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Tuesday, November 08, 2011

Could Avraham Avinu have been as tall as 74 men?

Parsha blog quotes the following from the end of Maseches Sofrim:
"The man [who lived in Chevron] was the greatest of the giants" (Yehoshua 14:15) -- This refers to our forefather Avraham, whose height was equal to that of seventy-four men. The amount of food and drink he consumed was enough for seventy-four men, and he had the strength of that many men as well.

R' Chaim Kanievsky is his sefer on Tanach (טעמא דקרא) takes this medrash literally and in fact offers an explanation of the source. However, from a strictly rationalist/scientific viewpoint it is very difficult to take this medrash literally.

On one of my trips to the US I bought a fascinating book called, The Physics of Superheroes, which explains many of the basic principles of physics using examples from comic book superheroes. One of the superheroes that he discusses is Giant Man, his power being that he could increase his size when needed. In his discussion in the book he points out that the size that a person could grow to is limited by the strength of materials (particularly bone) and gravity. A person's size is ultimately limited by the cube square law. For simplicity's sake let's model a person as a box. A box's volume is a product of length x height x width so a box that has a length, width and height of 5 feet (our person model) will have a volume of 125 feet cubed. Now assume that he grows to 4x times these proportions (20x20x20). He will now have a volume of 8000 cubic feet, in other words quadrupling his length increases his volume by a factor of 64. Now we need to consider density and mass. It makes sense to say as a person grows his density stays the same (otherwise he would simply thin out into nothingness). To maintain a constant density means that mass must increase at the same rate as volume so quadrupling height increases weight by a factor of 64. The problem is that as weight increases the ability of the skeleton to support that weight does not. The strength of an object depends on how wide it is, it's cross-sectional area. In our case here volume and mass increase much faster then the cross -sectional area of the bones.

Let's take the following simple example of someone who is 6 feet tall and 185 pounds. A single vertebra can support approximately 800 pounds. Now lets increase his height by a factor of 10 to 60 feet. His volume and mass grow by 1000 while his cross-sectional area only grows by a factor of 100. His vertebra can now support 80,000 pounds but his weight is now 185,000 pounds, meaning that his skeleton can no longer support his weight.

The bottom line is that if Avraham Avinu was 74 times taller then the average man (between 370 and 444 feet tall) his body would collapse of it's own weight (well before 74 times). It is a matter of simple physics.

Of course we could come up with all kinds of miracles and believe anything, but we know that Hashem tries to limit miracles and the world works with nature (the laws of physics). Therefore it doesn't make sense to assume that Avraham simply being able to stand (against the laws of physics) was a miracle. In fact, there are many interpretations of this medrash in a non-literal sense (see for example http://www.dafyomi.co.il/parsha/mishpat3.htm) which very nicely explain the medrash without having to believe that Avraham was literally 350 feet tall.

8 Comments:

At 6:43 PM, Blogger Milhouse said...

That's all very well, but what about Moshe Rabbenu? He was 10 amot tall, which is still much taller than any modern man could possibly be without being a cripple. And I don't see how one can take that maamar chazal figuratively; the context in which it appears is very practical.

 
At 6:54 PM, Blogger Lisa said...

Gah. He was not literally 10 amot tall. Nor was Avraham Avinu literally as big as 74 men.

 
At 3:30 PM, Blogger bluke said...

Lisa, you may not take it literally but many do up even today. R' Chaim Kanievsky in Taama de-Kra does understand this medrash literally.

 
At 4:00 PM, Blogger Lisa said...

Bluke, he does not take it literally. Like other rabbanim, he recognizes that midrashim, even midrashei aggadah, have to be consistent within themselves. So he discusses the topic within the world of the midrash. This is how midrashim are meant to be learned. They aren't just cute fairy tales; they're intended to be puzzled out. Riddled out for all the detail they contain. Taking what R' Kanievsky writes there are meaning that he thinks Avraham Avinu was literally the height of 74 regular men is an insult to R' Kanievsky.

 
At 4:10 PM, Blogger bluke said...

The Maharal in Chidushei Aggados Bava Metzia 84a (http://www.hebrewbooks.org/pdfpager.aspx?req=14192&st=&pgnum=37&hilite=) understands that Moshe was not really 10 amos tall and that Chazal are describing his spiritual attributes.
The Maharal writes:
אין זה שיעור גשמי רק כי היה ראוי לשלימות ומעלות נפשו עשר אמות

My translation:
This [Moshe being 10 amos tall] is not a physical measurement but rather that Moshe was fit for the perfection and spiritual heights of 10 amos.

 
At 4:12 PM, Blogger bluke said...

Lisa,

Of course he does, otherwise all his calculations make no sense. If the medrash meant that Avraham was equal spiritually to 74 people then it has nothing to do with the size of the camp etc.

 
At 3:17 AM, Blogger Chaim B. said...

The point of R' Chaim I think is that the number 74 is not just something pulled out of a hat -- it fits perfectly with the cheshbon. Whether it should be taken literally or not is a different question. The point is that in the context of Torah (in the broadest sense), the numbers add up, which is an amazing thing.

L'shitascha, what's the big deal here? There are dozens of examples where some Achronim take aggadita literally and make all kinds of cheshbonos to work things out while other Achronim take things symbolically.

 
At 3:17 PM, Blogger Jonathan B. Horen said...

It all works out, if you use the shortest man in the Bible:

Bildad the Shuhite

 

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