iSoul Time has three dimensions

Means and operations

The power means are defined for a set of real numbers, a1, a2, …, an:

The best-known of these are the arithmetic, geometric, and harmonic means, with p = 1, p → 0, and p = –1:

The other well-known power mean is the root mean square with p = 2:

These are all examples of quasi-arithmetic means:

The power means suggest power operations:

These include addition (p = 1), harmonic addition (p = –1), and the root sum squared (p = 2):

In order to avoid roots of negative numbers, the absolute value is often taken: | ai |. If the ai represent differences such as | xiyi |, then the operations are p-norms:

The best-known norm is the Euclidean norm or distance (p = 2):

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