measuring everything can't be done because any measurement tool has a resolving limit, from the measurement gears, or the conditions of the measurement.
also we hardly go look for what we do not know to exist. ^_^
now in the context of personal audio, the maximum quantity of data we can expect from a record is determined by the recording microphones and recording gears, and from that point we go down in resolution until the headphone/speaker being really not the best at keeping data clean. so the precision of the data is very much limited. and the variety of the data just as well as any signal recorded is no more than a voltage value changing as a function of time when we get it from a microphone, or send it to a headphone/speaker. not exactly overwhelming complexity. so the idea that we can't know everything of a signal we can represent in totality on a 2 axis graph, that's just plain ignorance.
usually people decide that sound is very complex and full of unknowns, because they project human constructs like pleasure or even more ludicrous like quantifying a perceived soundstage, and hope for a machine to tell them all of it in a simple graph... except that has very little to do with the audio signal and a lot to do with the person listening. they're not asking to measure the sound, they're asking to measure the guy and pretend like we're still talking about the sound. but stuff that are created by the brain, aren't acoustic anymore. even if the stimulus is sound, what needs to be studied if the human brain. so the unknowns are in the human(and placebo certainly is all about the human side), not in the sound.
I love it when technical aspects of this hobby lead to more philosophical discussion.
The trouble is, I love listening to music. I have until recently believed that if you have gear that is 99 % right you do not need to worry about the last tiny bit of performance.
Having bought a little amp/dac which seems to improve on the iPhone,
I am realising that musicality does perhaps lie in that last percentage of performance.
If this is the case it is highly unfortunate as this is the area where diminishing returns not to mention the snake oil merchants come into play.
It is also the area where psychoacoustics are very influential. A fact that the aforementioned snake oil purveyors thrive on IME.
The benefit of turning gear into a hobby,as we do here on HeadFi, may be the unlocking of exceptional musical performance.
Unfortunately it also leaves us open to wasting time money and effort on illusions.
I do not know how to avoid that if Science cannot help!
BTW. +1 for the biggest unmeasurable variable being the listener.