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Comment by jokabrink | Hacker News Reader

I am not sure what to take from this. The title certainly makes sense from a engineers perspective. But from a layman's? I don't know.

It seems, that he tries to explain an important concept in control theory but does not explain the meaning of "plane" at all. Even worse: He uses airplanes as an example.

Isn't it terribly confusing for non-control-theory people? If I don't know control theory, then how on earth would I know that he means a 2D-plane? And what's this "minimum-phase-system" he mentions once? Is a pole a number? And what about RHP poles?

I would be interested in how readers without a background in control theory and higher maths understood that article and what questions arose.

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As someone with a rapidly (exponentially?) decaying background in engineering, all the article did was create an insufferable itch of mathematical fuzziness about why these were called zeros until I got to the footnote and the actual article began.

Thanks for the tip, the rest made way more sense after reading that. I don't think I'm particularly poorly read or mathematically versed but I've never heard a pole called a "right-half-plane zero" before, so maybe the author could have lead with that (or even just called it a pole, which I have heard of so at least I'd have been less lost.)

The article wasn’t doing that, and specifically distinguished poles from zeroes:

>> Control theorists like to classify the behaviour of dynamical systems based on what we call poles and zeros. … Again roughly speaking, zeros describe mathematically how a system reacts to some input in the short term, while poles describe how a system reacts in the long term.

Whoops, adding that to my list of things to read again... >.>

Seemed a decent if over-long article to explain something I needed to know about feedback theory. Summary: to do x you may have to do, or briefly get, anti-x which you need to be aware of and account for. Key sentence where the importance clicked for me was:

"Let’s say our airplane is running in auto-pilot. We’ve sent a request to gain altitude, so the flight controller tilts the elevators to initiate a climb. But suddenly the airplane is losing altitude, moving farther away from our target? Do we pull up even harder?"

It's ok.

Talk about a borked example.

First of all, I'd call airplane/plane an "aircraft" instead, not because that's what aviators and Wikipedia editors do, but because it's super confusing in an article about some other thing called "plane".

And, as an aviator would probably tell you, in order to climb you should care more about the throttle (i.e. increase power) than about them elevators! So, in many cases there is absolutely no such dip.

And, I know of no aircraft capable of achieving that loopy flight path using just elevators. That would require quite a bit of kinetic energy, to say the least.

The bike counter-steering example clicked instantly with me, but I guess not many people have an intuition about that. I rode for decades before learning this and I think most other cyclists are not aware as well. (Most motorbike instructors teach that however.)

> The bike counter-steering example clicked instantly with me, but I guess not many people have an intuition about that. I rode for decades before learning this and I think most other cyclists are not aware as well.

Veritasium did a video on this:

https://youtu.be/9cNmUNHSBac

> And, as an aviator would probably tell you, in order to climb you should care more about the throttle (i.e. increase power) than about them elevators! So, in many cases there is absolutely no such dip.

An autopilot responds the same way, where an altitude error input affects the throttle control. (wincing... when implemented with classical SISO controls...).

I mean, to a layman like myself, the takeaway is something about stateful, irreversible systems where x is on both sides of the equation in unequal or inverse measures, and how those systems (maybe? sometimes?) progress toward equilibrium by going through unexpected phases that seem to contradict what you're trying to input. I read the whole thing as a metaphor for Fed policies or how we elect Democrats every time the economy is about to crash, and Republicans every time it's just recovered.

To the degree that some field of math can be best exemplified by various types of aircraft stalls, this didn't do a great job of explaining either the types of stalls or the feedbacks (what you might call negative REPL loops) leading to them.

I agree it's ok.

So, to me, this is just calibrating against a continuum. Right? I think of this as binary-searching a kinda normal'ish distribution? I'm not good at math so I had a hard time once the OP article got into differential equations

Fair enough, but then he wouldn't have needed to use control theory and just stuck with the examples.

Edit: removed ambiguity

As a mathematician it is just a lot of fuzzy rambling, until they have the actual definition. I really don’t know what an average person is supposed to take away, you can end up in some feedback loop, lol okay. Communicating maths to a wider audience you can still be correct but there is zero reason to make it fuzzy. It’s okay to use an analogy if there is something people can latch onto, carry it with them mentally, and then you slowly deform it into the correct statement, but you have to be careful to not be fuzzy.

If you are writing something just minimise the number of non informative sentences. They probably could have explained poles, planes, etc all in the same space instead of rambling. Cutting to the examples and then giving the definition would have been better.

Yeah, as someone with a math degree, I already know what the right half-plane refers to, I already know what zeroes and poles are (in a complex analysis way, not a control theory way), and I am just befuddled. The article doesn't really seem to have much concrete content at all, and could be cut down by a lot. Which is an achievement considering how short it already is.

Just cutting out this junk:

> Again roughly speaking, zeros describe mathematically how a system reacts to some input in the short term, while poles describe how a system reacts in the long term.

and similar waffle would be good. It's so vague as to be counter-productive.

The conclusions in the article aren't easily drawn from the vague tools we're given, in my opinion. Maybe I'm just not the target audience, but I don't really understand who that is.

At the beginning I didn't understand what the post was about. At the ending, it felt like I was at the beginning.

I never studied control theory, but I was fine with this. My pure maths education stopped at say first year undergrad. I didn't even consider that there were two kinds of plane. I thought the example was a good example of the subject.

To answer the confusion about poles...I think the teaching method of, 'here are some terms you won't understand until later' is very common, isn't it. I bet it even has a name

It's a nice explanation of the phenomenon of "getting tilted" in games:

Tilt originated from Poker and it's usually a state of emotional frustration and confusion.

It's most commonly used if you're going on a losing streak and then you become so frustrated that you start playing worse because you cannot focus anymore.

Part of it, as I see it, is that you are using that frustration to fuel further efforts, which ends up in a downward spiral feedback loop

https://gaming.stackexchange.com/questions/190507/what-is-th...

> I am not sure what to take from this

I think the author is using a lot of words to say "things often need to get a bit worse in order to start getting better"

And, critically, you potentially need to ignore the signal of "things getting worse". Otherwise you might creature a vicious cycle of more corrective action -> more things getting worse (at first) -> even more corrective action, until your system crashes and you never got into the phase where most of the desired result of the corrective action materialized.

And a second important point: You mustn't ever get into a state where the "things getting worse at first" already pushes you over a red line (see the example of the plane that loses even more altitude before it rises again. If you hit the ground in between you don't care that you theoretically would have risen later on).

That's only half of the story. The second half of the story is "if the getting worse temporarily cancels out the getting better, stop trying to correct, or you're going to crash!"

I think "when things get worse we tend to double down on what caused things to get worse, until everything around us crash and burn" would be more accurate, given the current state of affairs.

Not sure I share the pessimism. It seems to me that we're adjusting to situations pretty rapidly as a species. We're definitely at least attempting to find out what inputs lead to which short- and long-term outputs, which is a unique behavior among mammals.

To me, that immediately sounds like someone making excuses for their side and the midterm elections. I don’t care how much math there is.

It really all depends on how low to the ground you are when things begin to get worse.

For example, a virus that takes 10 IQ points off people who've been infected with it might make China more apt to consume Disney movies, while it might plow America straight into the ground.

> He uses airplanes as an example.

Oh wow, i didn't notice that. It's either pretty clever, or unfortunate wording.

Same. I ran to the comments to check my understanding.

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