I'm seeing the use of "random" instead of "arbitrary", etc., with increasing frequency. To me, "random" has a specific meaning and is not synonymous with these other words.
Is it correct to use it in this way?
The definition of arbitrary does include a link with random:
It is reflected by the usage "at random" (by chance), which is valid.
I typically use arbitrary when discussing planning or decision-making, or with respect to preference:
and random in cases where selection or ordering are the relevant aspect, or in mathematical or computer programming contexts:
That said, I don't think it's necessarily incorrect to use them interchangeably in some cases; it depends on the context:
Even in this case, for myself, the meaning of those two sentences has a slightly different color, but in essense they are interchangeable.
The difference becomes clearer when you consider the meaning of the word arbitrary.
Arbitrary, means something reached through the process of arbitration. An arbitration is the process of reaching a decision between two or more opinions or parties.
While a random sequence has no defined structure or pattern, an arbitrary one does. Random is the result of pure chance – like when we throw a dice – while arbitrary is a result of choice, deliberation, and often negotiations, sometimes extensive ones.
A random sequence of numbers is never wrong, while an arbitrary one can be. Whichever opinion underpins an arbitrary sequence or system, you will need to follow that sequence in order to get it right – whether you agree with the underpinning opinions or not.
A random sequence of numbers could be made into an arbitrary one – by choosing a sequence of random numbers, and making them “right” and thereby any other combination “wrong”. This is exactly what we do when we create a password, or a combination of numbers for opening a safe. They may start as random, but once we have chosen them, they become arbitrary.