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2.4.1
Introduction: What is an illion Series?
Defining an illion Series
Before we get started it would probably be best to define exactly what an "illion series" is. Everyone is familiar with numbers like a million, billion, and a trillion. Each of these are members of the standard illion series. Not every number name qualifies as a member of an illion series. It helps if it ends in -illion but this is not essential. One important property is that they name a power of a thousand, or at least a power of ten. Another important aspect is that it is part of a series of names which theoretical allow the naming of every number from 1 to the largest member of the series. An illion series, defined in this way, is really just an extension of counting. While every whole number can technically be "named" by simply reading out its digits, illion series' attempt to create "denominations" so that short names can be used for even very massive numbers. It is certainly possible to call 1,000,000,000,000 a thousand thousand thousand thousand, but its much easier and more clear to call it a trillion.
In this chapter we will be learning about a wide variety of illion type systems. Not all of them use powers of a thousand, but all of them provide short names for a series of powers of ten. First we will learn about the origin of the illions and their development to their modern canonical equivalents. After this we will consider the many systems myself and others have tried to devise to extend the canonical series to utterly absurd heights. It might surprise you how far people have actually extended these names. We will also be critiquing these systems to find out how far they can be extended, if they are free of ambiguities and are logically constructed, and considering how well they lend themselves to extension.
So how far have people gotten? That depends on the criteria by which we judge a systems extendability. I should note that we are not looking for the "largest named illion". It is a trivial matter to take 10^N where N is much larger than any number used to name a power of ten, call it "somethingillion" and claim to have the largest illion. Instead we are looking for a system which extends the furthest while maintaining names for all the intermediate names without ambiguity. This puts some very definite limits on how far the illions can really be extended, because we will be dealing with the confusing world of "recreational linguistics". I should also note that while numbers like a googol and a googolplex (of which we will learn more in chapter 3-1) while being powers of ten, do not qualify as members of any "illion scheme". An illion scheme must, at least in principle, allow for the naming of every number from 1 to its largest member. Do the terms googolplex and googol make it clear how we are to name terms between them?
The only two constructions we will be considering are power series, in which some base, N, is raised to successive powers N^2, N^3, N^4, etc. and each is provided a unique name. The second type of construction we will be considering are squaring series, in which some base, N, is repeatedly squared, N^2, (N^2)^2, ((N^2)^2)^2, etc. and each is provided a unique name. The squaring series are much more rare than power series, but they are also more extendable.
We have a lot of material to cover in this chapter, so let's get started. In the first article I discuss the origin of the canonical illions...
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