text: > go down
  You make your way down.
  
  This space seems more formed than it did the last time you were here.
  
  The space is now partially-formed, but it is still mostly unshaped matter. Besides the way up to the manifestation of one, you can now sense several more "paths" through the void: north, south, east, and west.
  
  > go west
  You make your way west through the void. 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.
  
  A large purple puppet is here, counting several coins laid out on the table. He is talking to himself. "... eight, nine, ten! Ten coins!"
  
  > look at the puppet
  The Count is not a man but a purple puppet. There is no one animating him, yet he talks and moves about. You're definitely dreaming.
  
  > look at the coins
  This is a huge pile of coins. You wonder if the Count knows exactly how many there are. He probably does.
  
  > ask Count about the coins
  It would be more polite to greet the Count first.
  
  > Greet count
  The puppet looks up at your approach. "I am the Count of this castle, and I love to count! But I have a problem. Maybe you can help.
  
  "I have ten different coins here that I have been flipping. I want to count how many ways I can flip the ten coins and have half of them come up heads and half come up tails. For example, one way is HHHHHTTTTT. Another way is HTHTHTHTHT. A third way is HTHHTTTTHH. That's three. But there are a lot more than that, and I can't seem to count them because I can't keep track of all the combinations!
  
  "Here are some ideas. I know that if I want 0 heads, then the answer is 1: TTTTTTTTTT. I know that if I want 1 head, the answer is 10: HTTTTTTTTT, THTTTTTTTT, and so on, with one head for each of the other coins. It took me a long time to find the answer with two heads, but I'm pretty sure I got it: 45. But with three or more I can't keep track of what I've counted and what I haven't.
  
  "If you know the answer, please tell me!
  
  "I will be happy to let you have one of my coins if you can help me."
  
  > ask Count about the big bird
  "I haven't seen him in a while," the Count says. "I probably should go visit sometime soon."
  
  > 99
  I didn't recognize that command. (There is a list of recognized commands in the HELP menus.)
  
  > go east
  As you move east, you feel an electrical impulse course through you. The space around you seems to fold in on itself.
  
  The space is now partially-formed, but it is still mostly unshaped matter. Besides the way up to the manifestation of one, you can now sense several more "paths" through the void: north, south, east, and west to the Great Hall.
  
  > go north
  You make your way north through the void. As you do, you feel an electrical impulse course through you. You find yourself in...
  
  You stand in the Lyceum, a collection of buildings and open spaces in ancient Athens. There is a stadium to the west, a temple lies north, and you can see a private home with an ornate doorway to the east. A road leads northeast out of Athens, and the rest of the city lies south.
  
  > go to the north
  Temple of Number, Southern End
  You stand in the southern end of the Temple of Number. The temple is made of white stone and features imposing Ionic columns. There is an inscription on the wall, the rest of the temple is to the north, and the exit to the Lyceum is south.
  
  > read inscription
  "Number is the origin of all things."
  
  > Go north
  Temple of Number, Northern End
  You stand in the northern end of the Temple of Number. The temple is made of white stone and features imposing Ionic columns. Instead of the half-expected statue of Athena Parthenos, though, stands a large statue of Pythagoras. Behind the statue is a small passageway heading north.
  
  An acolyte is here, silently cleaning up the area around the statue.
  
  You can also see a trash urn and a scrap of papyrus here.
  
  The acolyte picks up the scrap of papyrus from the floor. She reads it carefully, nods, and tosses it in the urn.
  
  > look at the urn
  This large urn is decorated with tasteful depictions of various numbers.
  
  In the trash urn is a scrap of papyrus.
  
  The acolyte polishes an already spotless part of the statue.
  
  > take the scrap
  Taken.
  
  The acolyte pokes at a corner of the temple with her broom.
  
  > read it
  This appears to be a piece torn from some religious scroll.
  
  "Number is the origin of all things.
  
  Number has two basic forms: The odd and the even. Each thing is odd or even or is a ΛΟΓΟΣ, or ratio, made from odd and even.
  
  1. Odd things include the statue of Him in our temple, which is one.
  
  2. Even things include the primary sources of light in our sky - the sun and moon, which are two.
  
  3. ΛΟΓΟΣ things include the seasons, which represent the ratio of
  one
  year into four parts.
  
  Nothing which is not odd, even, or a ratio from odd and even can exist."
  
  [If the Greek letters are not displaying correctly, you may type SYMBOLS OFF to turn off the use of Greek letters and mathematical symbols for the remainder of the game.]
  
  The acolyte polishes an already spotless part of the statue.
  
  > examine statue
  This large statue of Pythagoras dominates the north end of the temple. A small passageway is behind the statue, leading north.
  
  The acolyte picks up a speck of dust from the floor of the temple.
  
  > greet the acolyte
  The acolyte is focused on her cleaning, and she ignores you.
  
  The acolyte sweeps the area in front of the statue.
  
  > go north
  The acolyte stops you. She shakes her head silently.
  
  The acolyte polishes an already spotless part of the statue.
  
  > Inventory
  You are carrying:
  a scrap of papyrus
  your math book
  
  The acolyte pokes at a corner of the temple with her broom.
  
  > put the scrap in the urn
  You put the scrap of papyrus into the trash urn.
  
  The acolyte sweeps the area in front of the statue.
  
  > 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.
  
  > climb the statue
  That would be rather sacrilegious.
  
  The acolyte polishes an already spotless part of the statue.
  
  > Drop book
  Dropped.
  
  The acolyte picks up a speck of dust from the floor of the temple.
  
  The acolyte walks over to where you dropped the math book and looks around. Not seeing anything, she returns to her work.
  
  > take the book
  Taken.
  
  The acolyte gazes up at the statue with a reverent look on her face.
  
  > look at the statue
  This large statue of Pythagoras dominates the north end of the temple. A small passageway is behind the statue, leading north.
  
  The acolyte pokes at a corner of the temple with her broom.
  
  > look up Pythagoras
  (in your math book)
  Pythagoras was an ancient Greek mathematician. He also founded a quasi-religious order whose key belief was that numbers (by which they meant the positive integers) are the basis of everything in the universe.
  
  The Pythagorean Theorem says that the square of the diagonal of a right triangle is equal to the sum of the squares of the sides, or, in symbols, a² + b² = c². While this
  theorem
  is named for Pythagoras, there is no conclusive evidence that he actually proved the theorem. It probably led to the downfall of his religious cult, though. If you take a right triangle with sides of length 1, the Pythagorean Theorem says that the length of the diagonal must be the square root of 2. The proof that the square root of 2 is irrational - by one of the Pythagoreans - invalidated their key belief in numbers.
  
  The acolyte picks up a speck of dust from the floor of the temple.
  
  > examine the acolyte
  The acolyte is wearing pure white robes and wields a broom. She doesn't look much like the conversational type.
  
  The acolyte pokes at a corner of the temple with her broom.
  
  > look at columns
  These imposing columns are made of white stone and feature Ionic capitals.
  
  > Go south
  You stand in the Lyceum, a collection of buildings and open spaces in ancient Athens. There is a stadium to the west, a temple lies north, and you can see a private home with an ornate doorway to the east. A road leads northeast out of Athens, and the rest of the city lies south.
  
  > go to the east
  Some force blocks you from stepping through the doorway of the home. Ignorance may be bliss, but a little knowledge would go a long way here.
  
  > examine the doorway
  There is a rather ornate doorway here - but no door. Written above the doorway is the phrase "Let no one ignorant of geometry enter."
  
  > Go west
  This is a stadium in ancient Athens. The stadium itself consists of raised ground on either side of a race track about 200 meters long. The rest of the Lyceum is back east.
  
  Achilles sits by the side of the race track with his head in his hands.
  
  > greet Achilles
  Achilles looks up. "I'm the fastest man in Greece. Then this guy Zeno challenged me to a 200-meter race with a tortoise, under two conditions: (1) I had to be willing to give the tortoise a head start of 100 meters, and (2) every time I got to where I last saw the tortoise I had to look up and mark its position. Of course I can beat a tortoise, even with that much head start, right? But no. Watch."
  
  Achilles snaps his fingers, and from somewhere in the grass of the raised ground comes a tortoise. The tortoise ambles to the 100-meter mark, and Achilles heads to the start. They take off. When Achilles reaches the halfway mark, he looks up, and the tortoise is ahead of him. Achilles notes its position, races to that position, and looks up. The tortoise is still ahead of him. He does this again. The tortoise is still ahead. And again. The tortoise is, once more, ahead. Every time Achilles looks up he's closer to the tortoise, but he never quite catches up to it! Finally he stops running and looks over at you forlornly. The tortoise crosses the finish line, flashes a chelonian smile at Achilles, and disappears to wherever it was before.
  
  Achilles says, "You see? I can't catch up to the tortoise if every time I run to where it was before, it's still ahead of me!"
  
  > examine the track
  The race track is made of hard-packed clay and is about 200 meters long.
  
  > go south
  As you move south, you feel an electrical impulse course through you. The space around you seems to fold in on itself.
  
  The space is now partially-formed, but it is still mostly unshaped matter. Besides the way up to the manifestation of one, you can now sense several more "paths" through the void: north to the Lyceum, south, east, and west to the Great Hall.
  
  > go north
  You make your way north through the void. As you do, you feel an electrical impulse course through you. You find yourself in...
  
  You stand in the Lyceum, a collection of buildings and open spaces in ancient Athens. There is a stadium to the west, a temple lies north, and you can see a private home with an ornate doorway to the east. A road leads northeast out of Athens, and the rest of the city lies south.
  
  > go northeast
  This flat, paved road runs from southwest to northeast. However, you also spot a steep path leaving the road and winding its way north up the hillside.
  
  > Go north
  It's an arduous trek up the path. By the time you reach the top you are winded.
  
  You stand on top of a small hill just north of Athens. A winding path leads south, back down to the Royal Road.
  
  The great geometer Euclid is sitting here. He appears to be lost in thought.
  
  > greet the geometer
  "Oh! Hello. Sorry. Please accept my apologies if you've been standing there a while. Sometimes I don't notice what's going on around me when I'm doing geometry."
  
  You give Euclid a nod, as if to say that there's no need to apologize. He interprets it as interest.
  
  "I was just thinking about the postulates in my Elements.
  These are what I call the basic truths on which I build all of my geometric arguments. I'm happy with the first four, but the fifth one is too... I don't know... wordy?
  
  "It's basically equivalent to saying this: Given any straight line and a point not on that line, there exists exactly one other straight line that passes through the point and never intersects the first line. This is true no matter how far you extend the two lines. So there's exactly one other line that's parallel to the first line and
  that goes through the point.
  
  "I'm trying to figure out how to derive this one from the first four so that I don't have to claim it as a postulate. But I can't seem to do it.
  
  "Is it obvious that if you start with a point and a line, there's exactly one other line that goes through the point and never touches the first line? Or is that not even true?
  
  "If you have any ideas about how to prove this, or run across any examples where there are no lines or two or more lines through the point that don't touch the first line, please tell me about them!
  
  "And here. This will help you remember my postulates." He hands you a scroll.
  
  > read the scroll
  "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."