The End of Everything: How Wars Descend into Annihilation by Victor Davis Hanson
How can warfare lead to annihilation of entire societies? In many cases there are a distinct aims in warfare. One side may feel wronged and have specific goals in mind. The vanquished will often live to another day. However, in some cases, the entire society is destroyed. This book looks particularly at Thebes, Carthage, Constantinople and Tenochtitlan. These were each centers of great civilization. They had ruled empires and had been seen as somewhat invincible. However, they had gradually lost some of their strength. The invaders had come in and fully conquered them. In the process, they proceeded to wipe out the culture and civilization of the vanquished.
The conquered cities often occupied valuable geographic positions and were thus often occupied by the conquerors. Tenochtitlan was razed and became the location of Mexico City. The culture and society as replaced by a Spanish, Christian culture, with some bits of Aztec influence. Constantinople would become the base of the Muslim Ottoman empire and eventually be renamed to Istanbul. While many people today have some Greek ancestry, the culture remains Islamic.
How can civilizations be annihilated? In the case studies, there had already been a degree of falling away, combined with hubris. The cities had previously been great centers of power. However, they had lost some influence and strength. Despite this, they still held a greater view of themselves than their position warranted. Their military strength was inferior to their rivals. There were often cultural relics that made them more susceptible to defeat. (e.g. Aztecs warriors were prized on body count, and spent effort bringing back bodies rather than advancing position.) Today, weapons have become bigger and stronger and are more capable of large-scale physical destruction. Complacency is a continued concern.
Infinite Powers explores the evolution of calculus and the important roll that it plays in our lives. Both the concepts of "0" and "infinity" are key to the understanding of the world. However, these were not universally understood concepts in the ancient world. Many mathematicians did understand bits of it, but it wasn't until Newton and Leibniz separately put it all together.