Chapters (108)
- About the Author
- Title Page
- Copyright Page
- Dedication
- 1 - Outside Context Problem
- I
- II
- III
- IV
- V
- VI
- 2 - Not Invented Here
- I
- II
- III
- 3 - Uninvited Guests
- I
- II
- III
- IV
- 4 - Dependency Principle
- I
- II
- III
- IV
- V
- 5 - Kiss The Blade
- I
- II
- III
- IV
- V
- VI
- 6 - Pittance
- I
- II
- III
- IV
- V
- VI
- 7 - Tier
- I
- II
- III
- IV
- 8 - Killing Time
- I
- II
- III
- IV
- V
- VI
- VII
- VIII
- 9 - Unacceptable Behaviour
- I
- II
- III
- IV
- V
- VI
- VII
- VIII
- IX
- X
- XI
- XII
- XIII
- XIV
- 10 - Heavy Messing
- I
- II
- III
- IV
- V
- VI
- VII
- VIII
- IX
- X
- XI
- XII
- XIII
- XIV
- XV
- 11 - Regarding Gravious
- I
- II
- III
- IV
- V
- VI
- VII
- VIII
- IX
- X
- XI
- XII
- XIII
- XIV
- 12 - Faring Well
- I
- II
- III
- IV
- V
- VI
- Epilogue
The cloak went rigid underneath him and floated into the air, wrapping round him. He cried out and tried to fight against its enclosing black folds, but the buzzing came again and his vision faded even before the cloak finished wrapping itself round him.
8 - Killing Time
8
Killing Time
I
I
The usual way to explain it was by analogy; this was how the idea was introduced to you as a child. Imagine you were travelling through space and you came to this planet which was very big and almost perfectly smooth and on which there lived creatures who were composed of one layer of atoms; in effect, two-dimensional. These creatures would be born, live and die like us and they might well possess genuine intelligence. They would, initially, have no idea or grasp of the third dimension, but they would be able to live perfectly well in their two dimensions. To them, a line would be like a wall across their world (or, from the end, it would look like a point). An unbroken circle would be like a locked room.
Perhaps, if they were able to build machines which allowed them to journey at great speed along the surface of their planet - which to them would be their universe - they would go right round the planet and come back to where they had started from. More likely, they would be able to work this out from theory. Either way, they would realise that their universe was both closed, and curved, and that there was, in fact, a third dimension, even if they had no practical access to it. Being familiar with the idea of circles, they would probably christen the shape of their universe a ‘hypercircle’ rather than inventing a new word. The three-dimensional people would, of course, call it a sphere.
The situation was similar for people living in three dimensions. At some point in any civilisation starting to become advanced it was realised that if you set off into space in what appeared to be a perfectly straight line, eventually you would arrive back at where you started, because your three-dimensional universe was really a four-dimensional shape; being familiar with the idea of spheres, people tended to christen this shape a hypersphere.