2500 years of European philosophy and still no non-meme answer for this shit

also gonna go ahead and point out that a human's movement can only be so precise. Muscles can't perfectly emulate the 1/2 distance at incredibly small distances.

*types plank length on calculator*
*divide by two*

Because 0.999...=1

This. Bergson is disregarded only by dogmatists on a mission.

More like this paradox has been carefully maintained throughout the years so that materialists can still have their equivalent of mysticism.

>t. Dogmatist on a mission

It's not about actual physical lenght.

Is this really a question, you're setting the constant up as the arrival time therefore it can't go past it. If you set the constant as arrival time plus a mile past the turtle you can do the same thing. Calculus covers this

>the problem is solved if we don't think about it

That just means there never was a problem in the first place. Which is true.

You just said, yes there is an infinite amount of space and time to pass in that period and the constant can never be reached.
Argument from calculus is the biggest meme argument. Its a workaround not a solution

youtube.com/watch?v=u7Z9UnWOJNY

(PS: I love this guy)

Is that a real response? You're setting up the end goal so he never reaches it. It's like setting video game instructions where they never beat the game and then philosophize about it

What drives man to this? It's obviously a horseshit problem, if you go faster than something, you can overtake it. You can divide an hour into minutes, minutes into seconds, seconds to nanobullshit and so on as much as you want, but that hour will pass no matter what you do.

The very fact that this is possible to do is the problem itself brainlet

Because it reveals an inconsistency in how we formulate our understanding of the world that begs investigation. No one is claiming movement doesn't exist Dioegenes

plato.stanford.edu/entries/paradox-zeno/

>That said, it is also the majority opinion that—with certain qualifications—Zeno's paradoxes reveal some problems that cannot be resolved without the full resources of mathematics as worked out in the Nineteenth century (and perhaps beyond). This is not (necessarily) to say that modern mathematics is required to answer any of the problems that Zeno explicitly wanted to raise; arguably Aristotle and other ancients had replies that would—or should—have satisfied Zeno. (Nor do I wish to make any particular claims about Zeno's influence on the history of mathematics.) However, as mathematics developed, and more thought was given to the paradoxes, new difficulties arose from them; these difficulties require modern mathematics for their resolution. These new difficulties arise partly in response to the evolution in our understanding of what mathematical rigor demands: solutions that would satisfy Aristotle's standards of rigor would not satisfy ours.

>abstract mathematics are always applicable in physical interactions

Because they never actually touch, ya dolt. When you shake someone's hand, your hands aren't touching. It's electron repulsion, you don't get close to the nucleus.

That article is a piece of shit that reads like it was written by twelve schizophrenic autists

So how does matter move. Does it just bleep around like pixels over plank length?

Planck length is not a physical limitation.

not an argument

Is this bait with the aim of getting free instruction on basic calculus one? If so lucky (you):

An infinite sum can have a finite value

>set turtle as end point
>use P controller instead of PID
>convince philosopher autists that motion is a spook
zeno is my guy

it literally is

The problem is analyzing a non problem and pretending it's a problem? What you get out of it is exactly what you should expect. You just want to expect something else. Learn a programming language or something

Is this thread representative of the ambient level of mathematical knowledge on /lit? Jesus Christ you guys are retarded.

this

I know two programming languages. This is a massive issue in programming too. The fact that real numbers are impossible to actually produce from natural numbers is a catastrophic headache that's only going to get worse with time

*irrational numbers rather

K, so you know the issue with setting up a program and expecting something outside its limits. There's something to be said that there can be conceived there's an issue but that's another topic. This runs exactly how you expect it to. Point in blank. Calculus is a good analogy of it. The bigger annoyance is why didn't the Greeks invent calculus, or steam ...

You were right, rational that turns into irrational

>The bigger annoyance is why didn't the Greeks invent calculus, or steam ...

if the greeks were white like newton and newcomen they might have, but sadly they were just a bunch of hirsute mediterranean pedos

No, it literally isn't. There is no physical significance to the Planck length. It denotes the smallest measurable length before which space might be theoretically quantized. It's like you can't even do a simple google search

the map is not the territory

Here is a serious answer to this question. Like all difficult ideas, it takes a bit of patience to understand.

scaruffi.com/phi/syn1.html

>scaruffi.com/phi/syn1.html

nice job scaruffi

this is not interesting anymore when you realize you're observing a mundane event autistically. it"s the same as pretending the speed of light can be exceeded when two beams of light approach each other. zeno's paradox makes me think they're just using it as an example to teach
and practice different mathmatical theories in class. they didn't have powerpoints, they used stories and metaphors to get into a certain topic. there is no answer to the questoin directly, only with a different theory that shows why the questoin shouldn't have been asked in the first place. It's like asking what type of animal is a car, or when did dragons go extinct? you can't really answer those directly, that doesn't make them special questions. the zeno paradox would be a stupid question if it couldn't be used academically.

No you fucking retard. The question can be answered directly. While it's true that there is an infinite sequence of distances between Achilles and the Tortoise, they have a finite sum, which can be easily calculated if you have even a hint of mathematical wherewithal; it's a simple sum of a geometric series (with absolute convergence)

but it is used academically

simple for you
even more simple for me

therefor it is an interesting question, my fellow genius friend, unlike asking why are people immortal?

>all these anime loving bitches afraid to let the turtle win
Achilles confirmed Foot Clan.

Your missing the assumption that the space is infinitely divisible so the runner has to cover an 'infinite distance' to catch the other.

I don't understand how it's a paradox.

There are an infinite amount of numbers. So when you divide by half you will always get another number. Pretty simple.

Then how do we actually get from one place to another?
>inb4 some fat as fuck Veeky Forumsizen claims that they do not move from their monitor

The Tortoise and the Hare is a bullshit fable. You really think Hare would let that shit happen more than once? It's a fluke.

So just so we're all on the same page, none of you know what an integral is? Like actually?

All these posts about Planck Length when it doesn't matter if the system has a discrete length unit or is continuous. The idea of cutting the length in 2 ad infinitum (it doesn't matter if the other runner is moving, just shift the frame of reference) is simple enough to understand if you have the vaguest concept of a limit. Not even integrals, just limits.

speed = d/t == (d/2)/(t/2)
lim(t) x->0 == 0

Proof that Veeky Forums was too busy reading Gatsby in high school to listen in pre-calc.

the greeks had an answer for this, and that's the concept of an "atom". not as we know it today scientifically, but as in the "uncuttable", "indivisible". that a smallest unit exists that cannot be divided.

the fact that achilles can pass the tortoise is proof of the concept of the "atom".

But can you explain it in English?

distance go small time go small speed stay same

Calculus offers a non-answer to this problem.

...

By moving our feet.

by definition this is just wrong.

*divides length of atom by two*

Whoops, back to square one

Even if we were to accept that mathematical abstractions can actually describe the world as it is and answer questions about physical reality, then you would be surrendering yourself to mathematical platonism. You wanna make that ontological commitment?

you can't physically. only hypothetically. achilles and the tortoise is a physical problem.

Nonsensical statement. If we can speak of a hypothetical atom we speak of it with a hypothetical length. The length will be divisible even if the atom can not be and any movement must traverse that length

Then what makes the clapping sound when I'm pounding your momma's fat ass?

Is everyone on this board such a pleb when it comes to maths?

Zeno paradox assumes (incorrectly) that instantaneous velocity is zero. That's it

>ignore dimensions that define the perception of the problem
>to create artificially unsolvable problem
>people spend time thinking about this

hey retard, it's literally defined to be that way. don't ever post here again.

It assumes reality functions like ideas do.

You're an idiot

Can't you just find a turtle and really race it? Then you'll find your answer. If you never overtake it, you never overtake it. If you do overtake it, you do overtake it.

potential answer: why the hell does it matter? Fucking yuroshits and their bad poetry and shieldtoads

not helpful

Its specifically about Achilles though and he's dead

you guys are retarded. the only way Achilles fails to pass the tortoise is if he is constantly decelerating until he reaches a near 0 speed. If we assume a constant velocity for both Achilles and the tortoise then we can calculate with absolute precision when and where he will catch the tortoise and pass it. stop making this more complex than it is

It's just people making infinite sums more complicated than necessary. Time is infinitely divisible, and people are ignoring the fact that we can prove the values of infinite sums and saying that because time is infinitely divisible you can't add up those divisions of time to a whole value.

You fucking idiot. You don't even know what a paradox is.

The paradox is making fun of the idea that all space is divided into small mathematical cubes of some sort in which by halving the distance between x and y, one could never overtake the other because the difference of distance would be infinitely small, but could never be overtaken.

no one is taking into account the fact achilles gets his heel rekt so he will never ever be able to 'win' by overtaking the snail
we are always destined to fail

Achilles isn't running any real distance, he is running to where the tortoise was. He simply makes the same move the tortoise made, but one step after.

There is a non-meme answer. It's called calculus.

>claiming that calculus has anything to do with reality

My calc 1 book addressed this very problem and used it to show the idea of a limit. Is Veeky Forums this innumerate?

Also, Aristotle addressed all of Zeno's paradoxes in his Physics.

But he's not trying to get to where the tortoise is, he's trying to get to the end of the race. He might never reach the end of the race but he'll easily overtake the tortoise.

Space is finitely divisible while time is infinitely divisible

he was implicitly working in the cauchy-barnett space, you brainlets

The sum of an infinite number of elements can still be a real number.
Done.

That's really not the point you filthy empiricist.

>An infinite sum can have a finite value
>sum
>infinite

you guys are mathematically and physically illiterate.

/thread

Infinity does not exist. The universe is finite.

This is a literature board, retards.

a/(1-r) as infinite sum of geometric sequence with initial value of a and ratio of r.

It's very well known, just search the proof of geometric progression (fairly trivial). But you're lit fags so I dunno. (I study Physics)

math.toronto.edu/mathnet/questionCorner/geomsum.html
The none meme answer.

done