timeline

The History of Large Numbers

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Introduction

The development of large numbers has it's own history that parallels in many ways the development of human civilization. Very large numbers in history were rare owing to the fact that most were of no practical value and were highly theoretical. However very large numbers occurred even in antiquity for pragmatic, religious and theoretical reasons. It's not too inaccurate to think of the history of large numbers as developing in sequence with the size of the numbers, with larger and larger numbers being "discovered" over time. Thus we can think of a kind of progress in the search of large numbers through out history. In truth however, history is rarely so sequential. Large numbers were discovered independently in many places and many truths about them were rediscovered many times. It's only in recent history that a sequential development begins to take hold where previous discoveries forms the foundation of new discoveries.

Bits and pieces of large number history are scattered throughout the rest of this site, but the purpose of this page is to form a single clear narrative of that history as a whole.

The history will be broken up into highlighted dates followed by some entry on the significance of this time period. Like other information on this site, this list of dates is subject to revision and details will be added over time.

The Large Number Timeline

4,000,000,000 BC

Life begins on earth. I would argue that without sentient beings there are no numbers. Thus our progress with numbers really begins when life begins. Prior to this, if numbers simply exist regardless of who is thinking about them, then they always existed. But without anyone around to think about them we'd have to conclude that there could be no progress in the understanding of those numbers. The simplest organisms probably don't have anything we'd recognize as a thought, so therefore couldn't have conceived of number, but there was at least the potential that life would one day develop that ability. Thus I somewhat arbitrarily chose to begin the story here.

200,000,000 BC

Mammals arrive on the earth. Mammals are relatively intelligent life-forms which possess a fairly developed number sense. Most should be able to recognize the numbers one, two, and three intuitively. For larger numbers a intuitive estimation ability can be used. This is the same set of base numeric abilities that humans would inherit and would form the basis of our concept of "number"

65,000,000 BC

The estimated time when the dinosaurs died out. This event completely altered life on earth, and it marked the end of a strategy of "big and large" and the beginning of a new strategy: "small and resourceful". This was probably and important step in the evolutionary development of an intelligent species that would begin to think abstractly.

2,500,000 BC

This marks the beginning of what we would recognize as humanoid species appearing on the earth.

200,000 BC

This is an estimate on the first appearance of "modern humans". That is, human beings as we would understand them. At this early stage humans were already sophisticated hunters and tool markers when compared even to other humanoid species, but it is not certain how much they knew or cared about numbers. We can assume they had the basic number sense abilities pre-installed, but there would have been no words for numbers or even a clear concept of them distinct from actual objects.

33,000 BC

A bone dating from around this time has marks scratched on it that appear to be tally marks. It is the earliest record we have of "number". We can guess that around this time that people had no name for numbers (except maybe the smallest ones), but they had some sense that numbers had an exact magnitude even when it was difficult to discern. After all, the tally is a way to better discern a large magnitude. The largest numbers in such a time would have simply been the largest number a man could visualize. For example, the number of trees or beasts we could survey in his line of sight. Man must have had a least some sense of the vast expanse of the physical world, and that by necessity there must be quite large numbers out there. The largest number however he could actually quantify would be limited to the number of tally marks he could actually create. Since language includes a singular and plural form for many nouns its would seem that even early man would have had a sense of distinction between small numbers and large numbers.

4500 BC

Beginnings of Sumerian Civilization

Sumerian civilization is the earliest civilization we have physical evidence for. Historians speculate that Sumerian civilization began sometime around 4500 BC, although records only go as far back as about 2500 BC. The Sumerians developed the earliest known system of numeration, outside of tally marks. They used a base 60 positional system which is both surprisingly simple and sophisticated. It would have made "imagining" some very large numbers very easy. It seems very likely that some scribe in his idle thoughts must have wondered about numbers like 1000000000...000000 with 60 zeroes, in base 60. Such a number would be 60^60 which is approximately 10^106, and is even larger than a googol! This would not have been difficult to define in the Sumerian system, and the scribes mind was sure to be boggled when trying to contemplate just how large such a number actually would be. In fact it would probably be literally beyond his imagining since this number is much much larger than anything that could occur on the entire earth even is you counted every particle! How far did peoples idle thoughts go in the direction of large numbers? There is no way for us to know, because we only have written records to go on. The largest numbers in writing were probably not much more than a million since these numbers were used for actual commerce, and this suffices for most purposes.