TITLE: Random vs Unknown
QUESTION [20 upvotes]: Is there any distinction at all between a random quantity and an unknown quantity or is it impossible to distinguish?
Example: 5 minutes in the future, I plan to roll a die the the number of the die roll at that point in time is called X. Suppose the number X will happen to be 4 , although there is no way of knowing that at the current time (pretend I didn't say it was going to be 4, or that I retroactively inserted a 4 into the post after I witnessed it, but let's continue this discussion as if it were unknown). 
Is X a deterministic constant (in reality equal to 4), which is simply unknown (once again, pretend I didn't say it was 4)... or is it a random variable uniformly distributed from 1 to 6 (discrete)?
Does there exist any situation where we can say that a number is definitely a random variable and definitely not an unknown deterministic constant or vice versa (definitely an unknown deterministic constant and definitely not random)?
If there is no way to distinguish these two things, then is it possible they are in fact descriptions of the same thing i.e. everything we call random in the universe really just originates from lack of knowledge? Does there exist objective randomness which is not a function of the knowledge any specific observer has?
Thanks!

REPLY [3 votes]: In "Theory of Probability and Random Processes" by V.V.Tutubalin (it exists, alas, only in Russian: http://padabum.com/d.php?id=10681), the second half of the book is devoted to applications of probability to real world problems. Unlike most textbooks, it contains not an optimistic list of successful applications, but case studies and analysis of arising difficulties. After reading this book you may agree with the author that successful applications of probabilistic models to practice should often be viewed as miracles.
I like the book a lot. Retelling it is not for a MO comment, so let me give you just one quote. After saying that there is no accurate, systematic, and consistent way to apply mathematics to physics and engineering, Tutubalin writes (p.317): This is especially true for applications of probabilistic models due to the fundamental haziness of the notion of statistical ensemble.