Thursday, October 26, 2017

How tall was Avraham Avinu?

In this weeks Parsha we are introduced to Avraham Avinu. Maseches Sofrim states the following:
"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, it is clear that from a scientific basis it is absolutely impossible for a human being to be that tall.

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.


8 comments:

  1. Of course such a height is impossible. So how tall was he when he was born ? Was he regular size ? Then he must have a very abnormal growth rate. And if he was very large when born his mommy but have been a giant too. Rambam would probably not take this stuff literally. But maybe, just maybe the midrash is preserving some 'literal truth' in this sense. The Greeks had their giant gods, so maybe Avraham was at one time really just like one of those Greek gods. Or perhaps, the Jews heard about the Greeks bragging about their giants and so as not to be outdone they make Avraham a giant. P.S. There is numerous nonsense in the Talmud and you can write a book about it.

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  2. I find these sort of posts the most bizarre. Readers have a choice whether to take statements such as this literally or not. Those who do not have no such problem. Abraham was a giant among men, this will be considered as a statement of intellectual and / or moral / ethical values rather than physical proportions. I don't even find this a stretch, as these statements typically read very well allegorically.

    As for those who do read these statements literally, they clearly have a very different idea of how physics works. To me (and I presume you too), there is a presumption that the basic concepts of physics have been constant through time. Just as we see the world basically making sense from a bottom up physical perspective now, so too we presume it has always been the case. We don't suppose that there has ever been a miraculous shift in the way anything works. However to those that read these sort of passages literally, there is no such presumption. If Avraham's height could not be supported by current humanities bone structure then either he had bone made from different material, or the laws of phusics were miraculously suspended for him. Period. They simply don't view a question from physics as any sort of valid evidence or challenge against a statement that they consider sacrosanct.

    Anyone who has spent any significant amount of time in charedi academia (yeshiva, kollel, whatever) knows this as a simple fact, so I really don't see what you are trying to show in your post.

    I actually think that there might be a third category. People who take the stories at face value for the purposes of discussion and / or comparison with any other Torah facets but don't really believe them to be true in a factual sense. So basically they will argue the point ad infinitum when it comes to squaring it with halacha, medrash or whatever, but as soon as the question is from physiscs they aren't bothered as they don't really see it as a physical reality. I think if we can accept that approach then a lot of these sort of questions just fall away but without really giving in to fantastical thinking.

    OK, ow for my question on this Gemorrah, which I think is far more fundemental to ways 2 and 3 of thinking. If the average person is 4 amos (see Gemorra's everywhere) and Avraham was 74 times the size, i.e. 296 amos and Avroham kept the entire Torah. How did Avroham sit in a sukkah and / or light a menorah and / or set a korah on his mavoi as all of these are limited to 20 amos, roughly the height of Avroham's ankles!

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    1. Way 2 of thinking is simply burying your head in the sand. As Rav Aryeh Kaplan wrote:
      They say, “What do scientists know? Do they know what’s happening? Do they know what’s going on? They’re a bunch of phonies, a bunch of bluffers, a bunch of stupidniks! Do they really have a way of finding out the truth? They find a bone and they think it’s from a monkey.” But, I think to somebody who knows what science is, this is a very unsatisfactory approach. We have some idea of what is involved in paleontology. We have some idea what is involved in geology and in radioactive dating. We have some idea of what is involved in astronomy. We can casually speak about a star being a million light years away, and we do not stop to think, “Well, that’s a bit too much!” So I would say that if someone feels that science is ignorant and false, all well and good. Many people refer not to accept science as a worthy challenge. But I think that for many of us here, such an approach would be totally unsatisfying.

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    2. But saying that a medrash like that is literal *is* way 2 of thinking!

      Like I said, the approach is not unanimous by far, but that is effectively the worldview you are challenging. So if you challenge someone who is perfectly happy to say "They’re a bunch of phonies etc." that the physics of a 500 foot tall man just doesn't work out you are hardly going to make any progress.

      Your whole point in earlier posts is that you are not going for the obvious challenges (no there was not a global flood that wiped out 99.9999% of all terrestrial animal and human life 4,000 years ago) because you are looking at internal inconsistencies. But this is simply not an internal inconsistency the answer is always "itsamiraclestupid".

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  3. No wonder they couldn't have children for so long!

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  4. There's a neat explanation that compares Abraham's food ("Whoever partakes of a meal at which Talmidei Chachamim are sitting, is as if he has enjoyed the divine glory [Ziv Hashechina]") to the angels to the 74 people who ate on har Sinai:
    http://www.dafyomi.co.il/parsha/mishpat3.htm

    I have no problem with that.

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    1. That is fine, but many understand this Gemara literally and in fact in the Charedi world today if you don't understand teh gemara literally you are called a kofer.

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    2. True, the charedi world knows better than the Vilna Gaon!

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