Arachin 19a ~ The Mechanical Engineering of a Pledge

ערכין יט, א

אמר רב יהודה: האומר קומתי עלי נותן שרביט שאינו נכפף, מלא קומתי עלי נותן שרביט הנכפף.

Rav Yehuda says that one who says: It is incumbent upon me to donate my height, gives a thick rod that cannot be bent equivalent to his height. One who says: It is incumbent upon me to donate my full height, may give even a thin rod that can be bent, provided it is equivalent to his height.

What are we to do with a person who pledges to donate to the Temple the “amount of his height” ?Rav Yehuda comes up with an ingenious idea. Find a rod of the same height as the person, and the value of the rod would be donated to the Temple.

Rashi explains the passage along these lines:

קומתי - משמע כקומתו ונותן שרביט עב שלא יוכל לכופפו אם פירש כסף כסף ואם זהב זהב

My height: He means the same height as his own. He donates a thick rod which cannot be bent: if he agreed that it be made of silver, then it is the value of that silver rod; and if he agreed that it be made of gold, it is the value of that gold rod.

Last year, three mechanical engineers published a paper in the journal Hakirah which described some of the features of this '“rod that does not bend.” They noted that “technically speaking, “unable to bend” cannot be an exact term, as even the most brittle material has a Modulus of Elasticity (Young’s Modulus) and will bend under a load.” Good point; everything bends eventually. It’s gravity. To demonstrate this the authors consider a cantilever beam, one end of which is free (A), and the other is fixed (B) allowing for no translation or rotation. They continue:

The uniformly applied weight loading is the result of the Earth’s gravitational pull exerted on the cantilever of length and radius r, with the cantilever consisting of a homogeneous material of an isotropic Young’s Modulus E.

But wait. There’s more:

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And so things always bend. Gravity is a cruel mistress. In fact if you pledged to give your height in gold and you were say 1.7m tall (that’s 5 feet 7 inches for those of you in the US), a gold rod with a 10cm diameter would deflect a full 3.5 mm at its tip.

Deflection of a 1.7m cylindrical rod of Gold, Silver and Copper for a given radius. From Ehrenberg I. Siegel J. Erb B. The Tallest Column: On Monetary Value of Stature in Jewish Law.   Hakirah   2018:(25); 161-173

Deflection of a 1.7m cylindrical rod of Gold, Silver and Copper for a given radius. From Ehrenberg I. Siegel J. Erb B. The Tallest Column: On Monetary Value of Stature in Jewish Law. Hakirah 2018:(25); 161-173

Anyway the engineers continue to analyze the physics behind the various statements in today’s day of Talmud, but to follow their reasoning, I recommend you have a strong background in mathematics, Hooke’s law and “the moment-curvature relationship (𝑀 􏰁=𝐸𝐼𝜅).” Depending on the precise dimensions of the rod, they conclude that at today’s prices its value would range from $64 for a copper rod with a radius of 4.3mm to $112,710 for a gold rod with a radius of 5.3mm. So next time you donate the value of your height to the charity of your choice, be very explicit about what precisely, you mean, or it could cost you a great deal of money.

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