Uncertainty is the only certainty. Not a radical statement. As long as I live, dealing with uncertainty is inevitable. Unavoidable everywhere. I wouldn’t have it any other way, even if it can be uncomfortable.
Prominent Ancient Greeks may have travelled to Delphi for advice as to what the future may hold. There’re those three enigmatic witches who warn Macbeth of his fate. History and fiction are littered with references.
For me, I can pick-up a newspaper and look for a daily astrological prediction. One I like. I can flick around social media and see more prophecies than ever. Mostly gibberish. There are those convinced of their foresight.
Despite a cynical disposition towards the above, science can be applied to the world of uncertainty. Generally, the proposition is that an element of the past and present will be reproduced in the future. This is not absolute. However, human engineered systems tend to behave with a degree of predictability.
Empirical methods, where society collects data from the past and present, can be useful in trying to forecast what may happen next. The more deterministic the systems under study, the more useful acquired data can be. For these, forecasting challenges mount for the new, novel, or radically altered.
I’m writing this given the interest there is in probabilistic safety. There are figures that hit the headlines that are almost incompressible. If the rationale behind the numbers is not clear then incorrect assumptions result. Tiny numbers from 1 x 10-6 to 1 x 10-9 are quoted in the News (SI Units). What do they mean? Let’s start with simple probability.
If an occurrence is certain then a numerical value of “1” can be given to it.
Absolute certainty is a rare thing. I can say that the Sun will rise tomorrow, and most people will take that as a statement of certainty. Intriguingly there’s the most incredibly improbable case where the solar system is thrown into instability and the Sunrise isn’t as expected.
If an occurrence never happens then a numerical value of “0” can be given to it.
Absolute impossibility is only possible with absolute knowledge. So, again it’s rare. I can say that human time-travel, to and from the distant past, is only fiction to next discover that a way has been found.
Let’s say we live in a world where the probability of occurrences ranges from the 0.99999, with ever more “9s”, to a number as small as 1 x 10-30[1]. A quecto.
These extreme numbers are nice for physicists and astronomers to play with, but they are outside normal engineering practices. As yet, we do not have the means to operate at the level of these limits. Time will tell. Or I maybe wrong.
By the way, I used the word “occurrence” above to denote anything that can happen in an instant. When talking about undesirable happenings, that can mean an incident, accident, mishap, slip, failure, or error. Each of these has a definition. Often more than one.
Next. I’ll go back to the tiny numbers more commonly quoted.
POST: For extraordinary numbers we need look no further than the nimble electron. So far, the best measurement for the life of an electron suggests that one now will still be around in 66,000 yottayears (6.6 × 1028 yrs). That’s about 5-quintillion times the current age of our universe.