Another Apology

A computer implosion has robbed me of my computer for several days, and taken my only working pdf player. I've been trying to read a long FDA report to post on, but a bit more waiting is necessary.

Late Post Excuse

I started working on something for this post, but then arbitrarily decided that the subject was interesting enough to do correctly. So instead of that, you're getting a half assed apology post.

To beg your forgiveness, I am going to offer John Fahey's performance of "Red Pony":

Taxi Driver

Taxi Driver is one of the greatest movies ever made. Every time I see it, I'm shocked by it's power, leaness, beauty, and savagery. If you have never seen Taxi Driver I'm not going to describe the plot here but I am going to try to analyze it a little, so I'd recommend renting and watching the movie within the week before reading this analysis.

Taxi Driver is the self destructive impulses of a man without a society. It is hinted that he's scarred by the Vietnam War, but it's also hinted that these scars are yet another guise that Travis tries to put on.

Though the film is remarkably taught, the only scene that's just atmosphere is the beautiful final sequence, there are three scenes that I believe are the key to understanding the film.The first is Travis's clumsy first date with Betsy. When she picks the Kris Kristofferson song out of the air and connects him to it. Travis doesn't understand, and doesn't attempt to. It isn't the first time that it is clear that he can't adapt to his surroundings, but for the rest of the movie he attempts to make up for it. This scene is echoed in his very interaction with underaged prostitute Iris, his desperate attempts to seem both "cool" and "mature". His attempts to keep these masks on is as hilarious as Peter Boyle as the lying cabbie.Unfortunately, I can't seem to find a picture of what I think to be the pivotal scene in the movie. Travis has gone mad by this point, even if we allow that he didn't start there. He's begun his regimen, preparing to murder the people he blames for befouling the two women "in" his life - Palatine and/or Sport (we don't know which at this point). He's watching TV, and Jackson Browne is playing something soft on the TV. At the end of the scene he allows the television to fall to the ground (I don't recall him kicking it, but he might). This scene stuck in my mind for years, even beyond the iconic hyper-violent, self-destructive rampage just before the end it stuck with me. It shows his inability to comprehend his world, and his willingness to use violence to shape it how he wants it.

The third is, of course, the famous ending sequence, where Travis is seemingly beloved and rewarded for his actions. This final sequence is one of the greatest ever put to film, and I still can remember every glance that is made into the rear view mirror. In the end, Betsy fades out and all we see is Travis looking away at something. Finally, even Travis dissolves and only New York City remains. In his final act of self destruction he was only able to keep up his fantasy a few more seconds, and the world he could never understand envelops him.Wrapping up, I'd just like to mention Bernard Hermann's fantastic score which boils with ambiguity and indecision. Even in the opening scenes it melts between sleazy jazz sax and a foreboding base roar. It deserves a place in Hermann's great scores, which is no mean feat.

Peter Lorre

Peter Lorre is one of my favorite actors of classical Hollywood. Along with Bela Lugosi, Vincent Price, and Boris Karloff embodied the classic Hollywood horror movie, but only Lorre was able to shake typecasting consistently. Well, maybe Price.Lorre was, by most accounts, an amiable man. his friendship with Humphery Bogart led to roles in The Maltese Falcon and Casablanca. His performance in both movies steals every scene he's in - especially fortunate given his limited screen time but important role in Casablanca.Fat, bug eyed, and raspy voiced, Lorre was doomed to never be a romantic lead despite his acting talent. Sometimes, though, I think his stature was a blessing. He was one of the few people who could unironically make short, thin, pockmarked Humphery Bogart look like a physical god.Despite what I just said, Lorre could and did carry movies. The Mr. Moto series would not have flown without him, and his role in Mad Love is almost the only reason it's known today (the other two reasons:Karl Freund's last movie, and it's photographed by Gregg "Citizen Kane" Tolland).Of course, whenever one speaks of the past, the present becomes a looming topic. It is difficult to imagine Peter Lorre today. He is a man who I cannot imagine without the kinds of films he starred in, films of a style that no longer are made - indeed they were scarce even then! I do miss the classic Hollywood horror. I love many kinds of horror movie, and the self-similarity of the contemporary horror market should be thought of as unforgivable. Even the odd horror movie that does mix up the genre with fresh ideas - like No Country For Old Men - is now considered "not horror" because we expect such a mannered structure of cliches. True, the old Studio Hollywood was not a goldmine of innovation and creativity - but that does not forgive the sameness of today.Many thanks to the Peter Lorre Photo Gallery for contributing many of the photos in this post.

Big O-Notation

While Donald Knuth didn't invent O Notation, my knowledge of it came from his work.

I was explaining Big O Notation to a non-mathematically inclined friend recently and I suddenly found that I didn't buy it! It makes it very difficult to explain something, when you suddenly don't buy the foundation. Upon reflection I recovered, and I found the recovery process to be very interesting even to the non-mathematician. I will put a picture of a dinosaur where the math begins and a picture of a spaceship where it ends. Feel free to skip if you are familiar or uninterested in the workings of Big O Notation.

First, what is Big O-Notation? Well, first let me give it to you in words, then abstract, then a couple examples.

Big O Notation defines a function with a certain vagueness. Absolute precision is nice, but often impossible and even more often pointless. It's a bit of a wastebasket, but a precisely defined and predictable wastebasket. It's so useful it actually does a lot more than collect numerical inaccuracies. In fact, it's so good at certain things that it is actually more used for one thing in particular that it overshadows the original usage!

This usage is in evaluating the efficiency of computer algorithms. The reason it is useful for doing so is outlined below, but non-mathematically it works like this: in order to function as a wastebasket it tells us the order of magnitude of things we can throw away. So, if we use it on a function of time efficiency, it will tell us how much time we are going to throw away.

So how does this wastebasket work? Well, let me give you a few loose particulars.

This is from a comic called Devil Dinosaur, which is a fairly accurate depiction of what creationists believe.

Let there be two functions f(x) and g(x) (I'll do it with actual functions in a bit if these letters don't grab your imagination).

f(x)=O(g(x)) as x→∞
iff |f(x)| ≤ M*|g(x)| for x>a for positive real M & any real a.

Formally speaking, that is read aloud like this: The function f of x has order g when x goes to infinity if and only if there exists some positive real number M such that the absolute value of f is less than M times g for all x greater than some number a.

Informally, you'd just say "Foo is Big Oh Bar".

If you're wondering where M and a come from, it's because I didn't tell you because they aren't important. The important thing is that there exists a function that is always greater than f if we look far enough. Also, I hope you noticed that the equals sign used isn't a real equals sign. Arithmetic around O Notation can be tricky, but it's often a necessary sacrifice.

Let's first build an example of O notation, then look at two more examples in the contexts of it's main uses.

f(x)=5x^9+3x+2.

Subbing our first line, we can see:
f(x)=O(g(x)) becomes 5x^9+3x+2=O(???)

So how do we fine our g(x)? Well, let's look at f when a=1.
f(1)=5*((1)^9)+3*1+2=10.

Well, we can see, that x^9 is going to be the real growing power. So, if we let M=10, then we can see anything times that growing to the nineth power is going to sit on top of our function - because it's growing at the same rate and has a power that equals them at x=a=1.

So since |5x^9+3x+2|≤ 10*|x^9| for x>1, 5x^9+3x+2=O(x^9).

But who cares and why?

Well, let's look at a "simple" function:

e^x=1+x+(x^2)/2+O(x^3) as x→0

This function let's us know that we cannot be off by more than some multiple of whatever we choose for x taken to the third power. Since that gets smaller as we approach zero, this function can be useful for estimating a not at all obvious value in a simple way. We simply ignore the O notated portion if it is small enough!

Let's try it out

x=0
e^0=1+0+(0^2)/2+O(0^3)
1=1+O(0)
0=O(0)

At this point, the O notated error outright disappears! Now, if it gets larger as we go away from it, then the function will be worked properly as a wastebasket.

x=.5
e^.5=1+.5+(.5^2)/2+O(.5^3)
1.64872127=1.625+O(.125)
.023721270=O(.125)

Error now exists. I am committing an abuse of notation here, saying O(.125). Standard practice is to factor out any constant and write O(1). Looking at the part of the definition after iff shows this is possible pretty easily. I'm going to conform to standard practice from here down.

x=1
e^1=1+1+(1^2)/2+O(1^3)
2.71828183=2.5+O(1)
0.218281828=O(1)

The error is almost a tenth of the result! This is really much to high. We can see the error function absorb more and more.

x=2
e^2=1+2+(2^2)/2+O(2^3)
7.3890561=5+O(1)
2.3890561=O(1)

I think it's clear that this wastebasket conforms to expectations.

So, just one last function before we can leave. A realistic computational efficiency function. Let's say we have an algorithm that requires a sorting a list and selecting the middle value. If the list is even, then average the two "middle" values.

So, the time to compute is the time to: sort list+check evenness+select middle values+divide by two half the time. How can we find the amount of time this process will take? Well, using O notation, we can find the order of each element. The vagaries of O notation show that - as our intuition suggests - that this will run about as fast as the slowest section. We can then estimate the overall efficiency of the algorithm.

This can be seen if we accept that the sum of a series of Big O functions is the same as the largest function in the sum, which is not difficult to prove. I'd prefer not to do it here though.

I'm going to write from this point on assuming that you read none of the above.

Again, O notation tells you the scale of a function even as it increases. As I was explaining this I suddenly found myself disbelieving in the value of our wastebucket. I must have been in an odd state of mind. Maybe I explained it poorly and was having difficulty believing my own words. Still I will try to recreate my difficulty and why I think it is worth reading about.

Say you have the function 50*x^4+x^2. The wastebasket for that is O(x^4). I was stricken with an inability to swallow that was large enough to hold our function!

Think about what happens as x gets very large. If we take a million (10^6), we can see already that leaving out the x^2 makes little difference. But is not 50*x^4 still 50 times as much as x^4? How can we fit fifty things into one basket? In my defense, I had no paper to write out a function to see how miniscule this difference is. If you find it yourself, you will see. Also, I was actually thinking of the function x and O(x), where such things are slightly less obvious.

I thought of a million. I found myself unable to believe that any multiple of a million is just about a million. I retried with a billion. Again, 2 and 3 billion seemed far too distant to be considered on a scale with a million. Even the difference between a one and a couple trillion now has too much political reality.

And then I thought of a quadrillion. That's a thousand trillion, 10^12, or 1,000,000,000,000. Suddenly, like a light turning on, I was able to again grasp Big O Notation intuitively and simply. This, you see, is almost the count of cells in the human body. And if our cells were a bit bigger or smaller, who would notice? Most of our bodies are made of various smooth substances, not rough things. The O Notation can be seen as the smoothing out over time.

So what makes this interesting to someone not interested the vagaries of my mind - an audience I assume you are a a member of. Well, it illustrates something very interesting about how we think about scale.

Scale is one of the most important ideas for a person making sense of today's world. The human sphere is expanding, and understanding things at a small level no longer confers sense on the global scale.

It's arguable if it ever did, but certainly in modern times with airplanes, the internet, and the immediacy of international commerce we can no longer consider ourselves informed if we try to think.

The paradox of thrift is a simple case of Macro vs. Micro level thinking. The paradox is as follows: "If everyone increases the amount of money they save during a recession, then aggregate demand will drop - worsening the depression." Since saving and thrift is generally good for the individual, it presents an interesting dilemma. I'm told something similar happened in Japan. However, Economics is almost a science, so few schools agree on anything. Luckily, this is immaterial, the questions of scale simply changes form.economists disagree as to what is going on.

Richard Feynman

Feynman once said: "There are 10 to the 11 stars in the galaxy. That used to be a huge number. But it's only a hundred billion. It's less than the national deficit! We used to call them astronomical numbers. Now we should call them economical numbers."

I wasn't thinking of this when I was pondering O Notation, but I did conform to it's pronouncements. To my mind, the instant I thought of a billion or a trillion the economic scale came to mind. It was impossible for me to allow such blurring as the O Notation creates to occur, as to do so would be to ignore real world problems.

But it makes me think of other questions of scale. The budget for The United States Department of Defense in 2009 is projected to be $786 billion. How much does that mean in real terms? Is this the right scale?

It is the case that we as laymen don't know the accounts of the various sub-departments in detail to know the exact value of Defense. So the only political question here that we are capable of considering: What is the "right" scale for spending on defense? What about health? What about education? Energy? Veteran's Affairs?

This questions are left as an exercise to the reader. There is some evidence they are difficult.

But Wait, There's More!

This is my first post on my new schedule. For the conceivable future, there will be a new post every Monday. I'll see you next week!

Humor And the Formal Narrative

Yes, I am alive and well. After not posting for a while - and giving a load of crap posts - I feel compelled to write something worth reading. So this post will be about a particular kind of humor - the variety that comes from mocking "forms".

A form is a perceptual structure, an idea shape. Anything that has any kind of structure has a form. Often these forms are slightly fictitious. A piece of electronics has a corresponding circuit diagram as a form though the circuit and the diagram are two very different things. It is widely believed that there is a very high level form to both thought and reality (interestingly, the second would seem to imply the first).

Claude Shannon, information theorist, is useful as a human face for the concept of abstraction.

This form is generally considered to be mathematical in nature (to quote one man's opinion on it "Every science is a real science insofar as it is mathematics"), though certainly not necessarily mathematical in the ordinary sense - a system of closed form equations. It is possible very possible that the universe is better represented by iterative functions or differential equations or some other unknown process that may have no elementary solution.

But I digress... this post isn't about those implications except indirectly. Instead, I am going to write a little bit about humor. There is something both universal and intensely personal about humor. Humor can come from structure, charachter, and - even harder to define - aesthetics. Humor is difficult to encapsulate. There is a great deal of humor in seriousness. Is anything quite as funny as Robot Monster?

What precisely is the incongruity that makes this so funny?

Since this picture is certainly the only thing like itself, what are we comparing it to when we say it looks wrong? In fact, I don't think I would say it looks wrong but that it just looks wrong. As opposed to a subtle or complex wrongness, this is just laughable. One must always remember that functioning human adults made this movie. What led them to this ... aesthetic? Certainly, it wasn't mere poverty. There is a plethora of cheap black and white sci-fi movies which lacked this "aesthetic" and are now completely forgotten.

Are we imagining some sort of counter-factual image in which Robot Monster? What image do we have that a robot monster (which certainly the lead of a film called Robot Monster should be) should look like that this image is transgressing? Perhaps a more classical humor would help.

Classical Humor, but not the classic cast

Here The Three Stooges (Larry, Moe, and Curly-Joe) tussle with a more classic idea of a robot. It is large, gray, and highly unnatural looking. It is made out of simple euclidean shapes, in other words it looks engineered. Is this the idea we have of robots that makes Ro-Man so "unusual"? In a way it is very prejudicial of us.

I think we can agree at this point that comedy is a complex, mostly intuitive process. When one tries to pull it apart, humor only rarely arises. But this is by far from universally true! Indeed, one wellspring of comedy is the mockery of the various narrative forms.

A Sports Movie. Notice the deadly serious expressions on everyone's face.

There is probably a great deal of grammar for talking about this in art circles, but I am forced to develop my own out of ignorance. I have already defined form, it's close cousin formality comes next. Formality is the level of abstractness of the underlying form that one intentionally follows. Something with a high degree of formality is "very formal".

A sort of scale "exists": Monster A Go Go is as formless as Three Dimensional Random Walk. Coen Brothers movies are (mostly) fairly informal. Rock N' Roll follows strict forms, but mostly intuitively - leaving it at a sort of middle. Agatha Christie novels are pretty formal. Romantic Comedies are rigidly formal. Harry Stephen Keeler is formal to the point of incomprehensibility. I hope that this axis clearly indicates that there is not a direct relationship with formality and creativity or quality. There is more than enough room in any story structure to allow for play.

This is - as noted before - about a certain approach to formality, a perverse approach. I would call it being sly, some call it being subversive. Subversive is too political sounding for my tastes. When people mock sports movies they are not generally making a political statement about the role of sport or recreation in society. To be redundant, what they are doing is mocking sports movies. To do this one builds a sports movie but does it in a way that undermines the standard grammar of sports movies.

Though slyness is itself an approach, there are also many approaches one can take to being sly. The most obvious is the outright parody. In fact, one of the most common pitfalls of slyness is what could be called a "Shallow Parody", where rather than inventively mock the best parts and greatness of something one wallows in the underbelly. It results in a so-called slyness that is only as good as the weakest of the ideas stolen.

A good example of a parody is Screwy Squirrel - an almost pure parody of Tex Avery madness (done by the man himself).Generally, descending into self-parody is a Bad Thing. And truthfully, Screwy Squirrel isn't Tex Avery's high water mark. Screwy is so pure a parody that he doesn't really have a personality for himself.

It might behoove me at this point to define satire, which fortunately I have already done.

Anyway, Screwy Squirell also mocks the kinds of cutesy cartoons still being made at the time (or at least, only recently ended). They are abruptly dismissed, though there actually were some good ones. Avery's own I Love To Singa is the big cult classic there.Another point of Screwy Squirrel's mockery is the Cecil Turtle/Droopy Dog plot device that was a bizarre Tex Avery trademark.

Another method of mockery is the welding together of two genres so dissimilar that seriousness becomes impossible. In The Blow Out, (a long time favorite of mine - though I can never remember the name of the cartoon Lucille La Verne's evil voice is very memorable) Avery welds together a Pulp Fiction villain with a sanitized Little Rascals hero.

I just noticed that Avery again uses a bad guy mercilessly hounded by a good guy in this one. He must have found the whole idea hilarious.

Parody exists in music as well. Frank Zappa often parodied forms, he had a professed love of Doo-Wop. Zappa was equally capable of larger scale parody and out-right satire.

And now here's something you'll really enjoy!

Another type of slyness is the more general Rocky & Bullwinkle variety.Most fondly remembered was the self important Mr. Peabody and his boy Sherman.It is this kind of slyness that is perhaps the hardest to describe. It can't honestly be described as a parody. But it certainly isn't . It is a feigning of unintelligence while displaying obvious intelligence. Sometimes, it involves deliberate Camp, but not always. Like all forms of slyness is an approach, not a style. Ren & Stimpy had a similar slyness, but was entirely different in style.

This variety can also be found in music. Take the B-52s and Josquin des Prez also made effective use of imitation and humor.

This is Des Prez. You probably won't see the B-52s and Des Prez compared again.

The oeuvre of these musicians aren't really parodying something in particular. Rather there is a whole feel of play and humor that pervades the music.

It's interesting to think of the importance of words in these songs. While El Grillo is very light, Rock Lobster is rather perversely violent. Indeed, the fun of the song is in the contrast of the oddly serious surf-esque music with the absolutely kitschy imagery. We know that the music is humorous in intent - exactly how is what I'm driving at. Would a martian with no preconceived knowledge hear the song and interpret it as being much more violent than we with our shared ideas of kitsch? Would that make it less funny or more? It is difficult to say.

I don't want to imply that all musical humor comes from the spoken parts. Chopin's "Wrong Note" Etude (opus 25 - #5 in E minor), for instance is not only full of awkward dissonance, but is not quite rhythmically correct. Of course, playing it wrong perfectly is itself very instructive (it forces one out of finger ruts) - which is why it is in a lesson book. One bit that makes it funny is that it sounds like an amateur imitating Chopin - and an amateur exercise that could only have been written by a master is a funny concept indeed! I think the only time I've ever laughed out loud listening to a symphony though was during Charles Ives's Symphony no. 4 (I think it was four anyway). The way it blasted from outright incredible dissonance straight into an orchestral rendition of folk songs was hilarious! Absolutely Hilarious!

But as I was writing, we run into the same problem in music that we do in imagery - the Robot Monster Problem - how do we differentiate between "serious" uses from non-serious. How the question is framed is very important. We already can and do differentiate parody and non-parody. We can even tell the difference between Screwy Squirrel and non-parodic but also humorous cartoons, which is really quite the feat if one thinks about it.

Even on a basic level single word level we can find humorous names that seem to tweak something indefinable.What is it about the names Prescott Lowery or (Wal)ly Ballou that makes them so laughable? Both are fairly realistic smashing of syllables after all.

These are deep mysteries.

Sonny Terry

There is no music in the world quite like Sonny Terry's. He was a harmonica player, most famous as part of a duo with Brownie McGhee.
If Sonny Terry had a trademark it would be his wild whoops and hollers. If he had a style it would be his rolling and rollicking wave of sound. He loved to play and loved to blow the harp he was always bouncing more sounds out of it - never less.There is a whole chock full of videos available on YouTube from when Sonny & Terry did a show for Pete Seegar.

I don't know what I could write to follow up Sonny Terry. I mean unless I just jam out something great I might as well stop.