When you turn on a computer you get ... a universe.
To the extent the computer is yours, the universe is yours.
A universe is space.
The universe in one given computer either has things in it or does not have things in it.
A computer is a universe.
Imagine a computer which is a universe with nothing in it.
When you turn on a computer, it shows you an image of itself on the screen. A computer is a universe, so it is a universe, so an image of itself is an image of what's in it, so it's an image of nothing, on the screen.
Actually, a computer is a ship. This ship is in a universe. When you turn it on, you can use this ship to navigate that universe. You navigate by looking at the screen. The screen shows you images of things in the universe.
computer, show me the Google home page. computer, show me a page (the Google home page). computer, show me this page: (the Google home page).
Build your own operating system. An operating system is a program. What does it do?
It shows you imagery from a model.
The screen is a piece of film in a camera. You can tell the camera to look at this part or that part of the model.
But how are the parts of the model defined?
When you first create the model, there is nothing in it?
There is, however, something: the screen.
Is the screen in the model?
The question might not be answerable, but the screen defines the empty model.
From the center of your screen, project, towards you - you are in front of the screen, looking at it, seeing what's on it - an imaginary line, perpendicular to the screen and the same length as your screen's longer dimension or side.
Your screen is a rectangular plane segment. It is "on" a plane. It's center is a point on that plane. Imagine a line through that point and perpendicular to the plane. Measure from the point towards you on the line a distance equal to the length of the longest edge of your screen. This identifies a point on the line. Let us call that point the camera position.
I would like a nice table to work on. Quite a large one. I would like that table to be twenty feet long and five feet wide, no, six feet wide. Eight feet wide.
I would like a floor to put that table on, so I can put my camera on the same floor to take pictures of my table.
I would like a floor that is 100 ... no, 600 feet by 400 feet ... a rectangle that big ... a rectangular plane segment, with those dimensions, colored lightgrey.
The directions "below", "above", "to the left of", and "to the right of" can be defined from our camera.
The film has four edges, each of which is a line segment. The left edge meets the top edge at a point, and the two edges are perpendicular. The right edge meets the top edge at another point, and the right edges is parallel to the left edge. The point where the left edge meets the top edge is a point and it is called the top of the left edge. It is an endpoint of the left edge, and the left edge has another endpoint called the bottom of the left edge. Similarly the right edge has a top and a bottom, each of which is a point. The bottom edge is also a line segment. Its end points are the left edge and right edge bottoms.
Sorry about this.
The tops and bottoms of the left and right edges are called the corners of the screen. Imagine a line through each corner and perpendicular to the screen. We'll call these the box lines. Measure along each of those lines from the screen corners, which are points, a distance equal to the length one of the screen's longer edges. This creates two new points on each of the box lines. Connect one of those points on one of the box lines with one of those points on another of the box lines. If the resulting line is parallel to the screen plane, it is an edge of (naming this now) the viewing rectangle.
Build the four edges of the viewing rectangle. Each of its four corners intersects a line projected through one of the corners of the screen. It identifies a point on one of those four lines. If it intersects the line through the bottom left corner of the screen, it is the bottom left corner of the viewing rectangle, and so on.
Find the midpoint of the bottom edge of the viewing rectangle and the midpoint of the top edge of the viewing rectangle. Call a line through these two points the camera standard. The midpoint of the line segment connecting those two points is the viewing rectangle center, or viewing point.
I want to position my camera five feet above my floor. Measure from the viewing point along the camera standard five feet. This returns two points on the camera standard. Choosing one of the two points, measure along the camer standard to its intersection with the bottom edge of the viewing rectangle. If that distance is less than five feet, the point is five feet below the viewing point, in our model.
We have now identified a point on my floor. For convenience, let's say it is a corner of my floor. Define a line through that point and parallel to the above defined box lines. Find the point on that line 600 feet in front of the viewing plane.
We used certain procedures to define the directions above and below, to the left of and to the right of, the camera, and we will use the same types of procedures to define "in front of" and "behind" the camera. The screen plane is in front of the viewing plane.
The uninitialized computer displays, on its screen, an image of empty space, or, nothing. The screen defines units of distance and directions in that empty space.
It is also convenient to place on the screen certain controls. The "mark a point" control can be on the screen, and with it we can begin to define, um, things, in the universe that is the uninitialized computer. Defining things in the space defined by the uninitialized computer would be called "initializing the computer."
