Categories
mathematics

Random Facts: π and Six 9’s

A brief post on a mathematical curiosity.

I was introduced to the concept of “six 9’s” very recently. It is a definition of the (extreme) high availability of a system. This can be used to specify or demonstrate the required uptime and availability of, for instance, a computer server or related communications or information processing system.

The six 9’s themselves are 99.9999 and represent a percentage of expected uptime for the system to be defined as “high availability” to a spectacularly exacting standard of “six 9’s”. This means that over any defined timeframe, the acceptable downtime, failure or outage window for any system to still be considered as six 9’s “high availability” is 0.0001%. This approximates to 32 seconds (or less) of permissible downtime per year.

I randomly stumbled across another instance of six 9’s this evening. Pi (π) is an irrational number that is the ratio of the diameter of a circle to it’s curcumference. Most of us have at least passing familiarity with the beginning of the sequence: 3.1415… (etc.).

A curious feature of π is that it is a random sequence. It’s decimal expansion has been calculated into trillions of digits and no repetitive patterns have been identified. From the 762nd digit of π there are six consecutive 9’s, one after the other. This is called the Feynman point, after the famous (Nobel prize-winning) physicist and bongo drum player Richard Feynman.

This not particularly useful information and has absolutely no bearing on high availability systems. It is, however, just one of those weird and unexpected curiosities of numbers, number sequences and mathematics. Something to bring up at your next dinner party with IT industry types, if you ever go to those sort of things. For me, this will just get mentally filed away into my vast collection of useless but interesting information.

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