Small is Beautiful: Why the Small is Numerous but the Big is Rare in the World

Why are there more poor people with small bank accounts than rich people with big bank accounts? Why is the small almost always more numerous than the big in the world? Empirical examinations of real-life data overwhelmingly confirm the existence of such uneven size proportions in favor of the small. There are more small planets and stars than big ones in the cosmos. There are more small molecules than big molecules in the chemical world. There are more small families with few children than big families with many children. In geological data, there are more small rivers than big rivers, and there are more harmless small earthquakes than devastating big ones.

There are by far many more small creatures than big creatures in the biological world. There are only about two million big whales swimming the oceans, yet there are over 300 billion small birds flying the sky. Tiny little ants are even more abundant, with estimates of over 100 trillions of them walking the earth! In number theory as well, there are more small prime numbers than big prime numbers for integers. In census data, there are more villages than towns, more towns than cities, and more cities than metropolises. In history, there were more small wars with low death toll than horrific big wars with high death toll such as WWII.

The vast list of topics & disciplines obeying this quantitative law of nature confirms the fact that the phenomenon is nearly universal. This book discusses in detail several real-life case studies; presents three distinct explanations for the phenomenon; and numerically quantifies the small is beautiful phenomenon in order to obtain an exact measure indicating by how much the relatively small is more numerous than the relatively big.

Surprisingly, that numerical measure is found to be consistent and nearly universal across almost all data sets with sufficient variability having high order of magnitude. This nearly universal pattern across almost all data sets is termed ‘The General Law of Relative Quantities’ or simply GLORQ for its acronym. As it happened, Benford’s Law regarding the consistent digit distribution in almost all data sets with sufficient variability is demonstrated to be simply a mere consequence and a special case of GLORQ, leading to the conclusion that in a profound sense Benford’s Law springs ultimately from the small is beautiful phenomenon.

Why are there more poor people with small bank accounts than rich people with big bank accounts? Why is the small almost always more numerous than the big in the world? Empirical examinations of real-life data overwhelmingly confirm the existence of such uneven size proportions in favor of the small. There are more small planets and stars than big ones in the cosmos. There are more small molecules than big molecules in the chemical world. There are more small families with few children than big families with many children. In geological data, there are more small rivers than big rivers, and there are more harmless small earthquakes than devastating big ones.

There are by far many more small creatures than big creatures in the biological world. There are only about two million big whales swimming the oceans, yet there are over 300 billion small birds flying the sky. Tiny little ants are even more abundant, with estimates of over 100 trillions of them walking the earth! In number theory as well, there are more small prime numbers than big prime numbers for integers. In census data, there are more villages than towns, more towns than cities, and more cities than metropolises. In history, there were more small wars with low death toll than horrific big wars with high death toll such as WWII.

The vast list of topics & disciplines obeying this quantitative law of nature confirms the fact that the phenomenon is nearly universal. This book discusses in detail several real-life case studies; presents three distinct explanations for the phenomenon; and numerically quantifies the small is beautiful phenomenon in order to obtain an exact measure indicating by how much the relatively small is more numerous than the relatively big.