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What's the minimum (physics first) to get an oscillator?
Nominal Animal:
--- Quote from: RoGeorge on May 31, 2023, 06:42:27 am ---By explaining, I mean identifying the irreducible basic components that are needed for something to happen.
--- End quote ---
Righty-o.
One problem is that most (all?) things can be described in more than one way. Consider optics and Snell's Law, versus Fermat's Principle of Least Time: the former can be derived from the latter, making them equivalent. The two have very different 'explanations', too – even when they are mathematically equivalent. Ouch.
Second problem is that we cannot always even tell whether our mathematical description is correct, or only approximately correct to within some arbitrary decision within the region we can measure. An example of this is how Newtonian mechanics are indistinguishable from relativistic mechanics for small enough energies (masses and velocities).
Just like in mathematics, you always have some axioms that cannot be derived or proven in physics too. Physics is about modeling or describing reality, not defining it. (Thus, "physical law" = description or model that produces reproducible results matching real world experiments, not a dictat or requirement.)
_ _ _ _ _
Of course, when we consider say usable oscillators, the problem is not a show-stopper. We just need to outline what an "usable oscillator" is, and then analyse and group them so that we find their commonalities. The simplest set I can find is the division into discrete states or infinitely differentiable amplitude ones, with most "real" oscillators a combination of the two; and this is what my answers above tried to show.
Unfortunately, there are many valid answers (groupings and derived commonalities/requirements). Fortunately, it does not matter, because we can go back to the outline or definition of "usable oscillator", vary the definition or use case a bit, and pick the answer that yields the most useful properties.
Indeed, it actually is not unfortunate at all, because the set of different valid answers covers a larger set than any single answer alone; it just depends on the context and viewpoint which one happens to be most useful with respect to a given situation/problem/case.
If you think that is cheating or not true, do remember that even your own senses are approximations, inferences, and extrapolations. We don't normally use infinite precision arithmetic in microcontrollers, because it would be a waste of resources. Whenever investigating large molecules or systems of molecules, we don't use quantum mechanics derived ab initio models (because it would be too slow!), and use approximate/empirical ("descriptive") potential models instead. We don't use relativistic mechanics for satellite orbits, because Newtonian mechanics gives the same results with much less effort, and the noise (interaction with solar wind, upper atmosphere, and magnetosphere, among other things) causes larger unpredictable errors than the difference between the two. Perfect is the enemy of good: approximations and even guesses lets us advance, when requiring exact correctness would stall us.
In a very real way, even the 'irreducible basic components needed' kind of 'why' is almost impossible to answer, at least at this point. Even if we had the language to describe it, we don't have the context in which it would make sense, be understandable to us humans. It is annoying, but we are very imperfect beings. We have to settle for the best approximation we have for it, and make do.
Remember, modern physics is barely a century old.
Anyone claiming "most of physics has been discovered already", is just repeating a variant of the "640k of RAM is enough for everyone".
Or heck, what do I know; I could be utterly wrong here. :-// Just trying to help you find a useful point of view and understanding.
TimFox:
--- Quote from: RoGeorge on May 30, 2023, 09:02:06 pm ---Indeed, one can discover by observing mathematical results. It is even possible to make discoveries by crunching numbers (by simulation). And in the recent years there are more and more papers with discoveries made by AI exploration.
What bothers me is that they all fail to explain why something happens.
Would be great to have a new type of mathematics, with embedded causality in it.
--- End quote ---
Even though most occurrences have a cause, they do not need to have a reason.
jwet:
Nominal- There is a philosophy that teaches that there is only one ultimate truth but an infinite number of ways to observe it. The older I get, the more I believe this I think, though I'm no closer to knowing the ultimate truth. If this idea intrigues you, check out an interesting book - "The Surrender Experiment" by Michael Singer- it takes this to a very useful result.
One of the funny and useful things about online forums is that you see this at work- everyone brings their own truth to their understanding of the poster's problem.
I enjoy this thread- kind of a diversion.
CatalinaWOW:
--- Quote from: jwet on June 02, 2023, 04:49:28 pm ---Nominal- There is a philosophy that teaches that there is only one ultimate truth but an infinite number of ways to observe it. The older I get, the more I believe this I think, though I'm no closer to knowing the ultimate truth. If this idea intrigues you, check out an interesting book - "The Surrender Experiment" by Michael Singer- it takes this to a very useful result.
One of the funny and useful things about online forums is that you see this at work- everyone brings their own truth to their understanding of the poster's problem.
I enjoy this thread- kind of a diversion.
--- End quote ---
.
This post also hints at one of the qualities of a good teacher. The very best can identify the student's truth and provide explanations that are likely to be effective from that point of view, and ideally expanding understanding.
aneevuser:
--- Quote from: IanB on May 23, 2023, 01:39:00 pm ---From a mathematical and physics point of view, you need to have a second order time derivative in the differential equation that describes the system. This is the only way the solution will include a complex exponential which will involve functions of sin() and cos().
--- End quote ---
Interesting thread.
The quote above is too restrictive though. There are higher order DEs which can be proven to oscillate, though I'm not at all familiar with the methods (and as you note later, coupled first order DEs like Lotka-Volterra can also oscillate - do we count them as "really" second order?) - there is a branch of DE maths called oscillation theory which treats these problems.
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