## Monday, September 24, 2012

### The Physics of Superheroes as applied to עוג מלך הבשן (Berachos 54b)

Today's daf (Berachos 54) has 2 interesting discussions which relate to the size of Og. First the Gemara has a story that Og wanted to destroy the Jewish people by throwing a mountain on them. The Gemara says that the Jewish camp was 3 parsa by 3 parsa (approximately 12 square km) so Og picked up a mountain that big to throw on them (see the Gemara for how they were saved). Og obviously had to be quite huge to pick up such a large mountain. Later, the Gemara comments that Moshe was 10 amos tall, had a weapon 10 amos long, and jumped 10 amos to strike Og and only reached his ankles. Even using the smaller shiur of an ama, 18 inches, Og's ankle was 45 feet off the ground, meaning that he was 300-400 feet tall.

The Chafetz Chaim (או"ח סי' רי"ח) takes the first story quite literally. However, from a strictly rationalist/scientific viewpoint it is very difficult to take these gemaras literally, and in fact, both the Rashba and the Maharsha do NOT take these stories 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 Og was between 370 and 400 feet tall his body would collapse of it's own weight. 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 Og simply being able to stand (against the laws of physics) was a miracle and therefore the non-literal explanations of the Rashba and Maharsha (and probably others) are very useful here.