Michal Piekarczyk

June 22, 2024

random colloquialisms


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. 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. 

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 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. Fir 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 😂.