web analytics
July 2, 2015 / 15 Tammuz, 5775
At a Glance
Judaism
Sponsored Post


Daf Yomi

Daf-Yomi-logo

An Early Navigational Instrument
‘Rabbi Gamliel Used His Tube To Measure…’
(Eruvin 43b)

The Gemara tells us that Rabbi Gamliel had an instrument which he used to measure the 2,000-amah Shabbos boundary (see Rashi). The Geonim (cited in Meiri; Teshuvos Hageonim 28:314) explain that his tool was a narrow tube. When looking directly downwards through a tube, one can only see one’s feet. As one raises the tube, one can see farther away. An object was placed at an exact distance of 2,000 amos from the holder of the tube. The tube was slowly raised until it could see the bottom of the object, but no farther. Rabbi Gamliel marked the angle that the tube was held at which the object was thus viewed. From then on, he was able to determine the distance of the 2,000-amah Shabbos boundary by holding the tube at the same angle. This method was effective only when viewing objects on a straight plane.

High School Trigonometry

In his commentary to the mishnah, the Rambam seems to suggest that the instrument was more complicated than this. He writes that there is no need to explain at length the specifics of this mechanism. Those familiar with trigonometry, the study of triangles and the proportions between their sides and angles, will understand how these principles are applied in navigation. Those unfamiliar with trigonometry will not fully understand how Rabbi Gamliel’s implement worked. There are six parts to any triangle: three sides and three angles. According to the calculations developed by mathematicians, in almost all cases, any three parts whose measures are known can be used to find the measures of the other three parts, if at least one of the known parts is a side. It was such a computation that Rabbi Gamliel used in determining the distance of techum Shabbos.

Based on the Talmud Yerushalmi (Eiruvin 4:2), some suggest a third possibility of how Rabbi Gamliel’s instrument worked. As we know, the closer an object is, the larger it appears. It therefore takes up a larger portion of our field of vision. A building on a distant skyline takes up only a small part of our view. When we stand face up to it, it blocks our sight entirely.

Measure Distances With Fingers

Rabbi Gamliel had a tube with a simple piece of glass at its end, which did not magnify his vision. On this glass, he made markings equally distant from each other. For the sake of explanation, let us say that they were one millimeter apart. When an object was distant, it would cover only one marking, a small part of his view. When it drew closer, it would cover many markings, thus a larger part of his view.

When using such an instrument, the length of the tube also determines how many markings would be covered by a distant object. To demonstrate, hold your hand adjacent to your face, with fingers separated, and look at a distant object through the crack between two fingers. Slowly, draw your hand away from your face and you will see that the same object will appear through all the cracks of your hand. Similarly, with a shorter tube, the glass is closer, the markings appear larger, and the object viewed at a distance appears to equal only one of them. With a longer tube, the glass is farther, the markings appear smaller, and the object viewed appears to equal many of them.

Start With The Right Measure

Rabbi Gamliel would use this tool to measure the boundary of the techum Shabbos. He would take a pole that he knew to be one meter tall, place it a distance of 1,000 meters, and note that it appeared to equal one millimeter on his glass. He could then calculate that the object in sight was at a distance of exactly 1,000 times the length of the tube. This simplified measuring the boundary. Rather than drawing strings, and counting their lengths, an object of known height could be sighted from afar, and its distance calculated based on how large it appeared in relation to the markings on the glass.

In previous generations, the Romans, in application of precisely this principle, would build towers of set heights next to their ports in order to help navigators on incoming ships measure their distance from shore.

About the Author: RABBI YAAKOV KLASS, rav of Congregation K’hal Bnei Matisyahu in Flatbush, Brooklyn, is Torah Editor of The Jewish Press. He can be contacted at yklass@jewishpress.com. RABBI GERSHON TANNENBAUM, rav of Congregation Bnai Israel of Linden Heights, Boro Park, Brooklyn, is the Director of Igud HaRabbanim – The Rabbinical Alliance of America.


If you don't see your comment after publishing it, refresh the page.

Our comments section is intended for meaningful responses and debates in a civilized manner. We ask that you respect the fact that we are a religious Jewish website and avoid inappropriate language at all cost.

If you promote any foreign religions, gods or messiahs, lies about Israel, anti-Semitism, or advocate violence (except against terrorists), your permission to comment may be revoked.

No Responses to “Daf Yomi”

Comments are closed.

Current Top Story
investing-in-gold_4548807_lrg
What Sanctions? Iran Receives 13 Tons of Gold From S. Africa
Latest Judaism Stories
Rebbetzin Esther Jungreis

To my dismay, I’ve seen that shidduch candidates with money become ALL desirable traits for marriage

800px-Gustav_Jaeger_Bileam_Engel

Bil’am’s character is complex and nuanced; neither purely good nor purely evil.

Staum-062615

Amalek, our ultimate foe, understood that when unified, we are invincible and indestructible.

Torat-Hakehillah-logo-NEW

Perhaps on a deeper level, the mitzvah of parah adumah at this junction was not just to purify the body, but the spirit as well.

Halacha isn’t random; it’s a mechanism guiding individuals and society to a higher ethical plateau.

Question: Should we wash our hands in the bathroom with soap and water, or by pouring water from a vessel with handles three times, alternating hands? I have heard it said that a vessel is used only in the morning upon awakening. What are the rules pertaining to young children? What is the protocol if no vessel is available? Additionally, may we dry our hands via an electric dryer?

Harry Koenigsberg
(Via E-Mail)

Less clear, however, is whether the concept applies to the area of civil law such as the law of transfer of property.

The greatest of men, Moshe, had to wait for Hashem to sprinkle purifying waters on Bnei Yisrael to mark the conclusion of the period of death.

My Plate, My Food
‘My Loaf Is Forbidden To You’
(Nedarim 34b)

Of Chukkim “Satan and the nations of the world made fun.” They may appear irrational & superstitious

I realized from this story that I was sent as a messenger from above. Hashem has many helpers in this world to help do his work.

Tosafos answers that nevertheless the sprinkling is a part of his taharah process.

“What difference does that make?” replied Shraga. “What counts is the agreement that we made. I said two hundred fifty and you accepted.”

Zaidie’s legacy of smiles and loving words was all but buried with him, now the family fights over $

Israel’s complaining frustrated Moshe, making it increasingly hard for him to lead effectively

More Articles from Rabbi Yaakov Klass and Rabbi Gershon Tannenbaum
Daf-Yomi-logo

My Plate, My Food
‘My Loaf Is Forbidden To You’
(Nedarim 34b)

Daf-Yomi-logo

Not As An Asmachta?
“An Asmachta [In Beis Din] Does Acquire”
(Nedarim 27b)

Ulla’s Murderous Companion
‘Yes! Cut Him Even Deeper’
(Nedarim 22a)

An Enduring Text
‘If One Vows By The Torah…’
(Nedarim 14b)

Casting A Doubt
‘Shall We Say [They] Are Not Valid?’
(Nedarim 5a-7a)

The Honor Of Reading The Kesubah
‘Witnesses Sign Only After Reading…’
(Kesubos 109a)

Twice Promised
“Such And Such [I Give My Son]…”
(Kesubos 102b)

Seller’s Remorse
‘He Sold Because He Ostensibly Needed The Funds’
(Ketubbot 97a)

Printed from: http://www.jewishpress.com/judaism/halacha-hashkafa/daf-yomi-73/2013/04/17/

Scan this QR code to visit this page online: