4 ms·

Tje difference is because we cannot easily tell between “curve of second order” and “curve of other order”. You can get an idea when you try to understand why

Tje difference is because we cannot easily tell between “curve of second order” and “curve of other order”. You can get an idea when you try to understand why the function y=0 for x<0 y=x^2 for x>=0 has two derivativea but not three. But the issue is infinitesimal, so very hard to tell. Jerk you can “linearise” if you think of a car (with no air friction) and its accelerator. Somehow…

bowsamic 2y ago
> Tje difference is because we cannot easily tell between “curve of second order” and “curve of other order”. Why not, though? Why does third order "look like" second order but second order is starkly different to first order?
- Sharlin 2y ago
  Well, firstly, if you plot the first n degrees of monomials and keep the scale invariant, the visual difference between x^k and x^(k+1) literally gets smaller the higher up you go. Secondly, presumably the distinction of "straight" vs. "curved" is quite deeply programmed into the brain's pattern recognition machinery. The degree of curvature is a quantitative parameter on top of the qualitative categorization. This may or may not have something to do with the fact that a modern human sees straight lines everywhere (something that very much was not the case in the ancestral environment).
- tomek_ycomb 2y ago
  UHHHHHhhhh, it's because the last A*b is the only one that becomes a linear constant. For other polynomials, your derivative is a polynomial still, just different one. These are mathematical derivatives, I think of them as the slope of the thing it's derived of, aka the change in the thing that it's a derivation of. I think I don't have a sophisticated mathematical understanding, but my basic mechanic understanding makes it feel simpler than your question is acting.
- meindnoch 2y ago
  Because a line has an infinite radius, while a curve has a finite radius. The difference between infinite and finite is stark. The difference between two finite values is not.

bowsamic 2y ago

> Tje difference is because we cannot easily tell between “curve of second order” and “curve of other order”. Why not, though? Why does third order "look like" second order but second order is starkly different to first order?

Sharlin 2y ago
Well, firstly, if you plot the first n degrees of monomials and keep the scale invariant, the visual difference between x^k and x^(k+1) literally gets smaller the higher up you go. Secondly, presumably the distinction of "straight" vs. "curved" is quite deeply programmed into the brain's pattern recognition machinery. The degree of curvature is a quantitative parameter on top of the qualitative categorization. This may or may not have something to do with the fact that a modern human sees straight lines everywhere (something that very much was not the case in the ancestral environment).
tomek_ycomb 2y ago
UHHHHHhhhh, it's because the last A*b is the only one that becomes a linear constant. For other polynomials, your derivative is a polynomial still, just different one. These are mathematical derivatives, I think of them as the slope of the thing it's derived of, aka the change in the thing that it's a derivation of. I think I don't have a sophisticated mathematical understanding, but my basic mechanic understanding makes it feel simpler than your question is acting.
meindnoch 2y ago
Because a line has an infinite radius, while a curve has a finite radius. The difference between infinite and finite is stark. The difference between two finite values is not.