>>8946505
'sine wave' is defining the origin of the wave in time, and what it's phase is at the start of it. at the 0 time component.
so that means that . . . they would have also have had to have had (have to have had?) cartesian math, and an understanding of 'origin' points.
in fact waves don't really behave like that. And the locatin of an origin is rather arbitrary.
you know they came up with a math about minus infinity and plus infinity to do these transform things. the math basically includes all time. All time! so then they change that math to start at 'time zero'. Again, an arbitrary idea.
waves are all that exist, we know this. 'sine wave' is a concept from mathematics, and music, and it basically . . . is an abstract (but very useful idea) about waves and how to describe them.
but ancients didn't have 'sine waves' as a concept. Maybe starting sometime after Cartesian coordinate systems were crafted?
the idea that equations of x/y of t didn't go back to the begining of time was part of the reason that the wave theory and Laplace transfrom stuff was found to be very useful. If we always have to account for the part of an equation that happens long before we even start thinking about it . . . that's a whole long lot of time.
and then they were like, these math mind people, why don't we just look at the frequency equations and start them at zero time, an abstract time, yes, but more useful than negative infinite time in the past or negative infinite time in the future.
so they started breaking equations down into parts, and understanding when a equation was useful for a period of time.
And still they didn't get that the limits of modeling are such that it must match what is real in the world. or it's not a model but an abstraction of math.
and even though they understood that the model was not the thing, chaos theory didn't start happening until the 1960s: when the system of how much input (energy) was shown that the equation breaks. IE the actual physical system breaks. The 'linear' nature of the system breaks down at high energy input.
It's a veyr simple concept. And yet the models are seen as being the thing, not the actual stuff that is modeled. And eggheads mistake the math for the science.