Random variables
On, https://recompilermag.com/issues/issue-2/why-random-variables-are-neither-random-nor-variable/ . Cool article. I had some thoughts.
The author addresses this quote ,
"Why random variables are neither random nor variables"
Summarizing, the author would prefer I think "random variables" were renamed as
"probabilistically deterministic functions".
or maybe more verbosely,
"probabilistically deterministic functions mapping uncertainty to known possible outcomes".
The argument being, that, "random variables" are not variables because they are not single numbers but really intended to describe how a probabilistic distribution , say, maps to outcomes. I like that the author refers to these outcomes as "shadow numbers" 🙂. (And by extension I like the point that, just semantically, a number, "14" , is not random even if it was generated through a quantum event, because by definition the mapping function is what is random and not the numbers they produce).
And "random variables" are not random, per the article, that is, it is not true that we don't know anything about them. Instead they are "random" in a different sense that we do know something about them (perhaps the distribution).
My thoughts
Saying random variables are neither random nor variables is bait and switch in two ways. Saying a random variable say X, is not a variable, is not a useful statement, because variables are not variable either. If X is a mapping function from outcomes like sides of a die, to a measurable space such as 1/6, for each side as the probability of each outcome, as a mathematical definition, but in normal usage, we talk about X as the outcomes it takes on, as we observe them by rolling a die and we dont typically strictly mean the function. So its a double meaning .
But variable has a double meaning too, because if you ask someone whats a variable today, they'll tell you it represents a memory reference to some particular value, but its a misnomer because it doesnt "vary" on its own.
But variable has a double meaning too, because if you ask someone whats a variable today, they'll tell you it represents a memory reference to some particular value, but its a misnomer because it doesnt "vary" on its own.
That's why the "variable" in "random variable" relates to functions actually, since the output of a function also varies.
Then we have "random". This is a bait and switch because if random variables are functions powered by random events, but we choose to say the outcome itself, we observe is not random after its observed. But the random event is still random.
Also, the word random is colloquially an event that's surprising or not predictable. But speaking with definitions, it refers to the quantifiable uncertainty that can still be described with some precision. For instance we can say there's a 0.166... chance a fair 6 sided die will fall on a "3". So we have precision around the uncertainty here, but ultimately we are divijg into philosophy if we say that we are "not surprised". Ultimately we dont know what the die roll will be and so qualifying the random variable as not random is to ignore the random event that underpins how the state of the universe behaves .
I think bottom like, language is not as precise as math or code and so saying that "random variables are neither random nor variables" is funny joke territory at best and attempt at sounding clever at a party at worst 😂.