Waves

 

Anchors Aweigh

Anchors aweigh, my boys, anchors aweigh
Farewell to foreign shores, we sail at break of day, of day
Through our last night ashore, drink to the foam
Until we meet again, here's wishing you a happy voyage home

Let’s hear it for those who sail the waves. Not only are those waves alive, but those on those waves also keep us alive!

The dictionary definition of flatline is

“to die or be so near death that the display of one's vital signs on medical monitoring equipment shows a flat line rather than peaks and troughs. to remain at a continuous low level.”

It does not sound like being flat is such a good thing. Thus it is surprising that much of mathematics is based on the principle that a surface is flat, Euclidean. On the contrary it sounds like life should be a wave, not a flat line.

A single wave has peaks and throughs. Except on the wave itself, it is empty in the time between those peaks and troughs. An absolute should be a wave to be alive, but it should have no peaks or throughs. Rather than a single value, it should be any value within its amplitude, and thus it needs to fill in those empty spaces. An absolute should have an amplitude, but it should be the sum of all waves such that there are no empty spaces.

So why does this matter? Because every wave has a variance, which is twice the square of its amplitude. If an absolute is a wave, then by having an amplitude it by definition has a variance, which is the square of Standard Deviation. It is not only possible, but by its very definition, that an absolute, infinity, has no error. Standard Error, SE, is the Standard Deviation, SD, divided by the square root of its sample size. The limit of error as the sample size approaches infinity is zero. This is because the limit of SD/√n as n approaches ∞ is zero. It is NOT because its SD is zero. If that were true, then the SE for all values of n would be zero. Saying that the absolute is a wave and has zero Error does NOT mean that the absolute has zero Deviation.