My signals processing professor apparently knew one joke, and one joke only.
"A LOT (Polish airline) airplane is about to land in New York City; as they align for final approach, the first officer notifies the passengers that those seated on the right can now see the Statue of Liberty. A number of passengers get up from their seats left of the aisle and lean over the people seated on the right to get a glimpse of the statue. Plane promptly crashes.
Why? There were too many Poles in the right half of the plane.
I think this article is trying to make a political statement, "Our leaders have just done something that is going to cause a future problem, a crash".
I have only read the linked article, I think the followup might be available, but I'm not going to read it before posting this -- because this article was meant to be clickbait, to get you hooked and possibly mis-informed.
The article as it stands (incomplete) contains some classic argument fallacies.
It is an "appeal to authority", by attempting to explain control theory. This person knows something.
The examples all result in bad things, airplanes crashing, hard drives (crashing - perhaps a stretch). Bicycle at the edge of a cliff. Eating too much ice cream. Chernobyl. This is a possible "appeal to emotion".
The final issue is an "incomplete comparison". The graph at the bottom of the article shows housing prices -- all of the previous examples have mathematical models which can explain the behavior. For the last graph no model (the equations) is presented. Without a model you cannot use control theory to analyze the zeros and poles.
The last graph wants you to believe in a continuing upward trend, the fallacious argument, implies that whatever the Canadian political change that has been made is going to make this trend to zero, despite the intention to keep it trending upwards.
Background: A long time ago, as a mathematics undergraduate, I did take a course in control theory, it was run out of the engineering department. It was somewhat awkward as quite a few mathematical terms were not-quite-the-same. I get the same unease when reading this for poles, zeros and right-half-planes. Any engineering textbooks that use j for sqrt(-1) instead of i (because that is taken) is an indicator. Yup, this could be construed as an "appeal to authority".
There are, to me some language red flags. The followup article now uses "we' -- suggesting this is not the work of an individual. This was not present in the initial post.
An attempt is made to build a model. Curiously a visual programming model is now used. No explicit differential equations are given. If the equations are not given there is no way to check the model. So "pole" and "zero" analysis is mute.
There are no tests to validate this model against past situations - an easy and free test, the past history is known. If the model that has been created and can predict the future, why would was it not run it against the past and show the predictive success?
The built model is only presented against the current situation -- is it circumstantial / opinion based.
My understanding of science is -- build a model that can predict the future / what happens accurately, i.e. matches the measurements. The consensus agrees that this is the (current) best model.
Prices are ultimately influenced by a sentiment factor, a value derived from a I have no idea what human feeling / property. Some power "enabled" humans have been endowed with a much higher influence on this parameter. Where is this value expressed in the predictive equations?
That's not an appeal to authority. An appeal to authority is "P is a statement in the topic T. A is an expert in T. A says P is true. Therefore P is true." If I draw a parallel between two topics and proceed to explain one of them in order to argue something about the other one, that's not an appeal to authority.
It could be that the reader fails to understand the explanation and instead treats the writer as a trustworthy authority. That would not make the argument an appeal to authority or even fallacious.
It could be that the analogy is poorly justified, which would make the argument incomplete, or it could even be that the writer failed to understand some subtle aspect of the second topic that makes the analogy inappropriate. Neither of these would be appeals to authority.
The author of the article has had their understanding of systems eat their understanding of humans. Every time they make a realization about people, it immediately gets turned to getting more understanding and control over the world. Which doesn't leave any room to grow for their understanding of humans.
This makes it really hard for them to write an article for non-technical people. To do so, they would have to connect the human side of things to the systems theory side of things. Which they can't do, because they don't understand the human side of things.
They aren't using bad-faith arguments to convince you that they are correct. They simply have no idea how to talk to you. They are in fact trying to be helpful, by presenting what they think is really useful information to understand and control the world with. Their help is useless to you, but they are trying.
I agree. The author uses technical jargon but is clearly intending the reader to be non-technical. Otherwise, footnote 1 should just be in the main text. The rhetorical effect, intended or otherwise, is an appeal to (the author's) authority. As you say, the author then switches to a topic he likely much less expertise in (housing prices, inflation, etc.) while relying on the reader to believe that this new problem shares some mathematical foundations with the original set of problems.
I call it the "Ian Malcolm syndrome", in reference to the character (a mathematician) in Michael Crichton's Jurassic Park who tries to apply mathematical concepts to the dinosaur attraction to try to show why it is doomed to collapse.
There are a lot of similar posts online about people trying to use chaos theory (or what they believe chaos theory is), "systems theory", and other obscure concepts to explain why, for example, climate change will be the end of us all, or the global economy will enter a depression, or any other extremely pessimistic macro scenario. I see three reasons why these people are doing it. (1) To draw attention to themselves as someone with a superior intellect (which they actually aren't) (2) To construct an analysis no one has constructed before, in a "all these professional economists are saying the same thing, but here's why they're all misleading themselves, thanks to my ace card of a theory" kind of way, and (3) A love for the hyperbole, for dramatic outcomes.
A classic economic prediction like "Inflation pressures will potentially slow down growth in the short term, but the behavior of the economy over the next 12 months remains unpredictable" is not enough. It MUST be "A catastrophic economic collapse is inevitable", or "We are going back to the Middle Ages by the end of the decade", or "Hundreds of millions will die in the next few years".
This seems uncharitable. The author is trying to explain how knowing a bit of control theory could be helpful for understanding economics. Unfortunately they’re having trouble writing for a general audience, perhaps due to being too comfortable with the math. This doesn’t mean anything nefarious, just that they could use an editor.
Textbooks that use j instead of i are an indicator of what? Why is slightly different notation awkward? It's not as if notation is always consistent within the field of mathematics, right?
I’m curious what the right half plane zero in housing is. In general, we correct inflation through interest which we raise gradually waiting a month or two to observe the effects of a 0.5% raise. I think that should be sufficient to avoid the control feedback effects he talks about in this article.
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.
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.
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?"
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.
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
The greatest sin of undergraduate engineering education is sequestering signals and systems into electrical engineering curricula. I understand why it's done that way (I even had to fight to take the course early, sidestepping some prereqs for reasons).
But it's really so foundational to understanding concepts of stability, resonance, information/energy flow (from the conceptual perspective), and the simple analytical tools for building a solid conceptual base. It takes a semester to hammer home that step response matters, positive feedback bad, negative feedback usually good, and topologies are useful.
I went to school for mechanical engineering (though I now work in software). We were required to take signals and systems, but if I remember right it was a weed-out course for most MechEs (it certainly was a challenge for me, though I think that had more to do with the curriculum than the topic).
Those lessons might have been hard-won on my part, but I definitely still use them. The general concepts (feedback loops etc) are applicable basically everywhere in life, and I still find uses for literal actual math (like using a convolution kernel to do rolling window sampling in numpy).
I always thought my college education was backwards, with the exception that differential equations (and laplace transforms, which can help lay the groundwork for other transforms) came early enough that I could get by -- though it'd have been better if they were earlier, like high school, and if I hadn't been able to skip two semesters of calculus thanks to my HS calculus then differential equations would have come even later in college. But as a CE student at a school nominally more about video game making education I ended up first taking as CS electives an audio processing course, and then an image processing course, before the CE side reached control systems, which I had to retake after taking the next digital signal processing course, after which control systems made a lot more sense. It was only after graduating that I felt like I had reached a level of sophistication to go back and really grok all the related theory and go deep into applications. Maybe that's how graduate students are meant to feel? But I just went into full time enterprise work and 'retired' after 6 years of that, so I've since forgotten a lot... Still, the concept of feedback has proved useful in systems analysis from time to time, and it's a framework that I think could yield many low hanging fruit in other disciplines. (The book Behavior: The control of perception applies control theory to psychology in a convincing way but it's understandably been neglected by psychologists who aren't often very sophisticated mathematically.)
Can you recommend any good introductory books on the topics you mentioned for someone who studied (theoretical/mathematical) physics but never electrical engineering or signal processing? (Read this as: I am more or less familiar with Nyquist-Shannon's theorem but that's about it.)
Does anyone know of any courses which could explain concepts of stability, resonance, information/energy flow and help build a solid conceptual base for managers or entrepreneurs? These concepts are crucial when making business decisions. I've been building up an understanding of this through experience. If there was a way to shortcut this and provide such education deliberately, it would allow people to become better decision makers quicker.
The classic paper, Maxwell's "On governors". (1869) [1] This is the first theoretical analysis of feedback.
It will be seen that the motion of a machine with its governor consists in general of a uniform motion, combined with a disturbance which may be expressed as the sum of several component motions. These components may be of four different kinds:-
(1) The disturbance may continually increase.
(2) It may continually diminish.
(3) It may be an oscillation of continually increasing amplitude.
(4) It may be an oscillation of continually decreasing amplitude.
The first and third cases are evidently inconsistent with the stability of the motion; and the second and fourth alone are admissible in a good governor. This condition is mathematically equivalent to the condition that all the possible roots, and all the possible parts of the impossible roots, of a certain equation shall be negative.
That is, in the left half-plane.
(Terminology has changed. Maxwell says "disturbance" where today, the term "error" would be used.
Today, "disturbance" means an input which disturbs stability, while error is an output.)
Maxwell got so much right in that paper, and it was a long time before anybody picked up on that result.
Now, where it looks like the author is going is into economic territory. Basic economics talks about "economic equilibrium". The concept is that restoring forces will bring supply and demand into equilibrium. But basic control theory tells us that may not happen. Any system with delay in it can potentially be unstable. Too much delay, and even simple systems will not stabilize.
Shouldn't there be a diagram of the complex plane so that people can see what it's the right half plane of? On top of it, there's a picture of a plane which is confusing.
Fascinating subject though, in engineering class it was quite surprising how this bunch of functions tracing lines and dots on the complex plane would be relevant to just about everything. Perhaps the first lesson is that even if you know how a system works, you can't just take the inverse function to control what comes out.
> Shouldn't there be a diagram of the complex plane so that people can see what it's the right half plane of?
Author here. Yes! Very fair criticism. I was trying to strike a balance between making the concept approachable for those who don't have a background involving complex numbers, but that certainly leaves the name of the concept more confusing. I should add it in a footnote at least.
And I did honestly not think about the potential for confusion between plane // airplane. An airplane was the most familiar example system I could think of to explain the concept. Oops!
> Perhaps the first lesson is that even if you know how a system works, you can't just take the inverse function to control what comes out.
That's a great point too. It probably even deserves its own article.
I lost interest before I got to his political point (about inflation), but the comments made me go back and while it’s an interesting point, it ignores the fact that the current bout of inflation is almost certainly a consequence of the Covid stimulus plus the supply chain disruptions with a dose of war in Ukraine. And it turns out that inflationary pressures seem to be declining outside of the volatile food and energy sectors (see https://jabberwocking.com/inflationary-pressure-seems-to-be-...). I have a bit more faith in domain-specific analysis than abstract mathematical approaches.
Really should've run this by someone who knows how airplanes work, because they don't do what these hypothetical airplanes do. First off, "elevator flaps" is a howler. Elevators and flaps are two very different things. More importantly, you don't climb with the elevator; you climb with excess thrust. You can kinda sorta climb a little bit with just elevator, but unless you're making a very minor altitude correction, you'll slow way down and your climb rate will be really anemic, if you climb at all. But most importantly, an airplane won't just keep climbing and do a loop like that (unless you've got a thrust-to-weight ratio greater than one, which, to put it simply, you don't); the wing will stall way before you get anywhere near vertical, and the airplane will just stop flying until the angle of attack is reduced.
Always appreciate control theory articles. But this one needs some editing. Take ice cream example;that is not zero dynamics that's still pretty much convolution. Now zero dynamics examples must have no effect on the system. Thus it is not a zero if you continuously chugging ice cream. It is indeed a step input that you equilibriate at a constant ice cream input and some happiness comes out constantly. The moment you stop happiness goes away. That is not related to zero.
Also a pure zero action is supposed to cancel the input completely. Not at first but completely (restricting the discussion to linear systems).
Zeros effects are not so trivial to untangle as the article suggests unfortunately but fun read anyways and very nice flow.
> Now zero dynamics examples must have no effect on the system. Thus it is not a zero if you continuously chugging ice cream
Thank you for your input! I wonder if you might have misread that example. In this system there's indeed a RHP0 in the transfer function from ice cream consumption happiness. A continuously increasing rate of ice cream intake results in exactly no effect on the output.
It’s a bit disappointing that an article purporting to educate us about something we should know but may be unaware of, is completely wrong about the example of how an airplane climbs - you don’t climb by pitching up, you have to increase power.
For those wondering: this article is an introduction into inflation of house prices in Canada. You can easily find the next article (it's already online) by going to the substack's index.
Very good article, and well worth your time to read.
This is very well explained, but there should be a simpler name for this effect than right-half-plane zeros if the author wants to spread the concept beyond control theory.
> The danger of the right-half-plane zero is that it lures you into reacting to it, but that is precisely the wrong thing to do. Attempting to apply a new control input to cancel the inverse response only sets off an even worse chain of events, where the resulting secondary inverse reaction becomes even more severe, requiring even more corrective action, until finally you’ve slammed into the ground.
> In this situation, the flight controller’s only option is to ignore the initial misdirection and wait patiently until the airplane eventually begins to climb as intended.
Of course that is easier said than done; adding a sleep() to your control loop to ignore the initial misdirection is also very bad. The right way to solve this is to not just tell the control loop to "go up", but to plan a realistic trajectory that the control loop can execute. That way, the error between the desired trajectory and the actual trajectory will be much smaller, and the closer the error is to zero, the less chance of a control loop to go wild.
> the first important lesson of inverse response is: don’t ride your bicycle on the edge of a cliff
I don't know if many people often ride their bicycle on cliff edges, but many plane (as in airplane) accidents occur because it's difficult / impossible to recover from a stall near the ground.
This is some of the best non-rigorous writing about math that I've encountered. Far superior to the awful quanta articles that sometimes get posted here.
I would also mention, that we essentially design controllers to shift the poles and zeroes of the total system (which consists of the plant system and the controller system) to more desirable positions, than those of the plant system alone.
Comments: The OP is a troubling covert political statement. The real issue here seems to be US midterm elections / climate change / COVID / appeal to authority.
Great read. I’ve been thinking about how this applies to earth/climate change for a while, so I was surprised that the system he worries about is inflation/the economy.
> Countersteering on a bicycle is another example: To turn right, a cyclist will first steer slightly to the left.
It's very visible and pronounced on heavier bikes, like motorcycles. Especially if you try riding a very heavy cruiser bike -- you'll immediately notice that countersteering is the only way to turn it. No matter how you try to lean it, it won't respond and will just go straight, but it'll respond very easly to handlebar inputs.
As a layman, I had to think of drugs or other dopamine hits first - actions which increase well-being in the short term but are harmful in the long term.
But what he really talks about seems to be the opposite: Actions which case some mild harm in the short term but increase well-being in the long term. So I guess something like working out or going on a diet or making a downpayment for a house?
Except the failure mode is also counterintuitive: Normally, we tend to overvalue the short-term downsides of those actions and therefore shy away from them, missing out on the long-term benefits. But he talks about a situation where we overvalue the long-term benefits but ignore the short-term and overdo the action until the short-term harm becomes critical.
So, e.g. someone working out, getting muscle-ache - and then working out more to counter the ache - which will only lead to more of it until the workout actually starts to become detrimental to their health.
It's easy to see how this would trip up automated control loops, but I don't really see how this has practical application outside of control theory.
[+] [-] lb1lf|3 years ago|reply
"A LOT (Polish airline) airplane is about to land in New York City; as they align for final approach, the first officer notifies the passengers that those seated on the right can now see the Statue of Liberty. A number of passengers get up from their seats left of the aisle and lean over the people seated on the right to get a glimpse of the statue. Plane promptly crashes.
Why? There were too many Poles in the right half of the plane.
I'll lead myself out.
[+] [-] VogonPoetry|3 years ago|reply
I have only read the linked article, I think the followup might be available, but I'm not going to read it before posting this -- because this article was meant to be clickbait, to get you hooked and possibly mis-informed.
The article as it stands (incomplete) contains some classic argument fallacies.
It is an "appeal to authority", by attempting to explain control theory. This person knows something.
The examples all result in bad things, airplanes crashing, hard drives (crashing - perhaps a stretch). Bicycle at the edge of a cliff. Eating too much ice cream. Chernobyl. This is a possible "appeal to emotion".
The final issue is an "incomplete comparison". The graph at the bottom of the article shows housing prices -- all of the previous examples have mathematical models which can explain the behavior. For the last graph no model (the equations) is presented. Without a model you cannot use control theory to analyze the zeros and poles.
The last graph wants you to believe in a continuing upward trend, the fallacious argument, implies that whatever the Canadian political change that has been made is going to make this trend to zero, despite the intention to keep it trending upwards.
Background: A long time ago, as a mathematics undergraduate, I did take a course in control theory, it was run out of the engineering department. It was somewhat awkward as quite a few mathematical terms were not-quite-the-same. I get the same unease when reading this for poles, zeros and right-half-planes. Any engineering textbooks that use j for sqrt(-1) instead of i (because that is taken) is an indicator. Yup, this could be construed as an "appeal to authority".
[+] [-] VogonPoetry|3 years ago|reply
There are, to me some language red flags. The followup article now uses "we' -- suggesting this is not the work of an individual. This was not present in the initial post.
An attempt is made to build a model. Curiously a visual programming model is now used. No explicit differential equations are given. If the equations are not given there is no way to check the model. So "pole" and "zero" analysis is mute.
There are no tests to validate this model against past situations - an easy and free test, the past history is known. If the model that has been created and can predict the future, why would was it not run it against the past and show the predictive success?
The built model is only presented against the current situation -- is it circumstantial / opinion based.
My understanding of science is -- build a model that can predict the future / what happens accurately, i.e. matches the measurements. The consensus agrees that this is the (current) best model.
Prices are ultimately influenced by a sentiment factor, a value derived from a I have no idea what human feeling / property. Some power "enabled" humans have been endowed with a much higher influence on this parameter. Where is this value expressed in the predictive equations?
[+] [-] fluoridation|3 years ago|reply
It could be that the reader fails to understand the explanation and instead treats the writer as a trustworthy authority. That would not make the argument an appeal to authority or even fallacious.
It could be that the analogy is poorly justified, which would make the argument incomplete, or it could even be that the writer failed to understand some subtle aspect of the second topic that makes the analogy inappropriate. Neither of these would be appeals to authority.
[+] [-] CFLAddLoader|3 years ago|reply
This makes it really hard for them to write an article for non-technical people. To do so, they would have to connect the human side of things to the systems theory side of things. Which they can't do, because they don't understand the human side of things.
They aren't using bad-faith arguments to convince you that they are correct. They simply have no idea how to talk to you. They are in fact trying to be helpful, by presenting what they think is really useful information to understand and control the world with. Their help is useless to you, but they are trying.
[+] [-] yt-sdb|3 years ago|reply
[+] [-] Victerius|3 years ago|reply
There are a lot of similar posts online about people trying to use chaos theory (or what they believe chaos theory is), "systems theory", and other obscure concepts to explain why, for example, climate change will be the end of us all, or the global economy will enter a depression, or any other extremely pessimistic macro scenario. I see three reasons why these people are doing it. (1) To draw attention to themselves as someone with a superior intellect (which they actually aren't) (2) To construct an analysis no one has constructed before, in a "all these professional economists are saying the same thing, but here's why they're all misleading themselves, thanks to my ace card of a theory" kind of way, and (3) A love for the hyperbole, for dramatic outcomes.
A classic economic prediction like "Inflation pressures will potentially slow down growth in the short term, but the behavior of the economy over the next 12 months remains unpredictable" is not enough. It MUST be "A catastrophic economic collapse is inevitable", or "We are going back to the Middle Ages by the end of the decade", or "Hundreds of millions will die in the next few years".
[+] [-] skybrian|3 years ago|reply
[+] [-] any1|3 years ago|reply
[+] [-] TimPC|3 years ago|reply
[+] [-] jokabrink|3 years ago|reply
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.
[+] [-] loser777|3 years ago|reply
[+] [-] zasdffaa|3 years ago|reply
"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.
[+] [-] foxes|3 years ago|reply
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.
[+] [-] toomanydoubts|3 years ago|reply
[+] [-] jimnotgym|3 years ago|reply
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
[+] [-] pizza|3 years ago|reply
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...
[+] [-] unknown|3 years ago|reply
[deleted]
[+] [-] petesergeant|3 years ago|reply
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"
[+] [-] lagrange77|3 years ago|reply
Oh wow, i didn't notice that. It's either pretty clever, or unfortunate wording.
[+] [-] makach|3 years ago|reply
[+] [-] raydiatian|3 years ago|reply
[deleted]
[+] [-] duped|3 years ago|reply
But it's really so foundational to understanding concepts of stability, resonance, information/energy flow (from the conceptual perspective), and the simple analytical tools for building a solid conceptual base. It takes a semester to hammer home that step response matters, positive feedback bad, negative feedback usually good, and topologies are useful.
[+] [-] Agentlien|3 years ago|reply
The more I specialize in graphics the more I realize I need much more knowledge about signal processing than we were taught at the university.
[+] [-] nbadg|3 years ago|reply
Those lessons might have been hard-won on my part, but I definitely still use them. The general concepts (feedback loops etc) are applicable basically everywhere in life, and I still find uses for literal actual math (like using a convolution kernel to do rolling window sampling in numpy).
[+] [-] nabla9|3 years ago|reply
You need it in economics, biology, chemistry, physics, computer science, statistics, electrical engineering, robotics , automation, logistics, ...
It should be taught like calculus or linear algebra, so that everyone gets gist of the basics before learning to apply it into their specific field.
[+] [-] Jach|3 years ago|reply
[+] [-] codethief|3 years ago|reply
[+] [-] koliber|3 years ago|reply
[+] [-] trenchgun|3 years ago|reply
Thank you!
[+] [-] Animats|3 years ago|reply
It will be seen that the motion of a machine with its governor consists in general of a uniform motion, combined with a disturbance which may be expressed as the sum of several component motions. These components may be of four different kinds:-
(1) The disturbance may continually increase.
(2) It may continually diminish.
(3) It may be an oscillation of continually increasing amplitude.
(4) It may be an oscillation of continually decreasing amplitude.
The first and third cases are evidently inconsistent with the stability of the motion; and the second and fourth alone are admissible in a good governor. This condition is mathematically equivalent to the condition that all the possible roots, and all the possible parts of the impossible roots, of a certain equation shall be negative.
That is, in the left half-plane.
(Terminology has changed. Maxwell says "disturbance" where today, the term "error" would be used. Today, "disturbance" means an input which disturbs stability, while error is an output.)
Maxwell got so much right in that paper, and it was a long time before anybody picked up on that result.
Now, where it looks like the author is going is into economic territory. Basic economics talks about "economic equilibrium". The concept is that restoring forces will bring supply and demand into equilibrium. But basic control theory tells us that may not happen. Any system with delay in it can potentially be unstable. Too much delay, and even simple systems will not stabilize.
[1] https://en.wikisource.org/wiki/On_Governors
[+] [-] lordnacho|3 years ago|reply
Fascinating subject though, in engineering class it was quite surprising how this bunch of functions tracing lines and dots on the complex plane would be relevant to just about everything. Perhaps the first lesson is that even if you know how a system works, you can't just take the inverse function to control what comes out.
[+] [-] jbay808|3 years ago|reply
Author here. Yes! Very fair criticism. I was trying to strike a balance between making the concept approachable for those who don't have a background involving complex numbers, but that certainly leaves the name of the concept more confusing. I should add it in a footnote at least.
And I did honestly not think about the potential for confusion between plane // airplane. An airplane was the most familiar example system I could think of to explain the concept. Oops!
> Perhaps the first lesson is that even if you know how a system works, you can't just take the inverse function to control what comes out.
That's a great point too. It probably even deserves its own article.
[+] [-] rhn_mk1|3 years ago|reply
[+] [-] woojoo666|3 years ago|reply
[+] [-] dhosek|3 years ago|reply
[+] [-] _moof|3 years ago|reply
[+] [-] ilayn|3 years ago|reply
Also a pure zero action is supposed to cancel the input completely. Not at first but completely (restricting the discussion to linear systems).
Zeros effects are not so trivial to untangle as the article suggests unfortunately but fun read anyways and very nice flow.
[+] [-] jbay808|3 years ago|reply
Thank you for your input! I wonder if you might have misread that example. In this system there's indeed a RHP0 in the transfer function from ice cream consumption happiness. A continuously increasing rate of ice cream intake results in exactly no effect on the output.
[+] [-] tdubhro1|3 years ago|reply
[+] [-] once_inc|3 years ago|reply
Very good article, and well worth your time to read.
[+] [-] d--b|3 years ago|reply
[+] [-] gsliepen|3 years ago|reply
Of course that is easier said than done; adding a sleep() to your control loop to ignore the initial misdirection is also very bad. The right way to solve this is to not just tell the control loop to "go up", but to plan a realistic trajectory that the control loop can execute. That way, the error between the desired trajectory and the actual trajectory will be much smaller, and the closer the error is to zero, the less chance of a control loop to go wild.
[+] [-] bambax|3 years ago|reply
I don't know if many people often ride their bicycle on cliff edges, but many plane (as in airplane) accidents occur because it's difficult / impossible to recover from a stall near the ground.
[+] [-] voldacar|3 years ago|reply
[+] [-] lagrange77|3 years ago|reply
I would also mention, that we essentially design controllers to shift the poles and zeroes of the total system (which consists of the plant system and the controller system) to more desirable positions, than those of the plant system alone.
[+] [-] oh_my_goodness|3 years ago|reply
Comments: The OP is a troubling covert political statement. The real issue here seems to be US midterm elections / climate change / COVID / appeal to authority.
[+] [-] eigart|3 years ago|reply
[+] [-] deepsun|3 years ago|reply
It's very visible and pronounced on heavier bikes, like motorcycles. Especially if you try riding a very heavy cruiser bike -- you'll immediately notice that countersteering is the only way to turn it. No matter how you try to lean it, it won't respond and will just go straight, but it'll respond very easly to handlebar inputs.
[+] [-] xg15|3 years ago|reply
But what he really talks about seems to be the opposite: Actions which case some mild harm in the short term but increase well-being in the long term. So I guess something like working out or going on a diet or making a downpayment for a house?
Except the failure mode is also counterintuitive: Normally, we tend to overvalue the short-term downsides of those actions and therefore shy away from them, missing out on the long-term benefits. But he talks about a situation where we overvalue the long-term benefits but ignore the short-term and overdo the action until the short-term harm becomes critical.
So, e.g. someone working out, getting muscle-ache - and then working out more to counter the ache - which will only lead to more of it until the workout actually starts to become detrimental to their health.
It's easy to see how this would trip up automated control loops, but I don't really see how this has practical application outside of control theory.