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### Ten

One of the hardest concepts for humans to grasp is infinity. Normally when I think of infinity I think of some indeterminate end a long, long ways away, but every so often I am reminded that infinity also occurs between discrete numbers, and of the infinite number of discrete numbers, what happens between zero and one is often incredibly interesting. Consider one concept fundamental to real-time operating systems - achieving the highest possible probability of repeatable success. When the number one is defined as one hundred percent success rate, attempts to achieve ever greater success asymptotically approach one but never reach it. Consider another concept fundamental to real-time operating systems - the time slice that bounds the event. Ever smaller and smaller time slices asymptotically approach zero, but again, never reach it.

The number system Nature obeys is not positive and negative numbers on a continuous line, but a logorithmic sectioning where we define our location by what power of ten we exist in. It does not matter whether we are talking about time, temperature, or reliability. Stars live and die at scales of 10^6 degrees K, humans live and die over scales at 10^1 K, molecules live and die at scales of 10^-6 K. The half-life of a free neutron dwarfs that of a muon, tectonic plate migration dwarfs the lifespans of humans, and rotations of galaxies can be measured in thousands if not millions of rotations of solar systems.

Every day scientists achieve ever-closer temperatures to the posited absolute zero but it should be obvious that temperature operates on the same powers of ten scaling at the low end as it does at the high end. Today maybe it's 1 x 10^-7 K, tomorrow it'll be 1 x 10^-8 K. Sure, there's new and interesting things going on like Bose-Einstein Condensates, but in a scale that goes to infinity, this is no closer to absolute zero than the three million degree corona of our Sun. It's just a different segment.

In RTOS and uptimes, success rates are measured in ever-increasing N nines. Success can be shown to be identical to other aspects of nature by looking at the delta: 99.999% (also known as "five nines") is equal to 1 - .99999 = 1 x 10^-5. Six nines is 1 x 10^-6, and so on. In physics, a calculated value that is merely two or three times the measured value is irrelevant, but an order of magnitude difference, that's a mistake. Is RTOS any different? The competitive edge is in "The Nines," that area where one vendor can claim reliability to five decimal places, only to be trumped by a vendor that claims six. Nobody cares about the numbers between 10^-5 and 10^-6, like 3.14159 x 10^-6 and 7 x 10^-6, but there are more numbers between them than stars in this galaxy, or grains of sand on a beach, grains that look like mountains to paramecium.

In trying to define a narrow position within a power of ten, the landscape becomes fractal, where scale is irrelevant because it all looks the same. If the time slice bounding an event is one millisecond, attempting to determine when the event occurs exactly creates more time slices within the time slice, so that microseconds divide milliseconds, nanoseconds divide microseconds, picoseconds divide nanoseconds, ad infinitum. Yet, without the precise knowledge of when the event occurs and what time slice bounds it, claiming success to "n" decimal places is a statistical artifact borne of repeated testing instead of hard timing.

In the interview with Paul McKenney, three time scales emerged as regularly used time metrics in RTOS. I'll define them to be Human (medical research), Digital (heating systems), and Gaming (real-time physics). To this I'll add two more time scales - Geologic and Financial. Geologic is simple enough to comprehend. If the four and a half billion years the Earth has existed is represented on a time line where one millimeter equals one million years, the time line would be 4.5 meters long, or roughly fifteen feet. The time humans have been on the Earth would be less than the period at the end of this sentence.