֵּיהּ תְּרֵי כָסֵי בִּתְרֵי יְדֵיהּ

When Abaye would drink one cup, his mother would immediately place two cups in his two hands so that he would not inadvertently drink only one more cup and thereby expose himself to the danger of drinking in pairs.

Rav Nachman, who was a contemporary of Abaye, apparently had a personal butler, and followed a similar practice:

 וְרַב נַחְמָן בַּר יִצְחָק, כִּי הֲוָה שָׁתֵי תְּרֵי כָסֵי, מְנַקֵּיט לֵיהּ שַׁמָּעֵיהּ חַד כָּסָא, חַד כָּסָא — מְנַקֵּיט לֵיהּ תְּרֵי כָסֵי בִּתְרֵי יְדֵיהּ

 And similarly, when Rav Nachman bar Yitzchak would drink two cups, his attendant would immediately place one more cup in his hand, and if he would drink one cup, the attendant would place two cups in his two hands. These reports indicate that one should be concerned for his safety after drinking an even number of cups, even when he remains at home.

Isaac Baer Levinsohn On the origins of the Suspicion

Isaac Baer Levinsohn (1788-1860) was a Ukrainian Hebrew scholar and leader of the Haskalah. In a collection of his essays and letters called Yalkut Rival published in Warsaw in 1878 he addressed the origin of the Talmudic concern about pairs of things. Here it is:

Yalkut Riva’l, Warsaw 1878, p59-60.

Yalkut Riva’l, Warsaw 1878, p59-60.

The Babylonian Talmud, Chapter Arve Pesachim, (109–110), expounds at length on the matter of concern about zugot, even numbered events…

In early general literature, I found that both the Greek philosopher Pythagoras and his student Plato were most particular about the number two. They believed that it indicates very bad omen. During the era of Pythagoras, this belief was prevalent over the entire Italian region. The Romans also believed in the terrible powers of the number two. Since they customarily consecrated all evil things to the god Pluto, we find in mythological books of the early Romans that the second month of the year and the second day of that month were consecrated to this god…

Our Sages (who generally sought scriptural hints at established customs) noted [in Gen. Rab. 4:7] that the second of the six days of creation is the only one in which ki tov, “that it is good” [Gen 1:6–8], is not written. We also treat the fourth day of the week like the second day, and do not begin projects on it…

However, it is distinctly possible that the number four is considered to not be good because of zugot, as it is a double pairTractate Pesachim of the Babylonian Talmud [112b] also states that on the eve of the fourth day [= Tuesday night] Agrat bat Machlat ventures out (see my Bet Yehudah for speculation as to the original identity of Agrat, the qelipah “shell”). Finally, to defuse these primitive beliefs from the hearts of the masses, our sages maintained elsewhere that Monday and Wednesday are, in fact, excellent days to begin projects, with a mnemonic: Ba”D qodesh, “holy Monday and Wednesday,” literally “holy fabric.”

The fear of √2

It is not clear to which writings attributed to Pythagorus Levinsohn was referring, but it may be connected to the Pythagorean discovery (if it was indeed discovered by him) that the square root of two is an irrational number. In his sweeping history of mathematics The Universal History of Numbers: From Prehistory to the Invention of the Computer Georges Ifrah wrote (p.596) that the discovery that √2 is irrational (meaning it goes on and on forever without a repeating pattern, like π) “greatly perturbed the Pythagoreans, who believed that number ruled the Universe…”

The new numbers were called “unmentionable” and the existence of these monsters was not to be divulged to the profane. According to the Pythagorean conception of the world, this inexplicable error on the part of the Supreme Architect must be kept secret, lest one incur divine wrath.

Could this explain the origin of the fear of the number two, and from that the fear of doubles in general?

The Code of Jewish Law on auspicious days

In general, Jews are forbidden to pay any attention to superstitions, although as those of you who have spent time studying the Talmud will know, Jews are a superstitious lot. Here is the Shulchan Aruch, the Code of Jewish Law, on the topic:

שולחן ערוך יורה דעה 179

שלא לכשף לעונן ולנחש. ובו י"ט סעיפים
אאין שואלין בחוזים בכוכבים ולא בגורלות: הגה משום שנאמר תמים תהיה עם ה' אלהיך (ב"י בשם תוספות דע"פ ובשם ספרי) וכ"ש דאסור לשאול בקוסמים ומנחשים ובמכשפים (פסקי מהרא"י סי' צ"ו):

It is forbidden to turn to astrologers or those who forecast using lotteries. For it is written “You shall be perfect with the Lord your God”

So far so good. But then comes this:

נהגו בשאין מתחילין בב' ובד' גואין נושאין נשים אלא במילוי הלבנה: הגה ולכן נהגו ג"כ להתחיל ללמוד בר"ח כי אע"פ שאין ניח

We have the custom not to begin a project on the second day of the week, or the fourth day of the week

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Superstition in our Modern World

Our modern, rational world is still filled with superstitions. In the US, at lest 85% of buildings using an Otis elevator do not have a thirteenth floor. Actors still say to one another “break a leg” right before a show, reflecting a superstition that wishing an actor “good luck” was…bad luck. And there are any number of superstitions around boats and boating. Pairs and irrational numbers may no longer frighten us but just like our ancestors, we remain, sadly, a superstition-wary people.

אָמַר רַב פָּפָּא, אָמַר לִי יוֹסֵף שֵׁידָא: בִּתְרֵי קָטְלִינַן, בְּאַרְבְּעָה לָא קָטְלִינַן, בְּאַרְבְּעָה מַזְּקִינַן. בִּתְרֵי, בֵּין בְּשׁוֹגֵג בֵּין בְּמֵזִיד. בְּאַרְבְּעָה, בְּמֵזִיד — אִין, בְּשׁוֹגֵג — לָא

Rav Pappa said: Yosef the Demon said to me: “If one drinks two cups, we demons kill him; if he drinks four, we do not kill him. But this person who drank four, we harm him. There is another difference between two and four: With regard to one who drinks two, whether he did so unwittingly or intentionally, we harm him. With regard to one who drinks four, if he does so intentionally, yes, he is harmed; if he does so unwittingly, no, he will not be harmed.”
— פסחים קי, א -Pesachim 110a

For more on the fifth cup and magical pairs, see the excellent paper by Leor Jacobi from where the translation of Levinsohn’s paragraph on the origin of the suspicion was taken.

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