Nothing's univariate. That's a given. I'm saying, however, a univariate approximation is not destined to fail by design. It can, and does, work and we do it all the time in our day to day lives without even realising it.
I am trying to show you that your generalisation is overly broad and incorrect.
You tried but you failed and haven't provided a follow-up example. I just proved that the univariate approximation failed without considering the second variable. Where is your counter-example?
But that's not univariate. How sharp is too sharp? You need something to scale it against. I.E. A second variable detailing how much sharpness you can tolerate.
There is no need for a counter-example has you've haven't actually said
anything to counter the example provided earlier. I never said the situation ('how you should hold knife') was a situation that was one with only a single variable. It is certainly a situation with multiple considerations involved within it as I said (and you
reiterated: 'But that's not univariate. How sharp is sharp?').
Basically you're saying that the situation I describe is a multivariate situation and therefore my example fails.
Evidently, you're misinterpreting what I've been saying. I'm providing an example where a single variable assumption (blade is sharp) can apply to a multivariate (how sharp? how much will it cost for a hospital visit if I cut myself? what's the risk?) situation and be successful (risk of being cut by blade reduced by not touching it). I am NOT saying the knife situation is univariate as that would make the example irrelevant anyway.
I am demonstrating a successful use of a single variable assumption (the blade is sharp - do not touch) in a multi-variable situation (how sharp the blade is / consequences and risks of an accident).In other words, I contend that people do make a single variable assumptions ('it's a blade, therefore it will be sharp and hurt me; therefore I will not touch the blade'), without considering the 'amount' of sharpness however it is quantified. And, contrary to your prior assumption/generalisation that all single variable analyses are failures when applied to multivariate problems, they can be successful assumptions.