[captain11]

While I'm sure that you mean well, Base 4 IS literally an order of magnitude greater in complexity than Base 2.

Make that statement to a mathematician and best case, you'll get a puzzled look and a request to define complexity. Apparently you define it according to the number of values per digit.

In Binary you'd represent Base 2 as 10, while Base 4 would be 100.

You're confusing values represented in a base with the base itself. Stated precisely, this much is true:

• the decimal value 2 is represented in base 2 (binary) as "10".
• the decimal value 4 is represented in base 2 (binary) as "100"
• the decimal value 2 is represented in base 4 (quaternary) as "2"
• the decimal value 4 is represented in base 4 (quaternary) as "10"

100 is a single order of magnitude larger than 10, FYI...

Yes, it is. In any base, FYI.

[Southack]

"Make that statement to a mathematician and best case, you'll get a puzzled look and a request to define complexity. Apparently you define it according to the number of values per digit."

Design an experiment in which random, agitated matter inside a container is observed over time.

Now ask yourself, for this experiment, is it equally likely, more likely, or less likely that I witness "order" spontaneously (and without intelligent intervention of any sort) form from this chaos in which a two item pattern (e.g. 0,1) emerges in contrast to a four item pattern (e.g. 0,1,2,3) emerging?

I think that you'll eventually agree that the two-item pattern is an order of magnitude more likely to form.

[Southack]

100 is a single order of magnitude larger than 10, FYI.

"Yes, it is. In any base, FYI."

Surely you realize that was my intial claim...