Time Evolution or Displacement

Natural Time Evolution

(unit circle, unit cycle)           =   2 * Pi * frequency * time ,

= 2 * Pi * f * t

= ω * t ——> rad (units)

Radians are frequently omitted from mathematical expression, and are what should be in radians is in the form of number. All of trigonometry should be expressed in radians (rad).

The following measurement is used by computer engineers, such as the DOS engineers - and for all operating systems

frequency        = f

Natural time evolution (unit diameter, unit dimension)     = Pi * f * t

= ( ω/2) * t

The answer in information technology (IT) should be in rad. It is simply expressed as number. By this logic all numbers in IT are angles and should be expressed as rad, in the firmware and in software programming syntax. Naturally we do need to operate with radians in the display data. For better integration of logic we should employ the example of rad in the earlier information form.

Dimensional revolution or hypersphere

y   =   (( 1 ^ 2  -  ( x /2) ^ 2 ) ^ 1/2 is the spherical function for a sphere with radius 1/2 or diameter of 1, and a or amplification of 1. The clock, time is the independent variable. a^2 is the spherical, finite, upper of constraint of (x/2)^2.

The clock as mentioned above is understood:     time  =  t, the universal clock of physics - and now, mathematics. As the reader can see time has always been inherent, yet hidden in mathematics as the primary independent variable. By this example, x is only a dependent variable - not the most fundamental in mathematics.

No mathematics event space is ever mapped to real number set instantaneous. There is always a time component as mathematics is derived from the real universe - from physics, rather than the reverse scenario.

All mathematics can really be only proved by testing it in physics application. Both disciplines are governed, entirely, by algebra. Programming is a hybrid of standard algebra and word equations, as taught in primary school, universally. It follows the same rules of Physics for that reason.

Simpler Time Evolution

Eg 2 When working with natural or bounded cycles, use omega t to measure displacement or bounded/natural time evolution, 2 * Pi * f * t.

For linear or flat time evolution (artificial), displacement is:

                          θ =  2 * Pi * f * t / 2 * Pi

                       A = v * t , 

( λ/T ) * t,

= bitrate * clock()

f(x) = x

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