Basically, its a mathematical function where if you start at 0,0, you might falsely believe you are at the (or a) maximum or minimum of the function, as the slope at 0,0 is 0.
But, if you go any direction in the x axis, your function value rises, any direction in the y axis, your function value falls.
Thus a saddle point is an illusory, false impression of being at the extreme extent of a function, when in fact you are not.
The idea is that there is more to determining if you’re truly at a global max or min of a function than only finding a single point where the slope is 0.
Just have a continuous graph that looks like two little hills, but far away there is an even bigger mountain.
You’d then have two saddle points somewhere between those two little hills and the big mountain, though they might not be as visually distinctive as the image here.
Don’t think I said you cannot have local maxima that are not saddle points.
Hell, even the image of the graph shown could be some kind of small scale topographically phenomenon, and what look to be going off to infinity in this small scope might actually top off as local maxima.
The actual function isn’t shown.
It could be very simple, or it could be an absurdly complex polynomial that just looks like the simpler version when you zoom in.
sp3tr4l@lemmy.zip 2 weeks ago
en.m.wikipedia.org/wiki/Saddle_point
Basically, its a mathematical function where if you start at 0,0, you might falsely believe you are at the (or a) maximum or minimum of the function, as the slope at 0,0 is 0.
But, if you go any direction in the x axis, your function value rises, any direction in the y axis, your function value falls.
Thus a saddle point is an illusory, false impression of being at the extreme extent of a function, when in fact you are not.
The idea is that there is more to determining if you’re truly at a global max or min of a function than only finding a single point where the slope is 0.
rain_worl@lemmy.world 6 days ago
uhh, can’t there be two local maxima that aren’t saddle points? for example, x^2^-x^4^?
sp3tr4l@lemmy.zip 6 days ago
I mean … sure?
Just have a continuous graph that looks like two little hills, but far away there is an even bigger mountain.
You’d then have two saddle points somewhere between those two little hills and the big mountain, though they might not be as visually distinctive as the image here.
Don’t think I said you cannot have local maxima that are not saddle points.
Hell, even the image of the graph shown could be some kind of small scale topographically phenomenon, and what look to be going off to infinity in this small scope might actually top off as local maxima.
The actual function isn’t shown.
It could be very simple, or it could be an absurdly complex polynomial that just looks like the simpler version when you zoom in.
Something like a 3d version of this:
Image
rain_worl@lemmy.world 6 days ago
thought you implied the local maxima were AT the saddle points
ekky@sopuli.xyz 2 weeks ago
Hurr hurr, I’m gonna plot f(x,y)=x^2+y^3 where y=x for x limit inf. Checkmate science!