Call me clueless, but . . .
Since Pi is "The ratio of a circle's circumference to its diameter," how does adding any variable not included in the definition (e.g., velocity) have anything to do with the essential definition? (Rolling a ball along a straight path and another ball along a curved path at the same initial velocity will yield different time per distance traveled at the end of the measurement. So, what's that got to do with pi, the geometric constant?)
Here is an excerpt from the paper that DSKlausler linked to:
Some have taken exception to my way of stating that. They say that pi is 3.14... and can't also be 4.
They say I should come up with another Greek letter, at the least. But pi isn't defined as 3.14. Pi is
defined as the ratio of the circumference and the diameter. I have proved that when motion is involved,
that ratio is 4. Therefore, it is correct to say that pi=4.
Others have said that even if I am right, it is just a quibble, since in most cases pi will still be 3.14. But
that simply isn't true. In physics—and therefore in the real-world—almost all uses of pi include
motion. When pi is used in physical equations, 99% of the time those equations include a velocity of
Whenever I have posted in other forums about Miles's physics work, somebody always appears to discredit him saying "this is the guy that believes Pi=4." I personally think Miles shot himself in the foot by stating his claim in this way. I think it also adds confusion. The choice of Greek letter to represent a mathematical constant is fairly arbitrary. But once it's chosen, it won't do to say that actually that constant is a different number. It even more won't do to say it is different numbers depending on the situation. And in fact Miles is arguing that Pi=4 in some situations. So that only add to the confusion, because we usually think of mathematical constants as constant, so in a sense he is telling us that it's not constant but depends on the situation in which it's used.
I personally think he would have been better off choosing a different greek letter and making his argument something like: in situations X, we need to use Pi (=3.14) to calculate the circumference, but in other situations, we need to use (i don't know) Omicron (=4) to calculate the circumference. But Miles says he did it deliberately to be provocative, and he certainly succeeded in that.
But even then the whole business is confusing. One way to think about it: it takes more time to move in a circular path than in a straight line. When you're moving around a circle, it takes the same amount of time to travel 3.14 units of measurement as it does to travel to 4 units in a straight line. Another way of thinking about it is that anything moving in the circular path will necessarily take 4 times as a long as a linear motion across 1 diameter (whereas we would normally think it would take 3.14 times as long). The crucial point here is that it has nothing to do with velocity. The movement takes place at the same speed, as it were. It's not due to slowing down around the curve.
This latter point is crucial and is what makes it so mind-boggling.
The reason is that the distance around a curve is longer. Miles differentiates between length and distance: "A length is a given parameter that does not include motion or time. It is geometric only. But a distance is a length traveled in some real time, so it requires motion. A length is not kinematic, while a distance is." So if you're talking about lengths (such as those measured by a tape measure), Pi=3.14. When you're talking about distance (as he defines it), then Pi (or Omicron) = 4.
If you watch the video, what is not immediately obvious is that the length of the circular tube is the exact same length as the 'Pi' marking on the straight tube (you can do the calculations from the measurements given at the end). So if you straightened the tube, the balls would arrive at the 'Pi' marking at the same time, which for the shorter tube would be the end. Then if you bend it back into a circle, you'd see that the ball reaches the end of the circular tube at the same time as the ball in the straight tube reaches the 4 mark at the end -- even though both balls are travelling at the same speed
. And yet, if you measure it out and divide the length of the circular tube by its diameter, you'll get good ol' Pi=3.14. I don't know about you, but to me that's just bonkers.
Now, I would agree with criticism stating that we need better documentation/proof that the speed really doesn't change, although the video does offer a fair amount. Apparently Steve Oostdijk (who did the experiment and has been accused of being one of Miles's aliases/sock puppets) is going to redo the experiment to offer more evidence of this. I believe he will be vindicated.
I would also like to point out that this astonishing result ultimately arises from of one of Miles's key postulates or working assumptions, which is that there are no zeros or points in physics. Everything that exists must have physical extension. That being so, physical objects cannot be represented mathematically by a point or a zero or an infinitesimally small length. So you have to be careful when applying math and geometry to physical equations. Here I'll just quote from http://milesmathis.com/central.html
That oldest mistake is one that Euclid made. It concerns the definition of the point. Entire library shelves have been filled commenting on Euclid's definitions, but neither he nor anyone since has appeared to notice the gaping hole in that definition. Euclid declined to inform us whether his point was a real point or a diagrammed point. Most will say that it is a geometric point, and that a geometric point is either both real and diagrammed or it is neither. But all the arguments in that line have been philosophical misdirection. The problem that has to be solved mathematically concerns the dimensions created by the definition. That is, Euclid's hole is not a philosophical or metaphysical one, it is a mechanical and mathematical one. Geometry is mathematics, and mathematics concerns numbers. So the operational question is, can you assign a number to a point, and if you do, what mathematical outcome must there be to that assignment? I have exhaustively shown that you cannot assign a counting number to a real point. A real point is dimensionless; it therefore has no extension in any direction. You can apply an ordinal number to it, but you cannot assign a cardinal number to it. Since mathematics and physics concern cardinal or counting numbers, the point cannot enter their equations.
This is of fundamental contemporary importance, since it means that the point cannot enter calculus equations. It also cannot exit calculus equations. Meaning that you cannot find points as the solutions to any differential or integral problems. There is simply no such thing as a solution at an instant or a point, including a solution that claims to be a velocity, a time, a distance, or an acceleration. Whenever mathematics is applied to physics, the point is not a possible solution or a possible question or axiom. It is not part of the math.
Now, it is true that diagrammed points may be used in mathematics and physics. You can easily assign a number to a diagrammed point. Descartes gave us a very useful graph to use when diagramming them. But these diagrammed points are not physical points and cannot stand for physical points. A physical point has no dimensions, by definition. A diagrammed point must have at least one dimension. In a Cartesian graph, a diagrammed point has two dimensions: it has an x-dimension and a y-dimension. What people have not remembered is that if you enter a series of equations with a certain number of dimensions, you must exit that series of equations with the same number of dimensions. If you assign a variable to a parameter, then that variable must have at least one dimension. It must have at least one dimension because you intend to assign a number to it. That is what a variable is—a potential number. This means that all your variables and all your solutions must have at least one dimension at all times. If they didn't, you couldn't assign numbers to them.
This critical finding of mine has thousands of implications in physics...
Pi=4 in kinematic situations is just one of those implications.