text: > look around
  This is more of an abstract space than a physical place, but it gives you a sense of unity, wholeness, and beginnings. A hole leads back up to the positive axis. You sense another exit, too - one in a deeper, "downward" direction from this space.
  
  > Inventory
  You are carrying:
  a set (no longer empty)
  a square root
  a sapphire gem
  Elements
  a scribbled scroll
  your math book
  
  > examine the scroll
  This scroll is made from papyrus. Euclid has scribbled his five geometric postulates on it.
  
  > read it
  "First postulate: You can draw a straight line from any point to any other point.
  
  Second postulate: You can extend a finite straight line continuously in a straight line.
  
  Third postulate: You can draw a circle with any center and any radius.
  
  Fourth postulate: All right (90 degree) angles are equal to each other.
  
  Fifth postulate (rephrased, also known as the parallel
  postulate): Given a line and a point not on the line, there is
  exactly one other line that goes through the point that never touches the first line."
  
  > read Elements
  This is a copy of the Elements of Euclid. It's actually
  divided into thirteen books.
  
  Elements contains far too much material to read through.
  
  > go upwards
  You make your way up.
  
  Positive Axis: 1
  You find yourself in a deep dark blue - almost black - expanse of space that extends as far as you can see in all three dimensions. The space is broken up by the straight, flat white line floating in mid-air that you are standing on. The line stretches to the west and out of sight to the east. The number 1 is marked on the line. While the line doesn't appear to be supported by anything, there is a hole in the middle of it here, next to the 1.
  
  > go east
  Positive Axis: 2
  You are in a dark blue expanse of space, standing on a white line that stretches to the west and as far as you can see to the east. The number 2 is marked on the line here. There is a hole next to the 2 large enough for you to climb down into.
  
  > Extract root
  The root vibrates quietly, as it extracts the square root of the essence of the space around it. You feel yourself shift.
  
  Irrational: Between 1 and 2
  This is more of an abstract space than a physical place, but it feels large beyond your understanding, as if it encompasses infinitely more space than the single-number locations beneath the positive axis. A hole leads up to the positive axis.
  
  A proof is lying here.
  
  [Your understanding of Number Theory has increased. You
  estimate that your score on tomorrow's final has just gone up by two points.]
  
  > examine the proof
  This is a mathematical proof that the square root of 2 is irrational.
  
  > get the proof
  (putting your math book into the empty set to make room)
  Taken.
  
  > go upward
  You make your way up.
  
  As you step onto the positive axis, the hole behind you closes.
  Rather than standing at an unmarked spot between 1 and 2, you head back to 1.
  
  Positive Axis: 1
  You find yourself in a deep dark blue - almost black - expanse of space that extends as far as you can see in all three dimensions. The space is broken up by the straight, flat white line floating in mid-air that you are standing on. The line stretches to the west and out of sight to the east. The number 1 is marked on the line. While the line doesn't appear to be supported by anything, there is a hole in the middle of it here, next to the 1.
  
  > Go west
  You make your way west. As you do, you feel an electrical impulse course through you. You find yourself in...
  
  You are standing in the great hall of a large, cobwebby castle. A long table stretches from one end of the hall to the other. The entryway of the castle is to the east. Exits west and south lead to other parts of the castle.
  
  On the long table is a pile of old coins.
  
  The Count is here, sitting at the table. He mumbles something that sounds like "six."
  
  > Inventory
  You are carrying:
  a proof
  a square root
  a set (no longer empty)
  your math book
  a sapphire gem
  Elements
  a scribbled scroll
  
  > put the coins into the set
  (first taking the pile of old coins)
  Those belong to the Count. I wouldn't just take one without his permission.
  
  > Greet count
  "If you know, please tell me how many ways you can flip ten coins and have them come out half heads and half tails!" the Count says.
  
  > Show set to count
  The Count is unimpressed.
  
  > ask count for the coins
  (the Count first taking the pile of old coins)
  The Count ignores your request.
  
  > say 42
  (to the Count)
  The Count arches his eyebrow. "That's not the right answer."
  
  > say 252
  (to the Count)
  "That's it! That's it! I know that's it! Thank you, thank you, thank you!" The Count hands you one of the coins from his pile. "If you lose this one, feel free to come back and take another. I have plenty!"
  
  (You put the scribbled scroll into the set to make room.)
  
  [Your understanding of Combinatorics has increased. You
  estimate that your score on tomorrow's final has just gone up by three points.]
  
  > look at the coin
  This old coin is of eastern European origin. It is probably quite valuable.
  
  > go to the east
  On the long table is a pile of old coins.
  
  The Count is here, looking rather bored.
  
  > go east
  The Count calls after you, "If you find something else for me to count I would be grateful!"
  
  As you move east, you feel an electrical impulse course through you. The space around you seems to fold in on itself.
  
  > go north
  You make your way north. As you do, you feel an electrical impulse course through you. You find yourself in...
  
  > go north
  Temple of Number, Southern End
  
  > go north
  Temple of Number, Northern End
  An acolyte is here, silently cleaning up the area around the statue.
  
  You can also see a trash urn (in which is a scrap of papyrus) here.
  
  The acolyte polishes an already spotless part of the statue.
  
  > show the proof to the acolyte
  The acolyte is focused on her cleaning, and she ignores you. There must be some way to make her notice the proof.
  
  The acolyte picks up a speck of dust from the floor of the temple.
  
  > Go north
  The acolyte stops you. She shakes her head silently.
  
  The acolyte gazes up at the statue with a reverent look on her face.
  
  > read the proof
  Suppose the square root of 2 is rational. Then it can be expressed as a fraction x/y in lowest terms, so that x
  and y are integers with no common factors. Since
  x/y is the square root of 2, squaring
  x/y must yield 2, and so we get 2 = x² /
  y². This means that 2y² = x².
  
  Since y is an integer, so is y². Since x²
  is 2 times an integer, x² must be an even number. The only
  way that the square of a number can be even, though, is for the number itself to be even. Thus x is even. So x =
  2z, where z is some other integer.
  
  Substituting 2z for x, our equation now looks like
  2y² = (2z)² = 4z². Divide both sides by
  2
  to get y² = 2z². By the same logic as before, this
  means y is even. So x and y are both even.
  
  common factors. We now have a logical contradiction. Since our supposition that the square root of 2 is rational leads to a logical contradiction, the only possibility left is that the square root of 2 is, in fact, irrational.
  
  The acolyte picks up a speck of dust from the floor of the temple.
  
  > Drop proof
  Dropped.
  
  The acolyte sweeps the area in front of the statue.
  
  Then the acolyte picks up the proof. On her way to the trash urn, she glances at it. Then she stops and reads through it carefully. Her face tightens. She shakes the proof at you, spluttering. "This... this is blasphemy! All things must be odd or even or a ratio! You are in error! I will show it to you!"
  
  She reads over the proof again. "The error is here, in the second line. No... the mistake is in the assumption that... In this place, you can't claim that this follows from... Aarrrgghh! This proof is wrong! I know it is!"
  
  She reads the proof a third time. And then a fourth time. The anger slowly fades from her face. "How did you come by such sacred knowledge, and why, why did you share it with me?" Tears drop onto her cheeks. Giving you a last mournful glance, she runs sobbing out of the temple.