I'm going to introduce the subtopic of geometry that I want to consider with some useless (but somewhat interesting) trivia. Did you know that one of the biggest problems for blue whales is their tendency to overheat, even in frigid arctic waters? As Roger Payne wrote for PBS:
The requirement of being warm blooded would seem to make it impossible for a mammal to reach and harvest krill in polar seas-since those krill are living in an impregnable fortress: ice water, at the ends of the earth, where staying warm while immersed is simply not feasible for a warm-blooded mammal.For a 3 dimensional entity, surface area increases in proportion to the square of the increase in the length of the entity, volume increases with the cube of the length, and the ratio of volume over surface area increases linearly with the length. Considering the whale versus mouse comparison, a blue whale is about 200 times as long as a mouse. Thus, we would predict that a blue whale would weigh 2003 or 8,000,000 times as much as a mouse, have surface area 2002 or 40,000 times greater than a mouse, and have a volume to surface area of 200 times as big as a mouse. Given that a mouse weighs about 25 grams and a blue whale weighs about 150 tons, this gives a weight ratio of 5,376,000 to 1 which is pretty close to our prediction of 8,000,000 to 1. I'll bet you never knew that it takes over 5 million mice to balance one blue whale. There are only around 2,000 blue whales left on the planet, but those 2,000 whales have the equivalent weight and volume of over 10 billion mice. 2,000 whales are potentially endangered, while 10 billion mice are not.
Or is it?
Simply by being large an animal like a whale can take advantage of a simple but little-appreciated fact: the fact that the larger an animal's body, the smaller is its surface area in relation to the volume of that body. The reason this is important is that the volume of any animal's body is its furnace-the place where its metabolism generates heat, while the surfaces of its trunk, head, and limbs are its radiators, the things through which heat is lost. Tiny mammals, like mice, have relatively huge surfaces for their small volumes; which means that they have small furnaces and large radiators and therefore have to produce lots of heat to keep from cooling down. But large animals have relatively small surfaces for their large volumes-they have a large furnace and small radiators. That means that their problem is not losing heat but keeping from overheating-particularly when they exercise. Contrary to popular belief, blubber is not principally for keeping warm but for fuel storage.
The same sort of principle applies to large office space. For example, prior to its demise, the World Trade Center in New York was so large and therefore had such a high volume to surface area ratio, that it required the world's largest refrigeration plant, "with 60,000 tons of cooling capacity," to keep it cool, and the refrigeration capacity was utilized throughout the brutal New York winter (even worse than Afghanistan winters, turns out). Every light bulb, every person, every computer, every robot (well, not many robots) generated heat, and the exterior surface area wasn't enough to dissipate all that heat without help from the cooling plant.
Just as a 3 dimensional entity's surface encloses even more volume as it gets bigger, a 2 dimensional entity's perimeter encloses an even larger area as it expands. The formula here is that the area increases in proportion to the square of the increase in the perimeter. Also, the exact shape doesn't matter. The relationship holds for any convex shape.
At a given level of technology, there are a maximum number of people that can survive in a given isolated area. That population density, especially for a primitive people, is basically limited by the quantity of food that can be gathered and/or grown. Also for a primitive people (and maybe not so primitive), the population tends to expand to take advantage of the available food supply. The bigger the area, the greater the amount of available food, and therefore the greater the number of people. In other words, the number of people that can be supported is proportional to the area they live in.
A tribe has to be able to defend the area that they live in from other tribes that would like to slaughter them and take over their food supply. The defense happens at the (fairly fluid) border between the two tribes, along the perimeter. Assume each tribe is surrounded by other tribes. Then each tribe has to defend its entire perimeter. I realize that this is hugely oversimplified and ignores all sorts of military tactics and assumes a pre-aviation world, but I think the basic idea holds.
As an example, consider the very friendly and hypothetical Tuber Tribe (so named because the only somewhat anthropomorphic image I could find laying around on my computer is the potato person in the figure below).
Each tuber Tom requires one square of area of land to support himself. A Tuber Tribe of four requires four squares.
But the Tuber Tribe also needs to defend itself. In order to keep their area and the associated resources (i.e. food), the eight positions marked by bombs have to be defended from attacks by the surrounding tribes. In this case, only four tuber Toms have to defend eight positions.
A second Tuber Tribe has 16 members with the corresponding increase in area. It has four times as many members, but the perimeter only doubled. The 16 tuber Toms need to defend 16 perimeter positions. This is a one-to-one ratio instead of the inferior one-to-two ratio shown above.
In a nation of 1,000,000 tubers, there would be only 4,000 perimeter positions to defend. In this case 99.6% of the tuber Toms would not be needed for defense and could be employed doing something else.
In small primitive tribes, one of the things that is particularly brutal, is that every adult (male) needs to be involved in every war directly on the front, whereas even in the brutal wars of the 20th century, a far, far smaller percentage of the populations of the world actually fought.
So there is a major advantage for tribes to become as large as possible, in other words, to combine tribes in order to become nations. This is obviously true if a single large nation forms while all the rest of the people remain part of small tribes. The single nation is then clearly invincible and can also attack and conquer the small tribes with impunity.
However, it's also true that even as organizational methods spread such that many nations evolved from tribes, the size advantage was beneficial to all. All groups of humanity could still be at war, but a far lower percentage of each group needed to be involved in the actual fighting.
In summary, my conclusion is that because humankind engages in war by nature, genetic and/or memetic enhancements that enabled larger and longer lasting societies occupying larger areas were hugely advantageous for the warring groups, even if all of the groups were the same size.
In the next several parts of this series I'll look at some of the changes that enabled humans to organize into ever larger groups in order to capture the geometric area to perimeter advantage.