Can it also apply to the time until an event which hasn't yet happened? Ie. a system you have never observed crashing before, has been running for T hours. So being on average half way through its lifespan, will probably run another T hours without incident.
It works based upon the 100% certainty that whatever you are, at some point you will cease to be.
On average, regardless of what you are, you are in the middle of your life or existence (some very high variance here).
In order to generalise it to non-certain events, such as a program crash, you'd need to remove the certainty assumption and rejig the consequent statistics - it might be doable, but you wouldn't end up with something quite so clean and simple.
I am interested in this topic but never quite understood it. Is there a techincal reason why these organizations don't transpile COBOL to C? I imagine building such a compiler wouldn't be that hard, and even if it is, we've had decades to work on it.
Is it more of a process thing (having to change unit tests, code review, hire new people, etc) that prevents this? Or is it just too risky given the important roles of the mainframes?
Methinks you are replying to the wrong comment? But for the fun of it, the large three letter mainframe company made an effort to rewrite their COBOL compiler's backend to use the same JIT compiler they have for Java (check slides 5 and 8):
https://www.slideshare.net/MarkStoodley/under-the-hood-of-th...
Such a change would be transparent to the end user.. Except for gotchas like not all users have the source code for all of their dependencies. What happens if you want to update your program and you have a dependency on a binary from some vendor who went defunct 35 years ago? You're stuck compiling against whatever artifacts you have so does transpiling to C still work?
I don't see any issue, as long as you consider the time until the system crashes or stops for any other reason rather than the time until the system stops specifically due to a crash.
And note that the Lindy effect is about the expected value (mean). The statement "probably run another T hours without incident" could be interpreted as relating to the median, which is actually a little less than the mean. So the statement should either be "the expected value of the number of hours until the system stops is T", or "the probability of the system running for at least another T hours is a little less than 50%".
Edit: "A little" is inaccurate, the probability of the remaining lifetime being at least T is actually 25%[1]. And all this is assuming a "Lindy proportion" of 1 (which seems reasonable) and that no other information is known.
[1] Calculation: Lindy proportion 1 corresponds to a Pareto distribution with probability distribution function `a / x^(a+1)` where a = 2 and the range of x is [1, ∞). The cumulative distribution function is `1 - 1/x^a`. So the probability of the remaining lifetime being less than or equal to the observed lifetime is CDF(2) = 0.75.
