School

School is going well, teaching "ASEN3128" at CU.

I'm writing this mostly for myself, so apologies if you're a reader and find this post boring. Somehow writing for publication makes this seem easier than just scribbling it down somewhere. Or maybe it's because it's so easy, I don't know.

Anyway, I am developing a...

Lecture Style or Pattern

It has several parts: First there's a review. This is just repeating what happened in the last lecture.
Second, a hook.  To get them interested, calmed down, and foreshadowing the day's topic.  Sometimes I use the hook as part of the summary so I guess I'm not rigorous about it pertaining to the new material.
Next of course is the body of the lecture. There are lots of sub-topics here. Last is the crescendo. It's supposed to be a surprise opening up a new area to think about. Some examples will clarify.

Lecture 1: Hook: picture of an airplane window: nothing seems to be happening. It is as if there is no motion, and this is balance, this is trim. Course outline.  Discuss longitudinal trim, CMa and CMq and CMde. The many dichotomies of this course: trim vs perturbations. s vs z, Laplace vs integration, TF vs SS, Block Diagram Algebra vs Matrix notation, roots vs bode, decay vs oscillatory, Euler vs Quat. Numerical simulation of low pass, and hints of chaos. Of course these were discrete simulations, F(z), but we didn't touch on that much.

Lecture 2: The review was the stability derivatives & dichotomies. Hook was the chaos simulation, showing how its nonlinearity makes it insoluble. Direction Cosines, and the network diagram method of deriving them instantly. Crescendo: Quaternion is that one vector which is unchanged by a DCM. Stability Axes

Lecture 3: Hook = Close your eyes and imagine you're on a beach, running for the frisbee. Invert the scene with a rolling dive.  Here the hook was actually part of the review of DCM.  Meat was roll subsidence and stability axes. Stability derivatives with units of 1/t, and normalizations to get there. Introduction to block diagrams. Introduction to [A]x = sx as an eigenvalue problem: find eigenvalues of [sI-A]=0

Lecture 4: Hook = throwing tennis ball. Experts just catch it. Experts can guess the right answer. We will guess the answer is exp(at) or exp(st). Metapor for a match, which is a useful tool that separates us from the animals. We need to be good match (Laplace method) users.  Body of the class to discuss roll subsidence from two perspectives: Laplace method (d/dt --> s, crack the poly, then "just know" the pattern from roots to dynamics) and formal integration of the differential equation (much harder) required an integrating factor, integration by parts, homogeneous and particular solutions. Showed the root::dynamics correlations, speed for real roots, frequency & damping for imag ones.  The crescendo was discussing rolling a tennis ball across the floor: it would go forever. That was a *very* slow/large/long time constant, zero in fact. 1/(s+a) with a going to 0.  We did NOT get to Laplace Transforms, which is another method, requiring convolution and inverse-Laplace{F(s)}.  We did not get into numerical simulation but we certainly will.

Lecture 5: Bigger review 'since quiz next time. Homework review: what does a matrix [Cib] do to an eigenvector? Nothning; lambda was 1. How about a matrix [A] (multiply, to attenuate, but not to change). The bulk of the lecture will be on stability derivatives, and more trim, lateral this time.

Lecture 6: Quiz.

Lecture 7: Laplace transforms: computing some.  1, t, exp(at) sin?, L{f(t)}Using Lspecifically convolution of impulse response with step. LPF (something you might do explicitly in code)


Lecture 8: Pitch Short Period. Weathervane without a wing. Surprise, q integrates to give alpha (as well as theta). Without a wing that's clear.  It's a demonstration of Euler's equation, too. Full EOM (pitch)


Lecture 9: Rocket is not am inverted pendulum. Aircraft is not a pendulum. The force does not produce a feedback that changes the orientation & hence the force, as it does in the pendulum.

I need to do this for office hours a little bit too, because there's the one-on-one Q&A which is ineffective, but maybe necessary if students are afraid / embarrassed.  Just general Q&A about the homework is a good forum to explore confusions, but I'd like it if that were classroom-wide

Review of "Collapse"

Collapse: How Societies Choose to Fail or Succeed by Jared Diamond

My rating: 3 of 5 stars

Jared Diamond starts off with one star and an uphill battle since I thought GG&S was shameless profiteering from a pamphlet sized idea. That's prejudice for ya, folks! Don't worry though, my convictions are just as ductile as they are forceful. I'll be happy to eat these words later, like always.

Ok it's later...

I have warmed to Diamond's presentation somewhat, though I still think it a flaw to expand this idea to 500 page format. Lots of the details are fun if you're not in a hurry so I was going to let that cricicism go until late in the book we were treated to a comprehensive list of every baseball player from the Dominican Republic ever to make it in the big leagues. To no useful end, it is surely superfluous to add? Really, Jared? This book requires more skimming than anything, ever.

Tainter's Collapse is a great foil for this book. Here, I'd like to consider Greenland only, just as a case study, sort of comparing Tainter & Diamond's themes. While Diamond describes a panoply of factors and their various interactions, the short story is: they starved to death. My question is why the settlements collapsed catastrophically instead of finding a lower equilibrium within the carrying capacity of their environment?

As with Tainter, "control systems" provide an interesting insight that instability requires some kind of net "bad" feedback in order to run away out of control. Development of such instability is abetted by delays and momentum. There are fancy terms for these that I'll eschew, but you can imagine the effects of delay in noticing the trees are running out: you get "surprised" by a challenging problem. The basic question is how, in the face of diminishing returns on (technological) investment, population doesn't level off instead of collapsing? In microcosm of Greenland, I think Diamond makes a pretty good case for a terminal crisis.

In some good expansion years, population could rise while an insidious debt is being incurred, "flaying the outfield" for sod homes faster than it can be renewed, clear cutting timber, and raising sheep and cows that further degrade the turf. The population, their homes, their animals all represent the momentum needed to carry the economic balance between the Vikings and their environment from "challenging" over into "desperate." I describe it as "momentum" because you NEED those animals for cheese & meat, turf is NEEDED for fodder and homes, and so these are commitments from which you can't easily turn aside if the grass runs out. So, in the space of a couple of bad years, maybe precipitated by an atypical snowstorm, a crisis arises, the stock get gobbled and everybody dies.

Why did the Greenland Norse not see trouble coming and reduce their demands on the environment? Did they have no foresight at all? Here's a three part answer to that.

(a) tragedy of the commons (selfishness trumps global foresight),

(b) foresight's actually difficult to come by. (hey does America operate on a balanced budget, reducing the debt in "sunny" years? We STILL have no foresight, or at least don't act on it.) and

(c) well, no actually they really didn't see it coming: they didn't understand carrying capacity or soil erosion & so would have more vague ideas of impending environmental crisis.

He titled the book "how societies CHOOSE to fail or succeed," but I don't think it was all that conscious a choice.

Another thesis one could explore in this book is: "Religion takes the cheese, even if everybody starves." This is perhaps a more understandable root of the Mayans' more prolonged wilting, and draws attention to the joining of church and state. It's not religion per-se but the chiefs, which two groups in those days were nearly indistinguishable, that ruled, and continued to demand fealty shiny trinkets and big stone houses whatever the cost.

Last and scariest, what if it's (drum roll) CHAOS?! Not to go all Jurassic park on you, but we certainly don't understand all the ways life interacts and it's not written in stone anywhere that things are guaranteed to come out ok or behave in stable fashion. Maybe societies collapse for reasons that are essentially ineffable, or at least so complex and nonlinearly coupled as makes no difference. It's certainly possible the Norse didn't see it coming. The Easter Islanders? That's harder to excuse, isn't it? Chopping down the last tree and all. I'm tempted to blame them for a Onceler-ian selfishness & failure to cooperate; tragedy of the commons sort of collapse.

For us, for all of modern 21st century society, arguably doomed to stand or fall together, maybe it's gonna be Chaos (and chaos, too) since we can't so far agree on what the problems are and what to do about them.

But I am working hard to find some cohesion, some theme. Diamond makes no such attempt, beyond listing five factors which go beyond pedantic: warfare, trade, environment, I can't even be bothered to enumerate them. Environmental mismanagement is surely the core idea, though he won't quite come out and say it that clearly. Indeed his fifth cornerstone is actually made of three more minicornerstones, and they themselves vague and broad enough to support many fractal recursions thereupon, as "fleas hath smaller fleas... and so on ad-infinitum." Sigh.

A closing note, Tainter said something about us ALL not being able to collapse together as a unit, because he felt you had to collapse in relationship to something. So if human society is now one big monolith, then we can't formally undergo a collapse by Tainter's definition. (Interesting. I need to go back and reread that bit.) Yet, Diamond's cautionary tales of history surely seem to suggest something bad may happen. Let's just call it "severe, comprehensive involuntary lifestyle retrenchment. heh.

Last, to be unambiguous: this book deserves 3 stars for being thought provoking, not for itself containing cogent thoughts. Instead it's a compendium of factors. As for synthesis, Diamond just leaves us hanging in a maelstrom of minutae.





View all my reviews

Tribal Economy

Just listened to NPR's Planet Money on "the Past and Future of American Manufacturing."  It was quite a distressing podcast lamenting the loss of manufacturing jobs, wondering how good but unskilled laborers would fare in the future where manufacturing is about finesse and programming, not stamina.  The host, right after being told he would never be hired to program NC milling machines, wondered how the show's protagonist, a hard working aggressive young mom named Matty, could ever get uptrained.  The fearful conclusion was she wouldn't.

It's ironic how Adam Davidson worried about Matty's future, right after being told he himself also had no chance at that job either. I don't think getting everybody "trained up" to operate an NC mill is either needed or practical. We really do need only 1/100 as many combine drivers as scythe swingers. What an astounding efficiency gain! As they poignantly illustrated, there's tragedy here, because the machines have CREATED value, so overall life for everyone should be easier,, not tougher. Nor do I believe is it as simple as, "well there're are more of us now so the times are just as tough as ever."  Here's an illustrative fable.

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Thor paused, sweating.  His log was the biggest and he was in front, but he didn't need to rest.  The stop was because Ting the chief had just showed up on the crest of the next rise leading 4 of those strange new animals, "horses."  What would happen now?

The tribe was half way through their annual migration. Each year, the women built travois' and hauled the family's tent and few goods some 200 miles from the rich timberlands up north down to the arid grasslands.  The men hauled timber.  These logs were prized material to make bows & tentstakes among the hunter gatherer tribes of the south, and they'd trade food and furs that made the trip a productive annual event for the Ting tribe.  Some rich chiefs even had astounding "tents" made entirely of tree slabs stacked close, to keep out every whisper of icy wind.  They were luxuriously comfortable: the demand for the tribe's product seemed limitless.

Now old Ting had horses. He was even riding one.

"Thor," he said, looking down at his strongest haulsman while the others came up , variously puffing or wheezing according to their exertions and the ambition of their load, "things are gonna change around here."

"How, lord Ting?"

"We've got horses now.  We don't need all you men pulling.  A horse can haul as much as 3 men, and feeds itself along the way, so your job ends right here, on this hilltop.  From now on, your wife will ride, you can pull her travois with the tent on it."

"I can go twice as fast pulling that little thing.  Who'll keep up with me?"

"Well," Ting said, "the horses will be heavily loaded, so we won't go faster, but instead we'll just have more logs to sell.  If you get too far ahead each day, maybe you can do a little fishing, or nap.  Whatever."

~ ~ So, that's how it COULD have gone.  But as you know, on that day Ting instead left most of his tribe to fend for themselves. He had a horse and that made him rich and put the rest of the tribe out of business.  That pretty much set the pattern for the rest of history.

Why doesn't the largess of our technological advance translate into a more idyllic lifestyle for everyone?  

It's easy to do the "energy balance" and see that tools, animals, machines and oil have each multiplied our ability to get things done. These should have the effect increasing the potential leisure and comfort, supporting a greater population, or some combination of those. That we always choose option #2 seems like a problem in our programming.

Even if we preferred leisure over consumption, there is still a problem of distribution.Everyone needs to benefit from the technological improvement, but ownership tends to concentrate, as the return on investment allows Ting (and nobody else) to buy another horse. Would stock ownership allow the little guy to buy a small piece of the technology? Why hasn't that worked.?

If ancient Norse beer technology advancements doubled yield, why couldn't everyone just have two?  It seems a simple calculation, but maybe it's the problem as well. First of all, everybody has to increase their consumption to keep full employment or, in the case of items with intrinsically limited demand (ok so not beer, but there must be something...) the technological advancement, whether the horse or the automated brewery, brings a reduction in employment as a nominal consequence.

 The benefit is the commodity price drops thanks to lower labor, but what's the laborer supposed to do?  You obviously can't put the reduced price genie back in the bottle, nor is dragging logs by hand any longer a viable livlihood. You can't compete with a horse just as John Henry couldn't compete with a steam hammer. Is a requirement for growth the consequence of advancement?  Cold bloodedly, in the absence of consumption growth, starvation will eventually balance the labor market to the need. More hopefully though, assuming constant GDP (same number of logs dragged) a pair of hands has been idled, that's potential to create more wealth for us all to share. That's if we can gracefully repurpose and retask the displaced individuals, but why not?  Humans are flexible creatures. Maybe now Thor will carve totem poles the plainsmen can afford to buy since logs are cheaper. This is growth.Is there a problem?  Well, maybe. Another stable balance would involve MORE plainsmen consuming all the logs that could be supplied even with horses. Everybody's still pulling for all they're worth.  Subsistence, only more of it. This scenario need only arise if we wastefully expend every technological windfall in the name of more human mass until (see Collapse of Complex Societies) we are dependent on all the latest gizmos just to get by. Problematically, it seems the natural outcome.

Good day brewing yesterday. Hoping for a pilsner. It came out very strong: O.G. 1.059!