Another interseting concept I haven't discussed is the idea that two functions are "isomorphic". This is fancy math speak for "they have the same shape".

When we look at two nodes they sometimes are the same underlying math, but with different parameter meanings. For example, the Pow function and the Bias function are the same shape. Any shape you can make with one, you can exactly make with the other. But the values you use to create the same shapes will be different values.

This is a hard concept at first, but once you get it, it's a big time saver in learning the nodes. This is because when two nodes are isomorphic, they are actually the same, just using different control parameters, so once you understand one, you understand the other.

Example:

Definition of the add node: Value_1 + Value_2

Definition of the sub node: Value_1 - Value_2

Claim:

Add and Sub are isomorphic.

Proof:

Take whatever you're using in an add node, and negate the number in Value_2. It is now the equivalent subtract node.

Add(a, -b) = a + -b = a - b = Sub(a, b)
QED

Mul and Div are isomorphic:

Proof:
Mul(a, 1/b) = a * 1 / b = a / b = Div(a, b)

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