>>12754968ok yeah I get that it's an algorithm and not some end all be all axiom or something, I was just confused for this particular algorithm, about verifying uniqueness, if the way you do it is by solving backwards from obviously the linear borders, then the next points in that now have a defined 2 derivative value and so on, basically I was making sure what data you need to isolate a cubic function, two positions and a second derivative? I guess given the second derivative you can get the original function with remaining variables of cx + c, so then you have to use an (x, y) coordinate to solve for c... So yeah I was just trying to work through that particular algorithm
and yeah as you say that about having the correct number of variables to provide uniqueness does bring back some of the linear algebra I've read, with the solving systems of equations in matrix form and stuff
But yeah you answered my main question with the interpolation, I hadn't heard of that so I was just looking through the wikipedia page to see what was up with the different interpolation methods and how the algorithms worked, it's only been two years since I did calculus and I can't remember shit
But basically the interpolation answers my original question, do all data sets have a function that can trace them? Yes, there will be infinite functions that pass through your data points, so you use algorithms to produce usable and hopefully accurate extrapolations
And then obviously if you make stricter rules or increase the dimensions without increasing variables you won't have infinite functions, like if you bump the dimensions to 3 and try to find infinitely many traces of your x,y,z data set you'll get nothing if z>0
and yeah I really need to take some math classes, I got in a rut where I was only interested in physics and now I'm at a point where I'm not going any further without some new math
