Airplanes for CU!

Feedback from the class, some good: "Amazing lectures!" and... "Prof Krebs is great.  He does a great job of connecting the dots and gives is an intuitive understanding of what's going on, more than just writing down equations.  I have learned more in this class than any other class combined ."

...and some bad: "...doesn't explain what's the point in lectures, doesn't provide any context to what he's talking about. Does zero examples."  and "I don't like the disorganization.  I think it would be helpful if he came to class with a written out lesson plan rather than in his head."

Overall, there are stronger emotions behind the negative comments than the good, and more of them, too. :(

There is no mogul: ...the ontology of Outhouse.

In a cherished conversation with Miles, I once claimed you could ski bumps blind just by feeling the first one. The rest follow naturally, from the rhythm of the universe, the giant fft that is us all (or wavelets, if you like!).

The best quote from the matrix  has to be the kid breaking out, "Do not try to bend the spoon — that's impossible. Instead, only try to realize the truth: there is no spoon." Once mentioning the matrix, we cannot continue without reviewing Carl Sagan's apple pie. (and of course the musical rap cover.)

This post offers some notes on Ontology.

Here, we are going deep into Meinong's Jungle, wherein prowl pegasii and unicorns, which must subsist in some sense since we can talk about them.  This is Meinong's Gegenstandstheorie. Apparently, there are many levels of "real," if you think about it hard enough.

Oh my God, WTF is happening here? This blog has gone crazy!  Well, yes, sort of, but there is some scrap of coherence here, I think...  It all started when a student asked, "what is i, anyway?"  I was stumped, and I pretty much still am, but here is my answer anyway.  Obviously it's a complicated one, but, here goes!

First, let's get rid of the obvious canonical answer: i = sqrt(-1), but you knew that.

Now, what do we make of this?  Well, there is at least some major utility to it, eh?  Never minding whether or not i is an actual part of reality, I mean.  It's a nice tool, like a number line, or a bubble level: helps you figure things out. Sort of like saying "my very educated mother just served us nine *pies," it's a construct you can use whether or not it has any meaning grounded in reality.
(* Sorry, Pluto's not a planet.  Don't blame me, take it up with this guy.)

Let's look at some of the utility we get from i.  For one, consider helical antennas!  They make circularly polarized radiation and that is really neat. I once worked on a satellite that used those. That tubular structure in the picture is a multi-element quadrifilar helix.  The polar coordinate representation of exp(i*theta) is a visual model for all kinds of oscillatory phenomena, including the motion of airplanes.

Here's another example of something you can do with i. You can take the cube root of 1!  What, you're not impressed?  How many cube roots do you think there are?  (Hint:  thew sqrt of 4 = +/-2, right?  Why should it make sense to have two square roots and only one cube root?) Actually plain old +1 does have three cube roots (as it should) and they are 1 and  -1/2 +/- sqrt(3)i/2.  You don't want i just to get the root of -1, you want it even for mundane cube roots of plain old positive numbers!

Renee Descartes disagreed. He found i a lamentable necessity and saddled it with the pejorative "imaginary" label, but that, we'll see isn't really fair.

** ToDo: Put something intelligent here in the middle... ***

So the answer takes us full circle, back to the spoon only rephrased like this:  "Do not ask if there really are imaginary numbers. That's impossible. Instead, only try to realize the truth: the real numbers are all imaginary."

Holding The Bubble

Some days I go through life unconscious. Such days are indulgences, involving exercise, reading, food or music.  By "unconscious" is meant just letting the day happen without thinking too much about what's next. A summer hike in the mountains is one good example. Sunshine, the crack of a rock against another, a feathery misty rain I remember once, a sandwich & friends: these things make life somehow seem easy.  It's not hard to make recreational excursions graceful.

Other days, the world seems out to get you. Bad sleep, a hectic commute, an argumentative meeting; these are all minor stressors.  Concern about making payroll, paying for college, medical  worries, those long range planning activities are bigger issues.  It's a good goal to get through these things "gracefully."

Gracefully? That sounds crazy doesn't it?  I'm more of a straight-ahead person than a dancer so grace generally isn't my thing, but the word isn't entirely inappropriate.

Work is another story entirely. At some basic level, companies fight for survival. There are fights within companies too, or at least various agendas, some of them helpful and some just destructive.  I feel it's my job to create a bubble of safety and happiness, for my family, around my friends, and at work too.  That is meant to be a sunny place where people can feel they don't need their guard up.  Inside the bubble you can do your best work, you don't have to be on guard against enemies, your blood pressure can ease down.

I've realized I have even tried to make my office that way.. I mean the operation here as a whole, but my physical space too. It makes me feel good to be there & hopefully others too. Work ought to be a refuge of sorts from the big bad world.

The classroom's also a bubble. The kids don't realize it at first, but they're safe there. I'm trying to make them smarter, not fail them.  It takes a while for that to sink in.  I had an evaluation done, video taken, surveys tabulated.  The teacher said they're being hypnotized, they're not taking notes.  I need to engage them, break the spell they're under.  That's double edged! I'm glad they're in a trance in our little tribal meetings but of course they need to take notes.  Anyway, you get the point.

Sometimes though, it's work to hold the bubble up. Like an overcast of thick wet newspaper slurry wants to smack it down and I have to press back to keep the little sunny sphere open. It's tiring. I don't know how big a bubble I can hold open, how much longer.  Plus, it's cold out. We all need to help keep it going: it's a kind of magic, and it needs us.

Strange thoughts, eh?

Science Friday, speech decoding

On Science Friday Ira had one of his occasional fantastic guests. He was exploring the brain, recording and playing back words.  On the radio, you'd hear the actual spoken word, then you'd hear the consequent brainwave. It was intelligible, barely.  While the research was really cool, on reflection it didn't seem so strange that there's an electrical signal running around in your head that sounds like "chair" when I say "chair."

Then I started to think, "what will it sound like as they go deeper in?"

Following the signal chain from that word to the muscle commands that make you sit down, I'm expecting a more and more pulse-like burst of signal, less of a chair, and more of a databit.  What are the internal symbolic representations of words, the things with meaning?  Are they still vaguely "chair-sounding?" Or are they structurally encoded, just a data bit, but WHICH data bit, which networks activated that matter.

Writing it now it still sounds prosaic but I was really enthralled at the time. Maybe worth a listen.

Diamond vs Tainter

@Adam: I'm also very interested in the Tainter/Diamond comparison.

Diamond sez Tainter sez "how could you not anticipate a problem & fix it?" It's a fair assessment of some quotes from The Collapse of Complex Societies. (I linked my review.)
From that conundrum Tainter goes on to describe a dynamic (this oft mis-used word fits precisely here)wherein the society enjoys a benefit of technological progress, grows to consume the benefits, & thereby becomes irrevocably committed to it.  Tainter adds that more technology, our only solution (eg to world hunger) may actually not work because of diminishing returns.

This is a fancy way of saying "didn't see it coming"  so when Diamond cites that cause, he's agreeing with Tainter. Diamond divides and enumerates while Tainter tries to understand why. Both are forms of analysis, but not equally good. Diamond is exceedingly thorough, but fundamentally shallow. While both latch on to human self interest as impediment to doing the right thing, Diamond has only "didn't see it coming" and "tragedy of the commons" for rationale, though he takes a dozen pages to say it. Maybe I should say he takes 500 pages to say it! Tainter’s cause is far more nuanced, and complex enough to be the rationale for not foreseeing or effectively mitigating a problem, even if you wanted to.

Tainter’s approach is so tricky that he himself cannot explain it succinctly and instead has to spend much of the book illustrating the problem, carving away around the edges to indirectly describe it’s core. Thus, I’m sorely challenged to pack it in a nutshell! Here’s a try...

Tainter draws an arc of diminishing returns from technological investment that eventually flattens out entirely and then slopes downward!  How could this be?  Adam, I think you’ll like my answer that it’s essentially because of externalities. The accurate cost/benefit analysis in determining whether to buy the latest fertilizer is miscomputed by the farmer because the numerator is misquoted to him in the form of an incomplete accounting behind the price tag. Somewhere the last island of bat guano is being strip mined to make that cheap fertilizer, which lets Iowa support a larger population which intrinsically requires the higher crop yield. The people have to eat. The tractor has to eat. The people move off the farm and build iPods and strip mining machinery Then one day the fertilizer runs out.  Not so different from the last tree on easter island, but you can more easily see how it could sneak up on you. It's just the tragedy of the commons again, made indirect, far away and invisible.

Tainter would probably amplify on my example by describing interconnected webs of dependency, more fragile and less obvious than the fertilizer one. Have you heard Greenspan’s stump speech about the latte? (worth googling) A latte for a couple bucks is a triumph of technological society. Not so long ago, only royalty could aspire to such a concoction and now we all can, but it’s supporting infrastructure is not robust to challenge.   A big steel boat is efficient, but fragile. Put a hole in your wooden dinghy and at least it will still float and you with it.  

Why do we go over the cliff?  Why can’t we retrench to sustainable levels when something complicated gives way? Why are crisis and collapse required?  


When more children are born in Greenland and more outfield flayed to make their houses. You could go back, but some of those children would have to starve. I think Tainter would say the technology itself comprises the momentum, not just the bellies, but I can’t quite defend that part.  Can’t I un-commit to technology?

You can’t just rescale us without a nonlinearity.  There's this thing, the "back side" of the power curve.  There's a minimum drag point, fly faster or slower and you need MORE thrust.  Fly a little slower, add a little thrust, do that for a bit and you're in a tough spot because now it's unstable: if the thrust drops even just a little you can't get back to the normal linear range but instead will slow down until the nonlinearity: stall.  There's a solution in the airplane example just as there is in real life, but it's painful: you have to give in to the inevitable, dive and lose altitude (lose luxury, sacrifice population) to slide down to a sustainable situation.  This is a pretty good analogy, and the Lift-Drag curves even match Tainter's curves in the book.  

Maybe Tainter is wrong about a crystalline web or a house of cards: these are compelling images but are they apt?  What if the rubber supply for my espresso machine’s gasket fails? An alternative silicon gasket can get designed and produced in no time. Hell I’ve already got one. (a spare, actually. I can’t survive an espresso interruption, and after these doomsday books, I’ve taken steps.) Maybe our web of interdependence is resilient like a spiderweb, not fragile like ice, and surely it’s organic and self healing in the sense of trying to grow new bonds where there’s a need. Technology is our religion, a groundless belief that some nerd will invent a new kind of fertilizer and we’ll all be fine.  Even this example isn’t notional. Goog the story of the “Haber Process,”  wherein a smart boy invents a machine to make bat guano.  So maybe Tainter is wrong. Maybe this time. But that machine of Habers? It makes bat guano out of oil.

I like Diamond’s points, a lot. I agree with him.  But I never read a book before and said “duh” so many times.   Analysis by dissection is a tool but it’s too ponderous and just cutting stuff up into little bits doesn’t ADD anything. Tainter made me think & I’m still thinking.