The Story of The Unit Simulacrum and Whole PI

© 2004-2010

The names “The Bottom Up Solution”, “The Unit Simulacrum”, “Whole PI” and all equations, figures and schemes are copyrighted in 2004-2010 by William Craig Byrdwell.  No portion of the equations, figures or schemes may be used without acknowledging the copyright holder, William Craig Byrdwell. or

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To Continue Chapter Six

Chapter Six first posted to the Web on  Sunday, January 14, 2007



Mending the Sacred Hoop—

The Meaning of Whole PI


is in the process of editing.  It is not yet in its final form.

The equations in Figure 53 give the answers for circumference, area and volume in one, two, or three dimensions, respectively. When r=1, it is the Unit Radius. For the Unit Radius, the circumference, area and volume are 2p, p, and 4/3p, respectively. These are the characteristics of the Unit Radius Circle in Three Dimensions in our agreed reality.

But that is not the only way to see things.

Spectroscopy is a group of techniques used for studying wavelengths of light in different ranges of the electromagnetic (EM) spectrum. At different times in history, different types of spectroscopy from visible to infrared spectrometry to ultraviolet (UV) spectroscopy, to vacuum UV, to X-ray diffraction, to gamma-ray, and on up into super-high energy particle spectroscopy have been discovered, and our ability to perceive has been increased. In this way, our understanding of our reality has increased as our ability to perceive has expanded.

Each wavelength of electromagnetic radiation in our known (observed) universe is proportional to c, the speed of light in a vacuum, as we have scientifically measured it. It was, for a long time, believed to be the immutable upper limit of velocities for EM radiation in our universe. But look up the phrase ‘superluminal propagation’ and you’ll find numerous reports of instances where this once iron-clad constant is only one more milestone (Critical Limit) on the evolutionary trail of discovery.

All EM radiation is proportional to c, through the relationship E = hc/l. The energy is inversely proportional to the wavelength. A longer wavelength is lower energy, and a shorter wavelength is higher energy. Wavelength is proportional to energy through c. The constant c is itself is a velocity, which is a ratio of a distance traveled to time. To produce the ratio c, there must be a unit distance defined and a unit time defined. If a ratio involves two variables, each variable must have a unit definition and a number times that unit variable, or a fraction of that unit variable. The speed of light is usually measured in meters/sec, giving a value of 3.0 x 108 meters/second or 3.0 x 1010 centimeters/sec.

For another example, if I am driving in my car, there is a defined distance called a mile that I can count multiples of to keep track of distance traveled. To keep track of time, I will observe a clock to determine which fraction of a day’s time it takes to pass a certain distance. I’ll set a unit time of one hour, and I can count multiples of that unit time to count passage of time. Therefore, having the two unit variables, mile and hour, I can construct the ratio of miles to hours to determine the velocity of the car. Of course the car’s onboard computer isn’t waiting a whole hour to give me the miles per hour ratio. It subdivides the unit into small units and calculates the miles/hour ratio on a very short time scale, by calculating small fractions to the unit time.