Lol. I like this. In seriousness though, “normal” is as real a thing as any such concept can be- but “normal” is an extremely specific and subjective thing based almost entirely in perception. That is to say, I would find it highly abnormal to go to the kitchen right now and find my wife making dinner as I have no wife and my partner is currently traveling and I should be the only one in the house for 3 weeks. So “normal” in that regard would not be to find someone in my kitchen.
Beyond math “normal” exists as a helpful concept in technical fields not exclusive to math including sciences and engineering. Manufacturing and repair of mass produced machines are two examples where the concept of normal can be very useful. A general goal in mass production would be that each laptop is essentially identical and from when it leaves the factory to when it is retired should be essentially so. So “normal” can be generalized as “to specification.” We run in to a lot of trouble where the word…
.. “normal” is used for things that do not and often should not have a “specification.” Words carry certain context so something that may be called “abnormal” might be better described as “unusual,” and that which is generally expected might be said to be usually the case..” unusual has certain connotations too though. We might instead say “odd” or such but it is the case in English that most words which describe something that is “different” hold some sort of historically negative context. “Ordinary” and “out of the ordinary” are other pairs. They sound a bit stuffy- at least in modern American English, and while “out of the ordinary” isn’t necessarily as negatively perceived as some of these other examples, “ordinary” is often seen as insulting or has a sort of “plain” context.
Much the same we might call that we know and expect “common” and that which is otherwise “uncommon,” but this is another pair where “uncommon” doesn’t have the usual negative connotation of many words synonymous to “different,” but “common” has negative connotations. Continuing that theme- If we call that warranting comment for being not common to us “remarkable” and that which bears no special comment “unremarkable” we have two issues. “Remarkable” in modern American English is usually perceived as positive- often very complimentary and akin to “amazing.” “Unremarkable” is generally negative. To say “this burger is unremarkable” seems insulting and has a different perception than “this burger is not normal.”
“Strange” “weird” “off” are all some modern AE words for “not normal” and all have a generally negative connotation.
What’s important with people and such is to not project our concepts of normal onto others. We can know what is normal for us, that which is expected and/or what we are used to. It is also helpful to not apply “normal” to too general a scope. But- indeed the word is often overused, misused, and weaponized against anything or anyone who doesn’t conform to a standard set by another person or group often arbitrarily. It is also worth noting to the early points and to subjectivity that not being normal isn’t inherently bad. I would not consider it normal for diamonds to spring from my faucet and normally the food from the place down the street is not very well made but if they sent me some good food it wouldn’t be normal- but I’d be happy.
Beyond math “normal” exists as a helpful concept in technical fields not exclusive to math including sciences and engineering. Manufacturing and repair of mass produced machines are two examples where the concept of normal can be very useful. A general goal in mass production would be that each laptop is essentially identical and from when it leaves the factory to when it is retired should be essentially so. So “normal” can be generalized as “to specification.” We run in to a lot of trouble where the word…
“Strange” “weird” “off” are all some modern AE words for “not normal” and all have a generally negative connotation.