Mathis and pi

[Siggy_G]

From Miles' "The Extinction of pi" paper:
( http://milesmathis.com/pi2.html )

"If you add up those eight little lines segments along the steps, you find that they equal AD + DC. We have changed our path, but we have not changed our distance! We can draw eight steps or 64 steps or an infinity of steps, and it will not change a thing."

What Miles have got completelly wrong here, is that he states that the Greeks (or whoever) added the X and Y decompositions. It's the main vectors between these that is measured. This is elementary vector math.

From the image above, you add together the green vectors, not the orange and red decompositions. The result will be a length that is quite close to that of the arc, and certainly not AD + DC.

The reason for the subdivisions is for each piece (vector) to follow the arc more and more precisely. Then adding the subdivided vectors together (not the X and Y decompositions, but the "shortcuts"), they resemble the curve. More subdivisions = more precise resemblence of the curve. Here's why:

Also, if you imagine a rubber hose, shaped into a curve or a quad-circle, as it is straightened out, its length won't be as long as the rectangle surrounding it. So why insist that it does? (pi = 4) Miles insists that in a physical world the circumference of a circle is the same as a quad surrounding it (with sides = diameter).

[junglelord]

Pi does not equal four at any time for any reason.

[StevenO]

To move around a corner you will have to accelerate both in x and y direction. You will have to decelerate your speed in x and accelerate your speed in y. The total acceleration does not change whether you corner with a minimum or maximum radius.

[junglelord]

How does that make pi = 4 ?

[StevenO]

Well that's easy...because then you get four (straight) corners on a circle

[Siggy_G]

To move around a corner you will have to accelerate both in x and y direction. You will have to decelerate your speed in x and accelerate your speed in y. The total acceleration does not change whether you corner with a minimum or maximum radius.

I think I see your point about the "work space" of the acceleration being a quad. This is also the scenario when defining sinus and cosinus, as related to X and Y coordinates. See image:

But the resultant path is a curve, when you have this gradual acceleration/deceleration. If the X and Y velocity were linear, it would result in a straight diagonal line. In any case, the result is a shape that is smaller than the work space.

It's the circumference of the resultant shape (circle or circle segment) that is relevant, not the circumference of the acceleration's entire work space. In a physical world, painting a dot on a wheel and turning it one turn, will give a translation of the circumference. It will be 2 pi, where pi is an irrational number quite below 4...

I should also add that if the circular movement literally was only X-Y quad-steps, and not about the resultant path between each step, it would be a jagged outcome. The jagged path Mathis refer to (built up of X and Y decompositions), has a longer circumference than the actual arc or circle. It's like a curly hair straw - when you straighten it out, it gets longer.

[altonhare]

To move around a corner you will have to accelerate both in x and y direction. You will have to decelerate your speed in x and accelerate your speed in y. The total acceleration does not change whether you corner with a minimum or maximum radius.

There are no corners on a circle.

[StevenO]

One cannot understand this article from Miles about why pi=4 in kinematic situations without first understanding his articles on why the current calculus is wrong. Geometry is a poor way to describe physical motion.

[Siggy_G]

One cannot understand this article from Miles about why pi=4 in kinematic situations without first understanding his articles on why the current calculus is wrong. Geometry is a poor way to describe physical motion.

Perhaps, but isn't it Miles' application of geometry (here: X and Y coordinates) that results in the talk about quad and 4, as described in the post above about the "work space"? A circle is really defined as a center and circumfering points of constant radius. Waves from a stone dropped in water, just implies that one don't need to talk about how a circle is drawn. It can occur from a radiating point.

Whether you wrap the diameter around a wheel, or project the wheel's circumference on the floor, you'll still get that the ratio, pi, is the established irrational number (i.e. not 4). That ratio just happens to be somewhat incompatible with our numeral system.

[borut]

One cannot understand this article from Miles about why pi=4 in kinematic situations without first understanding his articles on why the current calculus is wrong. Geometry is a poor way to describe physical motion.

Perhaps, but isn't it Miles' application of geometry (here: X and Y coordinates) that results in the talk about quad and 4, as described in the post above about the "work space"? A circle is really defined as a center and circumfering points of constant radius. Waves from a stone dropped in water, just implies that one don't need to talk about how a circle is drawn. It can occur from a radiating point.

Whether you wrap the diameter around a wheel, or project the wheel's circumference on the floor, you'll still get that the ratio, pi, is the established irrational number (i.e. not 4). That ratio just happens to be somewhat incompatible with our numeral system.

By Miles in Kinematics there are no curved paths. Planets in orbits are traveling in straight line.( Even for Einstein that is true)
If you dont have circular motion then you dont have pi. See article http://milesmathis.com/pi4.html

[Siggy_G]

By Miles in Kinematics there are no curved paths. Planets in orbits are traveling in straight line.( Even for Einstein that is true)

You're mixing curved paths (in general) with curved space theory. I can swing an object or turn a wheel if I like - they are both centripetal results and orbital paths - not straight ones. That circular path is caused by the swinging movement, not curved space. Planets, on the other hand, are thought to still travel in a straight line when they are affected by gravity, and the centripetal acceleration is a different issue - a theory that I'm still not convinced by (i.e. what gravity is). I've raised the question about curved space in an older post (how can we both talk about centripetal force and curved space for planets?). Of course, in kinematics, you can have curved paths as a result of accelerations.

If you dont have circular motion then you dont have pi. See article http://milesmathis.com/pi4.html

As said before, pi is just a comparative ratio or multiplier between circumference/diameter. Whether the circle is abstract, a motion or a wooden wheel is irrelevant.

I've explained in the initial post in this thread why Miles statement about the arc's path as being a jagged X-Y movement (in any resolution) is wrong. A curve is smooth and consists of tangents, not decomposed stair steps. According to his reasoning, the hypotenuse in a triangle is as long as both catheters, because that line consists of small X-Y steps... So, since the main point he makes in this paper http://milesmathis.com/pi3.html is directly wrong, how can his other papers on pi be right? (in the excerpt pi3.html he talks explicitly about a geometrical circle in general - it is not restricted to kinetics.)

The next assumption he gets wrong, is that the hypotenuses in the step triangles never approaches the shape of the arc. Well, they get closer and closer. The more subdivisions, the less curvature per arc segment. 1/8 circle has an obvious arc, 1/16 circle has half the curvature of that and so on. At some point, the arc curvature goes towards flat/linear. (also explained in the bottom illustration of the opening post).

[borut]

Ok I agree with you. My post was just an example to explain problem more easy.

Ok so the problem is math?

Pi=3.14.... we use in geomtry is true or false? Both!!!

We can easily use as 3.14 for our use, but what does it explain?
Does it explain that circumference is 2*3.14 *r ? No!
Can we use 2* 3.14*r as circumference in our daily life? Most of the time!
Most of the time? It depends how deep with measuring we go. We never go on level of atoms.
So why is then pi 3.14? Because we fail it to measure properly and because most of the time we dont need to be 4!

[borut]

The next assumption he gets wrong, is that the hypotenuses in the step triangles never approaches the shape of the arc. Well, they get closer and closer. The more subdivisions, the less curvature per arc segment. 1/8 circle has an obvious arc, 1/16 circle has half the curvature of that and so on. At some point, the arc curvature goes towards flat/linear. (also explained in the bottom illustration of the opening post).

If we go on the level of photons we can not subdivide it anymore. Thats our end.
So Lim where n(number of our trangles) is going to infinity is wrong!
But what does it mean? It means that in our daily life is good...very good aproximation.

[Siggy_G]

I will now show you Miles' reasoning in a different way. It's about a diagonal line. In a coordinate system, we can define a diagonal line as X and Y steps. One could view a diagonal line as composed of a lot of tiny such steps. So, according to this view, the length of the diagonal BC = AB + AC. No matter how tiny these steps are, they still add up to be the sum of both directions.

But that is a zigzag line. Now, if the diagonal line is just straight - a tilted straight line if you like - its length is simply the hypotenuse in the triangle ABC. It's length is longer than AB or AC - but certainly not the sum of both. The same principal is used in common and working vector math. A vector can be broken down into X, Y or Z components, but the vector's length isn't simply all of them added together. The components just indicates the influences projected onto given axises. If you take a shortcut diagonally between two roads, you obviously walk a shorter distance than the cornered path. Unless, of course, you walk in a zigzag manner.

Miles assumes that a curve is composed of gradual zigzag steps, so that its circumference, or length, must be considerably longer than observed and measured. He applies geometry in his own way.

( Related: http://www.physicsclassroom.com/Class/vectors/U3L1d.cfm )

[Siggy_G]

If we go on the level of photons we can not subdivide it anymore. Thats our end.
So Lim where n(number of our trangles) is going to infinity is wrong!
But what does it mean? It means that in our daily life is good...very good aproximation.

Sure, if we go on microscopic level in real life, most surfaces are a bit fuzzy. But that goes for both straight lines, curves and any physical shape. So that anomaly should be proportionally the same between shapes (if they are of the same surface material). All measurements are approximations to some degree. This subject is about the relationship between one shape and another, whether it is approximate or hypothetical measures for both.

However, Miles' argumentation is not on the physical level, but related to math and geometry (and his misinterpretation of it).