[HN Gopher] You need to know what right-half-plane zeros are
       ___________________________________________________________________
        
       You need to know what right-half-plane zeros are
        
       Author : jbay808
       Score  : 393 points
       Date   : 2022-06-10 02:40 UTC (20 hours ago)
        
 (HTM) web link (jbconsulting.substack.com)
 (TXT) w3m dump (jbconsulting.substack.com)
        
       | bob1029 wrote:
       | This stuff is fun. Surprised I haven't seen direct mention of
       | state space representation yet:
       | 
       | https://en.wikipedia.org/wiki/State-space_representation
       | 
       | I recall going through this at university and it being a bit of a
       | struggle. Looking back at it now, this stuff makes a lot more
       | sense. A decade+ of practical experience probably helps.
        
       | lordnacho wrote:
       | 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.
        
         | rhn_mk1 wrote:
         | I felt that the article ended just where it was ripe to dig
         | into the maths.
        
         | jbay808 wrote:
         | > 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.
        
           | l33t2328 wrote:
           | > the potential for confusion between plane // airplane
           | 
           | This reminds me of the famous (possibly apocryphal) story of
           | the algebraic geometer of middle eastern descent who was
           | brought aside by Air Marshals for talking about how a
           | particular problem could be solved by "blowing up points on a
           | plane"
        
             | wbl wrote:
             | At Berkeley the legend is that there was a class on blowing
             | up with special application to local problems.
        
           | LeonB wrote:
           | Really good article. Make changes and corrections to it,
           | sure, but be careful not to over react to the criticism and
           | make too many changes such that you then get even more
           | critical feedback and make more corrections and get worse
           | feedback and bigger corrections and oh god help me worse
           | feedback and bigger changes and stop me please worse feedback
           | and help bigger changes seriously kill me bigger feedback
           | worse changes arggggh
        
           | ehvatum wrote:
           | If you haven't read it, I recommend:
           | https://www.gutenberg.org/files/6949/6949-h/6949-h.htm
        
           | yesenadam wrote:
           | The main thing missing for me: presumably if there's a plane,
           | you're graphing something vs something. What are the X and Y?
           | (or, uh, the x and y in the x+iy) Talk of a plane remains
           | rather vague without knowing that. Maybe I missed it, but I
           | looked twice, and read the comments on this page, and
           | couldn't see it mentioned at all. There are a couple of
           | graphs/planes, but they seem to be a different kind of thing.
        
             | mellavora wrote:
             | It is the complex plane, x is real, y is imaginary.
             | 
             | the author should have clarified this, you are correct, as
             | the author also makes clear he is writing for a non-
             | technical audience.
             | 
             | He probably forgot to mention it because the concept is so
             | fundamental to signal processing that he assumed it was
             | common knowledge.
        
             | stephen_g wrote:
             | Wikipedia has it highlighted on the graph:
             | https://en.wikipedia.org/wiki/Right_half-plane
             | 
             | Also see page 4 here:
             | https://web.mit.edu/2.14/www/Handouts/PoleZero.pdf
        
               | yesenadam wrote:
               | Uh that first link is just a picture of a right complex
               | half-plane... I know what that is, having done quite a
               | bit of complex maths, but the kind that uses _i_ , not
               | the kind that uses _j_ , e.g. I love _Visual Complex
               | Analysis_. I just don 't know what things are being
               | graphed in the article! Sorry I didn't explain better. Ok
               | thanks for the 13pp article, I will have a look sometime
               | soon. I was hoping someone could just tell me the answer.
               | 
               | edit: I looked at the first few pages of the paper but I
               | feel none the wiser, at all.
               | 
               | edit2: Ah... "the poles and zeros of a transfer function
               | may be complex, and the system dynamics may be
               | represented graphically by plotting their locations on
               | the complex s-plane". The transfer function (whatever
               | that is) is a rational function of the complex variable
               | _s_ , i.e. (in my words) it's a fraction with complex
               | polynomials for numerator and denominator. The _zeros_
               | are the roots of the numerator and the _poles_ are the
               | roots of the denominator.
               | 
               | Ok, I still don't know what the transfer function is or
               | means or comes from, but am much less in the dark, thank
               | you! :-)
        
               | jayjader wrote:
               | I see that /u/metaphor has given you some formal
               | references.
               | 
               | I'd like to chime in with a more intuition-based
               | explanation of what transfer functions are, from my
               | recollections of college control theory classes in both
               | electrical signals and a more general "systems
               | engineering" application:
               | 
               | Basically, the transfer function is a different
               | perspective on modelling/representing a system's output
               | as a function of its input. Classically, when modelling
               | and/or reasoning about a system in physics, the
               | perspective we adopt is that of "input" being the forward
               | advance of time (and sometimes initial conditions) and
               | "output" being the amplitude of the physical
               | quantity(ies) or dimension(s) of the system that
               | interest(s) us. The transfer function, then, is when we
               | switch perspectives to consider the "input" to be a
               | sinusoidal signal (characterized by amplitude and phase
               | over time), and the "output" is the new amplitude and
               | phase of that signal [after "traversing" the system]. Of
               | course, you're actually working with a closed-loop, but
               | most input/output systems can be modeled as a closed-loop
               | if you sufficiently broaden the system's boundaries.
               | 
               | This turns out to be useful for/in several
               | reasons/contexts:
               | 
               | - many physical phenomena are sine waves (or, thanks to
               | Fourier, a sum of sometimes many different sine waves),
               | and often times a system's purpose (to us humans) is to
               | control such a phenomena precisely along the lines of "do
               | this to the amplitude, and/or adjust the phase like so" -
               | dampening, feedback loops, more sophisticated processes
               | like hysteresis, maintaining a steady state given
               | incoming perturbations, etc. In these cases the transfer
               | function ends up being the mathematical expression of
               | that system's function in the "domain language" of that
               | problem, so to speak.
               | 
               | - It turns out that often, when working with systems
               | whose "classical" representation involve components like
               | exponentials or sine and cosine of time (which are "just"
               | complex exponentials of those quantities), the
               | corresponding transfer functions are "simple" fractions
               | of polynomials. More precisely, passing into the
               | Langrange domain allows transforming a differential
               | equation problem into a complex polynomial fractions
               | problem - often much easier to crunch/solve. Furthermore,
               | in the Lagrange domain, de-phasing a signal by pi/2 is
               | equivalent to simply adding 1/(j * signal's frequency) to
               | that signal (if I recall correctly). This makes much of
               | the math more accessible to human intuition, and
               | especially on more complex systems that have several
               | "moving parts" the linear quality of polynomials becomes
               | invaluable.
               | 
               | Personally, I remember quickly adopting, once I'd grokked
               | it, the transfer function perspective when trying to
               | reason about the effect of introducing a capacitor into
               | an existing circuit - analog or DC[0] - as well as things
               | like how the material properties of a door contribute to
               | its behavior as a low-pass filter on sound waves. Sitting
               | down and doing the math, the formulas that I would arrive
               | at spoke much more clearly to me. Also, you are sort of
               | adopting a "time-agnostic" (or perhaps time-invariant)
               | perspective, where the system itself does not change over
               | time. Instead, its' input is characterized by how it
               | behaves over time, and the transfer function (especially
               | when plotted) gives you a clear, direct sense of what the
               | output's "behavior over time" will accordingly be.
               | Notably, it's here that the zeroes of the OP become so
               | meaningful.
               | 
               | [0]: part of what initially started making things "tick"
               | for me was when a professor explained that an impulse on
               | an input signal (i.e. a quasi-instant variation, then
               | back to the preceding "steady state" value of it - i.e. a
               | DC current "turning on"), to a transfer function, "looks
               | like" a sine wave signal with a constant amplitude but
               | monotonously increasing phase offset - again I forget if
               | the rate is constant, polynomial, exponential or what.
        
               | yesenadam wrote:
               | You had me at "a more intuition-based explanation of what
               | transfer functions are". :-) Thank you so much for this.
               | 
               | edit: By "Lagrange" did you possibly mean to write
               | "Laplace"? I confuse those two gentlemen too. p.s. I just
               | learnt Lagrange was Italian! born Giuseppe Luigi
               | Lagrangia.
        
               | metaphor wrote:
               | > _I know what that is, having done quite a bit of
               | complex maths, but the kind that uses i, not the kind
               | that uses j_
               | 
               | Some things in life leave a lasting impression[1].
               | :eye_roll:
               | 
               | It sounds like what you're looking for is an explanation
               | of root locus analysis[2].
               | 
               | In the simplest control case, a transfer function is
               | nothing more than the expression of a continuous closed-
               | loop LTI system's output Y(s) over its input X(s) in the
               | Laplace domain, conveniently abstracted as its forward
               | path G(s) and negative feedback path H(s).
               | 
               | From there, Routh-Hurwitz method[3] can be used to
               | determine stability of the system.
               | 
               | ...and I will continue to use _j_ , thanks.
               | 
               | [1] https://youtu.be/1rqJl7Rs6ps?t=1828
               | 
               | [2] https://en.wikipedia.org/wiki/Root_locus
               | 
               | [3] https://en.wikipedia.org/wiki/Routh%E2%80%93Hurwitz_s
               | tabilit...
        
               | yesenadam wrote:
               | hehehe Thank you very much! :-) Funny video. I'll check
               | out that course. Thanks for the links.
               | 
               | edit: Took a lil while to work out that LTI system is
               | _Linear time-invariant system_.
               | 
               | https://en.wikipedia.org/wiki/Linear_time-
               | invariant_system
        
           | lordnacho wrote:
           | I'd definitely read a series about control theory. The first
           | time round was very badly presented at my university. A lot
           | of math, motivation hidden.
           | 
           | Stuff like Nyquist criterion just sort of appears out of
           | nowhere as functions.
           | 
           | I guess the big one is feedback being the magic, and then the
           | complex plane tells you where that blows up.
        
             | pid-1 wrote:
             | I went down this rabbit hole in grad and my opinion is that
             | Control Theory is good for writing academic papers, but has
             | few applications besides the classical ones (mostly in
             | mechanics).
             | 
             | Techniques often need very strong assumptions about the
             | systems being modeled, which severely limits their
             | usefulness.
             | 
             | In fact, CT is sort of the antitheses of the currently most
             | hyped way of modeling systems: Machine Learning.
        
               | alanbernstein wrote:
               | I think you're sweeping a ton of valuable applications
               | under the rug by saying "few applications besides the
               | classical ones" ?
        
               | jbay808 wrote:
               | I hope I will be able to change your mind!
        
               | lagrange77 wrote:
               | Interesting username for such an opinion.
               | 
               | Also systems modeling is not the same as control theory.
               | You could indeed utilize machine learning to model a
               | system, which you could then control by classical
               | controllers. On the other hand, _control algorithms that
               | use machine learning_ are a thing.
        
               | metaphor wrote:
               | > _Interesting username for such an opinion._
               | 
               | Perhaps just a coincidental namespace collision: Process
               | ID, not Proportional-Integral-Derivative.
        
               | lagrange77 wrote:
               | Yes, probably.
        
             | metaphor wrote:
             | > _Stuff like Nyquist criterion just sort of appears out of
             | nowhere as functions._
             | 
             | Black's canonical 1934 paper[1] _Stabilized Feedback
             | Amplifiers_ , which had an outsized influence on EE
             | classical control theory, may have something to do with
             | that:
             | 
             |  _Results of experiments, however, seemed to indicate
             | something more was involved and these matters were
             | described to Mr. H. Nyquist, who developed a more general
             | criterion for freedom from instability applicable to an
             | amplifier having linear positive constants._
             | 
             | ...which directly cites Nyquist 's canonical 1932 paper[2]
             | _Regeneration Theory_.
             | 
             | [1] http://archive.org/details/bstj13-1-1
             | 
             | [2] http://archive.org/details/bstj11-1-126
        
           | levi_n wrote:
           | Thank you for this article and the follow up. The information
           | is fascinating, and I eagerly await your next installments.
        
         | woojoo666 wrote:
         | Not to mention, it's not just a complex plane. It's the
         | s-domain, reached through the laplace transform.
        
       | iandanforth wrote:
       | TLDR; If you want to make something go up (or down, or left or
       | right) sometimes it goes down (or whatever the opposite is) a bit
       | first. If you were to try harder to make it go up at that point,
       | the problem gets worse, repeat until your system crashes. Times
       | like these are called right-half-plane zeros and any control
       | system you build has to be aware of them and designed to avoid
       | causing a feedback loop.
        
       | dhosek wrote:
       | 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.
        
         | civilized wrote:
         | It's like "I know math so take me seriously" but then the posts
         | don't use the math in any meaningful way.
         | 
         | Not that I think they _should_ use the math. Just skip the
         | systems lectures and the  "there is math behind this" and go
         | straight to the analysis.
        
       | sbf501 wrote:
       | Odd that OP would give a grim warning without an equation.
       | 
       | I graduated in 1991 with BSEE and the curriculum was a rush to
       | get us to diffeq and linear systems because 90% of the remaining
       | three years of classes were taught using S and Z plane analysis.
       | My engineering professors were incapable of introducing a concept
       | without starting with a differential equation.[1]
       | 
       | For the author to spend so much time explaining control theory,
       | then sort of give up on it, was disappointing. Ironically,
       | knowledge of control systems and warnings about them should
       | pervade the thought process of the thinker and prevent them from
       | making grandiose claims. Perhaps OP only has a topical knowledge
       | but can spin a good yarn.
       | 
       | [1] I'm a career programmer, but I always start my thoughts with
       | a d/dt: whether it's an RTOS project, a graph GraphQL endpoint,
       | or USB driver. I guess "if all you have is a hammer..."
        
       | nurettin wrote:
       | So sometimes it is better to cut losses rather than double down
       | because planes exist.
        
       | GistNoesis wrote:
       | Are they still important if you use something like model
       | predictive control ?
        
         | jbay808 wrote:
         | They are certainly something that your MPC controller will need
         | to account for, and they will constrain the theoretical maximum
         | performance you can get out of the system no matter how optimal
         | your control algorithm is.
        
       | _moof wrote:
       | 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.
        
         | tzs wrote:
         | > 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.
         | 
         | So what happens to something like a jet fighter that is in
         | level flight with the engines at maximum power if the pilot
         | uses the elevators to raise the nose?
        
           | _moof wrote:
           | It will climb (and slow down), but again, it's the thrust
           | that's producing the climb, and this is an extreme example
           | that isn't illustrative. Fighter jets produce enormous thrust
           | for their weight with many having thrust-to-weight ratios
           | greater than one. If they weren't air-breathing, they could
           | literally fly into space. A normal airplane, even if it
           | weren't air-breathing, couldn't do that.
           | 
           | Depending on the configuration an F-16 has a T/W a little
           | under 1.1, while a transport category aircraft (an airliner)
           | will have a T/W somewhere between 0.20 and 0.35. Totally
           | different performance characteristics.
        
       | entropicgravity wrote:
       | Not to mention poles in the unit circle.
        
       | raydiatian wrote:
       | The footnote is nonsense. Needs revision, author is currently
       | arguing that poles are indistinguishable from zeros.
        
         | oh_my_goodness wrote:
         | The footnote currently appears to be correct.
        
         | jbay808 wrote:
         | I'm not aware of what you mean.
        
       | lagrange77 wrote:
       | Great article and blog!
       | 
       | 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.
        
       | ali-preview wrote:
       | I'm nX 1 too<p>;)\n
        
       | thaumaturgy wrote:
       | The danger of "systems thinking" is that it misleads otherwise
       | clever people into believing they've found a cheat sheet for
       | subjects they don't have deep knowledge in. This article is a
       | fine example of that.
       | 
       | I didn't know what right-half-plane zeroes are. I knew some of
       | the examples it gave (Veritasium has a fun video on the bicycle
       | steering phenomenon), but not that there was a category they all
       | fit into. Neat.
       | 
       | But I got squinty when the author said the intended audience was
       | everybody, and got a hunch it was going to wander into the
       | current economy ... which it did, sort of, except that in this
       | case, "wandering" into the subject meant, "wrap it up with a
       | graph and then point at it and go, see! See! I can predict the
       | economy now!"
       | 
       | The follow-up at https://jbconsulting.substack.com/p/on-shelter-
       | futures-part-... goes into more detail and concludes that
       | interest rate hikes will increase inflation over the next 5-ish
       | years, but there's no "part 2" in the series to be found
       | (paywalled?).
       | 
       | There are lots of graphs and the author tries to build a case out
       | of several arguments, buuuuut in the end it _feels like_ that
       | IASIP conspiracy board meme. I smell a faint whiff of gish
       | galloping here and there, but one thing that stands out to me is
       | that the author chooses to normalize housing costs against
       | inflation, but there 's no mention of wage stagnation anywhere.
       | 
       | Rents and housing costs _can 't_ rise a whole lot more, certainly
       | not to the extent the author seems to be predicting, because
       | _people can 't afford them_. This is already a conversation
       | happening in every housing market in at least several countries.
       | In the US, pick literally _any_ local subreddit and ask if anyone
       | knows of an affordable place to rent, I dare you. There 's
       | already a huge epidemic of unhoused people and van-dwelling is
       | more popular than it has ever been, and consumers are currently
       | getting squeezed in a lot of directions. Here, one of the things
       | in my browser history before this article was this thread:
       | https://old.reddit.com/r/news/comments/v8knl5/gas_prices_hit...
       | 
       | So, if wages don't rise to meet these costs, then something big
       | is going to break way before the cost increases the article is
       | doomsaying.
        
         | robertlagrant wrote:
         | > Rents and housing costs can't rise a whole lot more,
         | certainly not to the extent the author seems to be predicting,
         | because people can't afford them.
         | 
         | House prices are passively controlled because there's only so
         | much money to spend on housing?
        
       | ali-preview wrote:
        
       | jokabrink wrote:
       | 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 air _plane_ s 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.
        
         | zasdffaa wrote:
         | 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.
        
           | kubanczyk wrote:
           | 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.)
        
             | Sohcahtoa82 wrote:
             | > 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
        
             | brandmeyer wrote:
             | > 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...).
        
           | padolsey wrote:
           | 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
        
           | noduerme wrote:
           | 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.
        
           | jokabrink wrote:
           | Fair enough, but then he wouldn't have needed to use control
           | theory and just stuck with the examples.
           | 
           | Edit: removed ambiguity
        
         | raydiatian wrote:
        
         | lagrange77 wrote:
         | > He uses air _planes_ as an example.
         | 
         | Oh wow, i didn't notice that. It's either pretty clever, or
         | unfortunate wording.
        
         | [deleted]
        
         | petesergeant wrote:
         | > 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"
        
           | nbadg wrote:
           | 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!"
        
           | Ialdaboth wrote:
           | 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.
        
             | noduerme wrote:
             | 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.
        
           | Perseids wrote:
           | 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).
        
           | chasd00 wrote:
           | 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.
        
           | noduerme wrote:
           | 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.
        
         | toomanydoubts wrote:
         | At the beginning I didn't understand what the post was about.
         | At the ending, it felt like I was at the beginning.
        
         | foxes wrote:
         | 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.
        
         | pizza wrote:
         | 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...
        
         | makach wrote:
         | Same. I ran to the comments to check my understanding.
        
         | jimnotgym wrote:
         | 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
        
         | loser777 wrote:
         | 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.
        
           | taneq wrote:
           | 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.)
        
             | SilasX wrote:
             | 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.
        
               | taneq wrote:
               | Whoops, adding that to my list of things to read again...
               | >.>
        
       | deepsun wrote:
       | > 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.
        
       | bambax wrote:
       | > _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.
        
         | LanceH wrote:
         | You can also get your weight to the inside of a turn for a
         | bicycle by leaning while riding straight.
         | 
         | Every time this comes up there is a big debate with a bunch of
         | people saying counter steering is required. Please, go out and
         | try it. Drive perfectly straight along a painted line. Lean
         | left, turn left. Lean right, turn right. There is no
         | requirement for counter steering.
        
           | bambax wrote:
           | I think it's somewhat speed-dependent. I ride motorcycles and
           | bikes. On a motorcycle at high speed it's impossible (in my
           | experience) to take a turn without counter steering. You
           | sometimes have to push really hard on the handle on the side
           | where you want to go.
           | 
           | Also, leaning is very similar to counter steering; counter
           | steering makes the bike "fall" on the side where you want to
           | go.
           | 
           | Interestingly, you can also steer a horse without doing
           | anything on the reins; the horse will usually go where you
           | put your weight; I think it's because it needs to compensate
           | for the weight differential; or maybe it takes it as a hint
           | about which way you're looking. In any case it works.
        
       | d--b wrote:
       | 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.
        
       | blauditore wrote:
       | Can someone provide a TL;DR? I don't have time to read the whole
       | article, and I don't even understand what's the topic based on
       | title and reading a few paragraphs, nor from googling "right-
       | half-plane zeros".
        
         | a_imho wrote:
         | The plane refers to the plane of complex numbers (a+b*i), the
         | right half is where the real part (a) is positive. If the zeros
         | of your feedback loop are on the right hand side that means it
         | is a unstable feedback loop, if they are on the left side it is
         | stable feedback loop (this happens because the zeros eventually
         | end up in exponents which either tend to infinity or to zero
         | with time).
         | 
         | If you squint a little bit most systems looks like a feedback
         | loop and my not very confident interpretation is, judging from
         | the last picture, that the author thinks we have a runaway
         | inflation problem (zeros on the right hand side of the plane)
         | and we might or might not have the controls to move them to the
         | left hand side to tame it.
        
           | layer8 wrote:
           | I thought this would be something about positive zero in a 2D
           | coordinate system, but seeing drawings of airplanes in the
           | article I concluded "bummer, it's not" and immediately hit
           | backspace. Thanks for the summary. :)
        
       | gsliepen wrote:
       | > 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.
        
       | ilayn wrote:
       | 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.
        
         | jbay808 wrote:
         | > 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.
        
           | ilayn wrote:
           | Your happiness shouldn't change if ice cream input has a
           | zero. Also it should be independent from the amount of ice
           | cream. In other words if we have an ODE say
           | 
           | ddot y + 2 dot y + y = dot u - 2 u
           | 
           | As long as my input is pure C exp(2t) independent of C I see
           | no happiness and it's not working on my mood. In your example
           | input u effect is cancelled by decay of y cancelling the
           | guilt. Making it not a zero.
           | 
           | In my personal case eating celery is a zero i see absolute no
           | point eating it :) no harm and no benefit just pointless
           | chewing
        
       | tdubhro1 wrote:
       | 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.
        
         | jbay808 wrote:
         | Fair. Perhaps a glider would have been a better example.
        
           | nosianu wrote:
           | How? A glider climbs when the air it is in rises faster than
           | the airplane sinks in that air to maintain its forward speed.
           | 
           | If you pitch up you can only exchange speed for a little bit
           | of altitude, briefly.
        
             | jacquesm wrote:
             | Exactly. A glider in air that doesn't rise is like a yo yo
             | on a string, you need to add energy to the system (rising
             | air, pulling up on the string at the right moment) to be
             | able to overcome the eventual return to the ground state.
        
         | rocqua wrote:
         | Just pitching up will have you climb, but at the expense of
         | losing velocity right?
        
           | jacquesm wrote:
           | Right up to the stall speed limit. You can't just keep
           | pitching up, you'd have to apply some power too if you don't
           | eventually want to run out of forward (air)speed.
           | 
           | In a glider you can't do that so there when in level flight
           | you have a limited amount of forward momentum available to
           | help you climb if the air itself isn't moving up, you are
           | continuously trading altitude for speed and vv (easy to see
           | in a dive: everybody expects you to gain speed in a dive
           | because can all relate so something falling, it's obvious the
           | reverse has to happen when you climb and the stall speed is a
           | design parameter of the aircraft at a given altitude combined
           | with a bunch of other factors).
           | 
           | https://aviation.stackexchange.com/questions/27693/how-
           | does-...
        
           | jhugo wrote:
           | Briefly.
        
       | Linda703 wrote:
        
       | once_inc wrote:
       | 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.
        
         | dools wrote:
         | It's funny as soon as I read the ice cream but I knew where he
         | was going with it.
         | 
         | The interesting thing is that his modelling concludes that
         | raising interest rates is inflationary which is what Warren
         | Mosler also says.
         | 
         | Anyone interested in what to do about inflation would enjoy the
         | recent Macro n Cheese podcast episode featuring Randall Wray
        
           | selimthegrim wrote:
           | Let's hope Erdogan doesn't read this
        
         | pcthrowaway wrote:
         | Link, because I assumed it wasn't out yet since the author
         | hadn't provided it: https://jbconsulting.substack.com/p/on-
         | shelter-futures-part-...
        
       | bsedlm wrote:
       | can anybody tell me what's f in this scenario?
       | 
       | dy/dt = dx/dt + Ax
       | 
       | is it the case that y = f(x,t)?
       | 
       | thanks
        
       | duped wrote:
       | 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.
        
         | nbadg wrote:
         | 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).
        
           | thrwyoilarticle wrote:
           | I can imagine it's used for car suspension?
        
             | dboreham wrote:
             | Wasn't control theory invented to understand the dynamic
             | behavior of steam engine governors?
        
         | koliber wrote:
         | 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.
        
         | Agentlien wrote:
         | I took some electrical engineering courses but mainly software
         | engineering with a focus on low-level details and graphics.
         | 
         | 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.
        
           | AB1908 wrote:
           | Could you demonstrate with an example?
        
             | Agentlien wrote:
             | I can give a few. In general, the theory behind rendering
             | generally treats what's on the screen as a discretization
             | of a continuous visual signal. Post processing especially
             | is largely about signal processing.
             | 
             | Anti-aliasing (AA) is a very clear example where the lack
             | of it leads to moire patterns and jaggies. Understanding a
             | lot of AA techniques is simplified by seeing the frame not
             | as a discrete set of pixels but as a continuous signal
             | being sampled (and can be sampled at multiple sub-pixel
             | points per pixel).
             | 
             | A lot of other screen effects are essentially filters
             | applied to the graphical signal (sobel, gaussian blur, ...)
             | and understanding them from a signal processing view helps
             | understanding how to modify and optimize them. A good
             | example here is identifying whether your effect is a
             | separable filter which can be split into a horizontal and
             | vertical pass.
             | 
             | Seeing the image as a continuous signal/field being sampled
             | is also the theoretical basis for a lot of visual effects
             | used in physically-based rendering and things like screen-
             | space ambient occlusion.
             | 
             | Finally, if you want to write your own ray-tracer it really
             | helps to be able to take this view of things once you get
             | past the basics.
        
         | nabla9 wrote:
         | _" signals and systems"_ - covering signals processing, systems
         | and control theory is very generic subject.
         | 
         | 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.
        
         | trenchgun wrote:
         | I was already thinking of taking it this summer, but you
         | convinced me to do it for sure.
         | 
         | Thank you!
        
         | Jach wrote:
         | 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.)
        
         | codethief wrote:
         | 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.)
        
           | scrlk wrote:
           | Signals & Systems by Oppenheim is a classic introductory
           | textbook.
        
           | lagrange77 wrote:
           | Not a book, but this series on Youtube is excellent.
           | 
           | https://www.youtube.com/watch?v=Pi7l8mMjYVE&list=PLMrJAkhIeN.
           | ..
           | 
           | > familiar with Nyquist-Shannon's theorem
           | 
           | BTW: In control theory there is also
           | https://en.wikipedia.org/wiki/Nyquist_stability_criterion
        
           | duped wrote:
           | ime the books are very loaded on theory and it's hard to
           | connect that to practice and concepts. I don't know of any
           | book that touches on what poles/zeros _mean_ or why they 're
           | useful outside what are (seemingly) contrived properties of
           | formulae like stability. It's one of those things that's just
           | useful to go through in a university course, even just
           | auditing it. The practical problems and lectures are
           | extremely useful, particularly due to the overhead of
           | notation (the practice is relatively young and derived from a
           | different tradition of education, and a lot of contemporary
           | notation can seem a little foreign, or is filled with
           | shorthand).
           | 
           | Applied Digital Signal Processing by Manolakis & Ingle is the
           | book I always turn to for reference and the code examples
           | don't suck. Oppenheim & Schafer is a classic but frankly only
           | useful as a reference, that tome is a bit dated otherwise.
           | The Scientists and Engineer's guide to DSP is also not bad as
           | a practical text.
        
       | dukeofdoom wrote:
       | If you are going slow on a bicycle, and want to turn right, you
       | might have to turn your front wheel left and then right, just so
       | you don't fall over and maintain upright balance. Which would be
       | a problem if you are riding along a cliff's edge.
        
       | eigart wrote:
       | 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.
        
         | jbay808 wrote:
         | Thank you for reading! I agree the Earth is a much worthier
         | system to be worried about than the economy, for sure.
        
       | LolWolf wrote:
       | Counterpoint: no you don't.
       | 
       | By the time you have a perfectly reasonable model of a system
       | that is good enough such that computing the transfer function's
       | poles actually tell you something interesting about the system,
       | there's way more you can say about the system than "it is
       | stable."
       | 
       | There are maybe some lessons to be drawn from basic "classical"
       | control theory, but many are better stated by just analyzing the
       | system directly.
       | 
       | (As a side note, I'm not saying there's Zero value in analyzing
       | transfer functions, just that it's a long way to the top from
       | there.)
        
       | lb1lf wrote:
       | 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'll lead myself out.
        
         | l33t2328 wrote:
         | I hate to be the guy to ask you to explain the joke, but why
         | would that make the plane crash?
         | 
         | I do know what a "pole" refers to, but I don't follow the crash
         | bit.
        
           | eftychis wrote:
           | tl; dr: The system is unstable as it has positive feedback
           | loops. You can "first day of class" think of it as the
           | implied series 1/(s-p) -- p the pole, s the Laplace variable
           | -- exists and converges. And in particular you want that
           | series to converge on the imaginary axis which means it does
           | not diverge in the frequency domain (Fourier transform).
           | Essentially, that means that you have regions of frequencies
           | where your system diverges/amplifies them excessively and
           | thus breaks down: is unstable. Filters do the opposite.
           | 
           | P.S. The other note is that for real linear time invariant
           | systems the region of convergence of the series/Laplace
           | transform of the system must be positive for the system to be
           | causal -- and thus real and implementable. So the joke could
           | also have been modified to get a magical and unstable plane.
        
             | pcthrowaway wrote:
             | > You can "first day of class" think of it as the implied
             | series 1/(s-p) -- p the pole, s the Laplace variable --
             | exists and converges. And in particular you want that
             | series to converge on the imaginary axis which means it
             | does not diverge in the frequency domain (Fourier
             | transform)
             | 
             | If this was the first day of any class I took, I would have
             | dropped it before the second day.
        
               | tinco wrote:
               | That makes me think of calculus in freshman's year. The
               | first week the prof explained all maths we had learned in
               | highschool, and then seemingly continued that same pace
               | every week, it was rough. Especially for some of the
               | smart kids who had never experienced learning material
               | coming at them faster than they could take it in. The
               | types who opened their textbook the night before the exam
               | and would ace it in highschool got a real test of
               | character.
        
               | angry_octet wrote:
               | That's why letting kids cruise in high school is a
               | terrible mistake. So many school systems are uninterested
               | in making sure everyone is challenged, especially in
               | maths.
               | 
               | University is good because you'll meet lots of people who
               | are smarter than you are.
        
               | Sohcahtoa82 wrote:
               | I don't even know how kids cruised in high school and
               | still got their diplomas.
               | 
               | I flunked out of high school despite getting A's and B's
               | on all my tests because I never did my homework which was
               | always at least 50% of our grade.
               | 
               | Trigonometry was so interesting to me as a 15 year old
               | that I decided to make it my internet alias. 95+% on
               | every test (even trig identities!), still got a C in the
               | class, with the teacher taking me aside 1-on-1 to tell me
               | "I'm breaking the rules to give you this C when I'm
               | supposed to be giving you an F because you only did 2 of
               | the 30 homework assignments."
        
               | hdjjhhvvhga wrote:
               | That's why I feel it's good to learn a bit about Laplace
               | transform for anybody doing anything technical. It has so
               | many applications you can hardly get away from it.
        
             | dreamcompiler wrote:
             | Acausal systems are implementable. They're common in signal
             | processing and even in some rather exotic control systems:
             | 
             | https://www.researchgate.net/publication/253627368_Feedforw
             | a...
        
           | Cerium wrote:
           | A control system with a pole (in the control systems sense)
           | in the right hand half of the plane will be unstable. If the
           | system changes during operation, the pole can move around the
           | coordinate plane.* As it goes from the left (stable) towards
           | the right (unstable) the system will begin to oscillate as
           | the pole crosses the Y axis.
           | 
           | In the joke, a Pole (person of Polish origin) was in the left
           | of the (air) plane. When they crossed the aisle to look out
           | the window, the (air) plane became unstable and crashed (pole
           | in the right hand plane).
           | 
           | *My control systems professor loved to explain using an
           | example of a driver as a control system. The system (car +
           | human driver) seeks to minimize error against the lines on
           | the road. If the driver starts drinking, one of the system's
           | poles will move right. The car will start overshooting first,
           | then will start weaving, before finally crashing when the
           | driver is too drunk.
        
           | dreamcompiler wrote:
           | Because if your poles are not in the left half [of the]
           | plane, the system is unstable.
        
           | [deleted]
        
           | ad404b8a372f2b9 wrote:
           | The weight imbalance from everybody rushing to the right made
           | the plane unstable.
        
             | 2-718-281-828 wrote:
             | this is the only answert to the question above and it's
             | being downvoted? welcome to hacker news ...
        
               | stephen_g wrote:
               | I didn't downvote it, because it's not a bad attempt at
               | an answer if you don't know the context, but the actual
               | joke is completely different and about calculus and
               | control systems. The right side of the plane is double
               | meaning for the right half of the _complex_ plane in
               | dynamical systems analysis, which is the area where the
               | real part of every point is positive. If your poles are
               | on the right half of the complex plane, then the system
               | is unstable and the output will tend towards exponential
               | growth (going out of control) for any change in input.
        
               | ad404b8a372f2b9 wrote:
               | The question is about the literal meaning of the joke, he
               | knows what a pole is within the context of calculus. He
               | didn't understand within the context of the joke what
               | lead to the crash.
        
               | lupire wrote:
               | It's a joke. There is no cause within the literal
               | context. The humor comes from word play.
               | 
               | After the plane crashed, one survivor was stranded in the
               | wilderness. Miles from civilization, he cried and
               | screamed until he got hoarse. Then he mounted the horse
               | and rode back to civilization. Back at home, he found
               | himself locked out of his house, since he lost his house
               | keys with his luggage on the plane. He sat on the porch
               | and sang various lamentations, until he found the right
               | key and unlocked the door.
        
               | ad404b8a372f2b9 wrote:
               | The joke relies on the fact that keys unlock doors, this
               | is the cause, just like the prior one relies on the
               | assumption that people rushing to one side crashes the
               | plane.
               | 
               | If there are 10 comments explaining what a key is in the
               | context of music and I add another that says "I
               | understand what the key refers to but how was the door
               | opened", one can only assume I lack the knowledge that
               | keys open doors.
               | 
               | Sometimes people understand the more complex behaviours
               | but somehow miss the simpler explanations, it's happened
               | to me before.
        
               | selimthegrim wrote:
               | There are enough actual LOT crashes he can form a model
               | on his own...
        
             | 22c wrote:
             | Interestingly, I recently spoke to a loadmaster who told me
             | that left/right side weight distributions are far less
             | important than forward/aft, to the point that for the
             | majority of aircraft they're loading, imbalance to the left
             | or right side of the plane aren't accounted for at all.
        
               | eftychis wrote:
               | Yes you want the center of mass to be more forward than
               | the center of lift. Otherwise, a small deviation in the
               | pitch becomes hard to impossible to recover -- the system
               | is unstable and stalls extremely easily. If that is a
               | fighter plane of course you want that, so you make sure
               | the opposite is true, and have a computer counteract that
               | during normal flight.
        
               | cwillu wrote:
               | I laughed the first time I made an airplane with the
               | centre of mass behind the centre of lift in Kerbal Space
               | Program.
        
           | tremon wrote:
           | A little bit broader than you asked for, but:
           | 
           | A dynamic control system is modeled by a set of dynamic
           | equations, usually expressed as partial derivatives. To
           | analyze the behaviour of such a system, the equation is
           | solved or approximated in the complex time domain. The
           | relevant part of the solution is where the real part of time
           | is positive, i.e. the right-half plane.
           | 
           | A pole is a coordinate for which the dynamic equations have
           | no solution (y = 1/z has a pole at z=0), which results in
           | undefined or uncontrolled behaviour.
           | 
           | (also see https://en.wikipedia.org/wiki/Zeros_and_poles)
        
             | JackFr wrote:
             | Honestly, this comment better than the article.
        
         | dreamcompiler wrote:
         | Did we have the same professor? Mine loved that joke too.
         | 
         | The students in the classroom next door always knew when Prof
         | Lipovski told his joke because everybody along the hallway
         | could hear the loud groan emanating from our room.
        
           | Natsu wrote:
           | I think all systems professors have the same joke book and
           | there's only one page in it :)
        
           | a9h74j wrote:
           | Heard a varient at Berkeley from a professor of Applied Math,
           | which you would probably no longer hear.
           | 
           | Generic airline, specifically Polish people were asked to
           | move to the left side of the plane. Because "Poles in the
           | right half plane cause instability."
           | 
           | (As for application in economics, economist Steve Keen, for
           | one, explicitly models time delays and dynamics, with results
           | worth learning from, AFAIK.)
        
         | ldite wrote:
         | And you know why the contour integral of Western Europe is
         | zero? Because all the poles are in Central Europe.
         | 
         | (sorry)
        
           | jimnotgym wrote:
           | As a resident of post-Brexit Britain, I was horrified as I
           | read this expecting it to have the opposite punchline and to
           | turn into an anti-immigration joke.
           | 
           | For those that don't know, Polish (and other Eastern
           | European) migration was a major issue raised by some in the
           | Brexit campaign.
        
         | selimthegrim wrote:
         | The real answer is Ilyushin made terribly finicky engines and
         | people skimped on maintenance but that's another story.
        
         | cperciva wrote:
         | There was nearly a disaster earlier in that flight too, when
         | the pilots got sick from food poisoning and the cabin crew had
         | to ask if any of the passengers knew how to fly a plane. As it
         | turned out, one of the passengers had flown many years
         | previously, and offered to try.
         | 
         | When he reached the cockpit, however, he took one look at all
         | of the controls on the modern aircraft and realized that he
         | wasn't going to be able to operate it. When the chief steward
         | asked why, he replied, "I am just a simple Pole in a complex
         | plane".
         | 
         | I'll follow lb1lf out.
        
           | [deleted]
        
           | drekipus wrote:
           | Now this made me laugh like crazy
        
           | danuker wrote:
           | It has a grain of truth to it. Poland could donate MiGs to
           | Ukraine, but other countries with US fighters could not,
           | because Ukrainian soldiers didn't know how to fly them.
        
             | Tuna-Fish wrote:
             | Actually not true. Many Ukrainian fighter pilots have
             | received training in the US, where they flew F-16:s. (That
             | is, before the current phase of the conflict.)
             | 
             | The hard part is actually the maintenance crews. A modern
             | fighter plane requires constant intensive mainentance, they
             | generally spend much more time being worked on than they
             | spend actually in the air. And this maintenance work
             | requires a lot of specific skills that don't necessarily
             | translate well or at all between aircraft types.
        
               | jacquesm wrote:
               | And a steady supply of parts.
        
           | jacquesm wrote:
           | Why did the man from Gdansk marry the woman from Zakopane?
           | 'Opposite Poles attract'.
        
         | gugagore wrote:
         | The article saying zeros (where the transfer function is 0)
         | when it should be saying poles (where the denominator of the
         | rational function is zero), right?
        
           | themeiguoren wrote:
           | Controls engineer here. The author's control theory knowledge
           | is correct - a RHP zero indicates that corrective action will
           | begin in the wrong direction (which the article compares well
           | with countersteering on a bike). The technical term is a "non
           | minimum phase system". It's possible this will lead to
           | instability, but in general the long term stability of a
           | system is determined by the location of its poles (which is
           | more applicable to the author's ice cream example). Poles in
           | the RHP will cause a system to blow up.
           | 
           | My gripe with the article is that the author tries to wow you
           | with some obscure technical points about a system which is
           | unmodeled and he does not understand, to wave his hands at a
           | vague conclusion. If he had made the same point using common
           | English phrases that encapsulate the idea ("positive feedback
           | loop", "we have to let it get worse before it gets better",
           | etc), then it would be a lot clearer how wispy his argument
           | is.
        
         | [deleted]
        
         | samfriedman wrote:
         | The version my professor told was, "Why is politics in Poland
         | so volatile? Because all the Poles on the right are unstable!"
        
       | woojoo666 wrote:
       | I don't think they should use the term right-half-plane zero if
       | they don't explain laplace transform and the s-domain. Just call
       | it an unstable system, or unbounded growth.
        
         | oh_my_goodness wrote:
         | The point of the article, perhaps not stressed enough, is that
         | there are _stable_ systems that can be very difficult to
         | control. Zeros in the right half-plane don 't indicate
         | instability. They indicate nulls in the transfer function for
         | unbounded inputs.
         | 
         | Poles in the right half-plane indicate instability. Zeros in
         | the right half-plane indicate something a little more subtle. I
         | believe the article is about the latter.
        
           | woojoo666 wrote:
           | Good point, I mixed up the two. However, the right-half plane
           | still refers to the s-domain so it doesn't make sense to keep
           | referring to the a right half plane without explaining what
           | plane it is
        
         | jbay808 wrote:
         | That would be a right-half-plane pole.
         | 
         | An explanation of the Laplace transform is coming! This is an
         | article, not a book.
        
       | parasti wrote:
       | This is weird to say, but I've never had this happen before: as
       | someone who's never heard of control theory, the initial
       | illustrations and the leading icecream example seemed highly
       | confusing and put me off from reading the rest.
        
       | magneticnorth wrote:
       | The follow-up article on inflation of shelter costs in response
       | to mortgage interest rates is also fascinating and worth a read,
       | imo [0]. The tl;dr is that in the medium and longer term, higher
       | interest rates will decrease inflation, but there's a right-half-
       | plane zero effect that will cause higher inflation rates in the
       | short term in response to interest rate hikes (with a lot of
       | simplifying assumptions).
       | 
       | [0] https://jbconsulting.substack.com/p/on-shelter-futures-
       | part-...
        
         | neilwilson wrote:
         | It's a little more complex than that because of the potential
         | feedback loop via the main price channel.
         | 
         | In other words if you can have a wage/price spiral you can have
         | a profit/price spiral and an interest/price spiral for the same
         | reasons.
         | 
         | [0]:https://new-wayland.com/blog/interest-price-spiral/
         | 
         | Once you abandon the concepts of general equilibrium and a
         | fixed amount of money for what happens in reality, then the
         | functional control mechanisms get a whole lot more interesting.
        
       | dukeofdoom wrote:
       | I watched this video in preparation for a Drone license test.
       | Really interesting stuff.
       | 
       | Human Factors for Drone Pilots
       | 
       | https://www.youtube.com/watch?v=UHYjl0u2UMA
       | 
       | Based on what real pilates need to know about human physiology as
       | it relates to steering airplanes.
        
       | [deleted]
        
       | voldacar wrote:
       | 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.
        
       | cheeselip420 wrote:
       | This is fantastic.
        
       | civilized wrote:
       | The article claims to be for a broad audience, and contains
       | insinuations of political relevance. But right-half-plane zeros
       | are a purely technical concept, and they're not explained with
       | enough technical detail to be air-dropped into the middle of a
       | broad audience piece.
       | 
       | It's almost good. It would be good if it dropped the pretensions
       | to technicality.
        
       | whycombinetor wrote:
       | The author lost all credibility when he said I have to
       | countersteer to turn my bike. The author is a "professional
       | engineer and consultant, specializing in feedback systems and
       | motors" too. There are >50 million cyclists in the US who would
       | presumably immediately recognize this as a false statement and he
       | didn't ask a single one of them to proofread.
       | 
       | Edit since some people are confused by this apparently: You can
       | steer your bike away from the edge of a cliff by _leaning to
       | initiate the turn instead of countersteering_. This makes the
       | author 's advice of "Don't ride your bicycle on the edge of a
       | cliff" much less critical.
        
         | mk12 wrote:
         | I'm curious how you're so confident about this. I think if you
         | ask most people (even most cyclists) what happens when you turn
         | the handlebars to the right, they'd say you turn to the right.
         | I cycle almost every day and I thought this for a long time.
         | Have you actually tried it? When I tried it, I found that it
         | forces me into a left turn.
        
           | whycombinetor wrote:
           | Have you tried leaning to the left while biking in a straight
           | line? It results in you turning left without your front wheel
           | ever having gone to the right (i.e., turning without
           | countersteer).
        
             | kazinator wrote:
             | > Have you tried leaning to the left while biking in a
             | straight line?
             | 
             | That is impossible. If you lean your body left while biking
             | in a straight line, the bike will lean right to keep your
             | center of gravity above the track.
             | 
             | For bike and body to be leaning left, the bike must already
             | be in a turn. Or else, it must be in the middle of a fall.
             | 
             | Two-track vehicles always begin a turn with a
             | countersteering move which induces a fall in the opposite
             | direction. Then the steering immediately switches in the
             | falling direction, to convert the fall into a turn.
             | 
             | (In the absence of wind anyway. A left turn could plausibly
             | start without a countersteer if a gust of wind blows over
             | the bike into a left lean; the subsequent left steer and
             | turn will supply the compensating acceleration to prevent a
             | fall.)
             | 
             | A bicycle is always countersteering. A bicycle whose
             | steering column is locked out, prevented from turning,
             | cannot be ridden. It will fall over.
             | 
             | A bicycle doesn't require a rider in order to maintain
             | balance, either. Above a certain speed, a bicycle can
             | correct itself. This is due to countersteering. Whenever
             | the bicycle accidentally steers slightly to the right, it
             | begins to fall to the left, and this provokes a left steer
             | which prevents a fall.
             | 
             | A rider who doesn't understand countersteering nevertheless
             | intuitively "bootstraps" the turn out of these small
             | wobbles, gradually increasing the tilt and and degree of
             | turn, through a sequence of small counter-steering
             | maneuvers.
        
         | adiM wrote:
         | One can always test the hypothesis via an experiment:
         | 
         | https://youtu.be/9cNmUNHSBac
        
           | whycombinetor wrote:
           | Indeed. I like this clip where they show bike steering to the
           | left, without its front wheel ever going to the right side of
           | its original path, by only leaning and no countersteering.
           | https://youtu.be/9cNmUNHSBac?t=445
        
             | kazinator wrote:
             | The video shows the exact opposite of your claim. The
             | bicycle is given an initial push by the experimenter. Its
             | steering is initially pointing a bit to the left. Because
             | of this, it begins falling to the right, and recovers by
             | steering in that direction, away from the guardrail.
             | 
             | The bike seems to be initially leaning to the left, because
             | it was induced into motion that way by the experimenter.
             | Yet in spite of this, it recovers by tilting to the right.
        
               | whycombinetor wrote:
               | Looks to me like 1. The bike is initially rolling
               | straight with no handlebar angle, and then starts falling
               | over to the left. 2. Due to the mechanic explained in the
               | video, this causes the handlebar to turn left.
               | 
               | If there was a human on that bike wanting to turn, here
               | they would continue leaning, turning, and pedaling in the
               | correct amounts.
               | 
               | But because there's no human to keep their weight leaned
               | to the left, then 3. The left turn of the handlebars
               | causes the road contact points to move to the left of the
               | center of gravity, so that 4. It starts turning right.
        
             | mk12 wrote:
             | That's with no rider on the bike. Earlier in the video when
             | he attempts to turn with the device that prevents
             | countersteering, he falls off every time. It seems unlikely
             | that 50M cyclists could easily do this but he could not.
        
               | whycombinetor wrote:
               | Now just imagine the possibilities _with_ a rider on the
               | bike. Being able to dynamically shift weight to either
               | the left or right side of the bike at will! You can even
               | do turns while riding with _no hands_.
        
               | kazinator wrote:
               | When you shift your weight to the left, the bicycle tilts
               | right to keep the center of gravity above the track line.
        
               | whycombinetor wrote:
               | If this were the case, you wouldn't be able to turn while
               | riding with no hands. Yet reality has us out here riding
               | bikes with no hands making turns.
               | https://youtu.be/_SWdCutqSWQ?t=73
        
               | kazinator wrote:
               | > _That 's with no rider on the bike._
               | 
               | That's irrelevant; bicycles countersteer to keep stable,
               | without a rider present (above a certain speed).
               | 
               | If the riderless experiment were repeated with a bike
               | whose steering is locked out, it would fall down rather
               | quick.
        
               | throwaway290 wrote:
               | The bicycle and riding style used in the video do not
               | provide a good illustration, I have no idea what he was
               | trying to do as he crashed repeatedly, and he did not
               | seem (or the frame prevented him) to use the ability of
               | his body to lean the bike into the turn, riding naively
               | (which didn't prevent them from talking down as if there
               | is a clear consensus in the field of bicycle dynamics).
               | 
               | At low speeds on e.g. a light MTB stop pedaling, lift
               | your butt off the saddle, lean bike far into desired side
               | balancing your body and handlebars to keep going
               | straight. You have most of what's needed to turn. You may
               | countersteer but your line does not veer into the
               | direction of countersteer, counter to illustrations.
               | 
               | Riding edge of a cliff is not a great idea anyway because
               | balancing a bicycle tends to require countless small
               | adjustments even due to pedaling alone.
        
               | kazinator wrote:
               | > _The bicycle and riding style used in the video do not
               | provide a good illustration_
               | 
               | It's good enough if you already understand it and know
               | what to look for; just not the best for convincing
               | someone who doesn't believe the physics.
        
           | dilyevsky wrote:
           | Heh was about to reply with the same video. It's really
           | counterintuitive even for people who ride a lot
        
             | CamperBob2 wrote:
             | It's counterintuitive to cyclists because we don't
             | countersteer. We lean instead, generally subconsciously. If
             | we didn't lean, it's true that we'd have to countersteer...
             | but nobody rides that way, making it a flawed analogy at
             | best.
        
               | dilyevsky wrote:
               | I'm not good downhill mtb rider but my understanding it's
               | really common technique there. Even on road i do that not
               | to take a spill in sharp-ish downhill turn going at speed
        
               | kazinator wrote:
               | You always countersteer; you're just not doing it
               | consciously. Because of that, you're doing it very
               | slightly. Because you're doing it slightly, you enter
               | into turns slowly. You're not able to take sharp corners
               | at a decent speed.
               | 
               | You cannot lean without countersteering first; the lean
               | happens because you induced a fall in the desired
               | direction, through a tiny countersteering move. With the
               | tiny, subconscious counter-steers, you induce only small
               | tilts. I suspect it takes multiple small counter-steering
               | maneuvers to "build up" a decent tilt for a sharp turn,
               | which takes time.
               | 
               | Once I learned to deliberately countersteer, I then
               | started doing it all the time. I hardly take any turn
               | (big or small) on a bicycle without pushing forward the
               | handle-bar on that side.
               | 
               | If you don't make deliberate countersteering your main
               | steering method, so that it becomes second nature, you
               | will not be able to count on yourself to use it in an
               | emergency.
        
               | CamperBob2 wrote:
               | Maybe you countersteer. I don't. I checked by riding
               | through a puddle, turning right, and then checking the
               | resulting trail left by the tires. No overshoot
               | whatsoever.
        
       | oh_my_goodness wrote:
       | OP: dy/dt = dx/dt + Ax
       | 
       | 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.
        
         | draw_down wrote:
        
         | dqft wrote:
         | Everything is fine. We are prepared and can handle the
         | situation(s). Everything is fine. It's fine. We have it under
         | control. Fine. We have the metrics and they're fine. Okay?
        
       | shreyshnaccount wrote:
       | My dynamical systems prof loved that xD
        
       | DeathArrow wrote:
       | Something I don't understand: on the one hand, people on HN seems
       | to enjoy this kind of articles. On the other hand, they upvote
       | any article who decries interviews where candidates are asked
       | things that involves knowing some theory.
       | 
       | So, if we think knowing theory is useful in cracking hard
       | problems, why is it wrong to asses its knowledge in an interview?
        
         | genezeta wrote:
         | While I don't claim to have _the_ answer to your question, I
         | think there 's a jump you're making that _may_ not be so
         | straightforward and somewhat explain things.
         | 
         | You say "people on HN seems to enjoy this kind of articles"
         | which seems reasonable, given the comments here. But then you
         | jump to "we think knowing theory is useful in cracking hard
         | problems".
         | 
         | Going from the first to the second is not quite so clear. That
         | is, someone may _enjoy_ such an article and even learning some
         | theory, but not necessarily because they think they will
         | directly apply it. People sometimes just enjoy learning stuff
         | or reading about it and then forgetting it.
         | 
         | You also make a second jump, because other factors may be
         | involved. Maybe the theory asked in the interviews is
         | completely unrelated to the things involved in the job. The job
         | may not even require cracking hard problems. These are frequent
         | occurrences -in my experience, at least-, and clearly seem
         | compatible with thinking that knowing theory is good in
         | general.
        
         | [deleted]
        
         | bee_rider wrote:
         | Programming and engineering are neighbors, so it is interesting
         | to see what's going on over there. But many engineering
         | analysis tools are not really useful for normal programming
         | jobs (unless you happen to be working on engineering software,
         | control systems, or something like that).
        
         | CamperBob2 wrote:
         | HN's readership isn't homogeneous. There's room for both points
         | of view.
         | 
         | I've done a lot of useful work in feedback systems without ever
         | really grokking Laplacian notation and the notion of complex
         | frequency in general. A lot of the actual numerical methods
         | used in real life boil down to a few canned formulas. But I
         | know enough about the underlying theory to appreciate where the
         | canned formulas come from, and fully intend to sit down some
         | day and go through the whole process. Articles like this are
         | interesting if only for the occasional gems in the comments,
         | such as John N.'s pointer to Maxwell's 'On Governors' paper
         | that I'd never run across before.
         | 
         | At the same time, I don't see much upside in making hiring
         | decisions on the basis of whether someone can regurgitate a
         | bunch of textbook math. I'd rather spend the interview talking
         | about control problems the candidate has dealt with personally,
         | how they were handled, and what the candidate learned from
         | them.
        
         | djmips wrote:
         | Because programming is rarely about cracking hard problems.
         | That's actually why the people HN enjoy the kind of article, it
         | takes them away from the drudgery of their job.
        
       | Animats wrote:
       | 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.
       | 
       | [1] https://en.wikisource.org/wiki/On_Governors
        
         | WanderPanda wrote:
         | In the real world all exponentials are sigmoids eventually, so
         | what we actually get is is a recession with a drastic
         | reallocation of resources (creative destruction).
        
           | duped wrote:
           | Not really, there are plenty that are sinusoids which are
           | just complex exponentials.
           | 
           | The real trouble with sigmoids is when the saturation point
           | is beyond physically meaningful quantities of the system. See
           | the tacoma narrows bridge collapse.
        
             | [deleted]
        
             | regularfry wrote:
             | Isn't it true to say that a theoretical exponential becomes
             | a practical sigmoid precisely because some property of the
             | system has become saturated and gone nonlinear?
        
               | LeonB wrote:
               | (Just trying to get this clear in my own head by writing
               | it down.)
               | 
               | When a real world system goes non linear (like the Tacoma
               | Narrows case) you don't get a sigmoid but something
               | catastrophic.
               | 
               | (If you graph the amplitude of the vibrations they
               | increase and increase -- and then -- if it was a sigmoid
               | they'd level out and stay at the max amplitude... but in
               | reality they go to zero as there is no bridge left to
               | vibrate.)
               | 
               | When a company is "growing exponentially" it may saturate
               | the market and then the growth slows in a nice sigmoid
               | function. That's common. But if, for example, the
               | investors insist that the company must maintain the
               | growth at all costs... it breaks laws, gets destroyed and
               | there's no company left to grow. No exponential curve, no
               | sigmoid, no signal at all.
               | 
               | Both the sigmoid and the total collapse are typical real
               | world results of what a simple model would expect to be
               | an unbounded exponential curve.
        
               | TheOtherHobbes wrote:
               | Control theory assumes the system is linear. As soon as
               | you get saturation the system stops being linear.
               | 
               | So in trad undergrad control theory instability implies
               | "And then the system blows up" - numerically, literally,
               | or sometimes both.
               | 
               | But depending on the system you can end up in regions of
               | recursive instability which are better modelled by
               | logistic/chaos theory:
               | 
               | https://en.wikipedia.org/wiki/Period-doubling_bifurcation
        
       | mattmaroon wrote:
       | I have a feeling this is going to be about interest rates and
       | housing.
        
       | steve76 wrote:
        
       | VogonPoetry wrote:
       | 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".
        
         | VogonPoetry wrote:
         | I have now read the followup article.
         | 
         | 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?
        
           | PragmaticPulp wrote:
           | I agree. The first article was interesting when it was
           | talking about control theory, but the hard pivot to economics
           | and politics at the end turned the article from potentially
           | informative to a disingenuous appeal to authority.
           | 
           | The author clearly knows a lot about control theory, but this
           | seems to have led to an idea that he knows a lot about
           | everything. This is a theme I see all too frequently in
           | people who list "systems thinking" as one of their areas of
           | expertise (like this author).
           | 
           | I have the benefit of the doubt and read the second article
           | looking for perhaps some actual modeling and references to
           | econ literature, but he merely refers to a couple papers and
           | then admits that his model was home-grown and will be
           | simpler. Some parts of it might be right, but this has too
           | many elements of "I'm an expert in one thing therefore I'm
           | qualified to talk about everything" for me.
        
           | dukeofdoom wrote:
           | Canada does not have 30 year mortgages. Most home owners have
           | mortgages with 3-5 year terms. Since 3-5 years ago rates were
           | low, and home prices were low, people's mortgage expenses are
           | still low. However that's about to end. As people either
           | bought at much higher prices in the last 2 years, and/or the
           | older mortgages are getting renewed at higher interest rates.
           | This will result in drastic increase in what people need to
           | pay to stay in their home.... possibly causing a market
           | crush.
        
             | VogonPoetry wrote:
             | Governments are in a privileged position to get this data
             | and they likely have it and have reasonable models.
             | 
             | The classic knob to influence inflation is interest rates.
             | This can be also be modeled. Non-politicised civil servants
             | have a good record of being able to do a reasonable job at
             | this - only if the politics are removed. In my opinion,
             | removing all political allegiance for civil servant
             | agencies is probably the best way to get better long term
             | stability and prosperity.
        
             | Sohcahtoa82 wrote:
             | > Most home owners have mortgages with 3-5 year terms.
             | 
             | As an American, this is easily misinterpreted to mean the
             | mortgages are expected to be paid off in 3-5 years, which
             | would be mind-blowing if true, because it would mean that
             | either houses are super cheap, or only the rich are buying.
             | 
             | IMO, adjustable-rate mortgages are almost a scam. Are there
             | any legal protections in place to disallow a bank from
             | deciding "In the next period, we're going to raise your
             | rate to 20% because fuck you the CEO wants another yacht"?
        
             | cecilpl2 wrote:
             | You are correct that in Canada we don't do 30-year fixed
             | mortgages. We only lock in interest rates for a 5 year
             | term.
             | 
             | However, we have what's called a stress-test. In order to
             | get a mortgage at the previously low 5-year fixed rates of
             | 2%, you still had to qualify as though the rates were >5%.
             | This means that if rates go up to 5% everyone should still
             | be able to afford their payments.
        
             | jimbob45 wrote:
             | 3-5 year mortgage? Aren't the monthly payments totally
             | destructive to one's financial health?
        
               | kspacewalk2 wrote:
               | The renewal periods are typically 3-5 years. The standard
               | mortgage amortization period in Canada is 25 years.
        
             | kspacewalk2 wrote:
             | >This will result in drastic increase in what people need
             | to pay to stay in their home
             | 
             | This will result in a drastic increase in what _a
             | relatively small number_ of homeowners need to pay to stay
             | in their home. Specifically, those who bought a house to
             | live in in the last 3-4 years.
             | 
             | >possibly causing a market crush.
             | 
             | Before losing their home, this relatively small number of
             | people (plus a larger number of those who will experience
             | much more moderate mortgage payment increases) will cut
             | back on spending for literally everything else. This will
             | have a very significant impact on the rest of our economy.
             | Which, in fact, is the whole point of inflation targeting -
             | cool down the economy when inflation is out of control.
        
               | btilly wrote:
               | _Specifically, those who bought a house to live in in the
               | last 3-4 years._
               | 
               | Also those who renewed in the last 3-4 years. Which
               | realistically means most of those who bought in the last
               | 20-25 years.
               | 
               | That's likely over half of all homeowners - not so small
               | a fraction after all!
        
               | davidgay wrote:
               | Yes, but interest is front-loaded on mortgages, so the
               | impact is much lower for those 20-25 years in.
        
               | kspacewalk2 wrote:
               | >Also those who renewed in the last 3-4 years.
               | 
               | No. Those who paid the exorbitant prices of the last 3-4
               | years. I've renewed recently, and borrowed the ~$100k
               | remaining on my mortgage at a historically low rate. If I
               | had to renew at twice that rate it would not make a huge
               | impact on my finances, because I'm currently paying
               | interest on a five-figure principal.
        
               | btilly wrote:
               | But it still would impact you.
               | 
               | Across all Canadians, we're talking about $1.5 trillion
               | (CAN) in mortgage debt. That's on par with the GDP. If
               | you hike the interest rates to match your inflation,
               | that's like sucking 5% of your GDP into interest
               | payments. This will be a pretty dramatic event, no matter
               | how it is distributed.
        
               | kspacewalk2 wrote:
               | It will certainly be a dramatic event, but it still
               | matters how it is distributed. To make up some numbers by
               | way of example, if 4 million people have to pay $50/month
               | more, I believe it has a significantly smaller effect on
               | the economy than 1 million people having to pay
               | $200/month more.
        
               | cecilpl2 wrote:
               | > Specifically, those who bought a house to live in in
               | the last 3-4 years.
               | 
               | No, everyone in Canada has to renew their mortgage at
               | least every 5 years, into whatever the prevailing
               | interest rate market is at that time.
        
               | kspacewalk2 wrote:
               | The vast majority of 28% of Canadian households who are
               | currently carrying a mortgage did not buy their house at
               | peak bubble prices, i.e. within the last 3-4 years. They
               | carry a much more modest debt load, have paid off more of
               | their mortgage, and this will significantly dampen the
               | effect of rising rates on their finance.
        
             | trelane wrote:
             | Wait, so all mortgages in Canada are ARMs by another name?
        
           | kspacewalk2 wrote:
           | I'll be that guy. Please don't hate me.
           | 
           | >So "pole" and "zero" analysis is mute.
           | 
           | Moot.
        
             | VogonPoetry wrote:
             | Yup, it should have been moot.
        
               | esquivalience wrote:
               | I spotted that but thought your original worked nicely
               | anwyay (it is silent on these things)
        
             | taylorius wrote:
             | I suppose if pole and zero analysis disagree with you, they
             | probably aren't going to say anything.
        
           | relaxing wrote:
           | Thank you for taking the time to write these follow-ups. I
           | was left with the same uneasy feeling at the end of the
           | article, and you've articulated perfectly why.
        
           | mellavora wrote:
           | > 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.
           | 
           | First person plural ("we") is normal in technical and
           | scientific writing.
        
             | VogonPoetry wrote:
             | Yes, agreed. It is a term of inclusivity that is applied to
             | observations and models, the testable items. I don't think
             | "we" it is acceptably used for individual opinions unless
             | it reflects the opinions of multiple authors.
             | 
             | The followup definitely uses the "I" (for opinion)
             | initially, but then switches to "we".
             | 
             | As a reader I am not a participant in "we" unless I agree
             | with the statements being made. I think it is this is what
             | made me frosty and say who is this other person, because it
             | isn't me.
        
         | Victerius wrote:
         | 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".
        
           | sebastos wrote:
           | Er, Ian Malcolm, the character who was introduced so that he
           | could arrogantly predict that the park would collapse, only
           | to get his satisfying come-uppance when... he turns out to be
           | completely correct?
        
           | Natsu wrote:
           | Why doesn't all the same analysis apply to your making of
           | "Ian Malcolm syndrome" itself?
        
         | starkd wrote:
         | I admit I was a bit disappointed by the end of the article. But
         | I don't think it was strictly an appeal to authority. The
         | author is evidently a very good writer, but he might have done
         | a better job at summing up a conclusion. It's very difficult to
         | tell just what point he was trying to make. He never even said
         | just what his inputs and outputs are in his housing model. Even
         | if he is saving that for a later article, he should have at
         | least mentioned that.
        
         | syntaxfree wrote:
         | "the math that I know is THE math to explain inflation,
         | political instability and more"
        
         | any1 wrote:
         | 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?
        
           | VogonPoetry wrote:
           | The context of the writer. Apologies if I implied that the
           | notation semantics were important -- letter exchange is free;
           | concept change is not. What I indented to mean was the use of
           | the terms poles and zeros is a bit wonky. Attempting to be
           | cute with a physicist's hat, a pole is a "black hole", an
           | entity you must not cross because the calculus will not work.
           | It is a discontinuity, a singular value. There are worse
           | things in mathematical generalizations; a cut / line in a
           | manifold. But tools to cope.
        
         | fluoridation wrote:
         | 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.
        
           | VogonPoetry wrote:
           | In this case the author (A) is setting themselves up as an
           | authority in (T). The statement (P) in this article has not
           | been revealed, but because (and I suspected separated) is in
           | the followup (which I have now read). The followup does refer
           | back to the "now you know about poles" -- the appeal to
           | authority.
        
             | hmry wrote:
             | Setting yourself up as an authority isn't a fallacy. It's a
             | rhetorical device. (Though I am not sure what makes you say
             | that anyway. The article didn't particularly strike me as
             | the author setting themselves up as an authority, beyond
             | what is inherent in writing an article that explains
             | something.)
             | 
             | If they made the argument "I am an expert in control
             | theory, therefore what I think about Canadian politics is
             | correct", that would be an appeal to one's own authority.
             | But I didn't see anything like that in the article.
        
             | fluoridation wrote:
             | >The followup does refer back to the "now you know about
             | poles" -- the appeal to authority.
             | 
             | How is that an appeal to authority?
        
               | VogonPoetry wrote:
               | In the classic social media sense.
               | 
               | You saw my post on X, now believe what I say on Y.
        
               | fluoridation wrote:
               | Would you mind pointing out in the second post the
               | sentence where that line of reasoning is implied?
        
               | yt-sdb wrote:
               | The person you're replying to already has answered this
               | question in a post you've already replied to. But to be
               | explicit, consider the first sentence of the follow up
               | post [1]:
               | 
               | > Now that you know what right-half-plane zeros are, in
               | this article I'm going to begin a deep-dive into a
               | control-systems-based analysis of a certain feedback
               | system that is drawing particular public attention today:
               | inflation.
               | 
               | In my mind, this is explicitly drawing a connection
               | between the author's engineering background, particularly
               | in control theory, and the current topic, inflation. To
               | be clear, it would be fine if the author wanted to make a
               | _mathematical_ connection between control theory and
               | inflation. However, since the author does not explain
               | right-half-plane zeros with any meaningful technical
               | detail, the rhetorical effect is an appeal: "just trust
               | me on this." Then the author switches topics _and
               | explicitly connects the two topics_. I cannot speak for
               | the person you're replying to, but this rhetoric is what
               | bothers me.
               | 
               | [1] https://jbconsulting.substack.com/p/on-shelter-
               | futures-part-...
               | 
               | EDIT: Looks like VogonPoetry already replied while I was
               | typing this up.
        
               | VogonPoetry wrote:
               | These:
               | 
               | "Now that you know what right-half-plane zeros are, in
               | this article I'm going to begin a deep-dive into a
               | control-systems-based analysis of a certain feedback
               | system that is drawing particular public attention today:
               | inflation."
               | 
               | And all of the statements made in the walkback "a bit of
               | a preamble" -- basically issuing caveats or disclaiming
               | all of what was said before. A classic "I got you here",
               | but I'm going to disclaim all of that, you are a fool to
               | read anything that follows.
        
               | fluoridation wrote:
               | I read that as "now that you know some of the concepts
               | and terminology used in systems theory, I can use them to
               | make an argument in economics, and you can use that
               | knowledge to judge for yourself whether the argument is
               | valid or not". It's literally the opposite of a appeal to
               | authority. As I see it, the only way it could be
               | dishonest would be if the systems theory explanation is
               | incorrect or purposely leaves inconvenient things out
               | (which it might).
               | 
               | It would be an (incompetent) appeal to authority if it
               | said "now that you've seen that I know my stuff when it
               | comes to systems theory, you know that this thing I say
               | about economics is true".
        
               | dahart wrote:
               | > As I see it, the only way it could be dishonest would
               | be if the systems theory explanation is incorrect or
               | purposely leaves inconvenient things out (which it
               | might).
               | 
               | That should be the default assumption, no? Today's
               | Control Theory has never been shown to be predictive of
               | the economy or politics, wouldn't you agree? The article
               | framed the discussion as if control theory is useful,
               | purposely implied it's utility, and did not state it's
               | _known_ lack of scientific validity, which is indeed
               | leaving some very inconvenient facts out, right? Saying
               | that they left it open with a 'judge for yourself' is not
               | a great counter to the critique of the argument style.
               | There is an intentional framing here that fails to list
               | the alternatives, tries to establish itself as 'correct'
               | via implication, and pivots to a separate topic that is
               | unproven to be relevant. Pretending to be unbiased while
               | presenting a one-sided set of "information" is a pretty
               | common type of appeal to authority.
        
               | fluoridation wrote:
               | I'm not particularly interested with whether the argument
               | raised by the article is valid or not, which is why I
               | left open several possible ways in which it _could_ be
               | fallacious. My point is solely that it 's not an appeal
               | to authority.
        
               | emaginniss wrote:
               | So if a school teacher taught you addition and then later
               | used it as the basis for teaching multiplication you'd
               | reject it because they were referencing their own work on
               | addition?
        
               | VogonPoetry wrote:
               | This is complicated. It involves identity, credibility
               | (accreditation), reputation and authority.
               | 
               | For me to be taught, my parents ceded authority to the
               | school to appoint credible teachers. Those teachers will
               | have an identity, qualifications and perhaps a
               | reputation. There are consequences for failing or abusing
               | this position.
               | 
               | This is the way a lot of traditional things work.
               | 
               | To directly answer your question, no. A teacher that
               | taught addition would likely be excellent for teaching
               | multiplication.
               | 
               | But, I don't think this is how the internet now works,
               | especially in the social media space. There is infinite
               | identity, which creates trust problems for reputation and
               | credibility. Applying traditional models breaks down. At
               | the moment the dominant factor appears to be who can win
               | a popularity content.
               | 
               | Hacker News is interesting in that karma is currency to
               | build credibility and reputation. This model has flaws
               | too. In my opinion, rewarding the most popular is not a
               | long term winning strategy for a society or community.
               | The demand for change only comes from dissenters.
               | Dissenters and different opinions are the engines of
               | change for any society / community, otherwise, without
               | change, it would stagnate and fall into decline.
               | 
               | But, in the face of infinite identity what is the
               | collective actually trying to say?
        
               | fluoridation wrote:
               | I find it pretty funny that you're accepting one claim
               | _because_ it comes from what you think is an authority,
               | while rejecting another because you think it relies on an
               | appeal to authority.
        
               | paledot wrote:
               | No, but I wouldn't trust them if they referenced their
               | math experience as a qualification to teach me SCUBA
               | diving.
        
               | relaxing wrote:
               | An elementary school teacher doesn't need to rely on
               | appeal to authority to teach math. The student can
               | quickly verify the method works themselves -- they don't
               | have to take the teacher's word for it alone.
               | 
               | In general, appeal to authority as a fallacy applies to
               | subjects that are opinion-based or contentious.
        
             | starkd wrote:
             | Actually, it seems more an effort to establish credibility.
             | "I have a degree in such and such" or "I have worked in
             | this field for over 20 years". That seems to be much
             | different than appeal to authority.
        
               | throw10920 wrote:
               | It seems to only be an appeal to authority when it's a
               | person or a position that one disagrees with. Otherwise
               | it's "experience" or "consensus".
        
             | Natsu wrote:
             | What makes appeal to authority fallacious is that one's
             | supposed expertise has no bearing on the truth of the
             | things one says. An appeal to authority is when someone
             | argues something like, "I'm an expert, I think X and so
             | should you" basing their opinion on X on their supposed
             | expertise and not actual logic.
             | 
             | When someone gives reasons, their argument rests on those
             | reasons, not on their supposed authority as an expert on
             | the topic.
        
         | TimPC wrote:
         | The follow-up article tries to argue there is an over five year
         | lag to interest correcting inflation based on undisclosed
         | principles of a model they don't provide equations for. Their
         | argument is in effect that the growth of roughly 30% of the
         | inflation basket of goods (housing) dominates the shrinking of
         | the other 70% of the inflation basket of goods. The analysis is
         | suspect as they don't seem to model how much the 70% shrinks or
         | slows in growth at all. They also aren't very numerically
         | precise on the interest effects on housing prices and
         | misanalyze how mortgages work in Canada.
         | 
         | Their analysis argues that roughly 4% of mortgages are replaced
         | every year while 96% retain the same rates. This makes it hard
         | to argue interest rates have the desired effect size but that
         | doesn't stop them from trying.
        
           | jbay808 wrote:
           | > The analysis is suspect as they don't seem to model how
           | much the 70% shrinks or slows in growth at all.
           | 
           | It doesn't model it at all. The trajectory of ex-shelter CPI
           | is taken as an input. For the provided scenarios, all non-
           | shelter components are assumed (as a scenario _premise_ , not
           | a prediction) to instantly return to a 2% growth rate and
           | stay there.
        
         | TimPC wrote:
         | 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.
        
           | jbay808 wrote:
           | The RHP0 in (Canadian) housing comes from including mortgage
           | interest payments -- a term that increases in proportion to
           | interest rates -- in the measurement of the CPI.
        
         | CFLAddLoader wrote:
         | 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.
        
         | yt-sdb wrote:
         | 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.
        
         | skybrian wrote:
         | 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.
        
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