> To me it makes much more sense to say. The Universe IS. ... There is no such thing as "time."
I think I see your problem. Without time, randomness is indeed impossible. There is no point in talking about random events when you can directly observe the entirety of space-time; from that perspective, there are no probabilities, only facts. This discussion, fortunately, was about a more human perspective, in which the past may be known but knowledge of the future is beyond our reach.
> If you get to reference something outside the sequence like "PI" then so should I. I will thereby reference the output of your transistor in my deterministic non-local Bohmian description of the dynamics of our static universe.
You can reference things outside of the sequence, but only if they are knowable before the sequence is generated. PI is known, being a fundamental mathematical constant, but the output of the transistor is not.
However, I would say that it is meaningless to talk about whether a specific _sequence_ is random; what matters is whether the _process_ of producing the sequence introduced new information into the system. (The same process must, of course, destroy some existing information in order that the entropy of the system as a whole remains monotonically increasing.)
If one can predict the result of a measurement with certainty using only information knowable beforehand, then the measurement itself introduces no new information, and thus is not random. Otherwise, the result of the measurement is random, with entropy greater than zero and less than or equal to the number of significant bits measured.
> Don't tell me something *IS* (in the descriptive sense) random just because you can't predict the next number.
It's not a question of whether you or I could predict the next number; the question is whether the rules of the system permit _anyone_ to predict the next number with 100% certainty, given all the information which it is possible for them to know. Even in a completely deterministic system it may not be possible, even in theory, for any one person to know all the initial conditions which can affect the result.