text: [Themes: math, surreal, ancient Greece, educational, adventure]
  
  > Look around
  This space is still filled with a bright light. While the light isn't painful anymore, it is still difficult to see. You can now tell, though, that the source of the light seems to be coming from the floor. In addition, there are exits north, south, east, and west, as well as the one above you to Gray Matter, Level Three.
  
  > go north
  You make your way north through the bright light. As you do, you feel an electrical impulse course through you. You find yourself in...
  
  The smell of tobacco hangs in the air in this small, dark pub. It is nearly deserted; even the bartender appears to have stepped out. An exit leads south.
  
  Cauchy is sitting at the bar, sipping from a glass of wine.
  
  Weierstrass is next to Cauchy, drowning his sorrows in a pint of beer.
  
  > examine cauchy
  Cauchy looks like he is trying to cheer up Weierstrass. He occasionally takes a sip from a glass of wine.
  
  > look at Weierstrass
  Weierstrass is deep into a pint of beer. He stares morosely into his mug from time to time.
  
  > look up weierstrass
  (in your math book)
  Karl Weierstrass, one of the great mathematicians of the 19th century, never actually completed a college degree. He is particularly famous for his precise definitions of limits and continuity, which helped put calculus on a solid theoretical foundation.
  
  > look up cauchy
  (in your math book)
  Frenchman Augustin-Louis Cauchy was the most prolific mathematician of the 19th century. While he made important contributions in many areas, he is particularly known for his emphasis on rigor in mathematics and his pathbreaking work in complex analysis.
  
  > go west
  You make your way west through the bright light. As you do, you feel an electrical impulse course through you. You find yourself in...
  
  Wires and pieces of metal indicate that highly complex experiments must have once been performed in this room. Now, though, they lie scattered haphazardly here and there: Someone has cleared this place out. There are open doors to the north and south, and the exit to the lab lies east. A door to the west is closed.
  
  Not all of the experiments are gone, though; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.
  
  There is also a large fan set into the east wall.
  
  A printout has fallen to the floor.
  
  > examine the platform
  Nothing is on the platform.
  
  > examine the panel
  The control panel is labeled "Transformation Matrix Prototype." It features numbers in a 3 by 3 matrix. Each number in the top row has a slider above it that controls the setting of that number. The numbers in the second and third rows, though, seem to be fixed. A button is next to the 3 by 3 matrix.
  
  The matrix currently looks like this:
  0  -1   0
  1   0   0
  0   0   1
  
  > examine the fan
  This is a large, industrial-strength wall fan. You wonder what experiments it was used for.
  
  The wall fan is currently switched off.
  
  > go to the north
  The seminar room is dominated by the large table running the length of it. A small window in the north wall looks out onto a courtyard, and a door leads south back into the lab.
  
  On the seminar table are some presentation slides.
  
  > look at slides
  There are seven pages to these slides. If you want to look more closely at them you should read a particular page.
  
  > read the page 1
  The first page begins a discussion of three-dimensional transformation matrices. It points out that the columns in a transformation matrix consist of the "inputs," while the rows consist of the "outputs." For instance, the entry in column 1, row 2 indicates the effect of the first, or x, dimension of the original object on producing
  the second, or y, dimension of the transformed object.
  
  > read the page 2
  Starting with the second page, there are some examples of three-dimensional transformation matrices. The first involves the matrix
  1  0  0
  0  1  0
  0  0  1.
  The fact that the first row of this transformation matrix consists of 1, 0, 0, means that, to produce the x coordinates of the
  output object the matrix takes only the x coordinates of the
  input object and multiplies each of them by 1. The 0, 1, 0 in the second row means that, to produce the y coordinates of the
  output object the matrix takes only the y coordinates of the
  input object and multiplies each of them by 1. The same is true for the 0, 0, 1 in the third row and the z coordinates. This transformation matrix doesn't really do anything, then; since none of the coordinates are changed, the output object is the same as the input object.
  
  > read the page 3
  0  1  0
  0  0  2
  simply doubles the z coordinates. The output object would be
  twice as tall as the input object.
  
  > read the page 4
  0  0  1
  0  1  0
  swaps the y coordinates with the z coordinates,
  while keeping the x coordinates the same. An object would be transformed via this matrix to a mirror image of itself that is also lying on its side.
  
  > read the page 5
  0  1  0
  0  0  1
  keeps the y and z coordinates the same from the
  original object to the transformed object. However, to create the
  x coordinates of the transformed object, it adds the
  x and y coordinates of the original object. A cube,
  for example, would be transformed into an object that looks like a box that has been partially crushed so that its sides are at an angle. (Technically the transformed object is a parallelepiped, a three-dimensional version of a parallelogram.)  This kind of transformation is known as a shear transformation.
  
  > read the page 6
  0  0  1
  0  -1 0
  keeps the x coordinates the same from the original object to
  the transformed object, makes the z coordinates in the
  original into y coordinates in the new object, and turns the
  y coordinates in the original into negative z
  coordinates in the transformed object. The effect of this is to rotate the object 90 degrees clockwise when viewed from the front.
  
  > read the page 7
  The final page mentions that combinations of these effects as well as other effects can be achieved by using different matrices. A three-dimensional object can even be turned into a two-dimensional or even a one-dimensional object by using the appropriate transformation matrix.
  
  At the end of the final page is a brief description of one of the graduate student experiments involving transformation matrices. Thus far the student has constructed a prototype that allows one to apply a transformation matrix to a physical object. For the prototype the transformations that produce the y and z coordinates
  are hard-coded; the user can only affect the transformations for the
  x coordinates of the new object. In addition, only a few
  choices have thus far been implemented for the top row of the matrix. Finally, the transformation effect is thus far permanent only for objects made of lead. Even for lead objects, though, the process seems to be permanent only once; subsequent transformations on a transformed lead object have so far only been temporary. The current hypothesis is that the transformation process changes something about the lead object at the atomic level.
  
  > Inventory
  You are carrying:
  Berkeley's lecture notes
  a toy mountain range
  some correspondence
  a set (no longer empty)
  Descartes's saying
  the trig homework
  a square root
  some exhaustion sandals
  your math book
  
  > go south
  Not all of the experiments are gone; near the west door is a platform, raised slightly off the floor. A control panel is attached to the wall near the platform.
  
  There is also a large fan set into the east wall.
  
  A printout has fallen to the floor.
  
  > look at the printout
  The note is a printout of an email. It reads, "To my graduate students: Greetings from Hawaii! I'm having a great time at the conference. It's too bad none of you could come.
  
  "Unfortunately, I have some bad news. Most of my funding has run out. While I have enough to support myself, I do not have enough left to support any of you anymore. Thus, all of your current projects are hereby cancelled. If you want to finish your degrees you'll need to find another adviser."
  
  Underneath someone has written an unprintable commentary on the contents of the email.
  
  > go south
  This office is small and cramped, although that hasn't prevented someone from squeezing several desks in here. A door leads north, back into the lab. A small window in the south wall looks out onto a dingy part of campus.
  
  > examine the desks
  The desks have all been cleaned out.
  
  > Search desks
  The empty desks are a sad testament to the graduate students who used to work here. They're not worth bothering with.
  
  > go south
  The window is closed. Even if it was open, though, you're too high up. There is no way you would survive the drop to the hard ground below.
  
  > go east
  You make your way east through the bright light. As you do, you feel an electrical impulse course through you. You find yourself in...
  
  Brass wheels, gears, knobs, and pipes emitting smoke are everywhere: This is a room out of some steampunk's dream. The south end of the room opens onto a gold-colored path. This path appears to be suspended in the air, with no apparent support, and to run for as far as you can see. You may also exit west.
  
  The room is dominated by a large, complicated-looking machine in its center.
  
  > examine the machine
  This machine is just as steampunk as everything else here, although there are several parts to it that look at least somewhat recognizable.
  
  For one, the machine has a switch that can be set to "Sequence" or "Series." It is currently set to "Sequence," although you could easily move it to the other setting by flipping the switch.
  
  There is a button labeled "Alternate" that is currently pushed off.
  
  The machine also has a dial that can be set to "Constant," "Identity," "Squared," or "Reciprocal." It is currently set to "Constant."
  
  There is a small circular hole near the button.
  
  Finally, there is a warning light on top of the machine. The warning light is dark.
  
  > look at the hole
  The circular hole is empty.
  
  > go south
  As you approach the golden path you take a look at it.
  
  The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are all the same: 1, 1, 1, 1, 1, and 1. The second numbers are the same as the first numbers: 1, 1, 1, 1, 1, and 1.
  
  Just before you reach the path, though, it shifts: The heights of the steps change. The first step is now up. After that, though, the path is level with the first step.
  
  You step onto the path and follow it for a while. It seems to stretch on forever, though, and so you eventually decide to turn back. As you step off the golden path back into the room with the complicated machine the path shifts once again: It returns to being level with the floor.
  
  > switch the switch
  You flip the switch to "Series." Some of the numbers on the golden path change. The warning light is still dark.
  
  > look at the light
  The warning light is dark.
  
  > Go south
  As you approach the golden path you take another look at it.
  
  The path is level with the floor of the room you are currently in. It consists of golden steps that seem to run on forever. Each step has two numbers appearing on it, although from here you can only read the numbers on the six closest steps. The first numbers on the steps are all the same: 1, 1, 1, 1, 1, and 1. The second numbers are 1, 2, 3, 4, 5, and 6.
  
  Just before you reach the path, though, it shifts: The heights of the steps change. The first step is now up. After that, the path rises evenly, each step just as much of an upstep as the previous one. In fact, the path looks like a set of stairs.
  
  You step onto the path and follow it for a while. It seems to stretch on forever, though, and so you eventually decide to turn back. As you step off the golden path back into the room with the complicated machine the path shifts once again: It returns to being level with the floor.
  
  > Go west
  As you move west, you feel an electrical impulse course through you. The space around you seems to fold in on itself.
  
  > Go south
  You make your way south through the bright light. As you do, you feel an electrical impulse course through you. You find yourself in...
  
  This rather plain room is dominated by a large window that fills the entire southern wall. An open doorway lies to the north.
  
  A tray is attached to the wall next to the window.
  
  > examine the window
  This window looks onto an endless flat, gray plane. You can see a large pile of discarded objects a short distance away in the plane.
  
  Standing near the pile, rocking back and forth and muttering to himself, is René Descartes.
  
  > look at descartes
  (René Descartes)
  Descartes is holding his head and muttering to himself, "I can't think here. I can't think here."
  
  > examine the pile
  This pile consists of a large number of unusual objects that seem to fade in and out of view.
  
  A square circle catches your eye for a moment before disappearing again.
  
  > examine the pile
  This pile consists of a large number of unusual objects that seem to fade in and out of view.
  
  A formula for solving the general quintic equation catches your eye for a moment before disappearing again.
  
  > look at the pile
  This pile consists of a large number of unusual objects that seem to fade in and out of view.
  
  A solution in positive integers to x^n + y^n =
  z^n for n > 2 catches your eye for a moment before
  disappearing again.
  
  > examine the pile
  This pile consists of a large number of unusual objects that seem to fade in and out of view.
  
  An algorithm to solve the Halting Problem catches your eye for a moment before disappearing again.
  
  > look at the pile
  This pile consists of a large number of unusual objects that seem to fade in and out of view.
  
  A proof of the continuum hypothesis catches your eye for a moment before disappearing again.
  
  > examine the tray
  The tray is made of metal. It looks like it could hold one thing at a time.
  
  > greet descartes
  (René Descartes)
  Descartes looks up at you briefly, a request for help in his eyes. Then he grabs his head once more. "I can't think here. I can't think here," he mutters.
  
  > put the saying in the tray
  (first taking Descartes's saying)
  You place Descartes's saying on the tray. The tray beeps softly, and a voice says, "Existence detected."
  
  > put the saying in the tray
  You place Descartes's saying on the tray. The tray beeps softly, and a voice says, "Existence detected."
  
  > go north
  You make your way north through the bright light. As you do, you feel an electrical impulse course through you. You find yourself in...
  
  Cauchy is sitting at the bar, sipping from a glass of wine.
  
  Weierstrass is next to Cauchy, drowning his sorrows in a pint of beer.
  
  > greet Cauchy
  You walk over to Cauchy. "Are you guys O.K.?" you ask.
  
  Cauchy looks up from his wine. "Hello," he says. "Weierstrass and I were just commiserating on the state of our research programs."
  
  Weierstrass snorts. "Cauchy is being kind. I don't have a research program! I need an important problem to solve, something to show the mathematical world I'm capable of more than teaching high school. Not that there's anything wrong with that," he quickly adds, "but it would be nice to have a university position.
  
  "Cauchy, though, is already internationally famous. He practically invented complex analysis, for one thing!" Weierstrass falls silent, staring back into his mug.
  
  > talk to Weierstrass
  Weierstrass grunts at you in response before returning to his mug.
  
  > talk to Cauchy
  Cauchy says quietly, "I'm worried about Weierstrass. I'm sure he's capable of being one of the great mathematicians of our age, but he needs the right problem to work on in order to prove it."
  
  > show the notes to Weierstrass
  Weierstrass lifts his head from his mug long enough to glance at the proffered notes. He grunts and starts to return to his mug - but then he stops. He takes the notes from you and reads through them. "Berkeley's criticisms of the foundations of calculus... Yes..." He thinks for a while.
  
  Then he turns to Cauchy. "The limit concept you've used in your work - I wonder if that would help here. But it needs to be more rigorous."
  
  Cauchy and Weierstrass are soon deep in conversation, scribbling mathematical symbols and scratching them out again on a bar napkin. About all of the conversation you can follow are the words "function," "distance," "error," and "limit," each repeated several times. Finally, Weierstrass says, "And if we use delta for 'distance' and epsilon for 'error,' that should do it!" He pockets the napkin.
  
  Weierstrass looks at you excitedly. "I think I've got some ideas that would put calculus on a sound theoretical footing! This should make my name, mathematically-speaking.
  
  "I owe you more than I can say, but I don't know how best to reward you. Perhaps I can improve something of yours with the power of the limit concept?"
  
  > show the sandals to Weierstrass
  (first taking the exhaustion sandals)
  Weierstrass takes the sandals and looks at them carefully. "These embody the principle of exhaustion, don't they?" he says. Then he closes his eyes and concentrates for a moment. The sandals begin to glow, and then they start to morph. Soon Weierstrass is holding a pair of shoes in his hands. "There," he says, opening his eyes and handing the shoes to you. "I've improved your exhaustion sandals to a pair of limit shoes.
  
  "Thanks again," he says. He stands up, an eager look on his face. "I need to explore these concepts further. I've got an idea for a continuous function that is not differentiable anywhere..." Weierstrass downs the rest of his beer, places his mug on the bar, and walks out of the pub. The bartender appears out of nowhere and whisks the mug away before disappearing again.
  
  Cauchy remains behind. "Weierstrass has expressed his personal gratitude," he says. "Let me offer my gratitude on behalf of mathematics as a whole. Weierstrass mentioned earlier that I know a little something about complex analysis. I can imbue an item of yours with the power of complex analysis, much as Weierstrass improved those sandals with the power of the limit."
  
  > look at what you're carrying with you
  You are carrying:
  some limit shoes
  Descartes's saying
  a printout
  a toy mountain range
  some correspondence
  a set (no longer empty)
  the trig homework
  a square root
  your math book
  
  > Show range to Cauchy
  Cauchy looks carefully at you for a while, as if reading your thoughts. Finally, he gives a satisfied nod.
  
  Then Cauchy takes the toy mountain range and looks at it carefully. Then he closes his eyes and rubs his hands over it. The mountain range begins to glow. After a while Cauchy opens his eyes again, and the toy stops glowing. "There," he says, handing the it back to you. "I've improved your toy mountain range. It should be able to differentiate complex functions now. However, unless you actually find a complex function the additional power won't be of any use. I think I can reward you better than this."
  
  > show the root to Cauchy
  (first taking the square root)
  (putting the correspondence into the set to make room)
  Cauchy looks carefully at you for a while, as if reading your thoughts. Finally, he gives a satisfied nod.
  
  Then Cauchy takes the square root and looks at it carefully. Then he closes his eyes and rubs his hands over it. The square root begins to glow. After a while Cauchy opens his eyes again, and the square root stops glowing. "There," he says, handing the square root back to you. "I've improved your square root. It should be able to extract complex numbers now.
  
  "Thank you, once again, on behalf of mathematics," Cauchy says. "The discipline will be stronger if Weierstrass can put calculus on a more solid foundation." He stands up and finishes the last of his wine, placing the glass on the bar before walking out of the pub. The bartender appears out of nowhere once more and whisks the empty glass away before disappearing again.