Please, could someone disect this frog for me?

https://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.Edit: This comment if mine has been sitting at 69 upvotes for a few days now, so uh… obligatory joke about taste testing each others saddle points or something, I don’t know.

uhh, can’t there be two local maxima that aren’t saddle points? for example, x

^{2}-x^{4}?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:

thought you implied the local maxima were AT the saddle points

No, I explained what a saddle point is and how a saddle point

*can*be misidentified as a local or absolute maxima or minima if all you do is look for a point where the slope is 0.… anyway, is this a glitch on my end or … how do most of your comments have 0 upvotes… and also 0 downvotes?

… I thought lemmy automatically gives every post 1 upvote by default.

you can remove your upvote, unlike reddit, where your vote doesn’t count, just no votes display as a score of 1

… And you do this, manually, to all or almost all of your posts?

Or is your user account from an instance where that is done automatically?

Hurr hurr, I’m gonna plot f(x,y)=x

^{2+y}3 where y=x for x limit inf. Checkmate science!Edit: the graph isn’t actually linear, man, and here I just thought it’d be that easy. :(