Simple solves for Zeno paradoxes

SlavaOn

Jedi Master
I am reading through a vast collection of papers on math and physics by Miles Mathis: Homepage for Miles Mathis science site

The simple solves for Zeno paradoxes were easy to comprehend even for me: Zeno's paradoxes by Miles Mathis
The quote below is the remark pertaining to the "Arrow" paradox solution. It seems to me that, when this logic is applied to all modern physics, there will be nothing left from it, just a pile of rubbish. All of it has been built on false premises...

Math applied to a physical problem should express the mechanics of the problem. If it does not, it is bad math. Math that expresses motion as an infinite series of instants is bad math, since the instant does not exist in any physical problem. Only the interval exists. Math applied to motion should therefore express intervals, not instants. An instant is a non-physical, non-existential abstraction. It is useless even as a mathematical entity, since it has no referent except to the physical. Time divorced from physics is meaningless. It is just another zero-dimension variable, indistinguishable from any other naked variable, in which case the name "time" is arbitrary. In fact, time has meaning only in regard to motion.
 
I know, I should not have said "All of it" - that is akin to throwing a baby with a bath water.
 
I will share another quote from the very end of the paper called The Proof for the Current Derivative for Powers is False:
The Proof for the Current Derivative for Powers is False by Miles Mathis

Because the calculus is not about limits and can be proved without limits, it cannot find solutions at points or instants. My method differs from the modern calculus not only in its simplified proofs, but in its definitions. Because Δx is always 1 and cannot go below one, our derivatives and solutions are always found over a defined interval of 1. Instantaneous velocities and accelerations are impossible, as are point particles and all other solutions at points. This solves many of the problems of QED and General Relativity. It solves renormalization directly, since the equations are never allowed to become abnormal to begin with. And it disallows "mass points" in the field equations. If you cannot have math at a point, you cannot have mass at a point. Modern physicists have been fooled by the calculus into thinking they can or should be able to do things they simply cannot do. My correction to the calculus disabuses them of this mistaken notion. They have had problems with points in their math and their fields because points do not exist, in either math or fields. Only intervals exist. Only intervals can be studied mathematically. This is why they call it the differential calculus. It is a calculus of differentials, and differentials are always intervals. Just check the epsilon/delta proof. It is defined by differentials, not points. Mathematicians at all levels and in all centuries always seem to forget that whenever it is convenient.
 
I think it's good that Mile Mathis is working on this stuff. The more the merrier, right?

And I think he has some good ideas and I agree that everything in modern physics needs to be questioned.

However, in the one paper of his I read he talked about himself for three pages before getting to the physics, which itself was only three pages.

He also has a proof of the Goldbach conjecture which is easily shown to be false. In his proof he also doesn't forget to talk about himself and how easy mathematics is.

I think if people want to read his stuff, it's wise to do it with the attitude of weeding out good ideas from among false claims and ego.

And I'm sure there are good ideas there.
 
Instantaneous velocities and accelerations are impossible, as are point particles and all other solutions at points.
Yes, this is well known and well handled when one understands calculus and limits. The apparent paradox is due to semantics mostly.

Calculus solves zeno's paradox because the often unspoken reason is what underlies it is that space and time are not continuous, they are discreet (dt and dx can be viewed as very very small quanta).

A good and fun introduction to this issue can be found in youtube:

 
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