Post #1362069
2026-04-02 20:55 UTC
Can't believe I'm nerd-sniped this easily. Very technically, the point at which a service should be considered unreliable or down is at γ nines, where γ = 0.9030899869919434… is a transcendental constant. γ nines is exactly 87.5% availability, or 7/8 availability, and it's the point at which a service's availability might as well be random. (Another one of the local complexity theorists can explain why it's 7/8 and not 1/2.)
Replies (2)
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@aio@awful.systems 2026-04-03 03:20
... why 7/8?
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@lagrangeinterpolator@awful.systems 2026-04-03 00:32
We can see that one 9 of availability is 90% = 0.9, two 9s is 99% = 0.99, three 9s is 99.9% = 0.999, etc. In general, for positive integers n, n 9s of availability is 1 - (1/10)^n, and we can extrapolate that to non-integer values of n. The value γ needed for 87.5% availability is the solution to 1 - (1/10)^γ = 7/8, or γ = log_10(8) = 0.903089987. γ is transcendental by [Gelfond-Schneider](https://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_theorem) (see [this](https://math.stackexchange.com/questions/2276970/is-my-proof-that-log-23-is-transcendental-correct) for a reference proof). Right now, Sora is at zero 9s of availability.