A somewhat later source puts it this way:

Lisa: My conscience is bothering me.
Homer: Your conscience!? Lisa, don't let that pushy little weenie tell you what to do.
Homer's Conscience: Homer, that's a terrible thing to say.
Homer: Aw, shut up!
Homer's Conscience: Yes, sir. (disappears)

As a motivator, guilt is often a miserable failure. Macbeth is a case study in guilt and how it can move a man to do more and more evil, not less. Lady Macbeth ridicules the very concept of guilt. She is a practical woman, not one to let the pale cast of thought get in her way. Her method for dealing with guilt is admirably practical: a little water clears her of the deed. She merely underestimated how much water she would need. Macbeth knew from the start that the multitudinous seas were not enough; he keeps his sense of guilt and his sanity. Does this make him a better person than his wife?

Lady Macbeth is ranked among the evillest of villainnesses in literature. But she balks at further killing. Again she is a practical woman, looking only to the immediate payoff: all she wanted was a contented life as Queen of Scotland in exchange for Duncan's murder. She did not get the contentment she wanted and knew she would never have it; she had spent her one chance for happiness and knew that she would never get another. The immediate gain was never enough for Macbeth, however, and as a result he drowns himself in blood. He finds no peace in the present, but looks vainly to find peace in the future, in murder after murder. He seeks comfort in fortune tellers and in the deaths of Banquo and Macduff--no, not merely in their deaths, but in the deaths of their futures. All the while his burden of guilt crushes him; even as he prepares for the last fight with Macduff he hesitates, unwilling if only for a second to add further to the charge of blood on his soul. But only for a second. Guilt was not enough to stop him.

But, you know, for all of that...Macbeth was right to feel guilty and Lady Macbeth was wrong. Don't you agree?

There's a reason I wrote the above paragraph but at the moment I haven't the energy to continue. The scream has grown more and more remote. Perhaps some other time.

There, I said it. Say what you want about George Lucas's tin ear for dialogue: The Empire Strikes Back has some of the worst lines in all the Star Wars movies, and I'm not forgetting Episode II.

UCLA students are a bit more pissed off than I thought.

I sympathize, believe me, even though the gesture is futile. No barricades in the streets of Paris will accomplish one damn thing these days.

Fourteen persons were arrested at the University of California Los Angeles when they protested a $2,500 increase in "fees" imposed gradually over the coming year. Note that this is not jacking up the tuition, merely "fees". Believe it or not, the University of California is still proud to say that tuition for residents of the state is still zero dollars. Affordable education for all!

In reality an undergraduate from California in a UC school can expect to pay about $26,500 a year including the cost of on-campus housing. If he lives at home, he can save $8,500, although bizarrely he will still have to pay $4,300 for "room and board" according to UCLA's own figures. An student coming in from another state will be socked for $49,200 in all.

The California Institute of Technology will cost a student about $49,500 whether he's from California or not. That is also the full cost including on-campus housing. What's more, when I was admitted (back in 1992 to be sure), I got a grant from the school covering some 40% of my tuition. From UC Berkeley, as I remember, I was told I would get almost nothing, so it actually ended up about the same to go to the upper-crust private country club as for the people's university.

The way things are going, too, it might actually be easier to get into Caltech these days. I wouldn't be surprised if the UC system announced that it wouldn't be letting in any new undergraduates at all because they're supposedly drowning in red ink.

I wonder. When I was still living in San Diego UCSD, the whole time I was visiting the place (I was an SDSU student but used the UCSD libraries regularly), was a nonstop construction site. The University of Washington, also said to be broke and also clamping down on new admissions, has similarly been knocking buildings down and rebuilding them for years. Indeed I've seen more on-campus construction this term than last, even though there's supposedly no money. I have also read in the UW newspaper that "The HUB", the large complex of buildings that houses the "Campus Department" and a lot of student facilities and organizations, is to be closed next year for a two-year renovation. What the--why? It's always for the students, we are told, it's only to help us. I seriously doubt whether more than a tiny segment of UW's students care about "The HUB" more than they care about affordable tuition and more seats in the classes they want.

There's something dreadfully wrong somewhere both here and in California. Is the dirty secret that universities don't really want to be teaching undergraduates any more? It was more than a secret at Caltech all those years ago. A couple of the heavy hitters in the physics department like Murray Gell-Mann openly advocated getting rid of the undergraduate program because it was dead weight. Caltech's real purpose, it was contended, was research, not nursing a pack of overgrown teenagers who more than likely would leave 'Tech on graduation and contribute nothing to the school's important work.

Maybe it's really like that everywhere, even at the schools that are supposed to be for all of us.

Where's it all going to lead? Sometimes I feel like the day isn't far off when the United States isn't producing any new college graduates in meaningful disciplines--no scientists, no historians, no masters of literature and language--only low-grade products of watery courses on business and "information technology".

The UW term is rolling into its last few weeks. It's been a tough one so far, especially in quantum mechanics. I don't know exactly how I'm doing in the class but I do know that I've spent hours and hours on homework without finishing it. I turned in the first take-home exam with only one question of four complete to my perfect satisfaction. I have it back now. In fact it's sitting maybe six feet away from me, face down. I don't know how I did; I haven't had the stomach to look. Nor have I picked up any of my graded homework assignments. It's not like the grade will change if I look at it, anyway.

On the bright side I'm doing well in electrochemistry, although that's the least important of the three classes I'm taking. I'm uncertain of my grade in molecular spectroscopy for a different reason: the prof hasn't handed anything back at all. We've had two tests so far with no results back from either.

I wonder what the quantum prof thinks of me. I've been a bit restive on certain matters. I've already mentioned my problem with Dirac notation both here and in class. I honestly think it's a barrier to understanding, at least for me, and I've done better with another quantum chemistry text that keeps its bras and kets to a minimum. I also have grumbled over the heavy dependence on mathematical software. I really shouldn't be doing this, not when my standing in the department is basically zero and my chances of acceptance into the program may ride on grades and personalities.

He's younger than me--that's always a little strange. Not that I actually feel that old, and the only external signs are a very few grey hairs and perhaps the general coarsening brought about by too many years of poor diet and excess of wine. But I do feel sometimes like I'm stranded among grade schoolers, and look it. On the up side, I did manage to say something clever in class today that I think actually impressed him--even if it did result from trying to make sense of his scrambled presentation of the topic of the method of time-dependent perturbation for predicting electronic transitions in molecules exposed to a varying electric field. I don't blame him for the scramble, although I think it'd help if he was working from a different textbook. But I realized that some particular product of integrals that was giving the class trouble made more sense when regarded as the Fourier transform of the convolution of two functions, a concept not introduced to us (I taught myself about it in a vain attack on some differential equations.) I told as much after class and he seemed to light up. Maybe I can actually regain some ground even if I can't raise my grades above mediocrity if I at least say the occasional intelligent thing.

Sometime in the '80s Douglas Hofstadter in his collection of miscellany, Metamagical Themas, described a game called "Nomic", which essentially is "Parliamentary Procedure, The Game". Or perhaps "Constitutional Law, The Game". Or maybe even "Free Will, The Game". The game is entirely recursive in definition: it establishes a central body of rules that define how one may build new rules and amend old ones. What the goal of a game of Nomic is and how winners and losers are decided...that I don't remember. I vaguely remember that the game does define at the start some currency or point system for rewarding players. Possibly it doesn't matter. The game is infinitely flexible (in contrast to games that provide only a rigidly circumscribed version of free will, like "Fluxx") and probably the only point of playing is to see how much power you can exert over the other players by defeating their rule changes and championing your own. An acquaintance of mind in Seattle a long while ago told me that she got into Nomic for a while with a group of friends; it tends to be an ongoing thing, I understand, sort of like keeping a D&D scenario running. One player succeeded in creating a semi-dictatorial position for a time by hewing out an office for herself somewhat like the chairmanship of the Rules Committee in the U.S. Congress, from which forcible men in the past have exerted an iron grip on legislation: this player got herself the power to decide whether new Nomic rules could be debated or not. She was eventually brought down, of course. All part of the game that, for all I know, never ended.

It is amusing to see a different sort of Nomic game play itself out on the Internet for stakes that are scarcely any more meaningful: the evolution of Wikipedia. If you consider how a self-moderating system like Wikipedia works, you must admit that it's a lot like a Nomic scenario: it begins with a nucleus of rules which in theory all players must follow equally, but as time goes on certain people get more power than others and can force through self-servicing amendments. How these amendments are debated and ratified is unknown to me, but their effects are visible to all. I wonder what sainted Wikipedia editor first gave the world ^{{citation needed}}. I wonder how he feels about his achievement, although it might easily have been accomplished by writing a script to insert the tag after every full stop or even every comma, which is the necessary and frequently seen outcome of the ^{{citation needed}}. Arguably the small but reliable dose of ego-stroking that comes from issuing a ^{{citation needed}} is the basic unit of Wikipedia's currency, small in value but cheap and plentiful, like pennies.

But there are so many new Wikipedia bank notes, new ones every month it seems. Another Wikipedia pioneer forced through a rule change allowing editors to flag not merely individual sentences but whole paragraphs, sections, and even entire articles with a few keystrokes. How powerful that must feel, to decide all at once that even the most detailed and best written articles "need cleanup" or "fail to meet style guidelines" or--Heaven forfend--have "multiple issues"! There are certainly multiple issues of new laws that all punish the same thing but which use new words to do so. There are "style guidelines" and also "quality standards" as well as "wikification" (seriously). If one tires of ^{{citation needed}} one can use its various spinoffs like ^{{verification needed}} and the puckish ^{who?} If you're one of the 0.0028% Wikipedia editors that actually contribute content instead of condemning someone else's, you have a kind of immunity clause to help you: by declaring an article a "stub", even a fairly lengthy article, you sharply decrease the probability of its being flagged for any reason, even with the headline proclamation that the article "needs expansion" that you sometimes see attached to much lengthier articles without the magic cloak of stubbiness.

Nobody ever removes the offensive uncited and unwikified material, of course, except sometimes if the article is about nothing important--popular-culture articles about TV shows or games, for example, are more fluid than most. Quite possibly the reason that Wikipedia articles are hardly ever truly edited is that it takes a few seconds' more typing than passing out yellow cards of ^{{citation needed}}.

The whole farce would be purely comical if so many persons didn't take it deadly seriously. Lord help us, the people who occupy themselves with creating self-serving rules believe that they are building a storehouse of information every bit as valuable and authoritative as the Encyclopaedia Britannica or Who's Who. They've published collections of Wikipedia articles as though they were a real encyclopedia deserving its own place on your bookshelf. They've even spawned the release of a new glob of cheap electronics devoted entirely to dishing up Wikipedia trivia, continuing the honorable tradition of open-standard bandwagon-chasers' creating ugly and poorly designed products that serve no useful purpose and appealing only to a miniscule audience composed of the sort of persons who carefully prepend "GNU" to every usage of "Linux".

This rant may contain some of the longest sentences I've ever written. Clearly one must "improve this polemic if you can."

Let's say you lived in Ashland, Oregon, and you hated Shakespeare. Most places you can get away with loathing Shakespeare but it would be more difficult in Ashland, which prides itself on hosting the great Oregon Shakespeare Festival every year. You woke up one day during 11th grade English class and proved to yourself by geometric logic that there was no legitimate reason for you to care about Julius Caesar. There are so many straws to grasp: the fellow stole all his plots, he was only a second-rater without enough education to merit consideration as a first-class poet, the only reason anyone remembers Shakespeare is because of the musty and outdated traditions of the English literary canon, the texts of the plays themselves are corrupt and untrustworthy, and in any case the man probably didn't even exist any more certainly than did Homer or Hesiod. Whatever the reasons, they comforted you whenever you decided to copy your essay homework from a website.

But here you are stuck in a podunk town on the Oregon border that, every year, dares to advertise to the country and to the world its reverence for some dead English guy who maybe but maybe didn't write some crappy plays forced on us all by a pack of white-haired and white-skinned male pedagogues. You've known the truth since you were old enough to hate Superman: William Shakespeare was a phony. How can you counter this centuries-old lie, drilled yearly into the heads of the good citizens of Ashland?

You see an opportunity: Ashland's Shakespeare festival isn't just about Shakespeare. There is money devoted to producing new plays and there's even something called "The Green Show" in which artists get a chance to enact anything they like, even if it's not a play, as long as it fits within thirty or forty minutes. And "that time of year" is good for interest in the dramatic arts generally; theatrical companies of all sizes get a crack at bigger audiences during the months of the Shakespeare Festivals. The spirits of Melpomene and Thalia are in the air, not just for those of us silly enough to like the old fraud from Stratford-upon-Avon. If you got together a bit of money and time you could use the opportunity of the Shakespeare Festival to present some kind of alternative or counter to Shakespeare. Perhaps you could kick some attention toward George Bernard Shaw, who disliked Shakespeare. Or maybe you felt that Rosencrantz and Guildenstern are Dead needed to be produced as a sort of antidote to Bard-worship.

Given that opportunity, it would be puerile indeed to squander it on devoting an entire thirty minutes of "The Green Show", or even more effort on an even larger stage in Ashland, to badmouthing Shakespeare and presenting nothing to replace him. Shakespeare may be a waste of time--the point can at least be debated, although I suspect that there is something awry in the soul of a man who hates Shakespeare--but, in that case, should not the time be filled with something worthwhile? Here you have a chance, not merely to tell the theater-goers of Ashland that there is something out there better than King Lear, but to show the people of Ashland what that better thing is. Instead you've nothing more in answer to the irrational tide of Bardolatry, no more mature a response, than to scrawl horns on all the posters and sneer at all the people buying tickets to Macbeth.

This is, more or less, what I think of the idiots buying "Yes, Virginia, There Is No God" billboard space in time for Christmas. Sad to say my faith in Shakespeare is less shaky than my confidence in the existence of God, although I came round to both at about the same age, after a period of youthful and pig-ignorant contempt. All the same I'm not totally unsympathetic to criticism of Shakespeare and I don't mind a good joke at his expense. If someone argued that we should devote all that attention instead to Bertolt Brecht and threw his efforts into building up a Medford Brecht Bash in opposition to Ashland's celebration of Shakespeare, I'd wish him the best even though I'm not a fan of Brecht.

I can't get behind the message that Shakespeare sucks, though. There's no message there, anyway, just the festering resentment of the bored high school student who never outgrew his petty hatred for boring old Hamlet. The "Freedom From Religion" crowd is right there with them.

I'd have been less put out if I learned that he was a young-earth Creationist or that he preferred potatoes to stuffing. God, I wanted so to tell him what I thought of it, but I think I'm probably in bad enough graces with him already.

Oh, yes, that makes it so much clearer.

This is a line from my latest physical chemistry assignment. The operation that this line of garbage represents is actually fairly simple: ψ is the linear combination of some eigenvectors a, b, and c with coefficients 1, 2, and 3. P₁ψ represents the "extraction" of the first coefficient by means of the inner product of ψ with the eigenvector a. In the usual case, when dealing with real-valued functions it means that you take the integral of ψ a:

⌠+∞
⎮ ψ(x) a(x) dx = 1
⌡-∞

Or you could use the notation of linear algebra:

<ψ,a> = 1

Written out either of these ways it's clear enough. But both professors and books insistently clobber us with Dirac notation, or "bra-ket" notation as it's sometimes called, because supposedly it's a nice shorthand, more compact and convenient than writing out integrals or inner products or whatever.

Poppycock. There's nothing convenient about "bras" and "kets" except for typesetters--who, I suspect, were meant to be the real beneficiaries of such obfuscated notation. Another that occurs to me is the subscript method of "simplifying" a partial derivative like ∂²u/∂x² into u_xx, which interferes with and confuses the normal usage of subscripts. Wilhelm Gottfried Leibniz had to endure Isaac Newton's jackassery on the way to giving the world a symbolic representation of complex maths that any sane man can grasp. Why throw Leibniz's gift away just so you can write everything out on one line that takes three weeks to parse?

Dirac notation flies in the face of every other symbolic use of parentheticals, too. When you see a '(' or a '[' or a '<' you naturally look forward for the ')' or ']' or '>' that tells us, "I contain a single operation within my walls." But in bra-ket notation you can have a '<' or a '>' all by itself. It displeases the eye and unsettles the mind, as though you were reading a novel and suddenly came across the last half of a parenthetical phrase without any beginning to match.

It is perhaps worth noting that Paul Dirac was a man devoid of social skills, incapable of engaging in human conversation. How fitting that he should have given us a scientific notation that is impossible to read.

Or the other way round, maybe.

I had a particularly heavy load of homework due today, two ordinarily difficult assignments and a take-home exam for quantum chemistry amounting to perhaps double the work of an ordinary weekly assignment. By no means did I leave all this work for the weekend. Going into the weekend I had already spent several hours on all three assignments.

Not one of them was entirely complete when I was forced to turn them in today, even after a desperate eleventh-hour push to finish it all early this morning. Of the four quantum chemistry questions--all multi-part questions, I should add--I only got all the way to the end of one of them. I scarcely made any progress on another. An intractable differential equation stopped me there; another equation prevented my completion of the electrochemistry assignment, even with the helpful hints in the text.

I daresay that I produced three pages of scrap for every page that I could consider even remotely complete enough to turn in. Sometimes I had to discard pages only because I had made some stupid error of transcription or transposition that spoiled all the work afterward. Yet more went in the bin because I had embarked on what looked like a promising attack that ended in a mess. I probably repeated myself a dozen times on certain problems.

It is often advised that, rather than grinding away on one problem for an hour or two, one should switch to another problem. I did this often and I now believe that it was a great mistake, at least the way I did it. I spent at least a half hour this morning sorting out all the pages that I had done out of order. I'm not entirely convinced even now that I didn't accidentally throw something out. What's more, the frequent switches between problems and assignments thoroughly scattered my attention and scrambled my memory of what I had already done. I perhaps could have turned in one complete assignment for one class at least, had I stuck to it rather than turning to something else.

I remain convinced that none of these assignments was beyond me had I spent my time wisely--had I taken sufficient care to avoid careless mistakes--had I begun just a little earlier and concentrated just a little better. But I have not done these things and now I'm gripped with the fear that I'm letting my chance slip away from me. My goal was not merely to get adequate grades but superlative ones that might better my chances of proper admission to grad school. Now I'm wondering if even a 3.0 is within reach.

Mind you I have no idea how the other students are doing. Some of them come across as awfully dense during lecture but a dull-seeming student may for all I know save all his intelligence for his homework, and do well. Maybe I'm actually in the upper quartile and don't know it. I almost would rather not know.

Whatever the context and whatever the cause, it is clear that my shambolic methods of study and doing homework cannot go on. The sad thing is that I never really have had the opportunity to learn to be a good student. At Caltech I refused to work hard; at SDSU I never really had to work all that hard except on some of the tougher Latin and Greek translations. A couple of the community college math classes were taxing but mostly because of the time needed for large volumes of busywork. But how to retrieve this situation? I wish I had any definite ideas.

I've finally gotten sick of my old clock-radio. Because of my poor eyesight without glasses I can't read the numbers from across the room, which is where Misha and I must put the radio if it's to stand any chance of getting us out of bad. The tuner is absolutely horrible, showing the poor selectivity and stability you'd expect from a Radio Shack kit or a $5 portable AM-FM radio made with transistors saved from the floor sweepings: a tiny display about two inches long, a dinky thumbwheel that is no doubt connected to a cheap variable capacitor that you can reliably tune within maybe 5° of its enormous 180° full range, a pointer that's fully 10% of the width of the display that's connected to the tuning knob with a piece of string. I decide to get a new radio.

I'm not sure how many of my few readers are old enough to remember the ubiquitous 12" or 13" black-and-white television. Even though U.S. manufacturers stopped making them in the '70s some time, so many of them flooded the market from Asia that even as recently as the late '80s and possibly beyond that you could go to an appliance store and still find, along with the 200-lb color sets, a selection of weensy B&W TVs made by bottom-of-the-barrel manufacturers like Goldstar and Samsung. I shouldn't knock them; I had that sort of B&W TV in my room in San Diego and watched it all through the '90s. But it was weird how even as the expected minimum in color TV size was getting bigger and bigger, ramping up from 17" through 24" and beyond, you could still get that minuscule Goldstar in all its black-and-blue glory. (Yes, blue, not white; the phosphors weren't so good in those cheap sets.)

I am astonished to find that the identical scenario exists with clock radios. No, it's even worse, because even though the appliance shops were still devoting shelf space for decades-obsolete B&W TVs they were stocking and displaying the hard stuff as well, even in the cramped home electronics sections of mediocre department stores. But I find that every single model of clock-radio I can find in the electronics department has an analogue tuner that is undoubtedly every bit as crude as the one in the piece of junk I've used. I don't understand it. Is it even possible, for example, to buy a car radio with analogue tuning any more? (For that matter, it is possible to buy one without a CD player?) I haven't seen an analogue-tuned car radio in any car built after the '70s. Early '80s, tops.

Oh, the top of the line (hah!) clock radios have all sorts of neat features. You can find huge displays, multiple alarm modes, talking alarms, even clock radios tuned to the VLF WWVB government station so you can keep the radio synchronized with the best clocks in the country. But they can't put in a tuner that cost more than 50¢ to build? Humbug. There must be a protective tariff or something that's causing this bizarre situation. Couldn't they at least put a proper vernier dial on the damn things? Hell's bells, I could build a more reliable radio. At least I know what a PLL is.

I have been accused of taking altogether too much time to do work on paper that these days can be done on the computer. This was perhaps even true in 1992, when I first went to college. Mathematica already existed by then although as I recall you couldn't ask too much of it. Of course no self-respecting teacher would accept homework that hadn't been done by hand (show your work!) although it was probably acceptable to use a computer for checking answers.

These days, as I have found out, teachers assume that you'll avoid adding two integers by hand if it can be at all avoided. There is, I suppose, a certain realism to this. It's numerical approximation that solves the problems of today and even the simplest methods of approximation are a nightmare to do by hand. My current physical chemistry professor freely recommends the use of Maple (a sort of runty cousin to Mathematica) in his homework and take-home test assignment. I have striven wherever possible to avoid using Maple until the last possible moment, and I have wasted perhaps too much time on trying to solve differential equations and tricky integrals by hand.

Here's the thing, though. Many years ago when I was still mired in the software industry I pulled out my old copy of Tom Apostol's Calculus to work some problems. I still remembered some basic rules of differentiation and integration, and I had a vague acquaintance with series approximations. I realized then, for one thing, that a lot of math (and science) that I thought I had learned in high school and at 'Tech had not in fact found a secure lodging in my brain. In returning to the material I resolved that I would not memorize anything that I had not first derived by hand. Then it all stuck in my head; I found myself wondering why such concepts as Fourier expansion had seemed so mysterious back in the day. I was flunking classes at 'Tech because of oversleep and weed, to be sure, but at the start I was also having legitimate trouble with homework problems that, several years on, looked perfectly straightforward. Since then I have made it a sort of personal philosophy that, ideally, I should be able to solve any math problem that might come up in chemistry or physics with nothing more than pencil, paper, a $10 calculator, and maybe one or two reference books. I should even be able to do without the calculator in a pinch. It's a stupid kind of pride to take, maybe, but I credit this do-it-all-by-hand principle with keeping me sharp.
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This is one of those days when I fume that college would so much more useful if it weren't for the frickin' students.

They say that the only stupid questions are the ones not asked. It's a noble sentiment but it is not true. The hitch is that stupid questions take time, especially when the questions are vague and confused, as stupid questions so often are. Also I suspect that teachers of upper-division classes aren't expecting their students to be ignorant of first-year physics.

Seriously, how do you get to a 500-level class without grasping what an electrostatic potential difference is? A simple diagram of an electrochemical cell with a voltage drop across each interface is giving one student at least no end of trouble. It confuses him that two electrodes made from the same metal, copper in this case, might be at different potentials. Durr, they're both copper, where's the potential difference coming from? Never mind that the concept of capacitance is practically the first thing you learn in E&M class after learning Coulomb's Law. All of electronics depends on potential differences between bits of copper--I just wanted to scream at him that he was holding the whole damn class up.

I shouldn't be harder on him than he deserves, I suppose. "Potential" is a word used somewhat sloppily depending on the subject. The underlying concept is the same, the idea of potential energy: work must be done to effect a physical separation of charge (electrical potential) or the interaction of electrons between chemical species (chemical potential) or the moving of an object through a gravitational field (gravitational potential) but it's all just different ways of putting energy into something. Maybe the real villain is inconsistent teaching at the first- and second-year level. In particular the concept of the "electrode potential" is taught apart from the notion of the "chemical potential", when in fact they are directly related. So I guess it's too easy to get confused. But...for heaven's sake at least have the wits to realize that you're bringing the whole lecture to a halt because you're muddled.

In my sophomore year at Caltech in Phys 2a I was assigned a problem out of the Berkeley "Waves" text. It was, in retrospect, a very simple problem: model the motion of a taut string struck at its center with a sharp blow. I had some vague idea how to do it; I knew it involved calculating the Fourier expansion of a step function, positive for a short interval about the string's center and zero everywhere else. But I gave up without a fight and never answered the problem. Not answering homework problems would become a habit.

Anyway, for the first assignment in Chem 550, quantum chemistry, we were given as a sort of warm-up a number of questions on classical wave mechanics. The last one of these was, basically, the same problem that I punted sixteen years ago. The professor directed us to use Maple--well, screw that! I did it by hand as I would have had to do all those years ago. It took an hour but I did it and it came out right the first time. *sighs* I feel better.

All the same I can still get an education from one of its professors. My father pointed me to an hour-long speech on global energy use and production, delivered by Dr. Nathan Lewis of Caltech. I had Dr. Lewis for Chem 1 oh so many years ago; he was also my undergraduate academic advisor, not that I sought much advice from him. I was too busy sleeping through lectures and reading comic books.

It's an excellent speech and I think anyone interested in energy policy ought to see it. Dr. Lewis gives us a concise and well-supported overview of the magnitude of the problem: how much energy we use, how much more we will use, how much of it would have to be "carbon-free" to keep atmospheric CO₂ below a reasonable threshold, and how woefully inadequate are all of the widely touted "clean" alternatives. The total amount of energy available in rivers, in tides, in wind and in geothermal heat, even if you assume maximum exploitation of the theoretically available quantity (impossible for all of these) simply isn't enough. Total available solar energy is more than enough on paper but the high cost of current solar cells and the shortcomings of current methods of energy storage mean that any solar plants built with contemporary technology cannot hope to supply enough carbon-free power to make a difference. As for nuclear, only breeder reactors offer hope for the long term because of the limited supply of uranium ore but nobody wants a lot of plutonium-producing nuclear plants around. (Well, I wouldn't mind.) Dr. Lewis concludes that the only chance for success in keeping CO₂ levels down resides in intensive R&D into solar power and storage of this power, breeder reactors, and carbon sequestration (i.e. trapping the CO₂ released from burning ordinary fuels), followed by massive deployment of these improved methods. Pessimistic? Oh, yes. But occasionally we need a real scientist to tell us how badly off we are, and how pointless it is to put up a few silicon solar panels and buy a Prius.

Every now and again I'm reminded of what good teaching can do. On my own I can absorb impressive volumes of information, in certain subjects anyway, but most of the time my mental organization of the material is terrible. The knowledge is there but not the structure to make the knowledge useful. That's when I need a steadier mind to push me and compel me to see things that I might very well miss on my own even with the help of a dozen books.

I had a moment like that yesterday. I'm taking "Current Problems in Analytical Chemistry" again this term and the subject is electrochemical methods of analysis. I've long been interested in such methods, not merely as a possible field of future academic work but also as something to play around with on my own. Polarography for estimation of heavy metals, for example, looks interesting. The difficulty has been that, for whatever reason, a solid and coherent grasp of the mechanism of the various techniques of electrochemical analysis escaped me. All I got from reading Skoog and West on my own was a jumbled assortment of factoids about half-reactions, electrode potentials, polarization, overvoltage, and so forth. How it interacted with external circuitry was also a bit mysterious to me.

The Chem 520 instructor yesterday began his overview of the field with a topic that, at first, seemed like beginning in the middle: he began with a description and explanation of the "electrical double layer" that exists around any metal electrode (any surface, really) immersed in an ionic liquid. The surface charge density of the electrode attracts to it a layer of ions of opposite charge, maintaining overall electrical neutrality. I was already familiar with the notion of the double layer through study of electroosmotic flow; you'll find discussion of the double layer in the relevant chapter of Skoog and West, somewhere in the middle. Why was the professor starting out this way?

Oh, he had the best reason. After describing the layer he brings up an illustration showing a simple RC circuit, showing a resistor and capacitor in series like you might find in the first chapter of any textbook of electrical engineering, and basically said, "The electrodes' layers of charge can be modeled as a capacitor and the supporting electrolyte between the electrodes can be modeled as a resistor." And then he went on to describe how this model predicted the behavior of an ideal electrochemical cell under various conditions like constant voltage, constant current, and so forth--all of it making perfect sense to me because it was all bog-standard EE material.

And then I realized that all of the electrochemical analytical methods were basically about measuring the departure of the real cell from the ideal behavior of the RC model. Accounting for non-ideal behavior is already an important aspect of circuit design; the simple capacitor model is better when modified to include series and shunt resistance, series inductance, and so forth. Could not Faradaic reactions at the electrodes of an electrochemical cell could be regarded in just the same way? Electrolytic reductions that consume electrons could be regarded as current sinks; oxidations that yield electrons correspond to current sources. The transconductance of these sinks and sources are functions of applied voltage, ideally zero at voltages below a certain threshold corresponding to the various standard electrode potentials. And so forth.

Skoog and West's electrochemistry chapter, while it treats in passing with the electrical double layer and its capacitance, does not employ an RC circuit model at all. I'm glad that the Chem 520 professor did. Now, if any electrochemical process seems mysterious to me, I know I can treat it as a problem in circuit design, which is something I already have practical experience with. Of course the analogies may be imperfect but I think even a flawed EE model can serve a useful purpose: it gets you to think in the abstract, about electrons moving and current flowing, and to avoid getting bogged down in the particulars of a given reaction or method.

Many years ago I first read the following passage from The Art of Electronics of Horowitz and Hill. I'm too tired to transcribe it so I'll post an image instead.

Darned impressive indeed. In very brief summary, a signal is modulated--a simple square wave will do--at some moderate frequency, say 1 kHz, then transmitted. At the receiving end the signal, now weak and buried in noise, is mixed with the "reference" output of a local oscillator whose frequency is exactly that of the modulation frequency and whose phase is adjusted to correct for phase shifts introduced in transmission and pre-amplification and so forth. Low-pass filtering the output of the mixer rejects the out-of-phase components, including it is hoped most of the noise, and yields a DC output that is (ideally) proportional to the original signal. The longer the time constant of the low-pass filter, the better the noise rejection, but at the cost of reducing the useful bandwidth in transmission.

I've been wanting to put this method to use for many projects--detection of the feeble radiance of Raman scattering, improving the sensitivity of transducers of all kinds, even radio broadcasting over the 160-190 kHz VLF band--in short, for any project requiring accurate reproduction and transmission of weak, slowly varying signals. The challenge of designing a photometric probe for titrations seemed like an excellent first opportunity to design a lock-in amplifier: both modulation and demodulation controlled by the same device, strong signal detected by a photocell, and a relatively short path length from the source to the detector. The example described in The Art of Electronics was also working with a modulated light source and a photocell detector, but with a much longer, unprotected path length and far more noise. If they could get a clean signal under those hostile conditions, surely I could manage at least as well?
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This unlovely mess is my first attempt at constructing apparatus for conducting photometric titrations. In conventional titration, such as you might have done once or twice in freshman chemistry or even at high school, you slowly add measured volumes of some reagent to the reaction mixture until some visible change occurs, usually the change in color of a pH indicator or other sort of indicator, marking the so-called "endpoint" of the titration. The limitations on visual endpoint detection are severe. Indicator color changes may be too subtle, too gradual, or too easily obscured if the solution is already colored.

What can't be easily seen with the eye, however, can often be detected with an instrument. Using a special probe dipped into the solution to be titrated a beam of light, often but not necessarily monochromatic light, is shone a short distance through the solution onto a photocell. The change in attenuation is monitored during the titration. Ideally the attenuation will change at an approximately constant rate leading up to the endpoint, whereupon it begins to change at a different rate. Thus, for example, if the color of a solution grows more intense during titration then reaches a maximum at the endpoint where it deepens no further, the photometric probe will detect a clean endpoint that is impossible to see visually. The same apparatus for monitoring the absorption of light by colored substances during titration, spectrophotometric titration, can be used for monitoring the scattering of light by solid particles, turbidimetric titration, enabling the titrimetric method to be applied to precipitation reactions, e.g. determination of barium by precipitation of barium sulfate.
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When I was at Caltech in 1992-94 the laserdisc hadn't yet fallen into darkness and I'd often go to the Tower Records shop near the campus to browse the discs for sale. I never bought any but I told myself that I would some day because I wanted movies on what looked like the coolest format of the time. Laserdiscs were especially attractive because of The Criterion Collection, a set of great movies from international cinema taken from the best possible prints and often featuring scenes cut from the theatrical releases available on videotape. Needless to say I never bought any Criterion discs and the old dream faded.

Now, though, the Criterion Collection is hot again and backing another trendy video format, BluRay. I was sold on BluRay after watching the BluRay release of Blade Runner on our widescreen TV--I have never, ever seen the film look so crisp and clean. Hence Misha and I have started to buy Criterion releases on BluRay, just a couple at a time--BluRay is still rather expensive--and only if one or the other of us thinks the movie is great enough to warrant the extra cost.

Last night we watched the first acquisition, Carol Reed's The Third Man. It must have been ten years or more since I last saw it on a VHS copy. At the time I thought it was one of best movies I'd ever seen, maybe the best. I can't be quite that enthusiastic after watching it again but I still put The Third Man in the top 10.

More behind the cut because there are spoilers.
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I've been wanting a magnetic stirrer for a while; I don't mind swirling flasks by hand, even during titrations lasting many minutes, but there are good reasons (aside from mere comfort and convenient) why hand-mixing is a severe limitation. I'm not the first one to have the idea of turning an electric fan into a magnetic mixer, but my early experiments with it went poorly: converting the fan isn't a problem but making one's own stir bar isn't so easy. One of my high school teachers had faked up stir bars by sealing lengths of thin iron rod in glass but I wasn't doing so well with that. Finally I broke down and bought a cheap Teflon-coated stir bar for two or three bucks and after that the rest was easy.

I have no idea where the fan came from. Misha dug it out of some piece of equipment years ago; the silly red and blue LEDs are built in. I can get some measure of speed control by running it off one of those Radio Shack "universal" wall wart power supplies. The magnets are from Amazing Magnets: Misha had ordered a bunch of small disc-shaped magnets for his Warhammer model work and they always throw in a bunch of miscellaneous ones of various shapes, including little cubes. Mounting the fan in a Gladware box was a brainstorm after noticing that the round divot in the lid was about right to hold a 250 mL beaker or Erlenmeyer flask as you can see in the photo. I hope it'll be enough for titrations.

I've been a lot of trouble with recent titration experiments that use standard solutions of oxidants or reductants for analysis. With the exception of potassium permanganate, which needs no indicator (its intense purple color even in very dilute solutions is sufficient to indicate when an excess has been added), there are very few substances that can function as indicators for redox titrations. With acid-base titrations there are dozens of pH indicators that give sharp, reversible color changes at a well-defined pH. Many dyestuffs change color on oxidation or reduction but most are useless as redox indicators for many reasons. I've tried a number of dyes that I already have on hand for oxidations with dichromate and with cerium(IV) and gotten poor results with all of them. Often a dye will seem promising in a "blank" test but fail with a real sample. It doesn't help that I'm dealing with solutions five- or ten-fold more dilute than is typical for run-of-the-mill experiments in volumetric analysis.

Therefore I need to start investigating non-visual, instrumental methods for detecting titration endpoints. There are many possibilities. Measuring the difference in voltage between a "working electrode" (which can be a special-purpose electrode like a pH glass electrode) and a standard reference electrode both immersed in the solution, potentiometric detection, is one of the best and most general methods but there are many others. Any property of the solution that can be measured continuously and whose second derivative changes sharply at the endpoint can be of use for titrations--electrical conductivity, absorption of light either by colored substances in solution or by solid particles in suspension, emission of light by fluorescence or chemiluminescence, even temperature. All of these methods, though, require some kind of probe or more than one to be immersed in the solution at all times during titration, preferably fixed in place. That rules out hand-swirling, which at any rate can only be done effectively and without danger of splashing anything out using a narrow-necked Erlenmeyer flask, which wouldn't leave much room for an electrode.

If only I could figure out how to heat and stir. New hot-plate-stirrers are expensive items and I'd not want to buy a used one. The standard device is I'm pretty sure nothing but a conventional electric hot plate fitted with a rotating magnet, but I have a crazy idea: could not the stir bar be itself used as the heating element by the method of inductive heating? Use a rotating steady field, horizontally oriented, to move the bar. Use a fixed, high-frequency field, vertically oriented, to heat the bar. A thermocouple in the liquid would be needed in a control loop to insure against overheating.