Hofstadter’s Law

Hofstadter’s Law: It always takes longer than you expect, even when you take into account Hofstadter’s Law.

(And it has right now a Wikipedia page that directly links to itself. Even the “Recursion” page does not do this.)

Hofstadter’s Law is a self-referential (or recursive) statement coined by Douglas Hofstadter in his magnum opus Gödel, Escher, Bach. It is a statement about time-taking projects, which seem to take more time than expected, even when the expected time is adjusted for delays.

Hostadter includes this at the end of a chapter on recursion, and particularly on a topic in which he shows how chess is analyzed recursively. He then recounts how programmers once (in the mid 1900s) thought chess could be mastered by a computer within ten years, but ten years later, it was still not even close to mastered, and it would seem to take even longer than ten years still!

Here is my illustration of Hofstadter’s Law:

Hofstadter's Law

The subtlety is of course that the graph is self referential. That is, Hofstadter’s Law as in the title of the graph refers to the last bar, “Actual Time.” At first you might expect that Hofstadter’s Law is present only in the fourth bar, but it is really the fifth bar that is Hofstadter’s Law. In fact, the “Actual Time” would be the “Worst Case Estimate, Taking Into Account Hofstadter’s Law” Taking Into Account Hofstadter’s Law. This leads to an infinite regress, as now the “Actual Time” is the new “Worst Case Estimate, Taking Into Account Hofstadter’s Law.”

Let the Right One In

(A 2008 Swedish vampire/romance/horror film directed by Tomas Alfredson.)

Let the Right One In (Swedish)

Rating: 10/10

Let the Right One In (in Swedish: Låt den rätte komma in) is based on a Swedish book by the same name, and I give it a perfect rating because it is by far the most unconventional serious movie I have ever seen. That may sound like an oxymoron, but it is true—this Swedish film contains ideas and scenes that American directors would not dare to show, for fear of being politically incorrect, and for fear of backlashes from material that might be, as a ridiculous euphemism goes, “corrupting the morals of youth.”

To be sure, this is a vampire movie, but it is NOT the same thing as Twilight (which I haven’t seen, but I am sure it must be Americanized). Let the Right One In deals instead with preteen children—or rather, preteen children and a 12-year old vampire who has been 12 years old for a very long time. And when these children and the child vampire begin to employ violence which is not condemned, and which becomes rather the object of sympathy, the film becomes markedly un-Hollywood, un-American.

The movie is quite chilling and also quite moving. As a viewer used to American films, I noticed that the Swedish film seemed slightly slow due to the lack of nonstop action, but this was all well done: I welcomed the time which allowed the deeper and more complex emotions to set in. There are scenes which I had previously imagined happening, but which I never thought would be put into a movie. It is no accident that this film is critically acclaimed—it won numerous awards and the movie has right now a 97% Fresh rating from 149 critics on Rotten Tomatoes.

An American remake of the movie, titled Let Me In, is scheduled for release later this year. I was skeptical at first when I read about this, as I thought it would Americanize the story and presentation too much; however, the director Matt Reeves has made it clear that he respects the ideas of the book and has even rejected a suggestion to change the ages of the main characters, saying that it would “ruin the essence of the story.”

Why is a Raven Like a Writing Desk?

A Mad Tea Party
John Tenniel's illustration of the Mad Tea Party.

This very famous question comes from Alice’s Adventures in Wonderland (by Lewis Carroll, Chapter VII, “A Mad Tea Party”):

The Hatter opened his eyes very wide on hearing this; but all he said was “Why is a raven like a writing-desk?


“Have you guessed the riddle yet?” the Hatter said, turning to Alice again.

“No, I give up,” Alice replied. “What’s the answer?”

I haven’t the slightest idea,” said the Hatter.

“Nor I,” said the March Hare.

Alice sighed wearily. “I think you might do something better with the time, “she said, “than wasting it in asking riddles that have no answers.”

(Here is a full text of this chapter, in case you wish to see the context.)

From Martin Gardner’s Annotated Alice, we learn that Carroll did not intend that there be an answer. In fact, Carroll wrote in the preface to the 1896 edition (I’ve emphasized the last sentence):

Enquiries have been so often addressed to me, as to whether any answer to the Hatter’s Riddle can be imagined, that I may as well put on record here what seems to me to be a fairly appropriate answer; vis: “Because it can produce a few notes, tho they are very flat; and it is never put with the wrong end in front!” This, however, is merely an afterthought; the Riddle, as originally invented, had no answer at all.

Here are some more answers, all documented in The Annotated Alice.

Because the notes for which they are noted are not noted for being musical notes.

Because Poe wrote on both.

Bills and tales (tails) are among their characteristics.

Because they stand on their legs, conceal their steels (steals), and ought to be made to shut up.

by Sam Loyd, American puzzle maven. The Poe answer is my favorite.

Because there’s a b in both.

Because there’s an n in neither.

by Aldous Huxley. In a philosophical manner, he responded to the nonsense question with nonsense.

Because each begins with e.

by James Michie.

Both have quills dipped in ink.

by David B. Jodrey, Jr.

Because it slopes with a flap.

by Cyril Pearson.

Because it can produce a few notes, tho they are very flat, and it is nevar put with the wrong end in front.

by Lewis Carroll. This is an updated answer, intentionally misspelling the word “never” as “nevar”, which is “raven” spelled backwards. The editor, however, mistook this for a typo and “fixed” it to “never.” Carroll died soon after, and so, “[w]hether Carroll was aware of the damage done to his clever answer is not known” (Gardner).

Because without them both Brave New World could not have been written.

by Roy Davenport.

Because one has flapping fits and the other fitting flaps.

by Peter Veale.

Because one is good for writing books and the other better for biting rooks.

by George Simmers.

Because a writing-desk is a rest for pens and a raven is a pest for wrens.

by Tony Weston.

Because “raven” contains five letters, which you might equally well expect to find in a writing-desk.

by Roger Baresel.

Because they are both used to carri-on de-composition.

by Noel Petty.

Because they both tend to present unkind bills.

by M.R. Macintyre.

Because they both have a flap in oak.

by J. Tebbutt.

Because it bodes ill for owed bills.

Because they each contain a river—Neva and Esk.

by Francis Huxley.

That’s all from The Annotated Alice: The Definitive Edition, and they are all very good. Here are some more I’ve found online and elsewhere:

Because a raven makes no sense, and so does a writing desk.

Because neither requires the other.

by Linus Connell.

Because neither one is made of cheese.

(Cannot determine origin of saying.)

Because you can baffle the billions with both.


Because they both stand on legs.


Because you cannot ride either one of them like a bicycle.


Because neither one of them is made from aluminum.


Because the raven wanted to be.


Reflections on High School

Today I took my final final exam in high school, and in a couple of days is graduation.

In my mind, however, school ended a long time ago (in a galaxy far, far—nevermind). I was mentally finished by the end of the first semester, when I began receiving college acceptances. I still remember December 15, 2009, the day I was accepted to the University of Chicago—it was my first real acceptance, as UT Austin accepted me earlier but I knew I was already guaranteed admission from the 10% rule. And though I’m not going to UChicago—I’m going to Cornell—that acceptance letter in my mind sealed away high school.

And when I say “sealed away,” I do not mean I stopped caring. I merely started to view everything from a philosophical, artistic point of view, by questioning things and by not being so rational, for no purpose other than being creative and trying new ideas. Most of my examples of this would come from second-semester during English class, in which I made liberal use of puns and tried to incorporate wit in many other ways. My particular memories include a discussion on Kafka’s Metamorphosis; a short play based on Shakespeare’s Othello and Stoppard’s Rosencrantz and Guildenstern Are Dead as a creative group project after study of the former; and the independent study project, for which my topic was the Physics of the Falcon Punch. My teacher, Ms. Gaetjens, was quite understanding—or perhaps forgiving—of my creative side.

I would elaborate very much on each of these, but the title of this post is “Reflections on High School” and not “Reflections on One Class in One Semester.” It is true that I already touched on many things relating to high school in my similar post at the end of the previous semester, in my Reflections on 2009, so I’d do best to cover the opposite of what I covered in that post.

To be continued… EDIT: Or not.

Waiting for Godot

Samuel Beckett’s Waiting for Godot (1949) is a play composed of two acts in which nothing happens.

Its sophistication lies not in the plot, however, as it doesn’t have any. It is rather the lack of plot which makes the play so compelling. Two characters wait for a person named Godot, and they are not sure whether Godot will ever come.

The very first spoken words are quite encompassing:

ESTRAGON: Nothing to be done.

VLADIMIR: I’m beginning to come round to that opinion.

These opening lines sum up the entire plot, as if the title didn’t already.

The play is very humorous nearly all the time:

VLADIMIR: You should have been a poet.

ESTRAGON: I was. (Gesture towards his rags.) Isn’t that obvious?

I read this last year (in class), so I don’t remember most of the nuances. The thing I remember most is the tree, which grows a few leaves between the two acts. It is otherwise barren. This epitomizes the nothingness of the story and the futility of change—or continuity.


Astute followers of this blog may have noticed a Random blurb on the right-hand column on Waiting for Godot. It has been here for a long time because this play was the thing that changed for the better my views on literature. As such, it receives from me much appreciation.

Better late than Godot.

I thought of this phrase as a more indirect and possibly more humorous way to say “Better late than never.” And I googled “Better late than Godot” in quotations and found zero hits, so yes, I’ll be taking credit for this. 😛