My Hero, Zero!
How wonderful
you are, why we could never reach a star
Without you, Zero, my hero, how wonderful you are
What's so wonderful about a zero? It's nothing, isn't it?
Sure, it represents nothing alone
But place a
zero after one, and you've got yourself a ten
See how important that is?
When you run out of digits, you can start all over again
See how convenient that is?
That's why with only ten digits including zero
You can count as high as you could ever go
Forever, towards infinity
No one ever gets there, but you could try
Zero IS my hero,
but what kind of zero.
There are three kinds of zero: 1) absolute zero, 2) relative
zero, and 3) repeating zero. Mathematically this can be expressed as
1.
0<x<∞, absolute zero;
2.
-∞<x<∞, relative zero; and
3. (n-1)*π*∞<x<n*π*∞, repeating zero.
It is confusing because absolute zero is often expressed using
a relative scale, but that does NOT make it a relative zero. Absolute zero occurs a temperature
of 0º on the Kelvin scale. But temperature is more often reported using the Celsius
or Fahrenheit scale, where e.g., 0º Celsius is the boiling point of water. -4000º on the Celsius
scale is undefined because absolute zero occurs at ‑453º Celsius.
Nothing exists below absolute zero.
By contrast a relative zero is only a reference point and infinity
exists before that reference point as well as after that reference point. For example
time is a relative zero where the refence point can be the birth of Chris, the
Common Era, the founding of Rome, the start of the Exodus, the Big Bang, etc.
A repeating zero is a recognition that zero may occur an infinite
number of times for example as in wave functions. It will pass though zero an infinite
number of times, periodically.
Not only are there three kinds of zero, but each also appears
to correspond to a dimension. Space is an absolute zero. There is no such thing
as negative space. There are three components of space: length, width, and height,
but as Minkowski showed, it is useful to combine them into a single dimension of
space. Time appears to be a relative zero with the reference event being now. There is an infinite amount time before that
event, the past, and an infinite amount of time after that event, the future.
Space and time are often taken together as space-time. This
defines reality and light is assumed to travel on a flat, Euclidean surface which defines a
light cone. However, it is only an assumption that space-time is flat,
Euclidean. The Earth's surface is spherical and is only perceived as flat because the radius
of the surface of the Earth is so large. Similarly if the universe were hyperbolic,
curved, then light would travel on that hyperbolic surface. and while there is an infinite amount
of space-time in which light can travel, the range of that space-time repeats
cyclically according to a hyperbolic function. If light travels on that hyperbolic
surface, it might be more useful to speak not of inverted light cones, but two sheets of a hyperboloid where the separation
between the two sheets is zero.
An absolute might then be represented as an infinite series of overlapping triangular waves. Each wave would have a sharp transition point
at its apex. However to an observer on
a hyperbolic surface that wave, and its discontinuity, would be perceived as
almost smooth and would repeat infinitely with each period of that wave, even
if the observer could perceive only the period in which the observer was located.
The sharp discontinuity at each half period would be perceived of as a single discontinuity. If the variance of the wave is perceived as 5/6
of the true variance, then the mean/median/mode/location of that wave might then
be assumed to be 6/5 of the true mean/median/mode/mode location of that discontinuity
in order to correct for this perception. Setting only the location, i.e. a User Optimal,
or only the variance, i.e. a System Optimal is inferior to setting, and correcting the perceptions, of both the location and the variance, i.e. a Nash
Equilibrium.
Zero is still my hero, but that includes all three kinds of zero!
