The operation of *raising-to-a-power* can be **base-free** just as an algebraic variable can be number-free when it applies to all numbers.

> specific bases are not necessary

We will interpret the round boundary as raising # to the power of its contents

(A) ☞ #A

For consistency, the square boundary then is interpreted as the base-free logarithm of its contents

[A] ☞ log# A

One convenient way to think about logarithms is that the Logarithm of a Number indicates the number of digits in that number.

The *Hash Mark*, #, is a meta-symbol that is neither part of the James notation nor part of the interpretation. # acts like a universal variable standing in place of an arbitrary base. In our interpretation, boundaries can stand in place of exponential and logarithmic expressions. In contrast, transformation within James forms is independent of the concept of a base. In effect, # is a convenience that permits the interpretation to remain uncommitted to a value of a base.

~

William Bricken, Iconic Arithmetic Volume I: The Design of Mathematics for Human Understanding (Unary press, 2019), p. 172–173.