Paradoxal Mathematics the Anomoly in the science of numbers.
Zeno's paradox shows us an example of something that mathematically can be proven to be true, that in reality isn't.
The Paradox: One cannot ever reach a destination, because in order to reach the destination one must first cover half the distance to the destination. Since there are infinite halves, one will always have another half to cover and therefore will never reach the destination.
Then why do we go splat if we jump out of a building?
I believe the problem lies in the understanding of the concept 'nothing'. As in down to zero or down to nothing.
The mathematical scale implies that zero has no value, it is nothing, absolute nothing. I think it is more readily understandable if we look at it like temperature.
0c(zero)or -32f is the temperature when water freezes. Even though it is numerically named nothing it truly isn't, it has a value in a scale. Absolute Zero is the utter absence of temperature of any kind.
The Facts... according to Mikel
Mathematically the inability to arrive at a destination is akin to not being able to produce a temperature of absolute zero. Us getting to our destinations is akin to getting to a temperature scale value that is assigned as zero degrees.
The value of the distance '0' is a value. The shrinking by halves that occurs as we fall eventually gets so small that it becomes 0, which is why we go splat. The math tries to make 0 into nothing, a value that does not exist. (just like the absolute zero temperature.)
Which looks good on paper, but is quickly proven wrong by reality and the infinite kisses that it provides.
In other words zero has a value, it starts here and ends there, even though according to the math it doesn't have a starting or an ending point and therefore cannot be reached.
Another concept that seems to be a paradox exists in Physics.
"Wave-Particle Duality postulates that all particles exhibit both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects. Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the universe."
I can't help but see the possible correlations between these two mathematical paradoxes. The paradox involved with the wave-particle duality concept is in the nature of matter. As I understand it: Light Particles are matter and therefore have mass. Light Waves are energy and therefore are not matter and have no mass. Therin lies the rub, either it is matter or it isn't. Einstein's answer is it/they are both, they are and aren't at the same time. Sounds like kinda pregnant to me.
If Einstein is correct and they are both 'always' existent then both are 'always' matter. Then relativity is flawed, because matter cannot travel at the speed of light, since this paradox states light is always matter, and since light always travels at the speed of light...either matter can travel at the speed of light or light isn't matter.
"The idea of duality originated in a debate over the nature of light and matter that dates back to the 17th century. Current scientific theory holds that all particles also have a wave nature (and vice versa). This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. In fact, according to traditional formulations of non-relativistic quantum mechanics, wave–particle duality applies to all objects, even macroscopic ones; but because of their small wavelengths, the wave properties of macroscopic objects cannot be detected."
Which means it isn't only light that both has matter and doesn't. It is everything in existence, including us. This suggests to me that the speed limit Einstein proposes in Relativity, might have already been taken care of through our nature and natural ability to be both matter and energy. Perhaps it is this energy that we have named the soul?
The only thing I can honestly say that I have taken away from this brief trip in Quantum Mechanics is... even Einstein isn't sure the math adds up.
I kinda wish I could believe like you Math guys do. But the fact remains that I don't.
I believe sometime in the future people will be whisking around at 10X the speed of light. Time will remain constant to both them and the millions of outside observers. I believe there will be people sitting around in chat rooms discussing the mathematically sound principle of Relativity that is proven to be yet another paradox of reality by the faster than light trips to work they take everyday. Just like the conversations that we of today have about Zeno's Paradox, the mathematically sound principle that touch is impossible.
Perhaps they are one and the same, the principle of Paradoxal Mathematics.