What Is a Curve?

This post is simply an abridged version of Miles Mathis's essay http://milesmathis.com/pi.html

I see this essay as the theoretical foundation of Mathis's system, so it is a good place to start in order to avoid confusion when reading Mathis's other essays.

par. 10

Drawing a circle is a real event, not an abstract event. In fact, any possible circle must take time into consideration. This is true of orbits, bugs walking in circles, whirlwinds, and so on. When we apply mathematics to any of these situations, we must take time into account. That is why we find accelerations in all circular motion, the most famous of which is the centripetal acceleration. Centripetal acceleration can be due to gravity or to some other force, but in any circular motion there will always be a centripetal acceleration.

par. 14

Here is an equation that is used everyday, right now, by the smartest people alive:

v = C/t = 2πr/t

     where v is the orbital velocity, C is the circumference and t is the period of the orbit. Newton used this equation. ... We have C in the place of x, as if C is a simple distance. [However,] C is not a simple distance. There is no way to express C with just an x-dimension. In fact, as I have just shown, C is three-dimensional, if you include time. This equation is including time, as you can see by the denominator. You cannot have a t in the denominator and claim you are ignoring time. You cannot put a curve over a time and have it come out to be a simple velocity. Velocity is defined as x/ t. The variable x is one-dimensional and therefore cannot curve.

par. 18

[S]ay you are in a tiny spaceship at the center of the circle. You are instructed to fly at a thousand miles per hour for one hour, then turn left at a 90o angle and keep going, not pausing or changing your velocity. You will say, “I need some method for calculating velocity. What if the background changes in some weird way after I make the left turn?” I answer, “Just measure internally. Meaning, use your onboard clock and check your engine’s rpm. Whatever the rpm’s were as you were going a thousand miles per hour along the first straight line, keep them there after you turn left.” You do as I say and after exactly one hour you come to a rosebush and a sign that says, “left here.” Miraculously you make the sharp turn without slowing down at all. After some time you come to the rosebush again and you think, “Is that the same rosebush? What is going on?” What is going on is that I turned on a big magnet as soon as you got to the rosebush. My magnet and I, sitting at the center of the circle [with r = 1000 miles], are causing you to circle us.

      According to this set-up, your velocity out to the rosebush would be r/t. You were instructed to keep this velocity, by a method that would guarantee it was kept. Therefore your tangential velocity is also r/t.

par. 20

Now, the question is, what centripetal acceleration must I apply to you with my magnet to keep you moving in a circle? Surprisingly, the answer is always the same. It doesn’t matter what your speed is going out to the rosebush or how long it takes you to get there or how far away the rosebush is. As long as you keep your speed the same before and after you turn, the acceleration I must apply to you with my magnet is. . . . π.

par. 29

Pi only applies if the tangential velocity is equal to r/t. But in orbits and most physical problems, this will not be true. The centripetal acceleration and the tangential velocity are independent motions. They are not necessarily related, much less equal. That is why we don’t find the value of pi for the acceleration in gravitational fields.

par. 33

To be even more specific, a = v2/r works in experiment because v = 2πr/t works in experiment. The equation v = 2πr/t is a very useful number to us even though it does not really express the orbital velocity, or any velocity. It is more useful to us than the actual orbital velocity or the actual tangential velocity, both of which aren't really that interesting in experiment except as theoretical numbers. The number 2πr/t is a number we can use, and if we mislabel it as a velocity, well, who cares as long as we mislabel it the same way throughout the centuries?

    Engineers aren't paid or trained to care about such things, but theoretical scientists understand that such mistakes ultimately lead to ruin. In the short term they may lead to simple engineering failures, which is bad enough. But in the long term they always lead to theoretical dead-ends, since a sloppy equation is the surest of all possible ways to stop scientific progress. A correct equation is almost infinitely expandable, since its impedance is zero. Future scientists can develop it in all possible directions. But a false or imprecise equation can halt this development indefinitely, as we have ample proof. Mislabelling variables is not a semantic or metaphysical failure. Is it failure of science itself.