Yoma 65b ~ Counting the Years

There is a special rule about selling a house in a walled city in the Land of Israel. The seller has the right to buy back his property for one year. If he fails to do so in that time it becomes the permanent property of the buyer. This is learned from a verse in Leviticus:

ויקרא 25:30

וְאִ֣ם לֹֽא־יִגָּאֵ֗ל עַד־מְלֹ֣את לוֹ֮ שָׁנָ֣ה תְמִימָה֒ וְ֠קָ֠ם הַבַּ֨יִת אֲשֶׁר־בָּעִ֜יר אֲשֶׁר־[ל֣וֹ] חֹמָ֗ה לַצְּמִיתֻ֛ת לַקֹּנֶ֥ה אֹת֖וֹ לְדֹרֹתָ֑יו לֹ֥א יֵצֵ֖א בַּיֹּבֵֽל׃

If it is not redeemed before a full year has elapsed, the house in the walled city shall pass to the purchaser beyond reclaim throughout the ages; it shall not be released in the jubilee.

The next question is, what is meant by “a full year”? This is the subject of a dispute on today’s page of Talmud:

יומא סה, ב

דְּתַנְיָא: ״שָׁנָה תְּמִימָה״, מוֹנֶה שְׁלֹשׁ מֵאוֹת וְשִׁשִּׁים וַחֲמִשָּׁה יוֹם כְּמִנְיָן יְמוֹת הַחַמָּה, דִּבְרֵי רַבִּי. וַחֲכָמִים אוֹמְרִים: מוֹנֶה שְׁנֵים עָשָׂר חֹדֶשׁ מִיּוֹם לְיוֹם

It was taught in a baraita: With regard to redeeming houses in a walled city the Torah states: “And if it not be redeemed within the space of a full year” (Leviticus 25:30), which indicates that he counts 365 days, in accordance with the number of days in a solar year; this is the statement of Rabbi Yehuda HaNasi. And the Rabbis say: He counts twelve months from day to day.

According to the great Rebbi Yehudah HaNasi (135-217 C.E.) a full year usually means a full solar year of 365 days. A solar year is the time it takes the earth to complete one revolution all the way around the sun. (Or for those of you living in a geocentric universe, that is the time taken for the sun to complete one revolution around the earth). Just like Rebbi, we assume that a solar year is 365 days long, but in fact it is a little less than 365 1/4 days: that is to say, 365 days 5 hours, 48 minutes and 46 seconds. Those extra five and a bit hours are the reason we have a leap year every four years or so, when they add up to almost another 24 hours. And there are other kinds of “solar” years.

The Solar Year

The solar year is the average amount of time it takes the sun to return to the same position as seen from the earth. It is usually measured from one vernal equinox to the next. (The vernal equinox is the day on which the length of day and of the night are equal.) You can see this on the drawing below, taken from H. A. Rey’s wonderful book The Stars (and yes, it is the same H.A. Rey of Curious George fame.) In the drawing, a solar year is the time it takes the sun (as seen from the earth) to orbit from one spring equinox to the next, which is about 365 days 5 hours 48 minutes and 30ish seconds, or 365.242 days.

The solar year is also known as the tropical year and it is also the length of our calendar year. In today’s page of Talmud when Rebbi referred to the “מִנְיָן יְמוֹת הַחַמָּה” or “the the number of days in a solar year” this is what he meant.

The sidereal year

Just like a spinning top the earth wobbles as it orbits the sun.

But there is another way of measuring the year, and it is the amount of time it takes the sun to appear against the same background of fixed stars. It is known as the sidereal year, from the Latin sidus meaning star. And a sidereal year is 20 min 24.5 seconds longer than a tropical year. The sidereal year is longer because of the precession of the equinoxes, the term given to the phenomenon that in addition to orbiting the sun, the earth is wobbling like a spinning top. As the earth returns to the same position it had one full solar orbit ago, the tilt of the earth is not now directly toward the Sun: because of the effects of precession, it is a little way "beyond" this. The sun does not line up against the background of the stars as it did one year ago, and we need to wait an additional few minutes for sun and earth to line up as they did then.

The lunar year

The rabbis were of the opinion that “the year” in question is the period of twelve lunar months that make up a regular (non-leap) Jewish year. That would be 354 days, which is 11 days and some shorter than a solar or sidereal year.

There is no “correct” way to count a year. It is a matter of convention. We have fiscal years and academic years, draconic years and sothic years. Today’s page of Talmud reminds us that so long as we are clear about what we are saying, a year can be defined in a number of different and interesting ways.

New Essay: The Plague Wedding

In the months following the worldwide COVID-19 pandemic there has been renewed attention given to what had previously been an obscure and long-forgotten Jewish ceremony. On March 18, 2020, a wedding took place at the Ponevezh cemetery in the city of Bnei Brak in Israel. It was reported in the Israeli press, and drone footage documented a huppa erected next to the wall of the cemetery, with a few dozen onlookers carefully weaving their way among the fresh graves.

Such a wedding acquired an unforgettable moniker: It was known in Yiddish as a shvartse khasene, a “black wedding,” and is sometimes referred to as a “cholera wedding” or a “plague wedding.”

The story travelled widely, and the ceremony has since been reported in The New York Times, The Los Angeles Review of Books, and on various blogs and websites. This unexpected attention to a little-known and often controversial Jewish response to pandemics raises many questions. What were its origins, how widespread was it, and what might be the halakhic and philosophical implications of this striking, and admittedly, bizarre ceremony? This paper, long in preparation before the COVID pandemic, is an attempt at some answers.

To read the full essay go to the Tradition Online site by clicking here.

Yoma 55a ~ Yom Kippur, Counting, and Why the Chinese Are Good at Math

A Mishnah that we studied a couple of days ago on page 53a described how the Cohen Gadol (High Priest) would sprinkle the blood of his sacrifice in Temple on Yom Kippur.

נִכְנַס לַמָּקוֹם שֶׁנִּכְנַס, וְעָמַד בַּמָּקוֹם שֶׁעָמַד, וְהִזָּה מִמֶּנּוּ אַחַת לְמַעְלָה וְשֶׁבַע לְמַטָּה

He entered into the place that he had previously entered, the Holy of Holies, and stood at the place where he had previously stood to offer the incense, between the staves. And he sprinkled from the blood, one time upward and seven times downward.

And then he would count to avoid any error:

וְכָךְ הָיָה מוֹנֶה: אַחַת, אַחַת וְאַחַת, אַחַת וּשְׁתַּיִם, אַחַת וְשָׁלֹשׁ, אַחַת וְאַרְבַּע, אַחַת וְחָמֵשׁ, אַחַת וְשֵׁשׁ, אַחַת וָשֶׁבַע. יָצָא וְהִנִּיחוֹ עַל כַּן הַזָּהָב שֶׁבַּהֵיכָל.

And this is how he would count as he sprinkled, to avoid error: One; one and one; one and two; one and three; one and four; one and five; one and six; one and seven. The High Priest then emerged from there and placed the bowl with the remaining blood on the golden pedestal in the Sanctuary.

Today’s page of Talmud comments on this interesting way of keeping track of the sprinklings:

יומא נה, א

תָּנוּ רַבָּנַן: אַחַת, אַחַת וְאַחַת, אַחַת וּשְׁתַּיִם, אַחַת וְשָׁלֹשׁ, אַחַת וְאַרְבַּע, אַחַת וְחָמֵשׁ, אַחַת וָשֵׁשׁ, אַחַת וָשֶׁבַע, דִּבְרֵי רַבִּי מֵאִיר. רַבִּי יְהוּדָה אוֹמֵר: אַחַת, אַחַת וְאַחַת, שְׁתַּיִם וְאַחַת, שָׁלֹשׁ וְאַחַת, אַרְבַּע וְאַחַת, חָמֵשׁ וְאַחַת, שֵׁשׁ וְאַחַת, שֶׁבַע וְאַחַת.

וְלָא פְּלִיגִי: מָר כִּי אַתְרֵיהּ וּמָר כִּי אַתְרֵיהּ

The Sages taught in a baraita that when sprinkling, the High Priest counted: One; one and one; one and two; one and three; one and four; one and five; one and six; one and seven. This is the statement of Rabbi Meir. Rabbi Yehuda says that he counted: One; one and one; two and one; three and one; four and one; five and one; six and one; seven and one.

The Gemara comments: They do not disagree about the matter itself that the High Priest sprinkles once upward and seven times downward. Rather, this Sage rules in accordance with the norm in his place, and this Sage rules in accordance with the norm in his place. In one place they counted the smaller number first, while in the other place they would count the larger number first.

WHo excels at math?

In a 1994 study of forty second-generation Chinese-American and 40 Caucasian-American preschoolers and kindergartners, the Chinese-American children outperformed Caucasian-American children on measures of mathematics, spatial relations, visual discrimination, numeral formation, and name writing. A 2011 study that explored cultural differences in young children’s early math competency prior to their school showed that Taiwanese children performed better than U.S., Peruvian, and Dutch children. More Taiwanese four-year-olds were able to count up to at least 21 when compared with children from the other three countries. There are more studies like these, but you get the idea. But why should some cultures be especially good at math? The answer, it appears, is in the language.

The Best language to learn math…is not english

From here.

It turns out that the way numbers are counted in different languages may make arithmetic easier - or harder. In a fascinating article in The Wall Street Journal, Sue Shellenbarger noted that Chinese, Japanese, Korean and Turkish use simpler number words and express math concepts more clearly than English. And this makes it easier for small children to learn counting and arithmetic. “The trouble starts at "11” she wrote:

English has a unique word for the number, while Chinese (as well as Japanese and Korean, among other languages) have words that can be translated as "ten-one"—spoken with the "ten" first. That makes it easier to understand the place value—the value of the position of each digit in a number—as well as making it clear that the number system is based on units of 10.

English number names over 10 don't as clearly label place value, and number words for the teens, such as 17, reverse the order of the ones and "teens," making it easy for children to confuse, say, 17 with 71, the research shows. When doing multi-digit addition and subtraction, children working with English number names have a harder time understanding that two-digit numbers are made up of tens and ones, making it more difficult to avoid errors.

These may seem like small issues, but the additional mental steps needed to solve problems cause more errors and drain working memory capacity…

This suggestion was supported by a more recent study that showed that among Chinese children language abilities were able to significantly predict both informal and formal math skills.

Language	17	27
English	'seventeen'	'twenty-seven'
Chinese	'ten-seven'	'two-ten-seven'
Japanese	'ten-seven'	'two-ten-seven'
Turkish	'ten-seven'	'two-ten-seven'
Hebrew	'seven-ten'	'twenty-seven'

Today’s discussion in the Talmud notes that there were different ways of counting the one “upward sprinkling” and the seven “downward” ones. Of course neither effected the way that numbers higher than eleven are counted in Hebrew, but it is a reminder that the order in which we count things plays a very significant role in how we might see the world. And how good we are at getting our sums right.

Yoma 44b ~ Gold

יומא מד, ב

אָמַר רַב חִסְדָּא: שִׁבְעָה זְהָבִים הֵן: זָהָב, וְזָהָב טוֹב, וּזְהַב אוֹפִיר, וְזָהָב מוּפָז, וְזָהָב שָׁחוּט, וְזָהָב סָגוּר, וּזְהַב פַּרְוַיִם. שֶׁדּוֹמֶה לְפָז. זָהָב שָׁחוּט — שֶׁנִּטְוֶה כְּחוּט. זָהָב סָגוּר — בְּשָׁעָה שֶׁנִּפְתָּח כָּל הַחֲנוּיוֹת נִסְגָּרוֹת. זְהַב פַּרְוַיִם — שֶׁדּוֹמֶה לְדַם הַפָּרִים. זָהָב וְזָהָב טוֹב, דִּכְתִיב: ״וּזְהַב הָאָרֶץ הַהִוא טוֹב״. זְהַב אוֹפִיר — דְּאָתֵי מֵאוֹפִיר. זָהָב מוּפָז —

Rav Chisda said: There are seven types of gold mentioned in the Bible: Gold, and good gold, and gold of Ophir (I Kings 10:11), and glistering gold (I Kings 10:18), and shaḥut gold (I Kings 10:17), and closed gold (I Kings 10:21), and parvayim gold (II Chronicles 3:6). The Gemara explains the reason for these names: There is a distinction between gold and good gold, as it is written in the verse: “And the gold of that land is good” (Genesis 2:12), which indicates the existence of gold of a higher quality. Gold of Ophir is gold that comes from Ophir. Glistering [mufaz] gold is so named because it resembles the luster of pearls [paz] in the way it glistens. Shaḥut gold is named as such because it is very malleable and is spun like thread [shenitve keḥut]. Shaḥut is a contraction of the words shenitve keḥut. Closed gold is so called because when a shop opens to sell it, all the other shops close, as no one is interested in purchasing any other type of gold. Parvayim gold is so called because its redness resembles the blood of bulls [parim].

רַב אָשֵׁי אָמַר: חֲמִשָּׁה הֵן, וְכל חַד וְחַד אִית בֵּיהּ זָהָב וְזָהָב טוֹב. תַּנְיָא נָמֵי הָכִי: בְּכל יוֹם הָיָה זְהָבָהּ יָרוֹק, וְהַיּוֹם אָדוֹם — וְהַיְינוּ זְהַב פַּרְוַיִם שֶׁדּוֹמֶה לְדַם הַפָּרִים

Rav Ashi said: There are in fact only five types of gold, the last five in Rav Chisda’s list. Gold and good gold are not independent categories; rather, each and every one of the types of gold has two varieties: Regular gold and a superior variety called good gold. That was also taught in a baraita with regard to parvayim gold: On every other day the coal pan was made of greenish gold, but on this day it was made of a red gold, and this is the parvayim gold which resembles the blood of bulls.

Illustration drawn for Talmudology by Yosef Itzkowitz (www.yosefpaper.com)

Not all Gold is “gold”

We usually think of gold as being the color of, well, gold. But that’s not its only color. While pure gold is a sort of reddish yellow, gold alloys vary in color depending on the proportion of the other metals that are found in it. (An alloy is a mixture of two or more different metal elements.) So an alloy of gold and copper will be more red, while an alloy of gold and silver (or gold and other metals like nickel or palladium) will give a white looking gold. You can see how this works in the figure below:

In addition, the purity of gold is measured in karats (also spelled carats, but certainly not carrots), where each karat is 1/24 (or 4.1667%) part of pure gold. Sixteen karat gold means that it is an alloy in which 16 parts are gold and 8 parts are another. Pure gold is, by definition, free of other metals and is therefore 24-karat (ie 24 parts out of 24) gold.

Where does “Parvayim Gold” come from?

Recent evidence suggests that gold is formed by the massive collision of neutron stars. “Every element on the periodic table heavier than bismuth…is forged by the rapid-process in these most extreme stellar surfaces” wrote the cosmochemist Tim Gregory in his recent book Meteorite (p.168). “This includes some of your most highly prized substances like …silver, platinum and gold.” This gold was incorporated into the earth’s mantle when the planet was being formed, and was incorporated with other metals, which is why different kinds of gold alloys may be extracted from different mines.

It is this feature that Rav Chisda and Rav Ashi were highlighting in today’s page of Talmud. Shauhut gold (זָהָב שָׁחוּט) which Rav Chisda noted to be so malleable that it could be “spun like a thread” (נִּטְוֶה כְּחוּט) was likely almost pure gold (i.e. 24 carat). Today, gold can be made into a thin sheet known as gold leaf that is an astonishing four to five millionths of an inch in thickness (0.1 to 0.125 millionths of a meter or micrometers, µm). And the “spinning into a thread” that Rav Chisda mentioned? Today it is possible to spin gold into a thread that is just one atom thick. One atom. Think about that.

Another kind of gold mentioned by Rav Chisda is Parvayim gold which was a red color that “resembled the blood of bulls” (שֶׁדּוֹמֶה לְדַם הַפָּרִים). This gold was likely an alloy with a high content of copper, (found towards the bottom right of the triangle above).

The Medicinal Qualities of Gold

The Jewish physician Abraham Portaleone was born in Mantua in 1541, and is best known for his work Shilte Hagibborim [Shields of the Mighty], in which he sought to identify the precise ingredients of the Temple incense mentioned in the famous talmudic passage called Pittum Haketoret (Grinding of the Spices). Portaleone was also very interested in pharmacology, and authored a Latin text De Auro Dialogi Tres (Three Dialogues on the Application of Gold in Medicine) about the possibilities of a medical use of gold “a topic halfway between alchemy and medical studies that still created heated scientific debate.” Here is the assessment of historian Alessandro Guetta in his 2014 work on the history of Italian Jewry:

Contemporary medical authorities were divided into two camps on this: those who denied gold’s powers and those convinced of them. Portaleone’s position lay midway between the two. In his view, the hypothesis that gold had powerful medicinal properties was true; nevertheless, it remained a mere hypothesis, since such properties do not reside within gold as we know it …but in its quintessence, a substance perfectly pure and balanced in composition. In truth, nobody had yet succeeded in extracting this essence…consequently, the long list of healings that ancient and modern doctors had attributed to attributed to the ingestion of “common gold” mixed with water or wine was the fruit of ignorance and charlatanism. As for gold’s capacity to cauterize wounds, it has this in common with many other metals with the same characteristics.

We are now some four centuries after Abraham Portaleone wrote his book about gold. And it is indeed now true that gold can be used as a medicine. Aurotherapy is used to treat some kinds of inflammatory diseases like rheumatoid arthritis, and may have a role to play in the treatment of some cancers and as an agent to improve wound healing. So to add to the Talmudic categorization of gold based on its color and malleability, we can now thankfully add another: how useful it is in treating disease.