Try to forget everything you already learned about geometry, numbers and your perception of ‘3-D’ reality.
This will be hard. Take off your glasses (if you can read without them).
We are going to create a completely different number-geometrical system based on the universe as it exists and the constants that it has revealed.
Forget points (especially). They are not real even in the context of the system that we currently use. If they are not real, and do not exist in and of themselves, forget them.
Let’s look at the things that are prevalent in the universe.
There are stars and planets. All of them are round, spherical. They have volume. They don’t have 3 perpendicular axes, defining x, y and z. They are best described using the tools of rotation, and circular motion.
Look at the stars and the things around us. They are all moving. Moving constantly. There is no Principal Coordinate System. No Zero. There is only motion and space. And Motion, always motion.
They too, are best described using the tools of rotation and circular motion.
Look at the constants that we know. The speed of light. Planck’s constant. They involve the relationship between time and length or rotation. Time is not an independent abstract. Time is the relationship between itself and length or rotation. It is not, and can never be, an independent variable, because without motion, there is no time.
This fact is totally ignored by the current ‘logical’ and ‘scientific’ thinking. Time is not an independent variable. Without mass, without motion, there is no time. Because, try as you might, without something being in motion, you cannot define time. It cannot and does not exist as an independent abstract.
And this is where Dr. Einstein failed. And Dr. Hawking, too. And everyone else.
Time is NOT an independent variable.
So in deciding where to start creating a different geometry, the first decision to make is: what is the most fundamental measurement possible?
Euclid said: The distance between two points. But he forgot about time. It always takes time to make a measurement.
So with that in mind, we’ll say that the first and lowest level measurement possible is a velocity. Distance over time. Now, according to previous chapters, we can’t actually see a velocity, and that is still true, but we can detect a velocity by noticing change, and using memory.
At this point, this must seem like just semantics, that we’ve just added a term that makes it look slightly different; but it’s not. This fundamental perceptual change has the power to influence virtually everything that is measured, calculated or constructed, as we shall soon see.
But for starters, think about this: we no longer need to tolerate the foolishness that a line is and must be made from a collection of points. A velocity makes a line. A continuous line, not a collection of dots that must, at some micro-cosmic level have some sort of separation to be distinct. No, a velocity creates a true continuous line, both in distance and in time.
This gets back to the concept discussed back in Chapter 9 about the differences between an approximation and the real thing. A line made from points is only and can only be an approximation, because each point must be distinct. A velocity is continuous, and therefore is the exact solution to the measurement.
Before going any farther with this, and before using this ‘newly’ discovered tool to build a geometry, there should be some discussion about its true nature, the universe in general and what exactly a dimension should be. Don’t worry, I’ll be brief.