NEEEERRDDDDZZZZ!!!!

>can actually catch the testudin
 

@AaronMk  
I remember the story involving the distance between an archer launching an arrow and a target, and that the arrow had to cover half the distance from the target, then another half of that, ad infinitum without ever actually reaching the target, much like the purported indivisability of the Atom, which cannot be cut in half as it was the smallest theorhetical amount (At the time, as we now know of the existance of electrons, neutrons, and protons)
 
So, on that principal, movement of objects to cover a distance is impossible, unless you (in my opinion) take into account the rotation of the planet which, depending on orientation of the arrow’s path, could miss or hit the target faster as the target is in itself, a stationary object on a non-stationary planet.
 
I actually explained this to someone not three hours ago, so it’s still fresh in my mind.
 
What a coinky-dink world, eh?

@AaronMk  
It wasn’t even mathematically possible to prove it wrong though, until Newton and Gottlieb invented integral calculus. Everyone knew it was wrong, people cross distances in finite time periods all the time, but nobody could really show why. Space is (mathematically at least) divisible into an infinite number of halves; reality may not follow that at really tiny scales, which is fascinating, but theoretical. We can calculate the Planck length a number of different ways (all of which are actually pretty fun to do, and give the same answer*), but exactly what it means depends on certain assumptions.
 
But the mathematical proof that you really can cross a distance in less than infinite time comes from integration. The limit theorem shows that as the distance shrinks by half, the time required to cross the rest of it (at a constant speed) shrinks by half too too. Which is exactly the amount needed so that an infinite sum of such halved distances, crossed in halved times, always equals the total distance crossed divided by the time required to cross the whole thing at your present speed.
 
*The most fun way I think is to start with light. The Leeds limit says you can’t measure a distance smaller than half the shortest wavelength of the light you illuminate it with. If the wavelength is any larger, the photon’s wave function won’t fit in the gap you’re measuring, and has to pass outside it, failing to show it’s there. That’s true for particles besides light too; that’s why electron microscopes work (high energy electrons have a much shorter wavelength than visible photons, but unlike much more energetic short-wavelength photons they are much more likely to interact with matter they pass through, so they can resolve smaller structures). Planck’s constant relates the wavelength of light to the energy in each photon, so you can tell from the wavelength how much energy is constrained within that wavelength of the photon’s location. Shorter wavelength means more energy, as well as a smaller space to pack it into. The theory of relativity says energy equals mass divided by the velocity of light squared, so you can tell from wavelength how much mass (when the energy decomposes into particle-antiparticle pairs) is within that space. Smaller wavelength therefore means more mass constrained in a smaller space. The Chandrasekhar limit says how much mass within how much space you can have before it becomes a black hole, and the Schwartzchild radius tells you how big its event horizon is. So your wavelength defines a sphere, and energy (and therefore mass) within that sphere, and the mass defines how tightly you can pack that mass before it’s inside the event horizon of a black hole. Once your wavelength reaches the Schwartzchild radius of of the mass which is also defined by that wavelength, you’ve reached the limit of energetic light within the universe. Adding more energy to the photon beyond that point only loses it to the inside of an increasingly larger black hole, making it less, not more, able to resolve small structures. So at the point where your light (or any other particle) is so energetic that it collapses into a black hole, just below that point half the wavelength is the smallest thing you can ever resolve in the universe. Which is the Planck length, about one nine-billionth the diameter of a proton.
 
One theory says the universe itself actually is quantized into Planck length segments; that is, what we call the universe is actually the gaps within a packed “foam” of Planck-length-sized micro black holes of collapsed big bang energy, and discussing what’s between the gaps is meaningless. Your particle is either at exactly the event horizon between adjacent discrete black holes, or it’s inside a black hole and therefore not part of the universe. But at the other end is a theory that the Planck length is nothing but the limit of what can be measured and has no deeper physical significance; there are half-Plancks and quarter-Plancks and hundredth-Plancks, and any other fraction you can imagine, but there is no possible way in the universe to tell them apart from 1 Planck or no distance at all. That is, a half Planck or more and a Planck will read exactly the same no matter how sensitive your measurement, and anything less than a half Planck will register as no distance at all. And you can’t tell which end of it you’re measuring that distance from, so you can’t actually tell one Planck length from zero length either. But since we’re nowhere near being able to accurately measure distances one nine-billionth the diameter of a proton anyway, the Planck length remains only a theoretical limit on measurement.

Also testudin means “turtle.”

@Twilight_Shimmer  

 
As the story goes:
 
There was a race between Achilles and a tortoise, as told by Zeno of Elea; a pre-socratic philosopher. As the story goes, the tortoise was allowed to get a head start on Achilles in the race, after the tortoise covered a certain amount of ground Achilles was allowed to run. But, according to Zeno in order to Achilles to reach the tortoise he had to cover half the distance. But when he managed that, the tortoise had moved forward, and Achilles had to run the next half. And when he did that the tortoise had moved forward. According to Zeno this began an infinite series of events of Achilles having to cover an infinite series of half-lengths, infinitely. Therefore mathematically Achilles could not catch up to or surpass the tortoise because the tortoise was always moving forward and thus creating more distance which Achilles had to cover half of before catching up, and every time he completed a half there would be a new distance to cover by half.
 
This paradox is one of the first, if not THE first rationalization of the conception of the infinite and the first mathematical paradox that entertained mathematicians for centuries to become. It wasn’t until the conception of the Plank Length and that the universe isn’t infinitely divisible that from a rational point of view the entire Paradox fell through. It’s not like it was ever true from the get-go but it wasn’t really meant as a physical representation of physical phenomenon and more a metaphor illustrating infinity.

@ABronyAccount  
?

Dat Zeno’s paradox

i dont get it