>> Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past.
How is this different from the observation that, say, a non-magnetic iron ball may have more than one possible velocity in a given gravitional field, depending on whether it was recently thrown upward or dropped from above?
With the ball in the gravitational field the state of the system is entirely captured by the ball's position and velocity. With hysteresis there is some extra state in the system that also affects the behaviour. The general pattern you see is that if you push the system from state A to B, then from B back to A, then it will take a different path in each direction. (you can of course create mechanical systems that have this property as well, it's not specific to magnetic fields, its just that magnetic materials tend to have this kind of state-storage effect).
If it was recently thrown upward, it is either still travelling upwards away from the centre of the Earth, or it is falling downwards towards the centre of the Earth.
So its past is kind of irrelevant. At some point if nothing is supporting it, it will fall towards the centre of the Earth.
You don’t need information about its past. Everything you need to know to predict its future state is contained in its current position and velocity at the moment you measure it.
Is there no measurable quantity in the current state of a magnetized ball that would predict its behavior in a magnetic field then?
I'd be surprised if that were the case: seems like it'd violate some sort of "locality", where the future should depend entirely on the present state.
Is it just that there's unidentified present state that's perhaps more easily characterized by knowing the history? Or is it somehow unidentifiable in principle?
Yeah, the current magnetization of the sphere carries all the history of the magnetic fields it's been in in its value.
The hysteresis in the material only means that if you apply 1T to it to magnetise (supposing the ball starts with zero magnetisation) it and then apply 0T to demagnetise it, the remanent field in the ball would be like 0.4T due to hystetesis, you need to apply something like -0.4T to leave it as it started.
Umm, either I'm misunderstanding or this holds for nearly every UI everywhere, no? Like if I click "reply" on HN I'm moved to the screen I now type this comment in. That means my current state depends on history, too, no?
If you click "reply" and copy the resulting link, there is no difference in behavior if you go straight to that link vs clicking "reply" to get there instead
Think of a state diagram: "you are at the reply screen" is one and only one state. "The tooltip is shown" is a behavior of more than one state, with different paths to get to those states
