Showing posts with label logic. Show all posts
Showing posts with label logic. Show all posts

Monday, May 4, 2015

Happy Star Wars Day...Chumps!


I was never a fan of Voyager, but Mr. Tuvok here does an excellent job of trolling the Star Wars fanbase. His many malapropisms are the perfect payback to all those people who think Star Track is a thing.

If you're bored, check out my solution to this Star Trek logic puzzle (and subsequent victory dance), which I had to amend recently, thanks to a pesky reader who detected a lacuna. (Ha ha, I'm speaking facetiously, of course: among the Seven Spiritual Works of Mercy is Instructing the Ignorant, which naturally includes Correcting the Wrong. I just hope I'm not in for any more mercy, as it makes me all sweaty and insecure to have my errors pointed out.)

*     *     *

After writing this rather frivolous post, I find that the actress Grace Lee Whitney, a.k.a. Yeoman Rand, has passed away. When I was a boy I thought she was just about the prettiest actress on TV...after Nichelle Nichols. She played a good strong character, as seen in episodes like "Charlie X" and "The Enemy Within," which also unfortunately reflect some of the attitudes toward female professionals at the time. But I guess that's been true of just about every incarnation of Star Trek since. Anyway, requiescat in pace, Grace Lee Whitney. Thank you for struggling to overcome your personal demons and serving as an inspiration to others.

Link

Thursday, April 2, 2015

You Are Likely to Be Eaten by a Grue

"Zork I box art" by The box/cover art can or could be obtained
from the distributor. Licensed under Fair use via Wikipedia.
In my last post I mentioned the Infocom games, which got me to thinking about such games and about interactive fiction in general. Infocom, if you don't know, was a computer company founded in 1979 and bought out by Activision in 1986. We had a number of their titles on floppy disks for our Commodore 64, including the three Zork games, Enchanter, Sorcerer, Planetfall, and I forget what else. I mostly played them around the late eighties and early nineties.

They're purely text-based, and form a bridge between the choose-your-own-adventure books that were popular at the time and visual adventure games like King's Quest or Police Quest. But the former were too simplistic to be engaging for long, while the latter, to me, left too little to the imagination. I loved the Zork games because playing them was a bit like being a character in a book. Also, because my parents wouldn't let me play Nintendo, and we didn't own a PC until winning a shopping spree a couple years later.

The beginning of Zork II, my favorite in the series.
The puzzles were extremely difficult, partly because the possibilities for action were basically limitless – you could try any simple command – and partly also because of misleading clues and useless objects. But of course, once you strip away the trappings, they're really just big logic puzzles, and I've mentioned my proclivity for logic puzzles here in the past. Part of the difficulty for me back in those Web-less days was that we had no instructions for any of them, since we inherited the games as part of a box of disks gotten rid of by someone else, but really that just added to my enjoyment.

I've done a bit of programming, beginning with BASIC at the same time I was playing the Zork games – which probably are what got me into programming – and continuing into C++ and other things in later years. Actually, just the other day I found some ancient C++ notes of mine with a map of Zork II drawn on the back. They're the classic games for geeks, and contain numerous programmers' in-jokes and obscure references, like 69,105. I've always wanted to try my hand at writing interactive fiction...

But all of that's not to say that the setting was nothing to me. Romantic that I am, I played the Zork games chiefly for their subterranean, half technological, half magical setting, exemplified by the opening above, in which the adventurer encounters an Elvish sword (which naturally glows in the presence of enemies) and a battery-operated brass lantern in an ancient barrow. The lantern's batteries, incidentally, have a frustratingly low life-span, leaving the hapless adventurer prey to lurking grues once the light goes out.

The interested reader can experience these games at the Internet Archive, which allows you to play them online in an Apple II emulator:
Enjoy!

Oh ye who go about saying unto each: "Hello sailor":
Dost thou know the magnitude of thy sin before the gods?
Yea, verily, thou shalt be ground between two stones.
Shall the angry gods cast thy body into the whirlpool?
Surely, thy eye shall be put out with a sharp stick!
Even unto the ends of the earth shalt thou wander and
Unto the land of the dead shalt thou be sent at last.
Surely thou shalt repent of thy cunning.

Thursday, March 12, 2015

Half-Breeds Like Us

In which I muse on my mixed ethnic background, the sense of isolation resulting from such a background, the history of negative mixed-ethnic stereotypes in letters and logic, and the weird ways in which these play a role in my writing.

Wagner's Hagen: half man, half dwarf.

Raymond Chandler's Playback is not his most well-known novel. It's meandering and depressing and mildly offensive, though it might have made a good noir film in the hands of the right director. In the course of this particular quest for truth, Marlowe finds himself extracting information from a parking garage attendant:
I let the door close and stood outside it waiting and a lean man in a long white coat came around the corner. He wore glasses, had a skin the color of cold oatmeal and hollow tired eyes. There was something Mongolian about his face, something south-of-the-border, something Indian, and something darker than that. His black hair was flat on a narrow skull.
Marlowe questions him, using his dope habit as leverage. In the course of their conversation the man reveals his ethnicity:
"You're not Mex?" 
"I'm part Chinese, part Hawaiian, part Filipino, and part n****r. You'd hate to be me."
Afterward:
He turned away and I went through the door and rang for the elevator. He was a queer duck, the attendant, very queer. Kind of interesting, though. And kind of sad, too. One of the sad, one of the lost.
Later on, Marlowe goes to find him at his house.
At the far corner of Polton's Lane there was an automobile agency. I followed its high blank wall, looking at broken crates, piles of cartons, trash drums, dusty parking spaces, the back yard of elegance. I counted the buildings. It was easy. No questions to ask. A light burned in the small window of a tiny frame cottage that had long ago been somebody's simple home. The cottage had a wooden porch with a broken railing. It had been painted once, but that was in the remote past before the shops swallowed it up. Once it may even have had a garden. The shingles of the roof were warped. The front door was  a dirty mustard yellow.
It goes on like this for a while. Then comes the inevitable discovery:
The man's scuffed toes almost touched the floor. His head was up in the darkness inches from the two by four that held up the rooof. He was hanging by a black wire, probably a piece of electric light wire. The toes of his feet were pointed down as if they reached to stand on tiptoe. [...]
I closed the door on him. I didn't go back in the house. As I went along the side towards Polton's Lane, that handsome residential street, the parrot inside the shack heard me and screeched "Quién es? Quién es? Quién es?"
A cruel but effective and not unsympathetic portrait of a person relegated to the interstices of society.

*     *     *

I am, as I have mentioned before, of rather mixed ancestry. Two of my grandparents were born in Puerto Rico, and their genes were a mixture of Spanish, Native American, and West African; my other grandfather came of Greek immigrants who entered the country by way of Ellis Island, and my other grandmother came of plains-dwelling Bohemians like characters in a Willa Cather novel. Practically speaking, what all this rich heritage means in is that I'm an outsider in every party.

When my Greek grandfather married my Bohemian grandmother, he was for a time persona non grata with her family. Her parents refused at first to let him in the house, or so the story goes. Being quite a likeable guy, though, he eventually won everyone over; actually, he became so integrated in the town that he hosted a polka program on the local radio station. They eventually settled elsewhere, and my grandmother had nine children – think My Big Fat Greek Wedding – while her brother had seven, giving rise to two very large but very distinct branches. The first is scattered from the West Coast to the East Coast; the second has tended to stay close to home.

A couple summers ago I went to a reunion in the old hometown. It was friendly, but I could sense a certain amount of tension. I suppose it didn't help that the cookout took place in a park dedicated to Hermann (Arminius, the titular protector of the Sons of Hermann), in the shadow of a terrifying statue of the hero that looms over the whole town from atop a towering dome, a kind of shrine where devotional souvenirs are sold. A relative lamented to me that her children aren't pure-blooded, as her husband isn't entirely of Germanic extraction. My children are purely human, and that's about it.

But back to my grandfather. On his own side he was regarded as having run off to marry an outsider. He made a choice – a sacrifice – to turn his back on his Greek heritage and embrace American patriotism like no other person I know. Similarly, my Puerto Rican grandparents raised my father to speak English, not Spanish. This was a conscious decision to integrate. My great-grandfather was a railroad worker; my grandfather was a sailor and airman and hardware store manager; my dad was a soldier and science teacher and counselor; and I'm what I am, such as it is. I guess we're slowly working our way in.

Incidentally, though, I'm not criticizing those who choose to retain a strong cultural identity in this country. On the contrary, I have an acute sympathy for them, because I know what happens when you lose it, and find yourself falling between chairs. I've sometimes regretted my family's sacrifice. But then again, I like existing.

*     *     *

There is a tendency, even among the diversity-minded, to view ethnicity as a matter of discrete categories or sets. To them, the "other" about which they are so solicitous tends to be a pure-blooded member of an ethnic minority, a view reinforced by bureaucratic check-boxes. In such a world the half-breed has no place. But of course ethnicity is really more like a collection of fuzzy sets.

In Aristotelian logic and classical set theory, an individual either does or does not belong to a set. The concept of the fuzzy set, developed by Lotfi Zadeh in the 1960s, allows for degrees of membership. Membership is valued as a real number μ such that 0 ≤ μ ≤ 1. In contrast to this, membership in ordinary or "crisp" sets is valued as 0 (not belonging) or 1 (belonging). In a rigorous sense, fuzzy logic is, I think, still insufficient to model ethnicity, because there clearly is a discrete element to genetics – inheritance is "digital" rather than "analog" (as, I believe, Mike Flynn put it, though I can't find the passage now) – and no ethnic category has a well-defined center, as though springing from a single progenitor like mankind from Adam. But as a metaphor, the concept at least captures the fact that we're not dealing with a black-and-white issue.

Thayer Watkins, whose website I consulted while reading about fuzzy sets, opines that Lotfi Zadeh's ethnicity is itself an example of a fuzzy set:
The question of Zadeh's ethnicity is difficult to answer sharply. His father was Turkish-Iranian (Azerbaijani) and his mother was Russian.
Dr. Watkins' site has some (alas, broken) links to discussions of the art of Paul Klee, a subject that fascinates me. It's interesting and possibly significant that the same people who were so fixated on the idea of racial purity were also the most suspicious of visual abstraction. (I wrote a bit about "degenerate art" here, and defended the art of Paul Klee here; these were part of a larger essay.) It's also interesting that A. E. van Vogt, who helped to popularize non-Aristotelian logic in the 1940s with his Null-A books (which I'm very fond of), apparently grew up speaking Low German in a Russian Mennonite community in Canada; whether he was ethnically diverse I don't know, but certainly he was personally acquainted with the idea of degrees of membership. It's the pitiably thalamic Enro the Reds of this world who feel the need to call black black and white white and fear or anathemize anything that falls between.

*     *     *

I sometimes read Nietzsche. How great a philosopher he was is debatable, but he had a penetrating insight, and was sensitive to the trends of his times and what was to come. At any rate I've found him useful. Henri de Lubac's Drama of Atheist Humanism has been helpful in this regard.

Nietzsche discusses the mixture of races at some length in Beyond Good and Evil. To wit:
In an age of disintegration that mixes races indiscriminately, human beings have in their bodies the heritage of multiple origins, that is, opposite, and often not merely opposite, drives and value standards that fight each other and rarely permit each other any rest. Such human beings of late cultures and refracted lights will on the average be weaker human beings: their most profound desire is that the war they are should come to an end. Happiness appears to them, in agreement with a tranquilizing…medicine and way of thought, pre-eminently as the happiness of resting, of not being disturbed, of satiety, of finally obtained unity, as a 'sabbath of sabbaths.'
It's hard to read this without reflecting on the way history went in the following century. There were the Nazi atrocities, and all else pales beside them, but even in our own country we had anti-miscegenation laws and the eugenics movement. Might not the still-current suspicion of the mixing of races be traced to the same origin? It's a little depressing to reflect that Alexis de Tocqueville predicted in Democracy in America that equality would never dawn until intermarriage created a smooth gradation between the races.

Anyway, Nietzsche goes on to describe how this leveling process sets the stage for the coming of the beautiful predatory one, the "Alcibiades" of history:
But when the opposition and war in such a nature have the effect of one more charm and incentive of life – and if, moreover, in addition to his powerful and irreconcilable drives, a real mastery and subtlety in waging war against oneself, in other words, self-control, self-outwitting, has been inherited or cultivated, too – then those magical, incomprehensible, and unfathomable ones arise, those enigmatic men predestined for victory and seduction… They appear in precisely the same ages when that weaker type with its desire for rest comes to the fore: both types belong together and owe their origin to the same causes. 
He later discusses Frederick II, better known as Frederick the Great:
Men were missing; and he [Frederick William I] suspected with the most bitter dismay that his own son [Frederick II] was not man enough… He saw his son surrender to atheism, to esprit, to the hedonistic frivolity of clever Frenchmen: in the background he saw that great vampire, the spider of skepticism; he suspected the incurable misery of a heart that is no longer hard enough for evil or good, of a broken will that no longer commands, no longer is capable of commanding. Meanwhile there grew up in his son that much more dangerous and harder new type of skepticism – who knows how much it owed precisely to the hatred of the father and the icy melancholy of a will condemned to solitude? – the skepticism of audacious manliness which is most closely related to the genius for war and conquest… This skepticism despises and nevertheless seizes; it undermines and takes possession; it does not believe but does not lose itself in the process; it gives the spirit dangerous freedom, but it is severe on the heart…
These ideas are profoundly repellent and fascinating to me. Repellent, because I embody everything Nietzsche saw in the degeneration of civilization: I'm not strong or ruthless or masterful, I'm racially impure, I have a developmental disability, I believe in the Beatitudes he so despised, &c. Fascinating, because they have a certain inner consistency and dramatic effectiveness, and even a romantic aura, if you're one of the pure-blooded. 

*     *     *

My ruminations on the subject gave rise to a pulp adventure story called "The Goblin King's Concubine." The plot outline was suggested by the story of Cynthia Ann Parker, mother of Quanah Parker, a story that also inspired Robert E. Howard's "The Vale of Lost Women," which has some disquieting racial elements. "Concubine" is the tale of a half-breed who falls between cultures. Write what you know, as they say. The character I identify with is Zilla. Maybe I shouldn't admit that! It's a dark tale and obviously made some people uncomfortable. But despite its origin it doesn't have a message or point. It's just a story written for entertainment.

And the half-goblin Zilla's biography extends far beyond it. He goes back almost twenty years in the history of my imagination, appeared in my earlier story, "Misbegotten," and plays a role in my forthcoming novel, Dragonfly. He is inspired by Nietzsche's Frederick the Great as well as Dostoevsky's Nikolai Stavrogin (The Possessed), Wagner's half-dwarf Hagen (Götterdämmerung), and, I must admit, Tolkien's "ill-favored" half-orc southerner in Bree. He comes from a desire to explode, from inside out, the negative stereotype of the suspicious half-breed, a role I've found myself assigned more than once. And by explode, I mean expand and dissect. But again, the objective is entertainment.

You see, I could write moralizing stories about virtuous half-breeds misunderstood and mistreated by their wicked pure-bred fellow citizens, but that would be obvious, stupid, and boring. No, my half-breed is not just suspicious and sneaky, but bad-ass, a great-souled warlock and conqueror who, far from being ill-favored, is so beautiful he has to wear a veil like Moses coming down from the mountain just to keep people from worshiping him.

So, yeah, Dragonfly, coming soon to an online retailer near you.

Sunday, December 14, 2014

Logical Self-Congratulation

Hey! My solution to the "extremely difficult" Star Trek puzzle I posted last week is reprinted today at io9 with my permission (scroll way down).

I worked the puzzle out while watching my students take a final exam. I was interested in it mainly because I teach a course on discrete math, covering things like formal logic, relations, and graph theory, and I'm always looking for interesting new problems. But as a mathemagician, I'm more interested in how to create puzzles like this than in how to solve them. I wonder how Professor Finkel did it? Perhaps he added one statement at a time until his program gave him a single solution. From a logical point of view, it was much simpler than it need have been, given that only one statement connected the two "parts" of the puzzle.

Robbie Gonzalez, the column's author, says this about the puzzle:
I'm going to come right out and say it: This puzzle is, in fact, "extremely difficult." It is not so much one puzzle as it is several logic puzzles. Some of those puzzles are nested, such that certain conclusions cannot be made until one has accurately arrived at some other conclusion or conclusions. This kind of puzzle can get very complicated very quickly, and solving it typically involves the use of a spreadsheet or some kind of table to keep track of all the relationships in play. 
It's also the kind of puzzle that begs for a programmatic approach. And, in fact, that's exactly how Finkel [the professor who created the puzzle] solves it himself. "This admission may come as a surprise," he writes me by email, "but I have no idea how to attack this puzzle with pen and paper!"
Well, now he and the rest of the Internet know. And maybe, because of that knowledge, the world is just a tiny bit less dark, a tiny bit less confusing. Maybe someone, somewhere, will go to sleep easier tonight, knowing which Enterprise NCC-1701-D crew member outranks which at Fizzbin. Just maybe. And that makes it all worthwhile.

Tuesday, December 9, 2014

A Star Trek Logic Puzzle [Updated]

♪Which one does not belong?♪
Yesterday I came across a cool logic puzzle at io9. They reproduced it from the website of Raphael Finkel, a professor in the Computer Science Department at the University of Kentucky. I am constitutionally unable to refrain from solving a logic puzzle; moreover, the puzzle uses characters from Star Trek: The Next Generation, which has nothing to do with the solution, but I'm superficial like that.

Here is the problem, for which I take no credit, quoted from io9 and Professor Finkel's web page (but don't look at the latter unless you want to see the solution):

Grobly Grizik is planning to write a novel fashioned after Star Trek: The Next Generation. In this novel, six of the crew members compete both at Fizzbin and at Tridimensional chess. Each crew member gets two independent rankings for ability at these games, with 1 ranked lowest and 6 highest. Every crew member has a personal hero among the crew, and every crew member is afraid of some crew member. Everyone is the hero of somebody, and everyone is feared by somebody. Nobody either fears him/herself nor counts him/herself as a hero. Nobody fears his/her own hero. From the given clues, discover every crew member's ranking at Fizzbin and at Tri-D chess, as well as whom he/she fears and whom he/she counts as a hero:
  1. Geordi ranks 2 at Tri-D Chess.
  2. Picard ranks two positions behind Troi at Fizzbin.
  3. Troi is feared by the person Geordi fears.
  4. Worf's hero ranks 3 times lower at Tri-D Chess than the crew member who is best at Fizzbin.
  5. Picard's hero fears Geordi.
  6. Data's hero is not Geordi.
  7. Data is the hero of Riker's hero.
  8. The person who is worst at Fizzbin is better than Troi at Tri-D Chess.
  9. The person ranked number 3 at Tri-D Chess is ranked 4 positions higher than Data at Fizzbin.
  10. Riker is feared by the person Picard fears and is the hero of Worf's hero.
  11. Riker is ranked 2 lower at Tri-D Chess than the crew member ranked 2 at Fizzbin.
Solution

Upon closer examination, we find that there are five statements dealing with only heroes or fear (Statements 3, 5, 6, 7, 10), five statements dealing with only Tri-D Chess or Fizzbin (Statements 1, 2, 8, 9, 11), and exactly one statement dealing with both (Statement 4). Let's renumber, and also break up Statement 10:

1A. Troi is feared by the person Geordi fears.
1B. Riker is feared by the person Picard fears
1C. Picard's hero fears Geordi.
1D. Riker is the hero of Worf's hero.
1E. Data is the hero of Riker's hero.
1F. Data's hero is not Geordi.

2. Worf's hero ranks 3 times lower at Tri-D Chess than the crew member who is best at Fizzbin.

3A. Picard ranks two positions behind Troi at Fizzbin.
3B. The person who is worst at Fizzbin is better than Troi at Tri-D Chess.
3C. The person ranked number 3 at Tri-D Chess is ranked 4 positions higher than Data at Fizzbin.
3D. Riker is ranked 2 lower at Tri-D Chess than the crew member ranked 2 at Fizzbin.
3E. Geordi ranks 2 at Tri-D Chess.

The puzzle of fears and heroes can be solved on its own, using only Statements 1A – 1F. The fact that each crew member is feared by some other member means that the correspondence is surjective; therefore, it must be bijective as well, and each must be feared by exactly one other member. So we can't have two members fearing the same member, etc. The same goes for heroes.

First, for fears, Statement 1A yields
F: Geordi → (???) → Troi 
and Statement 1B yields
F: Picard → (???) → Riker
For heroes, Statements 1D and 1E yield
H: Worf → (???) → Riker → (???) → Data
Now, Data must adulate someone. He could* possibly adulate Riker or Worf, if we had one of the following arrangements:
H: Worf → Data → Riker → Worf
H: Worf → (???) → Riker → (???) → Data → Worf
Both are compatible with the preceding. The latter leaves out a single crew member, because the unknowns can't be any of the three already listed, and, since no one can adulate themselves, this is impossible, leaving us with the former. But this would imply one of the following:
H: Picard → Troi → Geordi → Picard
H: Picard → Geordi → Troi → Picard
But both are impossible, because both violate 1C (Troi cannot both fear and adulate Geordi, and Geordi cannot fear himself).

So Data adulates neither Worf nor Riker, hence must adulate a third unknown, who in turn adulates Worf, so that we have
H: Worf → (???) → Riker → (???) → Data → (???) → Worf
where the three unknowns must be Picard, Troi, and Geordi. Statement 1F states that Data doesn't adulate Geordi, so Data must adulate Picard or Troi. If Picard, then Statement 1C implies that Worf fears Geordi. This would give us
F: Worf → Geordi → (???) → Troi
F: Picard → (???) → Riker
Five crew members are written explicitly here. So at least one of the unknowns already appears in one of these chains, and the only way the two chains fit together is if Picard is feared by Geordi, so
F: Worf → Geordi → Picard → Troi → Riker
But this creates an impossible situation. Worf must adulate Geordi or Troi. If Geordi, then this violates his fear of Geordi, since no one can both adulate and fear the same person. If Troi, then Troi would adulate Riker, violating her fear of Riker.

It follows that Data adulates Troi. We have
H: Worf → (???) → Riker → (???) → Data → Troi → Worf
Now, either Worf adulates Picard and Riker, Geordi, or vice versa. But Worf can't adulate Picard, or else Picard would adulate Riker, with the implication that Riker would fear Geordi (Statement 1C), resulting in
F: Picard → (???) → Riker → Geordi → (???) → Troi
which violates Riker's adulation of Geordi. So Worf adulates Geordi, and Riker, Picard. We've completed our hero chain:
H: Worf → Geordi → Riker → Picard → Data → Troi → Worf
Next, Statement 1C implies that Data fears Geordi, so we have
F: Data → Geordi → (???) → Troi 
F: Picard → (???) → Riker
The only way for these chains to fit together is for Picard to be the first unknown. So we have
F: Data → Geordi → Picard → Troi → Riker → Worf → Data
This completes our chain of fear. On to Tri-D and Fizzbin.

According to Statement 3A, Picard ranks 2 lower than Troi at Fizzbin, so he can't rank 5 or 6, and Troi can't rank 1 or 2. Similarly, Troi can't rank 6 at Tri-D (Statement 3B), and Data can't rank 3 at Tri-D or 3, 4, 5, or 6 at Fizzbin (Statement 3C); since Picard can't rank 5 or 6 at Fizzbin, Statement 3C also implies that Picard can't rank 3 at Tri-D. Also, Riker can't rank 5 or 6 at Tri-D (Statement 3D). Finally, we know for a fact that Geordi ranks 2 at Tri-D (Statement 3E). So far we have:
       |   Tri-D   | |  Fizzbin  |
       |1|2|3|4|5|6| |1|2|3|4|5|6|
  Data | |X|X| | | | | | |X|X|X|X|
Geordi |X|O|X|X|X|X| | | | | | | |
Picard | |X|X| | | | | | | | |X|X|
 Riker | |X| | |X|X| | | | | | | |
  Troi | |X| | | |X| |X|X| | | | |
  Worf | |X| | | | | | | | | | | |
(Excuse my crappy table; I have time to work out logic puzzles, but not to learn how to make tables in html.) We know that Geordi is Worf's hero, so Geordi is ranked 3 times lower at Tri-D Chess than the crew member who is best at Fizzbin. Since we already know Geordi is ranked 2, the person who is best at Fizzbin must also be best at Tri-D. This eliminates Data and Picard from being best at Tri-D, and Geordi, Riker, and Troi from being best at Fizzbin. So Worf must be best at both. Worf does not rank 2 at Fizzbin, so Statement 3D implies that Riker does not rank 4 at Tri-D.
       |   Tri-D   | |  Fizzbin  |
       |1|2|3|4|5|6| |1|2|3|4|5|6|
  Data | |X|X| | |X| | | |X|X|X|X|
Geordi |X|O|X|X|X|X| | | | | | |X|
Picard | |X|X| | |X| | | | | |X|X|
 Riker | |X| |X|X|X| | | | | | |X|
  Troi | |X| | | |X| |X|X| | | |X|
  Worf |X|X|X|X|X|O| |X|X|X|X|X|O|
Now, Riker ranks either 1 or 3 at Tri-D. If he ranks 1, then Troi must rank 3. It would follow that Troi ranks 4 places above Data at Fizzbin (Statement 3C). With the spaces available, the only way this could happen is for Data to rank 1 at Fizzbin and Troi to rank 5. But Statement 3D would imply that Troi ranks 2 at Fizzbin, a contradiction.

So Riker ranks 3 at Tri-D. He therefore ranks 4 places above Data at Fizzbin, placing Data at 1 and Riker at 5. We now know that Data did better than Troi at Tri-D (Statement 3B), so he can't rank 1 at Tri-D, and Troi can't rank 5 at Tri-D. We have:
       |   Tri-D   | |  Fizzbin  |
       |1|2|3|4|5|6| |1|2|3|4|5|6|
  Data |X|X|X| | |X| |O|X|X|X|X|X|
Geordi |X|O|X|X|X|X| |X| | | |X|X|
Picard | |X|X| | |X| |X| | | |X|X|
 Riker |X|X|O|X|X|X| |X|X|X|X|O|X|
  Troi | |X|X| |X|X| |X|X| | |X|X|
  Worf |X|X|X|X|X|O| |X|X|X|X|X|O|
Statement 3D implies that the person who ranks 2 at Fizzbin also ranks 5 at Tri-D; this means that Data does not rank 5 at Tri-D, hence must rank 4.
       |   Tri-D   | |  Fizzbin  |
       |1|2|3|4|5|6| |1|2|3|4|5|6|
  Data |X|X|X|O|X|X| |O|X|X|X|X|X|
Geordi |X|O|X|X|X|X| |X| | | |X|X|
Picard | |X|X|X| |X| |X| | | |X|X|
 Riker |X|X|O|X|X|X| |X|X|X|X|O|X|
  Troi | |X|X|X|X|X| |X|X| | |X|X|
  Worf |X|X|X|X|X|O| |X|X|X|X|X|O|
So Troi is ranked 1 at Tri-D, and Picard is ranked 5. It follows that Picard is ranked 2 at Fizzbin (Statement 3D), and Troi is ranked 4 (Statement 3A). Geordi must therefore rank 3 at Fizzbin.
       |   Tri-D   | |  Fizzbin  |
       |1|2|3|4|5|6| |1|2|3|4|5|6|
  Data |X|X|X|O|X|X| |O|X|X|X|X|X|
Geordi |X|O|X|X|X|X| |X|X|O|X|X|X|
Picard |X|X|X|X|O|X| |X|O|X|X|X|X|
 Riker |X|X|O|X|X|X| |X|X|X|X|O|X|
  Troi |O|X|X|X|X|X| |X|X|X|O|X|X|
  Worf |X|X|X|X|X|O| |X|X|X|X|X|O|
And we're done. To sum up:
  • Data fears Geordi, adulates Troi, ranks 4 at Tri-D, and ranks 1 at Fizzbin.
  • Geordi fears Picard, adulates Riker, ranks 2 at Tri-D, and ranks 3 at Fizzbin.
  • Picard fears Troi, adulates Data, ranks 5 at Tri-D, and ranks 2 at Fizzbin.
  • Riker fears Worf, adulates Picard, ranks 3 at Tri-D, and ranks 5 at Fizzbin.
  • Troi fears Riker, adulates Worf, ranks 1 at Tri-D, and ranks 4 at Fizzbin.
  • Worf fears Data, adulates Geordi, ranks 6 at Tri-D, and ranks 6 at Fizzbin.
Updated to correct an error brought to my attention by Robbie Gonzalez, who runs the puzzle column at io9 where this puzzle was featured.

* As pointed out by a correspondent with the infernal name of TartarosFalling, who wrote to correct a lacuna at this point.

Monday, February 18, 2013

A. E. van Vogt

The Golden-Age science fiction author A. E. van Vogt (1912 – 2000) was famously called "a pygmy with a giant typewriter" by Damon Knight. Well, I must be a pygmy of a reader, because I prefer van Vogt to every other science fiction writer of his period.

Part of the attraction for me, and part of the disappointment for other readers, perhaps, is that the innovations he explores are not primarily technological. He invents all sorts of futuristic gadgetry, but it's there just to make the plot possible and keep it going. What he's really interested in is putting human beings in new kinds of situations, conforming human society to new patterns, and seeing what happens. Ideas are more important to him than technologies.

There is, for instance, the running theme of The Voyage of the Space Beagle. Voyage is a fix-up novel about an intergalactic scientific expedition, knit together from four stories about encounters with alien life-forms. The stories are interesting in their own right—they must surely have provided inspiration for a number of Star Trek episodes—but what's more interesting to me is their contrast of scientific specialism with holistic understanding. Time and again the specialists come up short in crises through not being able to communicate with one another (or, worse, through academic gamesmanship), while the one "Nexialist" on board is able to integrate the results of their findings to arrive at a simple solution. The space voyage merely serves to isolate aspects of the interplay between the sciences, pragmatic militarism, and the crises that face civilization from time to time, and to point out the weaknesses in the modern framework. It's a disappointment that hypnotism and brainwashing—ideas van Vogt was much addicted to—take the place of rational persuasion at critical points.

The best of van Vogt's novels is surely The World of Null-A. In it, the world is divided into two classes: primitives who live as dictated by chemistry and emotion and think according to Aristotelian logic, classifying everything as black or white; and enlightened elites who recognize that there are…gray areas. Null-A is paralleled with null-E (non-Euclidean geometries) and null-N (non-Newtonian physics). Apparently, being null-A gives you powers to do pretty much whatever you want, including defeating an interstellar space fleet with sticks and stones. And the null-A protagonist, who's supposed to be a new breed of genius (he has two brains) seems bent on racing to his death for no apparent reason. (He actually dies at one point, but no matter: his memories are transported to a cloned body on Venus.) So, the null-A aspect of the novel is rather silly. But it's filled with so much beauty and so many interesting ideas that I can forgive its silliness.

The basic premise is this. Earth is ruled by those closest to grasping the null-A philosophy. Those who actually do grasp it are allowed to emigrate to Venus, a law-free utopia ruled by null-A principles. Examination for null-A proficiency takes place during periodic thirty-day games, reminiscent of the "testing hell" of imperial China. The games machine is a vast rational computer housed in a shining tower at the center of the futuristic capital city of Earth. Venus, on the other hand, is a sylvan paradise where the happy null-A live an idyllic pastoral existence. Much of the planet is forested with trees bigger than skyscrapers. The action moves from Earth to Venus and back to Earth again, as the protagonist, Gilbert Gosseyn, dies and lives again…through a cloned body with implanted memories.

(As an aside, it's interesting to note that van Vogt's identification of memory with identity goes hand in hand with his use of brainwashing techniques to influence recalcitrant antagonists. Brainwashing isn't unethical, because it isn't being done to anybody. There's no underlying person to whom this thing is being done. By changing feelings or memories, you're changing the person into another person, as a sculptor pushes his clay from one shape into another. He's doing something to clay, but it's an abuse of terms to say that he's doing something to a sculpture. There's no constant subject undergoing the operation.)

My wife and I like to read things aloud, and I once tried to read The World of Null-A to her. We didn't get very far. "What is going on?" she kept saying. It just seemed like a bizarre dream to her. And the book is weirdly and wildly incoherent. The characters apparently regard themselves as behaving quite sensibly, and they convince the reader of it from page to page, but if you put it all together it's pure irrationality. I suppose that's part of the draw for me. Life is a little like that, sometimes.

Van Vogt's protagonists tend to be smug adolescents (in maturity if not in age) who do bafflingly foolish or unethical things. In this connection, perhaps it's not out of place to observe that there's an understated, immature kinkiness in most of his characters' sexual situations: Slan ends with the adolescent protagonist's prospect of marrying and mating with two older women, one of whom is quite a bit older; The Weapon Makers is about an immortal man who maintains an imperial bloodline by occasionally wedding his own great-granddaughters; the two goddess-wives in The Book of Ptath can possess other female bodies to make love to their god-husband; Gilbert Gosseyn in The Players of Null-A has his mind projected into the body of a timorous weakling married to a gorgeous princess.
 
Beyond that, as regards the unrealistic action driving van Vogt's plots, Knight referred to him as being like a kid in a sandbox, and one can certainly see grounds for the charge. In a weird way, though, that's part of the draw for me, too. A more positive way of putting it would be to say that van Vogt's stories are naïve. Like an Henri Rousseau painting, they can seem rather silly and childish on the surface, but possess patterns of strange beauty for all that.

His work, sadly, is very uneven. He was a leader in the Dianetics movement that subsequently evolved into Scientology. His later novels, driven to a great extent by fad theories and pieced together from ill-assorted short stories, are his weakest. His best novels are his earliest, written during the forties. My personal favorites are Slan, The Voyage of the Space Beagle, The World of Null-A, The Players of Null-A, The Book of Ptath, The Weapon Shops of Isher, and The Weapon Makers.

Go to your local used bookstore or secondhand store, buy a few van Vogt titles in Ace paperback editions, and read them, savoring the garish covers, the yellow pages, the clumsy dialogue, the brilliant half-expressed ideas.