Eruvin 43b ~ Jews and their Telescopes

The chapter we are currently studying deals with the prohibition of traveling more than 2,000 amot (about 3,600 feet or just over a kilometer) in any direction on Shabbat unless an eruv, a legal boundary, had been built. Now what happens if you are on a ship that docks on Friday night, after Shabbat has begun? May you disembark? If the ship was within 2,000 amot of the port then you may leave, but if it was a greater distance than this you must remain on the boat until the end of Shabbat.

The Mishnah relates an incident when this question arose. Rabban Gamliel came to the rescue, and announced that he had determined that the ship was indeed within 2,000 amot of the port prior to the beginning of Shabbat.

ערובין מא, א

פעם אחת לא נכנסו לנמל עד שחשיכה אמרו לו לרבן גמליאל מה אנו לירד? אמר להם מותרים אתם שכבר הייתי מסתכל והיינו בתוך התחום עד שלא חשיכה

Once a ship did not enter the port until after nightfall on Shabbat eve. The passengers asked Rabban Gamliel, “what is the halakha with regard to alighting from the boat at this time? [In other words, were we already within the city’s limit before Shabbat commenced?] 

He said to them: You are permitted to alight, as I was watching, and I observed that we were already within the city’s limit before nightfall. [The port is therefore within the area on which we may walk on Shabbat.]

But how exactly did Rabban Gamliel know this? The Mishnah is silent on the issue, but the Talmud fills in some details.

ערובין מג,ב

תנא שפופרת היתה לו לרבן גמליאל שהיה מביט וצופה בה אלפים אמה ביבשה וכנגדה אלפים בים 

Rabban Gamliel had a special tube through which he would look and see a distance of two thousand cubits on land, and also determine a corresponding distance of two thousand cubits at sea.

Sidebar - which Rabban Gamliel was it?

There are several people in the Talmud who used the title of Rabban Gamliel. Given the context of the Mishnah, the one we are talking about here is Rabban Gamliel of Yavneh, also known as Rabban Gamliel the Second, the one who led the Sanhedrin immediately after the destruction of Jerusalem in 70 C.E.

And this is not the only time Rabban Gamliel was on a ship with Rabbi Yehoshua, Rabbi Akiva and others. In the tractate Horayot (10a) we read that Rabban Gamliel and Rabbi Yehoshua were sailing together when the latter demonstrated his navigational skills which involved a comet known today as Halley’s Comet. (You can read all about that here.) Rabban Gamliel seemed to know nothing of this comet, and yet here he is described as owning an instrument that allowed the precise measurement of distances. Perhaps Rabban Gamliel’s interests were only terrestrial.

“Rabban Gamliel’s tube is “one of the most puzzling scientific passages in the Talmud.””

Rabban Gamliel’s measuring device - according to Rashi

What then, was the nature of this special tube? According to the medieval exegete Rashi, who lived over one thousand years after Rabban Gamliel, the tube worked like this:

שפופרת.קנה חלול וכשהוא ארוך אין צופין בו למרחוק וכשהוא קצר צופין בו יותר והיתה שפופרת של רבן גמליאל מתוקנת למדת צפיית אלפים או בים או ביבשה

A tube: It was a hollow tube that when it is long you cannot see far though it and when it is short you can see farther. The tube of Rabban Gamliel was calibrated to measure 2,000 amot whether on land or sea.

That sounds rather like a simple telescope in which the focal length may be changed. However, telescopes which use lenses to focus were invented (at least in Europe) only around 1608. We do not know the name of the inventor, though in October of that year a Dutchman by the name of Hans Lipperhey had submitted a patent for a telescope. Did Rabban Gamliel really use a telescope over 1,500 years prior to this patent?

The Koren English Talmud suggests in a note that the tube was “a kind of precise protractor, similar to those used for astronomical measurements, i.e a type of sextant, the early form of which is known as an astrolabe.” The ArtScroll Schottenstein Talmud notes that Rabban Gamliel’s tube “operated without lenses, which were not invented until some fourteen centuries later.” It is challenging to figure out what exactly this tube was.

The Problem with Rashi

The mathematician and President of the Hebrew University of Jerusalem Selig Brodetsky (1888-1954) wrote a lengthy essay titled Astronomy in the Babylonian Talmud, which was published in English in 1979. Brodetsky calls the description of Rabban Gamliel’s tube “one of the most puzzling scientific passage in the Talmud.” And he describes Rashi’s interpretation as “even more puzzling.”

Rashi’s explanation can point to nothing else than a telescope. Are we then, to conclude that the Rabbis invented such an instrument fifteen centuries before European scientists became aware of its construction and capabilities? Or shall we baldly assert that someone has tampered with Rashi, and substituted an explanation in terms of instruments known to modern science? The second alternative is even more difficult to accept than the first, for no other reading of the Rashi is known.

The Astrolabe

In his Commentary on the Mishnah, Maimonides explained the the tube used by Rabban Gamliel was an astrolabe:

שמסתכלין בו החוזים בכוכבים ונקרא בערבי אצטרל"ב ואיני רוצה להאריך ולהזכיר איך יושג כי זה הדבר בזה הענין ארוך ואפילו באריכות לא יבין זה אלא מי שידע בחכמת התשבורת

…It was the device used by astronomers and known in Arabic as an “astrolabe.” I do not want to go into lengthy details and describe how it is used, because it is a lengthy process. And even then only those who are especially knowledgabe will understand

The astrolabe described here is a device that is used to measure the angular distance between stars or planets. As we have seen, this is the explanation offered in the Koren English Talmud. So according to Maimonides the tube did not provide any magnification.

The Nimrud Lens

The Nimrud Lens on display at The British Museum in London. It is 38 mm (1.5 in) in diameter and 23 mm (0.9 in) thick. And it is 3,000 years old

Brodetsky wondered how Rabban Gamliel could have used a telescope with lenses so long before it was “invented” in Europe. What he didn’t mention was that there is some controversial evidence that lenses were used millennia ago. The Nimrud Lens, discovered in Iraq in 1850, is a piece of crystal about 3,000 years old that appears to have been used to focus the rays of the sun, and perhaps even as a magnifying glass. Its function is however, a matter of academic dispute. Some have suggested that it was part of an ancient telescope. A curator at the The British Museum, where the lens is displayed, disagreed disagreed:

When it was found by Layard this oval piece of ground quartz or rock crystal was immediately identified as a lens, and it has come to be known as the 'Nimrud lens'. It could certainly have been used as a crude magnifying glass, with a focal length of 12 centimetres from the plane surface. Over the years it has been examined by a number of opticians, many of whom believe that it was deliberately manufactured as a lens. However, although this piece of rock crystal has been carefully ground and polished, and undoubtedly has optical properties, these are probably accidental. There is no evidence that the Assyrians used lenses, either for magnification or for making fire, and it is much more likely that this is a piece of inlay, perhaps for furniture. This is supported by Layard's statement that this object 'was buried beneath a heap of fragments of beautiful blue opaque glass, apparently the enamel of some object in ivory or wood, which had perished

Whether or not the glass was merely decorative or was used to magnify will never be known. But it raises at least the possibility that people were using lenses long before the time of Galileo.

Benjamin of tudela and the Mirror of Alexandria

Benjamin of Tudela (1130-1173) was a traveller who visited Africa and Asia, and wrote about his adventures in his Sefer Hamasaot (The Book of Travels). In the port city of Alexandria he described a tower or lighthouse, on the top of which

…there is a glass mirror. Any ships that attempted to attack or molest the city, coming from Greece or from the Western lands, could be seen by means of this mirror of glass at a distance of twenty days' journey, and the inhabitants could thereupon put themselves on their guard.

This is certainly not a telescope, but just what this mirror did (and how it did it) is not clear. Other texts mention this famous mirror, and many of them build on the description given by Benjamin. Now let’s jump forward by four-hundred years.

Azariah Figo on the Message of the telescope

Azariah Figo (1579-1647) was a rabbi who served in both Pisa and Venice during the era of the Italian ghetto. A year after his death his sermons were published in a work titled Binah Le’ittim, and since then they have been reprinted some fifty times. In a sermon delivered on Rosh Hashanah that happened to fall on Shabbat (like it does this year) he reminded his congregation about the wondrous ability of human creativity.

Azariah Figo. Binah Le’ittim. Benai Berak. Mishor 1994. p54. (In the original but less legible 1648 edition it appears on page 24b.)

The human being was given intelligence by the Source of all Wisdom and was given great strength…until He filled his heart on numerous occasions with the capacity to make artificial inventions which replicate that which is found in nature. Because of his weakness of matter or the deficiency in its preparation…man tries to correct and replace it by some discovery or invention drawn from his intelligence to the point where he will overcome what he naturally lacked.

We have seen people with poor sight, who because of a deficiency cannot see with their eyes things that are far away or even that which is close. But human intelligence was able to invent reading glasses that are placed on the bridge of the nose in front of the eyes. This improves their vision either a little or a lot, depending on the circumstances.

This was the case for the hollow tube of Rabban Gamliel, cited in the fourth chapter of Eruvin (43b), who said “I have already seen through it and I can verify that we are inside the boundary for Shabbat.

Figo was not giving a lesson in the history of science. Rather he was relating a spiritual parable, appropriate for Rosh Hashanah, the very day on which the sermon was delivered. Figo explained that just as we are able to make up for our physical deficiencies with eyeglasses and Rabban Gamliel’s tube, so too are we able to make up for our spiritual deficiencies with objects such as the shofar (the ram’s horn blown on Rosh Hashanah,) or the tzitizt, (fringes placed on the corners of a garment). Here is how the historian David Ruderman summarized the sermon:

Figo…was teaching his Jewish message by appealing directly to the immediate cultural context of his listeners. He was not teaching contemporary science to his coreligionists; he rather assumed that this knowledge was a commonplace in their experience with the world around them. As any wise preacher would do, Figo appropriated that experience to make his point about the religious message of the Jewish holiday.

And so the telescope became a scientific instrument that taught a religious lesson on Rosh Hashanah, the Jewish New Year, which we will celebrate again in two days.

Leon of Modena on the Telescope

Leon of Modena (1571-1648) was a contemporary of Azariah Figo and like him also served as a rabbi in Venice. Modena wrote at least a dozen books, including a commentary on the Ein Yaakov, which he called Haboneh (The Builder). In that commentary, Modena claimed that “there is nothing new under the sun” and that the telescopes of his day had been preceded by Rabban Gamliel’s tube.

“There is nothing new under the sun (Ecclesiastes 1:9).” The telescope which contains a few pieces of glass and which can be found today allows one to look many miles into the distance on land and at sea. It is wondrous to behold. And it had already been invented and used by Rabban Gamliel using his wide knowledge, which was greater than all his contemporaries…

Leon, like his contemporary, was also using the telescope to make a spiritual point. Modern inventions were predated by the Jewish sages, whose scientific knowledge eclipsed that of future generation (וגם חקרו רבן גמליאל בחכמתו הרהבח אשר גדל על כל באלה בתכונה).

ABraham Yagel on the Telescope

Abraham ben Hananiah Yagel was born in Italy in 1553. Although he was more interested in medicine than astronomy, he wrote several works that contain discussions of various astronomical phenomena. In his unpublished work Be’er Sheva he addresses both Galileo’s discoveries and the invention of the telescope (Ms. Oxford-Bodi. 1306: Be'er Sheva, Chap. 15, fols. 48a-53b). Here is what Yagel wrote about the new astronomy revealed by Galileo.

Our words were sincere, that in every generation things will be revealed to humanity which never were imagined by the ancients ... for behold you have seen among the fruits of the earth and the animals of the forest what we wrote in previous chapters of our composition, and also now in this chapter you shall truly see that my witness that is in heaven and my work that is on high will appear regarding the words of a wise Gentile man who in our day found several stars from the nebula which the ancients never saw and he placed their signs and their markings in a book and also spoke of the appearances seen on the moon and not in puzzles but the true opinion and what are the analogous figures to the human face [seen] from above ....

Yagel found two precursors in Jewish history that suggested the telescope’s invention long preceded Galileo. The first was Rabban Gamliel’s tube mentioned on today’s page of Talmud. The second is described again, by historian David Ruderman.

…he discovered in the tenth­ century commentary of the Sefer Yetsirah of the Italian Jewish doctor, Shab­betai Donnolo. In the introduction to this work, Donnolo describes his teacher in astronomy, an Arab named Bagdash. whose teaching agreed with that of the ancients and the Jews, especially the Baraita de-Samuel, and who taught him how to use an instrument which Yagel considered to be the same as Galileo's spyglass. "And thus this secret of the instrument in which the paths of heaven are seen was covered up, for our forefathers never imagined it and now it has been revealed, for there is nothing new under the sun."

Once again, the message is that the rabbis of the talmud had previously invented the telescope, long before it began to be used in Europe.

Delmedigo looks through Galileo’s Telescope

In the annals of Jews and telescopes one of the most remarkable stories is the relationship between Joseph Delmedio of Candia and his teacher Galileo. (Yes, that Galileo.) I have written about it in detail elsewhere, but here is his story in brief.

Joseph Solomon Delmedigo was born in Candia on the Island of Crete in 1591, where his family was the island’s most prominent Jewish family. They were wealthy and intellectually gifted, and both Joseph’s father and grandfather served as rabbis. Joseph received a traditional Jewish education that was based on the study of Talmud as well as a general secular education, and he fondly remembered his early years: “ . . . From my youth the study of Talmud was like a father to me; all of my ancestors studied in yeshivot and later spread Torah learning and raised many disciples.”

He was sent to Padua to study medicine, and when he graduated he traveled to Lublin, Vilna, and Livona, where he spent much of his time working as a physician. He ultimately settled in Amsterdam where he published his Sefer Elim.

In this long book book Delmedigo outlined the reasons he accepted the Copernican model of the universe, and in so doing he became the first Jewish Copernican. In addition to explaining all of the theoretical support for the heliocentric model, he cited experimental evidence. If the planets revolved about the Sun and were illuminated by it, the amount of light that they reflect would depend on their location and distance from the Earth. And this is precisely what Delmedigo and his famous teacher had observed through the telescope. 

“Galileo my Teacher” from Delmedigo, Sefer Elim, Amsterdam 1629. 148.

My teacher Galileo observed Mars when it lay close to the Earth. At this time its light was much brighter than that of Jupiter, even though Mars is much smaller. Indeed it appeared too bright to view through the telescope. I requested to look through the telescope, and Mars appeared to me to be elongated rather than round. (This is a result of its clarity and the movement of its rays of light.) In contrast, I found Jupiter to be round and Saturn to be egg-shaped.

This glorious passage reminds us that religiously observant Jews were sometimes at the very cutting edge of the new astronomy. How many could claim to have been instructed by the great Galileo himself? And one other thing: unlike his contemporaries, Delmedigo described the telescope as an object of science, rather than as a means of teaching a spiritual lesson.

Chofetz Chaim Shem Olam. Warsaw 1895. Vol 1 p. 59.

Chofetz Chaim on the invention of the telescope

Much closer to our own times, Yisrael Meir (HaKohen) Kagan (1838 –1933) also used the telescope to make a spiritual point. Known popularly as the Chofetz Chaim, he was a giant of the last century. He authored the Mishnah Berurah, a widely used compendium of of Jewish law, as well as several books of ethics (mussar). It was in one of those works of mussar called Shem Olam that he made a connection between the invention of the telescope and the decline of religious observance. Its invention was a way to remind us of God’s providence in the world. Just as we can use the telescope to see high into the heavens, so too can God look down on us.

To understand properly the significance of the telescope, it is important to know that in the previous generation faith in providence was very strong. Everybody had perfect faith that even though God dwells above, nevertheless He supervises from His lofty abode all the inhabitants of the Earth… In that generation it was not necessary to have such things as telescopes.

However now, because of our many sins, we find many people who deny Providence and claim that God does not see or pay attention to what occurs in the world since He is so far away in Heaven. To counteract this false claim, God shows us clearly - by giving the inspiration to build the telescope - that even lowly man has the ability to see at the great distances from the Earth to the Heaven. So we realize that surely God has the ability to see from above to below concerning all matters… It follows from our discussion that all the scientific knowledge and technological advances that have occurred in our time - is not an indication that we are greater and more knowledgeable than previous generations. In fact it is only to validate for us the idea of Providence.

It is not clear to which generation the Chofetz Chaim was see referring. Was it that of Galileo, in whose era the telescope was perfected, or his own? And was Jewish observance in either of these times so much weaker than any other? In any event it is inconceivable that he was referring to the talmudic times of Rabban Gamliel, which means that the Chofetz Chaim was of the opinion that Rabban Gamliel’s tube could not have been the telescope as we know it.

AND A telescope named after a JEWISH FEMALE ASTRONOMER

Let’s end with a Jewish astronomer who just had an entire observatory named in her honor - Vera Rubin (1928-2016). She was born to Jewish immigrants in Philadelphia, educated at Vassar, Cornell and Georgetown, and moved to the Carnegie Institution in Washington in the 1960s. She studied the rotation of galaxies, and discovered that something other than their matter must be holding them together. As her obituary in The New York Times noted, “her work helped usher in a Copernican-scale change in cosmic consciousness, namely the realization that what astronomers always saw and thought was the universe is just the visible tip of a lumbering iceberg of mystery.” Being a woman in a man’s field had tremendous challenges, and called for ingenuity:

…she still had to battle for access to a 200-inch telescope on Palomar Mountain in California jointly owned by Carnegie and Caltech. When she did get there, she found that there was no women’s restroom. …Dr. Rubin taped an outline of a woman’s skirt to the image of a man on a restroom door, making it a ladies’ room.

Vera Rubin was elected to the National Academy of Sciences, and last year the Large Synoptic Survey Telescope was renamed the National Science Foundation Vera C. Rubin Observatory in recognition of her contributions to the study of dark matter and her outspoken advocacy for the equal treatment and representation of women in science. Dr Rubin now holds the distinction of being the Jew with the largest telescope named for her.

in conclusion

To sum, telescopes have served a number of different purposes for both rabbis and lay Jews.

• For Rabban Gamliel it was used as a measuring device, (though it likely wasn't a telescope at all).

• For Benjamin of Tudela is was a wondrous device to see for a distance of twenty days’ journey (though it was not a telescopes as we know them today, but some kind of mirror).

• For Azariah Figo it was a device that taught a religious lesson: just as physical weaknesses may be overcome with human ingenuity, so too might spiritual weaknesses be overcome.

• For Leon of Modena it was a proof of the greatness of Rabban Gamliel, who had used the device centuries before it was used in Europe.

• For Avraham Yagel, it was was a similar message: the rabbis of the Talmud had previously invented the telescope, long before it began to be used in Europe.

• For Joseph Delmedigo it was a scientific device that demonstrated the truth of the Copernican model.

• For the Chofetz Chaim its invention reminded us of God’s providence in the world. Just as we can use the telescope to see high into the heavens, so too can God look down on us.

• And for Vera Rubin, it was used as an object of honor for an extraordinary career.

NEXT TIME ON TALMUDOLOGY:

HOW RABBAN GAMLIEL USED TRIGONOMETRY

—

[Many thanks to Dr. Howard Adelman from Queens University in Canada for his help in finding the original reference to Figo, and for pointing me to one about Leon of Modena.]

Eruvin 18a ~ Adam's Tail and the the Recapitulation of Phylogeny

On today’s page of Talmud we read the following:

כְּתִיב: ״וַיִּבֶן ה׳ אֱלֹהִים אֶת הַצֵּלָע וְגוֹ׳״, רַב וּשְׁמוּאֵל: חַד אָמַר פַּרְצוּף, וְחַד אָמַר זָנָב 

 it is written: “And the tzela, which the Lord, God, had taken from the man, He made a woman, and brought her unto the man” (Genesis 2:22). Rav and Shmuel disagree over the meaning of the word tzela: One said: It means a female face, from which God created Eve; and one said: Adam was created with a tail [zanav], which God removed from him and from which He created Eve.

The Talmud then investigates how the claim that Adam was created with a tail can be supported from the text of the Bible, and it is a discussion that need not concern us here. But Tosafot actually takes the time to consider which of the two explanations of the word tzela is correct, and concludes that it is the opinion that Primordial Man was indeed created with a tail, from which Primordial Eve was created.

The suggestion that for a time, Primordial Man had a tail is actually well known to those who study embryology and human development. To understand why, we need to take a detour into the thought of a German named Ernst Haeckel (1834-1919) who, at least according to Wikipedia, was a “zoologist, naturalist, eugenicist, philosopher, physician, professor, marine biologist, and artist.”

Ernst Haeckel - A warning

Before we go any further, we must point out that Haeckel was a social Darwinist, and an advocate of scientific racism. He believed that some human races were inferior to others, as this sample from his book The Wonder of Life makes abundantly clear:

These lower races (such as the Veddahs or the Australian negroes) are psychologically nearer to the mammals (apes or dogs) than to civilized Europeans; we must therefore assign a totally different value to their lives.

The fact that Haeckel thought that the Jews were located “at the same highly developed level as the Germans and within the same species” should not comfort us. Scientific racism is malodorous and to be fought at every turn, regardless of which race or group are claimed to be at the top. We, of all peoples, should know this to be true. So to quote Haeckel in a post about the Talmud might be just too distasteful for some. If this resonates with you, please read no further, and join us again for the next post, which will discuss telescopes. But if you can hold your nose for a while, read on and see why Haeckel springs to mind when learning that Adam was created with a tail.

“[Haeckel’s] evolutionary racism; his call to the German people for racial purity and unflinching devotion to a ‘just’ state; his belief that harsh, inexorable laws of evolution ruled human civilization and nature alike, conferring upon favored races the right to dominate others ... all contributed to the rise of Nazism”

— Stephen J. Gould . Ontogeny and Phylogeny. Harvard University Press 1977. 77.

Ontogeny Recapitulates Phylogeny

Haeckel’s contribution to science was his suggestion (now largely discredited or re-interpreted) that “ontogeny recapitulates phylogeny.” Ontogeny is the study of the organization and development of an organism; phylogeny is the study of how a species evolves. The meaning of this phrase boils down to this: as an organism grows inside the womb, or the egg or whatever, it goes through stages that mimic the previous development of its species over millions of years. The theory was especially pertinent to higher animals, like mammals, which, so the claim goes, go through embryological stages analogous to the adult stages of organisms from those species in its evolutionary history.

Haeckel believed that when you look very closely at the development of a human embryo, there are several stages in which it appears to have more in common with a fish, a species thought to have been ancestors of humans. His textbooks contained illustrations of this principal, like this one:

TOP LEFT: Dog (left) and human (right) embryos at 4weeks

TOP RIGHT: Dog (left) at six weeks, human (right) at eight weeks.

BOTTOM RIGHT: Turtle (right) at six weeks, dog (left) at eight weeks.

From Haeckel, E.

As you can see from the illustration, the dog and the human embryo resemble one another in the early stages of development, tails and all. Haeckel also observed that during a period of its development, the human embryo temporarily has slits on the sides of its neck, which resemble fish gills. This was an echo, he claimed, of our origins from fish.

Adam and his tail

So if Adam was created with a tail (as indeed Tosafot rules to be the case), does this lend support to the suggestion that ontogeny recapitulates phylogeny? Might the tail of the human embryo be an echo of this distant past in the Garden of Eden?

No. First, the creation story told in the opening of the Torah cannot be easily reconciled with the scientific understanding of human evolution. They are two different domains, and for every example where the order of creation seems to foreshadow what we now understand to be the story of the creation of the universe, there are many more examples that simply cannot be reconciled with our scientific understanding of how we got here. The great Rabbi Shimshon Raphael Hirsch (d. 1888) wrote that “it is not the aim of the Holy Scriptures to teach us astronomy, cosmogony or physics, but only to guide man to the fulfillment of his life’s task within the framework of the constellation of his existence.” To his list of things that the Torah does not teach us about, we should add evolution.

But there is a second reason why Adam’s tail cannot be found in the developing human embryo. It is because Haeckel seems to have been not altogether accurate in how he depicted the stages of development. Some have accused him of outright deception, while others more generously blame the poor equipment with which Haeckel had to work.

“True human tails are rarely encountered in medicine. At the time when Darwin’s theory of evolution was a matter of debate, hundreds of dubious cases were reported. The presence of a tail in a human being was considered by evolutionists as an example that “ontogeny recapitulates phylogeny.” As the discussions on Darwin’s theory subsided, so did the reports on this interesting feature. A recent review summarized 33 cases of patients with a bona fide tail. ”

— Speigelman R. et al. The human tail: a benign stigma. J Neurosurg 63:461-462, 1985.

But humans do sometimes have tails

Sometimes babies are born with a defect that resembles a tail. Here, for example, is a photo from a 1985 case reported from the Department of Neurosurgery at The Chaim Sheba Medical Center and The Sackler School of Medicine in Israel.

From Speigelman R. et al. The human tail: a benign stigma. J Neurosurg 63:461-462, 1985.

The “tail” on this baby, and on others reported, contained no bones or vestigial spinal cord. It was largely made up of fatty (adipose) tissue, and did not connect to the spinal cord. It was removed surgically without incident.

The Israeli authors point out that the normal human embryo has a tail protruding from the trunk, and that

during the 7th to 8th week of embryogenesis, the tail regresses as the vertebrated portion retracts into the trunk and the caudal vertebrae fuse to form the coccyx. The nonvertebrated apex remains as a temporary pro- trusion, but finally also disappears. In 1901, Harrison suggested that the rare vestigial human tail probably arises from this distal, unvertebrated portion of the embryonic tail. This possibility could explain the two features noted in all reported human tails: namely, the lack of vertebrae and the absence of associated spinal cord malformations.

Another case report of a human tail, published in The New England Journal of Medicine in 1982, notes that this malformation provides no support for Haeckel’s theory. The rudimentary tail contains no bones, has no connection to the rest of the skeleton, and is often not even located in the midline. It is a reminder, the author claims, that some elements needed for the formation of a tail are somehow buried deep in our genes, because we are related to other tailed primates, from whom we diverged “some 25 million years ago.” Perhaps they are a rare reminder too that in Jewish thought, there is no shame in having a tail. Just ask Adam.

Eruvin 14a ~The value of Pi in the Talmud

Today we discuss maths (as it is called in the UK, Ireland and Australia,) or math (as it is called in the US and Canada). We will focus on that most magical of numbers, pi, also known as π.

The Talmud determined the that value of π is 3. How does it know this? Because of this verse in the Book of Kings:

מלכים א פרק ז פסוק כג 

ויעש את הים מוצק עשר באמה משפתו עד שפתו עגל סביב וחמש באמה קומתו וקוה שלשים באמה יסב אתו סביב 

And he made a molten sea, ten amot from one brim to the other: it was round, and its height was five amot, and a circumference of thirty amot circled it.

So one of the vessels in the Temple of Solomon was ten amot in diameter and 30 amot in circumference. Since π is the ratio of the circumference of a circle to its diameter (π=C/d), π in the Book of Kings is 30/10=3. Three - no more and no less. From this, today’s page of Talmud teaches a general rule:

תלמוד בבלי מסכת עירובין דף יד עמוד א 

כל שיש בהיקפו שלשה טפחים יש בו רחב טפח. מנא הני מילי? - אמר רבי יוחנן, אמר קרא : ויעש את הים מוצק עשר באמה משפתו עד שפתו עגל סביב וחמש באמה קומתו וקו שלשים באמה יסב אתו סביב 

"Whatever circle has a circumference of three tefachim must have a diameter of one tefach."  

But PI is more than three

However, this value of π =3 is not accurate. It deviates from the true value of π (3.1415...) by about 5%. Tosafot is bothered by this too.

תוספות, עירובין יד א

והאיכא משהו. משמע שהחשבון מצומצם וכן בפ"ק דב"ב (ד' יד:) גבי שני טפחים שנשתיירו בארון ששם ספר תורה מונח שהיא בהיקפה ששה טפחים ופריך כיון דלאמצעיתו נגלל נפיש ליה משני טפחים וכן בתר הכי דמשני בספר דעזרה לתחלתו נגלל ופריך אכתי תרי בתרי היכי יתיב משמע דמצומצם לגמרי וקשיא דאין החשבון מדוקדק לפי חכמי המדות

Tosafot opens the objection with these words: “But [pi] is a little more [than 3]. Which means that the value [of pi] is rounded down” Tosafot can't find a good answer to this obvious problem, and concludes "this is difficult, because the result [that pi=3] is not precise, as demonstrated by those who understand geometry." 

PI IN THE RAMBAM

In his commentary on the Mishnah on which today’s discussion is based, (Eruvin 1:5) Maimonides makes the following observation:

פירוש המשנה לרמב"ם מסכת עירובין פרק א משנה ה 

צריך אתה לדעת שיחס קוטר העיגול להקפו בלתי ידוע, ואי אפשר לדבר עליו לעולם בדיוק, ואין זה חסרון ידיעה מצדנו כמו שחושבים הסכלים, אלא שדבר זה מצד טבעו בלתי נודע ואין במציאותו שיודע. אבל אפשר לשערו בקירוב, וכבר עשו מומחי המהנדסים בזה חבורים, כלומר לידיעת יחס הקוטר להקיפו בקירוב ואופני ההוכחה עליו. והקירוב שמשתמשים בו אנשי המדע הוא יחס אחד לשלשה ושביעית, שכל עיגול שקוטרו אמה אחת הרי יש בהקיפו שלש אמות ושביעית אמה בקירוב. וכיון שזה לא יושג לגמרי אלא בקירוב תפשו הם בחשבון גדול ואמרו כל שיש בהקיפו שלשה טפחים יש בו רוחב טפח, והסתפקו בזה בכל המדידות שהוצרכו להן בכל התורה

...The ratio of the diameter to the circumference of a circle is not known and will never be known precisely. This is not due to a lack on our part (as some fools think), but this number [pi] cannot be known because of its nature, and it is not in our ability to ever know it precisely. But it may be approximated ...to three and one-seventh. So any circle with a diameter of one has a circumference of approximately three and one-seventh. But because this ratio is not precise and is only an approximation, they [the rabbis of the Mishnah and Talmud] used a more general value and said that any circle with a circumference of three has a diameter of one, and they used this value in all their Torah calculations.

Is the Value of Pi hidden in the Bible?

There are lots of papers on the value of pi in the the Bible. Many of them mention an observation that seems to have been incorrectly attributed to the Vilna Gaon.  The verse we cited from מלאכים א׳ spells the word for line as קוה, but it is pronounced as though it were written קו.  (In דברי הימים ב׳ (II Chronicles 4:2) the identical verse spells the word for line as קו.)  The ratio of the numerical value (gematria) of the written word (כתיב) to the pronounced word (קרי) is 111/106.  Let's have the French mathematician Shlomo Belga pick up the story - in his paper (first published in the 1991 Proceedings of the 17th Canadian Congress of History and Philosophy of Mathematics, and recently updated), he gets rather excited about the whole gematria thing:

A mathematician called Andrew Simoson also addresses this large tub that is described in מלאכים א׳ and is often called Solomon's Sea. He doesn't buy the gematria, and wrote about it in The College Mathematics Journal.

A natural question with respect to this method is, why add, divide, and multiply the letters of the words? Perhaps an even more basic question is, why all the mystery in the first place? Furthermore, H. W. Guggenheimer, in his Mathematical Reviews...seriously doubts that the use of letters as numerals predates Alexandrian times; or if such is the case, the chronicler did not know the key. Moreover, even if this remarkable approximation to pi is more than coincidence, this explanation does not resolve the obvious measurement discrepancy - the 30-cubit circumference and the 10-cubit diameter. Finally, Deakin points out that if the deity truly is at work in this phenomenon of scripture revealing an accurate approximation of pi... God would most surely have selected 355/113...as representative of pi...

Still, what stuck Simoson was that "...the chroniclers somehow decided that the diameter and girth measurements of Solomon's Sea were sufficiently striking to include in their narrative." (If you'd like another paper to read on this subject,  try this one, published in B'Or Ha'Torah - the journal of "Science, Art & Modern Life in the Light of the Torah." You're welcome.)

Did the rabbis of the Talmud get π wrong?

So what are we to make of all this? Did the rabbis of the Talmud get π wrong, or were they just approximating π for ease of use?  After considering evidence from elsewhere in the Mishnah (Ohalot 12:6 - I'll spare you the details), Judah Landa, in his book Torah and Science, has this to say:

We can only conclude that the rabbis of the Mishnah and Talmud, who lived about 2,000 years ago, believed that the value of pi was truly three. They did not use three merely for simplicity’s sake, nor did they think of three as an approximation for pi. On the other hand, rabbis who lived much later, such as the Rambam and Tosafot (who lived about 900 years ago), seem to be acutely aware of the gross innacuracies that results from using three for pi. Mathematicians have known that pi is greater than three for thousands of years. Archimedes, who lived about 2,200 years ago, narrowed the value of pi down to between 3 10/70 and 3 10/71 ! (Judah Landa. Torah and Science. Ktav Publishing House 1991. p.23.)

Still, don't be too hard on the rabbis of the Talmud. The rule that the circumference of an object is three times its diameter is pretty close to being correct, and is usually a good enough approximation. But it is not accurate, and never will be.

[Repost from Pi Day 2016.]

Eruvin 7a ~ Trephination

The new tractate of Eruvin, which we started to learn last Tuesday (named in Latin dies Martis, and see Shabbat 156 for an explanation) is concerned with the various legal definitions of public and private thoroughfares, and the prohibition against carrying on Shabbat. But in today’s page of Talmud we take a brief detour, (for reasons that need not detain us here) into questions of ritual impurity.

Although human remains transmit ritual impurity, if they are missing a bit they may not transmit a certain kind of ritual impurity called tumat ohel. Which brings us to the case of a skull with a hole in it. How much needs to be missing for the skull to be incapable of causing others to become impure?

ערובין ז,א

דִּתְנַן: הַשִּׁדְרָה וְהַגּוּלְגּוֹלֶת שֶׁחָסְרוּ — וְכַמָּה חֶסְרוֹן? … וּבַגּוּלְגּוֹלֶת, בֵּית שַׁמַּאי אוֹמְרִים: כִּמְלֹא מַקְדֵּחַ, וּבֵית הִלֵּל אוֹמְרִים: כְּדֵי שֶׁיִּנָּטֵל מִן הַחַי וְיָמוּת. 

We learned in a Mishnah: The skull…that is incomplete do not impart ritual impurity… How much is considered a deficiency in the skull for this purpose?…Beit Shammai say: It must be missing a piece the size of a drill hole, and Beit Hillel say: It must be missing an amount that, when removed from a living person, would cause him to die, [which is a larger amount].

What is this Drill hole all about?

But just how big is Bet Shammai’s “size of a drilled hole?” The commentators are silent on the matter here. The late and very great R. Adin Steinzaltz, (who died just nine days ago at the age of 83 and those intellectual output and infectious smile will be sorely missed) translated the passage without explanation. The medieval commentator Rashi, however, directs us elsewhere, telling us to “see Bechorot chapter three where this is explained.” If we take Rashi’s advice and revisit Bechorot (38a), we read a passage cited from a Mishnah in the tractate Oholot (2:2), where the dimensions of this drill are outlined by Rebbi Meir:

בְּאֵיזֶה מַקְדֵּחַ אָמְרוּ, בַּקָּטָן שֶׁל רוֹפְאִים, דִּבְרֵי רַבִּי מֵאִיר

It it is the size of “the small drill hole, used by physicians” (בקטן של רופאים). Good, we are making progress.

Maimonides in his explanation of this Mishnah explained that implement was a small mallet used to open up “wounds and abscesses.” However that type of surgery is carried out on the skin and so is performed using a sharp knife, and not a drill (or a mallet). The implement was more likely to have been a drill in the modern sense of the word. Indeed this is the explanation given by Samson ben Abraham of Sens (1150-1230), better known as the Rash Mishantz, who also describes how it was used to drill into the skulls of both living animals and living people.

So around the first century BCE there were physicians going around drilling holes (of various sizes) into the skulls of the living. Why on earth would they do such a thing, and just how common was this practice?

Trephinated skull of a 50 year-old woman found in Corseaux-En Seyton, Switzerland. Growth of the bone around the burr-hole indicate that the the patient survived the procedure. From the collection of the Cantonal Museum of Archeology and History, Lausanne Switzerland.

Trephination - a hole drilled into the skull

Let’s start by introducing you to a word you may not have heard of. Trephination. It is the art of boring holes into people’s heads, and is also known as trepanning. The word is ultimately derived from the Greek trypanon, which was the instrument used to bore these head-holes. That is what the Talmud refers to as “the small drill hole, used by physicians” (בקטן של רופאים).

Trephination, the removal of a piece of the skull of a living individual without penetration of the underlying soft tissues goes back a long, long way. In fact it is the oldest surgical procedure known to humanity, and it predated Bet Shammai by at least 4,000 years. Oh, and by the way, many victims survived the procedure, as we can tell by noting the smooth edges around the hole. This indicates that there was some boney growth, and hence a living person, after the procedure.

Trephinated skulls from ancient Israel

Left: Round trephination found in Jericho. Right: Angular trephination, found in Timna. Angular trephination was associated with a very low rate of survival, indicated by lack of healing of the wound in the skull. It may have been practiced for ritual rather than for therapeutic reasons. From Arensburg B., Hershkovitz I. Cranial deformation and trephination in the Middle East. Bulletins et Mémoires de la Société d'anthropologie de Paris, XIV° Série. Tome 5 fascicule 3, 1988. pp. 139-150.

Trephinations in Israel and South Sinai by type, healing status and period. From Arensburg B., Hershkovitz I. Cranial deformation and trephination in the Middle East. Bulletins et Mémoires de la Société d'anthropologie de Paris, XIV° Série. Tome 5 fascicule 3, 1988. pp. 139-150.

Archeologists in Israel have discovered many trephinated skulls. According to Prof I. Hershkovitz from the Department of Anatomy at Tel-Aviv University these include trephined skulls from the 7th century BCE at Tel Duweir, a trephinated skull found in a tomb near Timna, roughly dated between the 6th century B.C.E. and the 3rd century C.E, and a skull from the Hellenistic-Roman period in Acco. Two trephinated skulls from the Middle Bronze Age I (~2,200-2,000 BCE) were found in Jericho, one from the Early Bronze age was found in Azor, and a trephinated Iron Age skull was found in Yavneh. But the very earliest skull found around the Land of Ancient Israel was uncovered in a a large cemetery at Wadi Hebran in the Southern Sinai. It belonged to a man aged between 35 and 40, who was buried around 4,000 BCE; that’s over 6,000 years ago. So yeah, trephination is a really old procedure.

“According to anthropologists who have studied trephined skulls, patient survival rate varied greatly. One scientist found advanced healing in 250 of 400 skulls, for a survival rate of 62.5%. Other scientists have found the survival rate to be between 23.4% and 55.3%.”

— Froeschner, E. Two examples of ancient skull surgery. J Neurosurg 1992; 76: 550-552.

Around the world with trephination

Evidence of trephination is by no means unique to ancient Israel. Trephinated skulls have been found in Peru, India, and Africa (where it is still practiced). The procedure was practiced in several different and geographically remote populations, which demonstrates that it independently evolved in each. Why would that happen?

In 2015 the neurosurgeon Miguel Faria suggested the following as an explanation. Neolithic man would have noticed that while massive blunt head injuries were invariably lethal, milder head injuries were not. There might be an extended period of unconsciousness to be sure, but some victims would, having been left for dead in the back of a cave, “miraculously” recover and become “undead.” Today we would call this period a “coma”, and, so the claim goes, it would have been supposed that “something in the head had to do with undying.” Then this:

“..an opening in the head, trephination, could be “the activating element,” the act that could allow the demon to leave the body or the good spirit to enter it, for the necessary “undying” process to take place. If deities had to enter or leave the head, the opening had to be sufficiently large…The head was chosen for the procedure, not because of any particular intrinsic importance or because of magic or religious reasons, but because of the unique and universally accumulated experience observed by primitive man in the Stone Age with ubiquitous head injuries during altercations and hunting. Otherwise, the pelvic bone or femur could have served the same purpose. We must recall that even the much more advanced ancient Egyptian, Mesopotamian, Hindu, and even Hellenic civilizations believed the heart to be the center of thought and emotions, not the brain. In fact, the association of the heart with emotions lingered to the present age.

And so it was that the procedure came to be practiced across the world. This may also explain how it also ended up being used in ancient Israel, and trickled down into a teaching about ritual impurity cited by Bet Shammai.