I like to remind people that math is an excellent tool, but to remember that math exists no where in the known universe except as that - in a human’s head.
Likened to an extra long perfect kinda stick for getting the ants at the bottom of a deeper hole (on the Savannah) but, to remember that is all it is.
For example, math is not science, it is not a arbiter, even though it is a factor and an important one. But that it cannot stand in stead of logic and open minded analysis.
That we like to use numbers in analysis and would love to try to frame, corral, and label human desires. And thus own desires and perception as a tradable, saleable, storable, repeatable, fully known and owned commodity.
People have been trying to do this for thousands of years, and have pretty well gotten no where. But they sure have mastered the basics...(think modern media manipulation of the masses)
Then we want to quantity and commodify human hearing. That turns out to be a waste of time, as we don’t fully understand the limits of human perception, let alone that each and every one of us is different in such to the point that no perfection in such desires to quantify--can be found..
If we could only get one more decimal point of accuracy! Sorry dude, not happening....
As, in audio we talk limits of perception, not the basics. Basics, we all got them. Quantification can and does happen there, no disagreement from anoyne on those parts.
Limits is the deal...Peaks, absolute peaks... and there, it is all fuzzy and 100% individual in level. It’s like IQ tests..when you get beyond the basics with such testing, it gets less and less relevant and when reaching the most intelligent, IQ tests are useless. Absolutely useless.
One of those chicken and egg problems that not enough people understand the huge scope of it as existing. From those, you tend to get argument that audiophiles can’t hear what they say they do and here’s the numbers to prove that.
Where if one even begins to understand what I wrote about, it is not possible to be more incorrect than that position about extreme audio and those who hear things in it.
One could write a book on the subject and not make a single misstep. But the contrarian spitting vitriol would have to be open minded enough to not just read it, but to understand it. To be stable enough to be open.
Like Bruce Lee said, "Do not concentrate on the finger or you will miss all of the heavenly glory!"
When science and math have a problem they can’t unravel, it (as a pair) can quite likely find itself being forced to ground to go to first principles, which are rooted in philosophy and logic. Philosophy being the actual parent of it all, in effect, or... Logic and the attempt to make logic provably, repeatedly - functional.
We won't get into engineering attempting to be to be the logic poseur that it is when it tries to express itself in scientific exploration... this is due to the literal construction of engineering as a dogmatic form. Repeatability, is what that is about. Engineering has nothing to do with formal and actual science, engineering is a end point , in repeatability, of the application of proven science.
Thus, beware the engineering mindset that tries to dogmatically push numbers and book learning... into a frameworks and area of scientific exploration ....where all the realities are not even remotely known.
Like that of high end audio and human perception.