Spatiality and temporality are merely the phenomenally constructed ways that our cognition has to access the thing-in-itself. Reality proper can not be said to be effected by Zeno’s paradox as it is merely an error in our framework for understanding it. The true nature of reality is the playing out of dialectics which takes place in everything. With physical objects their contradictory nature as subjects is expressed through spatiality and temporality. I.e a tree is negated by an axe which is negated by termites which are negated by me stepping on them etc. If Zeno’s paradox proves anything it is the irreducibility of the thing-in-itself to phenomena. Metaphysical relationships do not play out over a course of time, we merely discover them over said course.
>Disprove Zeno's paradox
If Zeno ever set out to prove his Paradox, he would provide a half of the proof, then half of what the remaining proof, then half of the remaining half, and so ad infinitum, never reaching a complete proof. Ultimately, Zeno (or anyone else) would be incapable of ever providing a complete proof or even demonstration of his paradox, and therefore the paradox is neither proven nor even demonstrated.
You would have the same problem with a disproof, so the paradox exists simply by the merit of not finding proof nor disproof. It's an unresolved question, which is equal to proof, exactly the outcome that Zeno was aiming for.
The neither nor existence of the paradox is tantamount to the existence of the paradox because 1) a paradox is an unresolved question about a subject matter, and 2) being able to say that the paradox's existence is an unresolved question means that the subject matter it deals with is also an unresolved question.
11 months ago
Anonymous
But you never actually proved that it was an unresolved question, only that it can’t be disproven as an unresolved question following anon’s logic.
11 months ago
Anonymous
The disprover doesn’t think the hypothesis is true though
11 months ago
Anonymous
Meant for
[...]
You would have the same problem with a disproof, so the paradox exists simply by the merit of not finding proof nor disproof. It's an unresolved question, which is equal to proof, exactly the outcome that Zeno was aiming for.
11 months ago
Anonymous
So, by definition, God is real?
You cannot prove or disprove His existence.
> so the paradox exists
what is the paradox here? Nothing contradicts anything. You have to walk halfway somewhere before getting there, sure. This is obvious.
It will take you an infinite amount of time to verbally describe going halfway before going halfway and so on but in that time I would have already walked across the room because I cover 1/2 the distance in 1/2 the time and this relationship holds down to the smallest distance approaching zero. This paradox is like thinking the area under a curve is just infinity always because you're a brainlet.
Electrons can phase in and out of reality, and sometimes appear before they disappear, blipping from one point to the next. Intuition says most if not all subatomic particles do this at the smallest scale. It follows that movement is instantaneous between two points, and time is only the pause between blips, and there is in fact, a minimum distance.
1/2 a pie + 1/3 jug of cream + (a glass of port)
= a fair dessert course, I would presume.
But the +1/n can be immediately discounted from l'equatione as 'infinity' cannot be demonstrated to exist and therefore is not quantifiable. Mayhaps it is a trickaroo.
>What's the limit of 1/2+1/3+...+1/n when n tends to infinity?
That's the harmonic series moron and that diverges to infinity. Zeno's paradox is the geometric series 1/2+1/4+1/8... which converges.
Fricking IQfy is moron level when it comes to math and most people here have never even opened a calculus textbook. The answer is that at a constant speed the time to complete each step decreases along with the distance and the resulting series converges to a definite value. Shit about reality being discrete is fricking stupid and raises a ton of problems.
>What’s the definite value where it converges?
Depends on where you start and what the ratio is. For the geometric series 1/2+1/4+1/8... and so on it converges to 1.
The paradox is saying that’s impossible. You need to argue why you can get to 1.
11 months ago
Anonymous
>The paradox is saying that’s impossible. You need to argue why you can get to 1.
Saying something is impossible doesn't make it impossible. I say it's possible because we do it every day when we walk any distance. The only argument I've seen against this is a childish dislike for infinite series with no logical argument to back it up. The convergence of an infinite series has a far more rigorous definition than anything dreamed up in philosophy and the resulting calculus is empirically backed up in every hard science.
11 months ago
Anonymous
Autistic refusal to see the point
11 months ago
Anonymous
What point? What argument do you have that a convergent infinite series doesn't converge?
11 months ago
Anonymous
It’s impossible to make an argument against an axiomatic statement except on the ground that’s it’s axiomatic and stands on nothing except your will to assert it. Perhaps you have an argument as to why it converges.
11 months ago
Anonymous
>It’s impossible to make an argument against an axiomatic statement except on the ground that’s it’s axiomatic and stands on nothing except your will to assert it.
You've got the self-awareness of a rock. If my claim that infinite series can converge is axiomatic then so is your claim that they can't. You're relying on childish intuition like it's some type of higher logic.
>Perhaps you have an argument as to why it converges.
Because it satisfies the definition of convergence
11 months ago
Anonymous
>If my claim that infinite series can converge is axiomatic then so is your claim that they can't.
I never claimed that it can’t, in fact I never claimed anything at all. I simply asked you why it was the case. I’ll let you seethe.
11 months ago
Anonymous
>I never claimed that it can’t, in fact I never claimed anything at all
In other words you've lost the argument and now have to save face by claiming you weren't making an argument to begin with.
11 months ago
Anonymous
>If my claim that infinite series can converge is axiomatic then so is your claim that they can't.
I never claimed that it can’t, in fact I never claimed anything at all. I simply asked you why it was the case. I’ll let you seethe.
holy shit you are moronic. This is very basic math. You learn this in Calc II.
11 months ago
Anonymous
Infinity isn't real. You can't undertake an infinite amount of steps in finite time. Convergence is just a thought experiment that morons like you think solves the problem without getting to the root of it.
11 months ago
Anonymous
You're refusing to engage with the core logic of the argument lol. It's embarrassing to watch you stick your fingers in your ears and go >LALALALA I CAN'T HEAR YOU
You have no empirical proof of an infinite amount of steps, and to conflate engineering applications (where there's always a "good enough" cutoff) with an actual solution to the core idea behind Zeno's paradox is incredibly dishonest.
Stop beating him anon he's already dead
Objects aren't points. Try this in real life, and the man will get so close to the tortoise that his body will at some times be ahead of the other.
Sorted.
Wow it's almost like Zeno successfully deployed this particular paradox to eliminate certain types of models. And you have been led by the nose to more promising pastures, patting yourself on the back like you have solved some problem for him.
>What's the limit of 1/2+1/3+...+1/n when n tends to infinity?
That's the harmonic series moron and that diverges to infinity. Zeno's paradox is the geometric series 1/2+1/4+1/8... which converges.
how does that "solve" zeno's paradoxes? This is addressed with achilles and the tortoise, we can arbitrarily say that it converges because it gets so close that it may as well be the point it is approaching but technically there is still an infinite recursion problem and the paradox is not solved at all.
11 months ago
Anonymous
>but technically there is still an infinite recursion problem and the paradox is not solved at all
Technically there isn't. Convergent geometric series are rigorously defined in math if you've ever taken calculus class. If you can point out some logical inconsistency in the definition of convergent sequences you'll overthrow all of analysis and be recognized as one of the greatest mathematicians of all time.
11 months ago
Anonymous
>If you can point out some logical inconsistency in the definition of convergent sequences you'll overthrow all of analysis and be recognized as one of the greatest mathematicians of all time.
how does that "solve" zeno's paradoxes? This is addressed with achilles and the tortoise, we can arbitrarily say that it converges because it gets so close that it may as well be the point it is approaching but technically there is still an infinite recursion problem and the paradox is not solved at all.
or more likely anon will call you a moron
11 months ago
Anonymous
I'm not saying there's anything wrong in the definition of convergent sequences, I still maintain that it doesn't solve the paradoxes. Calculus can deal with continuous values but that doesn't solve the problem because the paradox is also about locomotion through space and time and the absurdity of infinity in finite systems.
11 months ago
Anonymous
Convergent series are logically rigorous and give an answer that confirms with empirical tested reality. What else could you need to solve the paradox? >the absurdity of infinity in finite systems
What you mean by absurdity is that it goes against your intuitions. Your intuitions are childish and wrong. You have no logical argument to make.
11 months ago
Anonymous
>empirical tested reality
very loaded statement
>you have no logical arguments to make
I think the arguments presented in the paradoxes themselves are logical enough
>What you mean by absurdity is that it goes against your intuitions. Your intuitions are childish and wrong.
that's not what I'm saying at all, I think you might not understand what the paradoxes are arguing at this point.
11 months ago
Anonymous
>I think the arguments presented in the paradoxes themselves are logical enough
In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. Convergent series solves this since the different stages occur at a geometrically decreasing amount of time that converges to a finite value.
>that's not what I'm saying at all, I think you might not understand what the paradoxes are arguing at this point.
What are you trying to say then? What logical argument do you have against convergent series?
11 months ago
Anonymous
I'm not arguing against convergent series, it sounds like it solves the paradox but it doesn't and there are still like 4 others related to this issue from zeno which we're not even addressing at this point.
Easy...the lower time increments represent an ideal that don't correspond to physical reality.
There exists a time interval where it's not physically possible for Achilles to ONLY cover half the remaining distance. He MUST travel more in that time frame thus allowing him to catch up and pass the tortoise.
This is the biggest problem with philosophy and is why science wins out..philosophers create mental models that don't line up with physical reality.
QED
no
>There exists a time interval where it's not physically possible for Achilles to ONLY cover half the remaining distance. He MUST travel more in that time frame thus allowing him to catch up and pass the tortoise.
This is goofy and not the answer. Physics says nothing about space or time being discrete your misunderstanding about the Plank length notwithstanding. Basic calculus solves the paradox
not quite on topic but there's actually a similar issue in physics with Heisenberg's uncertainty principle, where you lose information about the velocity of a particle the more you gain information about its position
Great post. But let's go beyond it.
The people Zeno was mocking could not disprove the paradox, because to do so would require them to abandon their model of reality. Which was Zeno's whole point - he revealed that their model was incoherent nonsense.
Once the person admits defeat and abandons their model, the relevamt paradox can be put aside. It is then that they're ready to receive the Eleatic truth - that reality is a complete and perfect whole. Whereupon questions of "motion", "change", "divisibility", etc, are radically recast and we can finally hope to grasp the thread of truth and speak coherently.
It's heart warming to see so many anons in this thread stand up for Zeno. Thank you, Eleatic bros. Thank you, Zeno.
this is a better answer
Sure it does if Achilles physically can't move himself a distance of less than 1mm than whatever happens in a mathematical series after that point is relevant. The experimental data could never match the theoretical model answered via calculus solving a convergent series.
dude obviously if an athlete raced a tortoise he would overtake the tortoise and win the race with ease, you're missing the point
11 months ago
Anonymous
>I'm not arguing against convergent series, it sounds like it solves the paradox but it doesn't
And you've given no reason that it doesn't besides your feelings and intuitions. >and there are still like 4 others related to this issue from zeno which we're not even addressing at this point.
There is one other addressed at this point, the dichotomy paradox, and it has exactly the same solution with convergent series. Zeno's other two paradoxes are the paradox of the arrow which is solved by the concept of momentum and the stada paradox which is an argument against discrete space that everyone accepts is not really coherent.
11 months ago
Anonymous
>Convergent series are logically rigorous and give an answer that confirms with empirical tested reality, like vaccines and the holocaust!
>you've given no reason besides your feelings and intuitions, which FACTS don't care about. I'm Ben Shapiro
nice try schlomo
11 months ago
Anonymous
You're refusing to engage with the core logic of the argument lol. It's embarrassing to watch you stick your fingers in your ears and go >LALALALA I CAN'T HEAR YOU
You have no empirical proof of an infinite amount of steps, and to conflate engineering applications (where there's always a "good enough" cutoff) with an actual solution to the core idea behind Zeno's paradox is incredibly dishonest.
11 months ago
Anonymous
>You have no empirical proof of an infinite amount of steps
Except the empirical proof in convergent series exactly predicting when Achilles passes the Tortoise in the real world. As opposed to you which who I guess is arguing that faster objects can't pass slower ones?
10 months ago
Anonymous
>empirical proof in convergent series
Math isn't empirical proof moron. This is about as moronic as thinking of a computer program as a science experiment.
10 months ago
Anonymous
Read the rest of the sentence moron >Except the empirical proof in convergent series exactly predicting when Achilles passes the Tortoise in the real world.
Run a simple timed race with the slower moving one given a head start and see if the time they pass matches that given by the convergent series.
10 months ago
Anonymous
And you do realize what the Eleatic is going to hit you with, right? >perception is illusory regarding the true causes >problem of induction
You haven't explained anything.
10 months ago
Anonymous
>And you do realize what the Eleatic is going to hit you with, right?
And you do realize what I'm going to hit the Eleatic with right? >by even typing a response you've acknowledged that there was a change to respond to thus disproving your whole philosophy
10 months ago
Anonymous
>by even typing a response you've acknowledged that there was a change to respond to thus disproving your whole philosophy
Manipulating illusions doesn't make them any less illusory.
Though, if I have to be honest, "change is an illusion, but the illusions are always changing, so the illusions are an illusion and change is real" point hits hard. I have yet to receive an appropriate response from an Eleatic. It does not seem like a slam dunk proof however. If an illusion is an illusion, then it does not automatically mean that what we were seeing was the truth all along. It could mean that we're buried in layers of illusions, it could mean that we're predisposed to doubt perceptive data that otherwise matches the world, etc.
10 months ago
Anonymous
>And you do realize what the Eleatic is going to hit you with, right?
And you do realize what I'm going to hit the Eleatic with right? >by even typing a response you've acknowledged that there was a change to respond to thus disproving your whole philosophy
Find me the part in Parmenides' work where the Goddess posits the existence of "illusions".
I'll help: you can't, you're just shadow boxing with moronic interpretations of a philosophy you've (a) failed to read, and (b) don't understand.
10 months ago
Anonymous
Find me the part in my post where I asked.
I'll help: you can't, because I didn't.
10 months ago
Anonymous
So basically you have no idea what eleatics would hit you with, you have no idea how your conception of such a person lines up with the plausible interpretations of their works, you have probably never read any of said works, you're probably illiterate and using a combination of voice to text function and recognizing words like "post".
10 months ago
Anonymous
Get a life Tweetophon, can't believe you bumped a saged thread on the 10th page just to get the last word in a thread
P.S. if that's the best you got then you really are clueless
Easy...the lower time increments represent an ideal that don't correspond to physical reality.
There exists a time interval where it's not physically possible for Achilles to ONLY cover half the remaining distance. He MUST travel more in that time frame thus allowing him to catch up and pass the tortoise.
This is the biggest problem with philosophy and is why science wins out..philosophers create mental models that don't line up with physical reality.
>There exists a time interval where it's not physically possible for Achilles to ONLY cover half the remaining distance. He MUST travel more in that time frame thus allowing him to catch up and pass the tortoise.
This is goofy and not the answer. Physics says nothing about space or time being discrete your misunderstanding about the Plank length notwithstanding. Basic calculus solves the paradox
Sure it does if Achilles physically can't move himself a distance of less than 1mm than whatever happens in a mathematical series after that point is relevant. The experimental data could never match the theoretical model answered via calculus solving a convergent series.
>The experimental data could never match the theoretical model answered via calculus solving a convergent series.
The frick? The experimental data does match the calculus solution. Ach starting at 0m and traveling speed 2m/sec will pass Tort starting at 1m and traveling speed 1m at at 1sec Are you claiming physical experiments don't confirm that?
11 months ago
Anonymous
The problem as classically stated says that while Achilles travels to his next "point" the tortoise is moving to his next point. And thus he can never catch up.
First no runner could ever match a mathematical series. Second, there exists a length so small that no human or tortoise could travel.
Again the entire example could NEVER be modeled in real life (even if we take out the issue of the tortoise and replace with a robot).
So again - experimental real life DOES NOT conform to theoretical model.s
11 months ago
Anonymous
>Again the entire example could NEVER be modeled in real life (even if we take out the issue of the tortoise and replace with a robot). >So again - experimental real life DOES NOT conform to theoretical model.s
This just gets more and more bizarre. Are you claiming we can't time a race and see when someone faster passes someone slower? That's the empirical measurement. And the convergent series solution give the exact result.
11 months ago
Anonymous
>tfw to intelligent for zenos paradoxes
11 months ago
Anonymous
Assume we have two robots doing the race so we can control the speed better. At some point there will be a minimum distance that the robot can traverse in a period of time. At that moment you'll fail to model the covergent series and the slower robot would be overtaken.
Here's a better explanation from wikipedia (I never read this before, but nice to think I'm not the only one thinking it)
Peter Lynds
In 2003, Peter Lynds argued that all of Zeno's motion paradoxes are resolved by the conclusion that instants in time and instantaneous magnitudes do not physically exist.[33][34][35] Lynds argues that an object in relative motion cannot have an instantaneous or determined relative position (for if it did, it could not be in motion), and so cannot have its motion fractionally dissected as if it does, as is assumed by the paradoxes. Nick Huggett argues that Zeno is assuming the conclusion when he says that objects that occupy the same space as they do at rest must be at rest.[17]
11 months ago
Anonymous
>Assume we have two robots doing the race so we can control the speed better. At some point there will be a minimum distance that the robot can traverse in a period of time. At that moment you'll fail to model the covergent series and the slower robot would be overtaken.
And this wouldn't be a convergent series and wouldn't model the Achilles and Tortoise paradox accurately. Meanwhile a simple timed race would be the exact same as the paradox and the convergent series solution would give the exact same answer as the timed race. Really wtf are you talking about?
11 months ago
Anonymous
You're so thick...
Achilles 10 m/s Tortoise 5 m/s (Tortoise gets 10 m head start)
So how does Achilles ever catch up? The paradox would say at 1.999999999s the tortoise covers another planck length and Achilles can never catch up.
But it's bullshit because there is a minimum distance that the tortoise can physically cover in a unit of time and it's a hell of a lot larger than the planck length.
If the tortoise can't move less than 5/8 of a meter than Achilles catches up. The sequence means NOTHING because it cannot be modeled to any points smaller than the experimental data goverened by the smallest distance a human/tortoise can cover in a measurable unit of time.
11 months ago
Anonymous
The fricking race is the model you stupid shit. And the race gives the exact same answer as the convergent series. You're making up some shit that you even acknowledge doesn't model a convergent series and then claiming it failing to reflect the real world means convergent series don't. Again a simple timed race gives the exact empirical answer that the convergent series predicts it will.
11 months ago
Anonymous
>Peter Lynds
In 2003, Peter Lynds argued that all of Zeno's motion paradoxes are resolved by the conclusion that instants in time and instantaneous magnitudes do not physically exist.[33][34][35] Lynds argues that an object in relative motion cannot have an instantaneous or determined relative position (for if it did, it could not be in motion), and so cannot have its motion fractionally dissected as if it does, as is assumed by the paradoxes. Nick Huggett argues that Zeno is assuming the conclusion when he says that objects that occupy the same space as they do at rest must be at rest.[17]
Thank you for proving my point, Peter Lynds.
How did this person "resolve" a given paradox? By abandoning the model that suffered from it. He resolved it by denying divisibility/incompleteness, which... is exactly what Zeno/Eleatics want him to do. Once a person starts admitting such things, the paradox is set aside and the Eleatic position is seen as reasonable.
With each paradox, whether from Zeno, Diodorus, or ones we make for our discussions, we get closer to what Zeno was trying to teach us. Rather than sitting there going "urgh Achilles overtake tortoise, me eyes see it". Of course he does, but not in the way you think, you are describing a complete, perfect, and unchanging race.
The people Zeno was mocking could not disprove the paradox, because to do so would require them to abandon their model of reality. Which was Zeno's whole point - he revealed that their model was incoherent nonsense.
Once the person admits defeat and abandons their model, the relevamt paradox can be put aside. It is then that they're ready to receive the Eleatic truth - that reality is a complete and perfect whole. Whereupon questions of "motion", "change", "divisibility", etc, are radically recast and we can finally hope to grasp the thread of truth and speak coherently.
It's heart warming to see so many anons in this thread stand up for Zeno. Thank you, Eleatic bros. Thank you, Zeno.
IIRC, Hegel said that infinity expresses itself through finite.
There are an infinite amount of elements in which you can divide existance.
It's like god is everything (infinite) because everything can be divided into infinite finite elements.
Saying that an infinite amount of steps are required for Achilles to reach the tortoise is understanding that God is infinite, while we are finite (in its infiniteness) so we are unable to make an infinite number of actions, but only through a finite number of actions we will be able to surpass the tortoise, while the elements (which we are made of) will be capable of reaching the tortoise in an infinite number of actions.
Elements are singular, not finite. Their infinite numbers prevents us from knowing these elements, because we are finite.
My guess is that the paradox exists because we don't know of the elements I talked about, while it is solvable because we are finite and everything finite has an end.
I don't study philosophy, theology or mathematics.
Well, think of another one of Zeno's paradoxes. Does it always take an amount of time to cross a given space? Yes or no.
If it always takes some amount of time to cover a space, and there is an unlimited number of spaces/divisions of time, then the amount of time it takes to get anywhere will have no limit. Also, it would seem to take as much time to walk to work as to walk to your bathroom, because both would be limitless.
Zeno asks the same question about weight/magnitude. If we divvy up an object, does each division have some magnitude? If yes, and there's no limit to the division, then we will have no limit to the result and a pea will be infinitely heavy and just as heavy as everything else.
And indeed you would never begin the journey or the divvying up of an object, because you will not be able to identify the first step/the first cut. Where will you first move to? Oh no there is a space before that, etc.
There is a way around these paradoxes, as noted before. Some are failures, like trying to treat infinitees as numbers and cancel them out, and successful ways, such as by denying divisibility in that sense and accepted chronology/spatially as a complete whole.
You won't even get to start the division in a presentist model, because you won't be able to identify where the first step is made. Similarly, you won't be able to stop the series unless you also assume the destination and accept the whole race or scenario as a complete whole. When those concessions are made the Eleatic already has what he wants, but if he wants to continue getting into the weeds he will just show further absurdities of trying to posit limitless processes and treating an "infinite" as a number or otherwise as something with definite qualities we can apply. Rather than inaccurate shorthand for our broken models to approximate the truth for practical purposes.
>Zeno asks the same question about weight/magnitude. If we divvy up an object, does each division have some magnitude? If yes, and there's no limit to the division, then we will have no limit to the result and a pea will be infinitely heavy and just as heavy as everything else.
sounds like he was joking then.
>sum of infinite number can be a finite number
/thread
that makes more sense. Given, as I pointed out earlier, than an 'infinite' number cannot be said to exist and so the person doing the calculation must simply skip it for the equation to be completed.
if, as a random anon said, the 'n' represented infinite.
Fricking IQfy is moron level when it comes to math and most people here have never even opened a calculus textbook. The answer is that at a constant speed the time to complete each step decreases along with the distance and the resulting series converges to a definite value. Shit about reality being discrete is fricking stupid and raises a ton of problems.
This thread demonstrates why Plato said you should know math before you take up philosophy. IQfyoids proved themselves to be utter brainlet posers.
>Plato said you should know math before you take up philosophy
it was probably only ever intended to lead the mind to discarding what cannot be said to exist. You guys think that these Stoics (who we know were teaching real-world logic; causes etc.) were sitting around coming up with sudoko puzzles? Only after 1,400yrs of doctrinal faith in non-existence does humanity arrive at such nonsense.
He was making a joke of other people's models, yes. That's the whole point, he saw that reality is complete and can't be divvyed up and altered in the way other people claimed.
So it's even funnier when brainlets try to come in and say they "disproved" Zeno.
11 months ago
Anonymous
Ha that is pretty funny. I tend to ignore numeracy (because I know I know better) but that budding mathematicians would approach Zeno only to find that he was dunking on mathematics is pretty cool.
>It's not that we don't understand 1+1=2 it's just that one apple placed on a table next to another apple by itself doesn't mean there are two apples on the table. This is philosophy not math
You're a fricking midwit. Think about it: in what sense are we talking about the addition of an apple? We aren't denying the accepted result of the race/the idea that there are two apples on a table. We are criticising how the process of motion/change is being modelled, and by extension criticising the overall model of reality/metaphysics. You mathcels get dragged kicking and screaming every inch of the way, utterly incapable of contextual thought. Literal beep beep bloop bloop human calculators who should be enslaved and put to work in the fields so philosophy chads can put their feet up and do the big thinks without you.
11 months ago
Anonymous
The solution is this simple—instead of plotting distance on the X axis and time on the y axis, plot time on the X and distance on Y. Should help you realize you’ve been spooked.
11 months ago
Anonymous
Non-responsive
Let's play another game. I'm about to leave the office and I need to walk to my car. In this magical infinitely divisible wonderland, what location or space do I move to first?
11 months ago
Anonymous
Your inability to see atoms is not evidence against motion.
11 months ago
Anonymous
non-responsive
>I'm about to leave the office and I need to walk to my car. In this magical infinitely divisible wonderland, what location or space do I move to first?
In a magically divisible wonderland, the idea of a discrete space doesn't make sense. You don't move to a grid location 'first'. You move continuously.
Yes, that's my point, it doesn't make sense. So one must accept a different metaphysical framework. So, what does "divisible" mean to you, if you are positing that we "move continuously"?
If you are saying that this is a complete picture, "my journey from my desk to my car", and I am smeared across it, I could agree with that and the conversation would go a different direction. At any rate, as a result of such a model, the presentist accounts of change that people advocate are destroyed. The chronology is complete and change/motion is a relative term. The journey is already complete, I have already "moved" everywhere possible, it is all necessary. This is is the conclusion that Zeno is leading us towards
If you doubt the above, though, then please tell me what you mean. Because those people who believe in genuine change are screwed when faced with this question. They will posit me at moment 1 at a certain fixed location, and they need to "create" a moment 2 (that is not) where I am at a different location. So they need to identify a moment 2, and they cannot because of the issue with their acceptance of unlimited divisibility.
humans can catch turtles in real life, so I don't see how this scenario is realistic.
> that's just saying that Zeno is right by admitting that reality is a smooth continuity and not made up of discrete units.
p much the story in any Zeno conversation, people are led by the nose by Zeno's paradox to a better metaphysical position, but they don't know what's going on and they think they've "solved" something themselves.
11 months ago
Anonymous
>I'm about to leave the office and I need to walk to my car. In this magical infinitely divisible wonderland, what location or space do I move to first?
In a magically divisible wonderland, the idea of a discrete space doesn't make sense. You don't move to a grid location 'first'. You move continuously.
funny that it's basically the other way around and you're the one completely missing the point (and thinking you're smarter because of it)
>You have no empirical proof of an infinite amount of steps
Except the empirical proof in convergent series exactly predicting when Achilles passes the Tortoise in the real world. As opposed to you which who I guess is arguing that faster objects can't pass slower ones?
this is so fricking funny dude holy shit
>Right, because we live in a continuous world in which "motion" and "change" are just the internal rearrangements of one enormous continuous body
So you admit the positions of Achilles and the Tortoise are rearranged at the time during the race predicted by calculus. Why did it take you so long to just admit you were wrong?
Calculus doesn't solve the paradox because being able to sum up an infinite series doesn't actually answer how something can jump between discrete states. >b-b-but the reals are continuous!
Then you're admitting that Parmenides was right and that we do not live in a universe made up of discrete units but rather one of pure, infinitely divisible, continuousness.
Right, because we live in a continuous world in which "motion" and "change" are just the internal rearrangements of one enormous continuous body. This is literally what I said in
Calculus doesn't solve the paradox because being able to sum up an infinite series doesn't actually answer how something can jump between discrete states. >b-b-but the reals are continuous!
Then you're admitting that Parmenides was right and that we do not live in a universe made up of discrete units but rather one of pure, infinitely divisible, continuousness.
, so I'm not sure why you decided to agree with me.
Thank you for the (you), though.
11 months ago
Anonymous
>Right, because we live in a continuous world in which "motion" and "change" are just the internal rearrangements of one enormous continuous body
So you admit the positions of Achilles and the Tortoise are rearranged at the time during the race predicted by calculus. Why did it take you so long to just admit you were wrong?
11 months ago
Anonymous
See
Calculus doesn't solve the paradox because being able to sum up an infinite series doesn't actually answer how something can jump between discrete states. >b-b-but the reals are continuous!
Then you're admitting that Parmenides was right and that we do not live in a universe made up of discrete units but rather one of pure, infinitely divisible, continuousness.
, this was already explained The paradox, like all of Zeno's Paradoxes, can be summed up as "what makes something move between two discrete states?".
It should be noted that the people Zeno was opposing would reject the idea of summing up an infinite series in the first place.
11 months ago
Anonymous
That might be true, but I don't want to talk about Greek philosophy, I want to talk about calculus.
11 months ago
Anonymous
you're in a greek philosophy thread autist
11 months ago
Anonymous
And this is patently moronic. Even the fact that you're replying to me shows you know it's moronic to because if there was no change there would be nothing to respond to. Every (you) you give shows how wrong you are. You sound like one of the advaita cranks who keep getting beat down here.
If that's the case, why did you choose to do this on /lit? Go make this thread on IQfy. If you hurry you'll get it up just in time for peak Americans-are-home-from-work hours and will be able to beat the seed oils and vaccines spam.
11 months ago
Anonymous
Because the accepted solution to Zeno's paradox is given by calculus. If you're obsessed with some culty shitskin gibberish like advaita it's easy to see why you would hate such a clearly logical refutation of similar beliefs
11 months ago
Anonymous
>Because the accepted solution to Zeno's paradox is given by calculus
No it isn't. See
Calculus doesn't solve the paradox because being able to sum up an infinite series doesn't actually answer how something can jump between discrete states. >b-b-but the reals are continuous!
Then you're admitting that Parmenides was right and that we do not live in a universe made up of discrete units but rather one of pure, infinitely divisible, continuousness.
. Calculus can't explain Zeno's Paradoxes because in order to do that it would have to demonstrate a world where calculus doesn't work. If you can sum up a series of infinite points, then you're saying that Zeno and Parmenides were right.
If you want to prove them wrong, then explain how you can move between discrete quantized states that do not have any continuity between them.
11 months ago
Anonymous
>If you can sum up a series of infinite points, then you're saying that Zeno and Parmenides were right. >If you want to prove them wrong, then explain how you can move between discrete quantized states that do not have any continuity between them.
Bro I think you're kind of confused. I suggest going back and reading Zeno's paradox and going over some basic calculus.
11 months ago
Anonymous
Read the thread, this was already addressed in
Calculus doesn't solve the paradox because being able to sum up an infinite series doesn't actually answer how something can jump between discrete states. >b-b-but the reals are continuous!
Then you're admitting that Parmenides was right and that we do not live in a universe made up of discrete units but rather one of pure, infinitely divisible, continuousness.
11 months ago
Anonymous
oh the accepted solution, it's settled science!
11 months ago
Anonymous
So calculus solves Zeno's paradox which is exactly what I've been saying for multiple posts. Glad to hear you agree. >It should be noted that the people Zeno was opposing would reject the idea of summing up an infinite series in the first place
No shit. Calculus would be invented for another 1500+ years.
11 months ago
Anonymous
how does calculus explain how you can move between two discrete states that cannot be further subdivided?
11 months ago
Anonymous
integer addition
11 months ago
Anonymous
so how do you add the integers?
11 months ago
Anonymous
the entire proof is 86 pages long, but you can find the whole hog in Principia Mathematica by Alfred North Whitehead and Bertrand Russell
11 months ago
Anonymous
Shorthand notes + "we'll define the process of addition in regards to motion later" = image attached
Yes, as a result of the nature of Being. I think the other anon is wrong to say that Parmenides posited infinite divisibility, but he's right in terms of purity and continuity. There are other details, too, for as the goddess says the signs regarding the nature of Being are many.
11 months ago
Anonymous
And this is patently moronic. Even the fact that you're replying to me shows you know it's moronic to because if there was no change there would be nothing to respond to. Every (you) you give shows how wrong you are. You sound like one of the advaita cranks who keep getting beat down here.
11 months ago
Anonymous
You just keep digging your hole. The Eleatics were right, Zeno successfully dealt with the ridiculous systems he encountered, and a mathcel like you should move on because you are incapable of considering the ramifications of this.
11 months ago
Anonymous
So you are an advaita crank lol. Called it lol. See this post
And this is patently moronic. Even the fact that you're replying to me shows you know it's moronic to because if there was no change there would be nothing to respond to. Every (you) you give shows how wrong you are. You sound like one of the advaita cranks who keep getting beat down here.
and feed me your (you)s
11 months ago
Anonymous
Never read advaita in my life. Keep seething, midwit.
11 months ago
Anonymous
>Never read advaita in my life. Keep seething, midwit.
According to you you've never read anything in your life since that would mean transitioning from not having read something to having read it. And you claim change doesn't exist.
11 months ago
Anonymous
>You just keep digging your hole.
Rofl what are you responding to? I thought change didn't exist? A response requires a change to respond to. You can't defend yourself without implicitly admitting you're wrong
11 months ago
Anonymous
Change doesn't exist as the targeted models/philosophers posit it. Same goes for multiplicity/division/independent existence. The Eleatics are putting forward an account of reality as a perfect whole. There is still a youth and a goddess, there is still a series of events that constitutes their conversation. Whatever account of "change" we posit will need to be relative/eternalist, for what-is cannot literally become something else/"what is not".
But that conversation is beyond you. You are a midwit because you cannot think contextually. You cannot think of any other system, you cannot process the ramifications of certain metaphysical truths and how they would play out, intellectually you are an npc and incapable of philosophy.
11 months ago
Anonymous
Again you respond. What are you responding to? It can't be to anything I wrote because then that would mean something has changed for you to respond to. >you cannot process the ramifications of certain metaphysical truths and how they would play out
I can process it well enough to know how ridiculous it is. How can you type a response to me unless you admit something has changed to respond to? By even presenting your philosophy you've already disproven it to me since it's a change in my awareness
11 months ago
Anonymous
Listen to yourself. I said that I accept an eternalist account of change. I referenced Eleatic works to indicate that it should generally be acceptable given the characters and events described. And what do you? Prove that you cannot think contextually, you live a blinkered existence and will just continue down your lane. You'll forgive me if I leave it at that, you were never really part of this conversation.
11 months ago
Anonymous
>I said that I accept an eternalist account of change
Rofl. So you do believe in change. Calculus solves Zeno's paradox and the CHANGE of position of the individual racers. They change position in the same way you change your arguments in response to me.
11 months ago
Anonymous
very npc response, may as well be talking to chatgpt or reddit
11 months ago
Anonymous
If chatgpt is capable of pointing out a gaping logical flaw in someones argument it has some value after all.
Dumb. The map is not the territory. Xeno has not uncovered a mystery of physics. He has simply described ordinary life in a way that is confusing to you. It’s a Chinese finger trap for the mind. Stop looking at it as a problem of space, and consider it in relationship to time. The trick works because Xeno keeps shrinking the time interval while your imagination is focused on the distance traveled.
the entire proof is 86 pages long, but you can find the whole hog in Principia Mathematica by Alfred North Whitehead and Bertrand Russell
>If you can sum up a series of infinite points, then you're saying that Zeno and Parmenides were right. >If you want to prove them wrong, then explain how you can move between discrete quantized states that do not have any continuity between them.
Bro I think you're kind of confused. I suggest going back and reading Zeno's paradox and going over some basic calculus.
Zeno was a student of the philosopher Parmenides. Parmenides held that reality was one giant continuous infinitely divisible mass. Some other philosophers disagreed, arguing that the world was made up of a large number of discrete states and things just jumped between these discrete states while spending no time in between them. Zeno created a series of situations that are, if you assume the world to be made up of discrete states, paradoxical. There's no paradox if you believe the world to be continuous and infinitely divisible, however, they're only paradoxical if you disagree with Zeno and Parmenides.
Yes, Achilles will obviously reach and surpass the tortoise, that's Zeno's argument for why we live in a continuous infinitely divisible world where all motion and change are just illusions caused by the huge mass of everything shifting around. If we didn't live in such a world, Zeno is arguing, Achilles would have to jump an infinite number of times between discrete states. Because there's an infinite number of states between start and finish, Achilles can never complete the action. Achilles can never complete "walk to where the tortoise was, then walk to where it was, then walk to where it was, then..." not because he can't run faster than the tortoise or because he has to move an infinite number of steps through a finite distance, but because he's moving through an infinite distance in an infinite number of steps. If you hold the world to be discrete, he can't actually do this, because eventually he and the tortoise will meet as they're both moving the minimum number of units.
Zeno DOES have another paradox, the Dichotomy Paradox, which is about summing up an a finite distance that is cut up infinitely, however.
You can just say "but asymptotes", but that's just saying that Zeno is right by admitting that reality is a smooth continuity and not made up of discrete units.
11 months ago
Anonymous
I’m familiar. You’re not. Motion and time are tied together. The seeming paradox only appears when you focus on the sequential changes of space. This is a distraction from the sequential change sin time. For each fractional movement, you are also observing a fraction of the time. What Xeno and Parmenides observe is not the infinitive divisibikity of reality, but the infinite divisibility of numbers. You can theoretically discuss the difference between 1/infinity inches and 1/(infinity plus 1) inches. But you must also remember to tie these theoretical distances with their partners in time. Obviously if you try to examine motion at 1 Infinitieth of a second, it will look like movement’s impossible. But all this really says is that motion is proportionate to time. It’s no paradox at all. It’s just common sense.
10 months ago
Anonymous
>What Xeno and Parmenides observe is not the infinitive divisibikity of reality, but the infinite divisibility of numbers
What's the difference, really? Are numbers not part of the fabric of reality?
>We cannot hope to disprove Zeno if we can't even disprove 0.999... = 1.
Rofl I can't wait to hear the morons who hate calculus have to say about 0.999...=1. It's going to be like every internet forum full of 12 years except they're all going to think they are philosophically brilliant.
more like >points on a plot I place on a piece of paper after some movement has occurred have the effect of reaching back into time and applying a force to the moving object stopping it until I place the next dot.
math so powerful!
Movement goes from a place to another, in a discontinuous fashion. Then, you can always decompose the distance between those two places.
Anyway, with Zeno's method, you can also show that Achilles never reaches the end of its first step, because he should first reach half of it, then half of the remaining distance etc.
Every successive step takes exponentially less time and time is passing steadily so the two will meet. The idea of needing infinite steps is poor framing by the human but an error in the universe. The steps are nothing more than arbitrary distinctions in the mind.
The infinite divisibility of space is actually necessary if there is to be any motion at all, because it means that after each division you still have a finite number of "parts". The real problem would be if the turtle had to go through an infinite series of infinitely small parts.
How the frick is it a paradox? It's an illustration of a simple as frick mathematical concept. The racers could be anything. >duh if da race car never passes da earfworm, it will nevuh be in da first place uh durrrrrrrr
1. Pick reference frame that of a tortoise(I.e. he will be standing still in ~~*this*~~ reference frame
2. Subtract tortoise speed from that of a bozos' and you'll get his relative speed in specified reference frame.
3. Just divide handicap distance with aforementioned speed and you'll get time in which handicapped distance is reached by achilles in the ~~*relative motion frame*~~
4. Profit idk >le infinitesimal calculus
le Occam's razor b***hes
It is only a paradox BECAUSE it is disproven every single day by everything that moves. Because there are particles which are "as small as is physically possible," and all matter is made up of such, the movement of such a particle must have a "smallest possible distance" which would constitute movement.
What refrains you from choosing a reference frame witch moves with a speed that of a tortoise? That makes the tortoise to be standing still while Achilles covers the distance in between them in a single iteration.
P.s. let me remind you that for even such a simple problem there can be invented infinite amount of solutions with infinite levels of complexity but this is why Occam's razor exists to cut off that lard of extra complexity whenever possible.
This paradox assumes no other points in existence, and works only in a two dimensional plane deviod of time where the speeds of each entity are related to each other as their only point of reference. If speeds are held constant the paradox doesn't arrise, as it would only take time for the faster entity to gain the lead.
Achilles would easily outrun the tortoise in real life. Also it presupposes that Achilles can only go twice as fast as the then current speed of the tortoise. This would mean his speed is actually incostitent to stay in tune with the tortoises.
I don't have to. Reality comes in minimal chunks. Therefore the pixels of the universe makes them catch up eventually.
it looks like if it kept going itll be like that mandelbrot set thing in appearance, pretty cool
It’s a joke, not a paradox.
*shoots you in the head*
Paradox disproven.
*disappears into the shadows again*
Spatiality and temporality are merely the phenomenally constructed ways that our cognition has to access the thing-in-itself. Reality proper can not be said to be effected by Zeno’s paradox as it is merely an error in our framework for understanding it. The true nature of reality is the playing out of dialectics which takes place in everything. With physical objects their contradictory nature as subjects is expressed through spatiality and temporality. I.e a tree is negated by an axe which is negated by termites which are negated by me stepping on them etc. If Zeno’s paradox proves anything it is the irreducibility of the thing-in-itself to phenomena. Metaphysical relationships do not play out over a course of time, we merely discover them over said course.
Did this homosexual really say that? I refuse to use my copy of the phenomenology for anything except to roll weed on
>Disprove Zeno's paradox
If Zeno ever set out to prove his Paradox, he would provide a half of the proof, then half of what the remaining proof, then half of the remaining half, and so ad infinitum, never reaching a complete proof. Ultimately, Zeno (or anyone else) would be incapable of ever providing a complete proof or even demonstration of his paradox, and therefore the paradox is neither proven nor even demonstrated.
QED
Umm... zenosisters? Our response?
You would have the same problem with a disproof, so the paradox exists simply by the merit of not finding proof nor disproof. It's an unresolved question, which is equal to proof, exactly the outcome that Zeno was aiming for.
Wouldn’t it neither exist nor not exist?
The neither nor existence of the paradox is tantamount to the existence of the paradox because 1) a paradox is an unresolved question about a subject matter, and 2) being able to say that the paradox's existence is an unresolved question means that the subject matter it deals with is also an unresolved question.
But you never actually proved that it was an unresolved question, only that it can’t be disproven as an unresolved question following anon’s logic.
The disprover doesn’t think the hypothesis is true though
Meant for
So, by definition, God is real?
You cannot prove or disprove His existence.
I couldnt finish reading your message unfortunately
> so the paradox exists
what is the paradox here? Nothing contradicts anything. You have to walk halfway somewhere before getting there, sure. This is obvious.
It will take you an infinite amount of time to verbally describe going halfway before going halfway and so on but in that time I would have already walked across the room because I cover 1/2 the distance in 1/2 the time and this relationship holds down to the smallest distance approaching zero. This paradox is like thinking the area under a curve is just infinity always because you're a brainlet.
ive seen this pic many times and ive never understood it. am i moronic?
google "turtles all the way down" and you'll probably get it
It’s an illusion. Time is constant.
>Time is constant
This. It only seems like a paradox if you keep halving time.
Electrons can phase in and out of reality, and sometimes appear before they disappear, blipping from one point to the next. Intuition says most if not all subatomic particles do this at the smallest scale. It follows that movement is instantaneous between two points, and time is only the pause between blips, and there is in fact, a minimum distance.
You all are idiots, and Xeno is a pseud.
>Zeno's paradox.
refresh my memory on what this is supposed to be? I see various things be said in this thread and they can't all be to the point.
>existence
>reality
>time
What's the limit of 1/2+1/3+...+1/n when n tends to infinity?
1/2 a pie + 1/3 jug of cream + (a glass of port)
= a fair dessert course, I would presume.
But the +1/n can be immediately discounted from l'equatione as 'infinity' cannot be demonstrated to exist and therefore is not quantifiable. Mayhaps it is a trickaroo.
I’m pretty sure it’s just about 2. Which proves Xeno wrong. If you can’t see that, you’re filtered.
>What's the limit of 1/2+1/3+...+1/n when n tends to infinity?
That's the harmonic series moron and that diverges to infinity. Zeno's paradox is the geometric series 1/2+1/4+1/8... which converges.
Who cares?
The universe is not continuous so eventually a minimal distance would be reached.
Fricking IQfy is moron level when it comes to math and most people here have never even opened a calculus textbook. The answer is that at a constant speed the time to complete each step decreases along with the distance and the resulting series converges to a definite value. Shit about reality being discrete is fricking stupid and raises a ton of problems.
What’s the definite value where it converges?
>What’s the definite value where it converges?
Depends on where you start and what the ratio is. For the geometric series 1/2+1/4+1/8... and so on it converges to 1.
The paradox is saying that’s impossible. You need to argue why you can get to 1.
>The paradox is saying that’s impossible. You need to argue why you can get to 1.
Saying something is impossible doesn't make it impossible. I say it's possible because we do it every day when we walk any distance. The only argument I've seen against this is a childish dislike for infinite series with no logical argument to back it up. The convergence of an infinite series has a far more rigorous definition than anything dreamed up in philosophy and the resulting calculus is empirically backed up in every hard science.
Autistic refusal to see the point
What point? What argument do you have that a convergent infinite series doesn't converge?
It’s impossible to make an argument against an axiomatic statement except on the ground that’s it’s axiomatic and stands on nothing except your will to assert it. Perhaps you have an argument as to why it converges.
>It’s impossible to make an argument against an axiomatic statement except on the ground that’s it’s axiomatic and stands on nothing except your will to assert it.
You've got the self-awareness of a rock. If my claim that infinite series can converge is axiomatic then so is your claim that they can't. You're relying on childish intuition like it's some type of higher logic.
>Perhaps you have an argument as to why it converges.
Because it satisfies the definition of convergence
>If my claim that infinite series can converge is axiomatic then so is your claim that they can't.
I never claimed that it can’t, in fact I never claimed anything at all. I simply asked you why it was the case. I’ll let you seethe.
>I never claimed that it can’t, in fact I never claimed anything at all
In other words you've lost the argument and now have to save face by claiming you weren't making an argument to begin with.
holy shit you are moronic. This is very basic math. You learn this in Calc II.
Infinity isn't real. You can't undertake an infinite amount of steps in finite time. Convergence is just a thought experiment that morons like you think solves the problem without getting to the root of it.
Stop beating him anon he's already dead
Wow it's almost like Zeno successfully deployed this particular paradox to eliminate certain types of models. And you have been led by the nose to more promising pastures, patting yourself on the back like you have solved some problem for him.
solvitur ambulando
Because he was starting from false preconceptions about reality and that’s not how the real world works.
This thread demonstrates why Plato said you should know math before you take up philosophy. IQfyoids proved themselves to be utter brainlet posers.
this thread should really be in /vg/
If I don't know what happened to the cookie therefore God exists.
all of zeno's paradoxes were already refuted in ancient greece why are we still making threads about this stuff
no they weren't and still haven't
Convergent geometric series. Seethe more
how does that "solve" zeno's paradoxes? This is addressed with achilles and the tortoise, we can arbitrarily say that it converges because it gets so close that it may as well be the point it is approaching but technically there is still an infinite recursion problem and the paradox is not solved at all.
>but technically there is still an infinite recursion problem and the paradox is not solved at all
Technically there isn't. Convergent geometric series are rigorously defined in math if you've ever taken calculus class. If you can point out some logical inconsistency in the definition of convergent sequences you'll overthrow all of analysis and be recognized as one of the greatest mathematicians of all time.
>If you can point out some logical inconsistency in the definition of convergent sequences you'll overthrow all of analysis and be recognized as one of the greatest mathematicians of all time.
or more likely anon will call you a moron
I'm not saying there's anything wrong in the definition of convergent sequences, I still maintain that it doesn't solve the paradoxes. Calculus can deal with continuous values but that doesn't solve the problem because the paradox is also about locomotion through space and time and the absurdity of infinity in finite systems.
Convergent series are logically rigorous and give an answer that confirms with empirical tested reality. What else could you need to solve the paradox?
>the absurdity of infinity in finite systems
What you mean by absurdity is that it goes against your intuitions. Your intuitions are childish and wrong. You have no logical argument to make.
>empirical tested reality
very loaded statement
>you have no logical arguments to make
I think the arguments presented in the paradoxes themselves are logical enough
>What you mean by absurdity is that it goes against your intuitions. Your intuitions are childish and wrong.
that's not what I'm saying at all, I think you might not understand what the paradoxes are arguing at this point.
>I think the arguments presented in the paradoxes themselves are logical enough
In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. Convergent series solves this since the different stages occur at a geometrically decreasing amount of time that converges to a finite value.
>that's not what I'm saying at all, I think you might not understand what the paradoxes are arguing at this point.
What are you trying to say then? What logical argument do you have against convergent series?
I'm not arguing against convergent series, it sounds like it solves the paradox but it doesn't and there are still like 4 others related to this issue from zeno which we're not even addressing at this point.
no
not quite on topic but there's actually a similar issue in physics with Heisenberg's uncertainty principle, where you lose information about the velocity of a particle the more you gain information about its position
this is a better answer
dude obviously if an athlete raced a tortoise he would overtake the tortoise and win the race with ease, you're missing the point
>I'm not arguing against convergent series, it sounds like it solves the paradox but it doesn't
And you've given no reason that it doesn't besides your feelings and intuitions.
>and there are still like 4 others related to this issue from zeno which we're not even addressing at this point.
There is one other addressed at this point, the dichotomy paradox, and it has exactly the same solution with convergent series. Zeno's other two paradoxes are the paradox of the arrow which is solved by the concept of momentum and the stada paradox which is an argument against discrete space that everyone accepts is not really coherent.
>Convergent series are logically rigorous and give an answer that confirms with empirical tested reality, like vaccines and the holocaust!
>you've given no reason besides your feelings and intuitions, which FACTS don't care about. I'm Ben Shapiro
nice try schlomo
You're refusing to engage with the core logic of the argument lol. It's embarrassing to watch you stick your fingers in your ears and go
>LALALALA I CAN'T HEAR YOU
You have no empirical proof of an infinite amount of steps, and to conflate engineering applications (where there's always a "good enough" cutoff) with an actual solution to the core idea behind Zeno's paradox is incredibly dishonest.
>You have no empirical proof of an infinite amount of steps
Except the empirical proof in convergent series exactly predicting when Achilles passes the Tortoise in the real world. As opposed to you which who I guess is arguing that faster objects can't pass slower ones?
>empirical proof in convergent series
Math isn't empirical proof moron. This is about as moronic as thinking of a computer program as a science experiment.
Read the rest of the sentence moron
>Except the empirical proof in convergent series exactly predicting when Achilles passes the Tortoise in the real world.
Run a simple timed race with the slower moving one given a head start and see if the time they pass matches that given by the convergent series.
And you do realize what the Eleatic is going to hit you with, right?
>perception is illusory regarding the true causes
>problem of induction
You haven't explained anything.
>And you do realize what the Eleatic is going to hit you with, right?
And you do realize what I'm going to hit the Eleatic with right?
>by even typing a response you've acknowledged that there was a change to respond to thus disproving your whole philosophy
>by even typing a response you've acknowledged that there was a change to respond to thus disproving your whole philosophy
Manipulating illusions doesn't make them any less illusory.
Though, if I have to be honest, "change is an illusion, but the illusions are always changing, so the illusions are an illusion and change is real" point hits hard. I have yet to receive an appropriate response from an Eleatic. It does not seem like a slam dunk proof however. If an illusion is an illusion, then it does not automatically mean that what we were seeing was the truth all along. It could mean that we're buried in layers of illusions, it could mean that we're predisposed to doubt perceptive data that otherwise matches the world, etc.
Find me the part in Parmenides' work where the Goddess posits the existence of "illusions".
I'll help: you can't, you're just shadow boxing with moronic interpretations of a philosophy you've (a) failed to read, and (b) don't understand.
Find me the part in my post where I asked.
I'll help: you can't, because I didn't.
So basically you have no idea what eleatics would hit you with, you have no idea how your conception of such a person lines up with the plausible interpretations of their works, you have probably never read any of said works, you're probably illiterate and using a combination of voice to text function and recognizing words like "post".
Get a life Tweetophon, can't believe you bumped a saged thread on the 10th page just to get the last word in a thread
P.S. if that's the best you got then you really are clueless
Easy...the lower time increments represent an ideal that don't correspond to physical reality.
There exists a time interval where it's not physically possible for Achilles to ONLY cover half the remaining distance. He MUST travel more in that time frame thus allowing him to catch up and pass the tortoise.
This is the biggest problem with philosophy and is why science wins out..philosophers create mental models that don't line up with physical reality.
QED
>There exists a time interval where it's not physically possible for Achilles to ONLY cover half the remaining distance. He MUST travel more in that time frame thus allowing him to catch up and pass the tortoise.
This is goofy and not the answer. Physics says nothing about space or time being discrete your misunderstanding about the Plank length notwithstanding. Basic calculus solves the paradox
Sure it does if Achilles physically can't move himself a distance of less than 1mm than whatever happens in a mathematical series after that point is relevant. The experimental data could never match the theoretical model answered via calculus solving a convergent series.
>The experimental data could never match the theoretical model answered via calculus solving a convergent series.
The frick? The experimental data does match the calculus solution. Ach starting at 0m and traveling speed 2m/sec will pass Tort starting at 1m and traveling speed 1m at at 1sec Are you claiming physical experiments don't confirm that?
The problem as classically stated says that while Achilles travels to his next "point" the tortoise is moving to his next point. And thus he can never catch up.
First no runner could ever match a mathematical series. Second, there exists a length so small that no human or tortoise could travel.
Again the entire example could NEVER be modeled in real life (even if we take out the issue of the tortoise and replace with a robot).
So again - experimental real life DOES NOT conform to theoretical model.s
>Again the entire example could NEVER be modeled in real life (even if we take out the issue of the tortoise and replace with a robot).
>So again - experimental real life DOES NOT conform to theoretical model.s
This just gets more and more bizarre. Are you claiming we can't time a race and see when someone faster passes someone slower? That's the empirical measurement. And the convergent series solution give the exact result.
>tfw to intelligent for zenos paradoxes
Assume we have two robots doing the race so we can control the speed better. At some point there will be a minimum distance that the robot can traverse in a period of time. At that moment you'll fail to model the covergent series and the slower robot would be overtaken.
Here's a better explanation from wikipedia (I never read this before, but nice to think I'm not the only one thinking it)
Peter Lynds
In 2003, Peter Lynds argued that all of Zeno's motion paradoxes are resolved by the conclusion that instants in time and instantaneous magnitudes do not physically exist.[33][34][35] Lynds argues that an object in relative motion cannot have an instantaneous or determined relative position (for if it did, it could not be in motion), and so cannot have its motion fractionally dissected as if it does, as is assumed by the paradoxes. Nick Huggett argues that Zeno is assuming the conclusion when he says that objects that occupy the same space as they do at rest must be at rest.[17]
>Assume we have two robots doing the race so we can control the speed better. At some point there will be a minimum distance that the robot can traverse in a period of time. At that moment you'll fail to model the covergent series and the slower robot would be overtaken.
And this wouldn't be a convergent series and wouldn't model the Achilles and Tortoise paradox accurately. Meanwhile a simple timed race would be the exact same as the paradox and the convergent series solution would give the exact same answer as the timed race. Really wtf are you talking about?
You're so thick...
Achilles 10 m/s Tortoise 5 m/s (Tortoise gets 10 m head start)
Time Achiles pos Tortoise pos
0 0 10
1 10 15
2 20 20
3 30 25
So how does Achilles ever catch up? The paradox would say at 1.999999999s the tortoise covers another planck length and Achilles can never catch up.
But it's bullshit because there is a minimum distance that the tortoise can physically cover in a unit of time and it's a hell of a lot larger than the planck length.
So our data would be something as follows :
1 10 15
1.5 15 17.5
1.75 17.5 18.75
1.88 18.75 19.38
2 20 20
If the tortoise can't move less than 5/8 of a meter than Achilles catches up. The sequence means NOTHING because it cannot be modeled to any points smaller than the experimental data goverened by the smallest distance a human/tortoise can cover in a measurable unit of time.
The fricking race is the model you stupid shit. And the race gives the exact same answer as the convergent series. You're making up some shit that you even acknowledge doesn't model a convergent series and then claiming it failing to reflect the real world means convergent series don't. Again a simple timed race gives the exact empirical answer that the convergent series predicts it will.
>Peter Lynds
In 2003, Peter Lynds argued that all of Zeno's motion paradoxes are resolved by the conclusion that instants in time and instantaneous magnitudes do not physically exist.[33][34][35] Lynds argues that an object in relative motion cannot have an instantaneous or determined relative position (for if it did, it could not be in motion), and so cannot have its motion fractionally dissected as if it does, as is assumed by the paradoxes. Nick Huggett argues that Zeno is assuming the conclusion when he says that objects that occupy the same space as they do at rest must be at rest.[17]
Thank you for proving my point, Peter Lynds.
How did this person "resolve" a given paradox? By abandoning the model that suffered from it. He resolved it by denying divisibility/incompleteness, which... is exactly what Zeno/Eleatics want him to do. Once a person starts admitting such things, the paradox is set aside and the Eleatic position is seen as reasonable.
With each paradox, whether from Zeno, Diodorus, or ones we make for our discussions, we get closer to what Zeno was trying to teach us. Rather than sitting there going "urgh Achilles overtake tortoise, me eyes see it". Of course he does, but not in the way you think, you are describing a complete, perfect, and unchanging race.
Great post. But let's go beyond it.
The people Zeno was mocking could not disprove the paradox, because to do so would require them to abandon their model of reality. Which was Zeno's whole point - he revealed that their model was incoherent nonsense.
Once the person admits defeat and abandons their model, the relevamt paradox can be put aside. It is then that they're ready to receive the Eleatic truth - that reality is a complete and perfect whole. Whereupon questions of "motion", "change", "divisibility", etc, are radically recast and we can finally hope to grasp the thread of truth and speak coherently.
It's heart warming to see so many anons in this thread stand up for Zeno. Thank you, Eleatic bros. Thank you, Zeno.
Infinite series can converge. In this case, his series converges to 2, so the hare passes the turtle after two meters.
IIRC, Hegel said that infinity expresses itself through finite.
There are an infinite amount of elements in which you can divide existance.
It's like god is everything (infinite) because everything can be divided into infinite finite elements.
Saying that an infinite amount of steps are required for Achilles to reach the tortoise is understanding that God is infinite, while we are finite (in its infiniteness) so we are unable to make an infinite number of actions, but only through a finite number of actions we will be able to surpass the tortoise, while the elements (which we are made of) will be capable of reaching the tortoise in an infinite number of actions.
Elements are singular, not finite. Their infinite numbers prevents us from knowing these elements, because we are finite.
My guess is that the paradox exists because we don't know of the elements I talked about, while it is solvable because we are finite and everything finite has an end.
I don't study philosophy, theology or mathematics.
>Hegel said that infinity expresses itself through finite.
Thanks for reminding me to never read Hegel.
>t. filtered by calculus
Nah, I was a math major. Just read that Hegel bullshittery at the start of the post and disregarded the rest.
Then how have you avoided expressing the infinite through the finite in even the most basic limit problems?
Nothing to avoid. I don't see the problem.
Exactly why is it supposed to be impossible to cross infinitely many points in finite time?
Well, think of another one of Zeno's paradoxes. Does it always take an amount of time to cross a given space? Yes or no.
If it always takes some amount of time to cover a space, and there is an unlimited number of spaces/divisions of time, then the amount of time it takes to get anywhere will have no limit. Also, it would seem to take as much time to walk to work as to walk to your bathroom, because both would be limitless.
Zeno asks the same question about weight/magnitude. If we divvy up an object, does each division have some magnitude? If yes, and there's no limit to the division, then we will have no limit to the result and a pea will be infinitely heavy and just as heavy as everything else.
And indeed you would never begin the journey or the divvying up of an object, because you will not be able to identify the first step/the first cut. Where will you first move to? Oh no there is a space before that, etc.
There is a way around these paradoxes, as noted before. Some are failures, like trying to treat infinitees as numbers and cancel them out, and successful ways, such as by denying divisibility in that sense and accepted chronology/spatially as a complete whole.
The flaw lies in that as subdivisions happens, the magnitude of each reduces in turn.
An infinite sum can result in a finite final value
You won't even get to start the division in a presentist model, because you won't be able to identify where the first step is made. Similarly, you won't be able to stop the series unless you also assume the destination and accept the whole race or scenario as a complete whole. When those concessions are made the Eleatic already has what he wants, but if he wants to continue getting into the weeds he will just show further absurdities of trying to posit limitless processes and treating an "infinite" as a number or otherwise as something with definite qualities we can apply. Rather than inaccurate shorthand for our broken models to approximate the truth for practical purposes.
>Zeno asks the same question about weight/magnitude. If we divvy up an object, does each division have some magnitude? If yes, and there's no limit to the division, then we will have no limit to the result and a pea will be infinitely heavy and just as heavy as everything else.
sounds like he was joking then.
that makes more sense. Given, as I pointed out earlier, than an 'infinite' number cannot be said to exist and so the person doing the calculation must simply skip it for the equation to be completed.
if, as a random anon said, the 'n' represented infinite.
>Plato said you should know math before you take up philosophy
it was probably only ever intended to lead the mind to discarding what cannot be said to exist. You guys think that these Stoics (who we know were teaching real-world logic; causes etc.) were sitting around coming up with sudoko puzzles? Only after 1,400yrs of doctrinal faith in non-existence does humanity arrive at such nonsense.
Plato can also suck dick.
>sounds like he was joking then.
He was making a joke of other people's models, yes. That's the whole point, he saw that reality is complete and can't be divvyed up and altered in the way other people claimed.
So it's even funnier when brainlets try to come in and say they "disproved" Zeno.
Ha that is pretty funny. I tend to ignore numeracy (because I know I know better) but that budding mathematicians would approach Zeno only to find that he was dunking on mathematics is pretty cool.
>sum of infinite number can be a finite number
/thread
all of zeno's paradoxes have yet to be disproven
This thread is so disappointing. When do all of you go back to school?
tell me you love me in binary code
How is it that none of you have taken calculus?
Zeno explains why we shouldn't bother and why reductio ad numismatic is an absurd proposition.
it turns out. i'm inclined to believe this.
He types on a computer
it's not that we don't understand, there must be some missing information or miscommunication going on in this thread
>It's not that we don't understand 1+1=2 it's just that one apple placed on a table next to another apple by itself doesn't mean there are two apples on the table. This is philosophy not math
You're a fricking midwit. Think about it: in what sense are we talking about the addition of an apple? We aren't denying the accepted result of the race/the idea that there are two apples on a table. We are criticising how the process of motion/change is being modelled, and by extension criticising the overall model of reality/metaphysics. You mathcels get dragged kicking and screaming every inch of the way, utterly incapable of contextual thought. Literal beep beep bloop bloop human calculators who should be enslaved and put to work in the fields so philosophy chads can put their feet up and do the big thinks without you.
The solution is this simple—instead of plotting distance on the X axis and time on the y axis, plot time on the X and distance on Y. Should help you realize you’ve been spooked.
Non-responsive
Let's play another game. I'm about to leave the office and I need to walk to my car. In this magical infinitely divisible wonderland, what location or space do I move to first?
Your inability to see atoms is not evidence against motion.
non-responsive
Yes, that's my point, it doesn't make sense. So one must accept a different metaphysical framework. So, what does "divisible" mean to you, if you are positing that we "move continuously"?
If you are saying that this is a complete picture, "my journey from my desk to my car", and I am smeared across it, I could agree with that and the conversation would go a different direction. At any rate, as a result of such a model, the presentist accounts of change that people advocate are destroyed. The chronology is complete and change/motion is a relative term. The journey is already complete, I have already "moved" everywhere possible, it is all necessary. This is is the conclusion that Zeno is leading us towards
If you doubt the above, though, then please tell me what you mean. Because those people who believe in genuine change are screwed when faced with this question. They will posit me at moment 1 at a certain fixed location, and they need to "create" a moment 2 (that is not) where I am at a different location. So they need to identify a moment 2, and they cannot because of the issue with their acceptance of unlimited divisibility.
> that's just saying that Zeno is right by admitting that reality is a smooth continuity and not made up of discrete units.
p much the story in any Zeno conversation, people are led by the nose by Zeno's paradox to a better metaphysical position, but they don't know what's going on and they think they've "solved" something themselves.
>I'm about to leave the office and I need to walk to my car. In this magical infinitely divisible wonderland, what location or space do I move to first?
In a magically divisible wonderland, the idea of a discrete space doesn't make sense. You don't move to a grid location 'first'. You move continuously.
funny that it's basically the other way around and you're the one completely missing the point (and thinking you're smarter because of it)
this is so fricking funny dude holy shit
and this is icing on the cake
Calculus doesn't solve the paradox because being able to sum up an infinite series doesn't actually answer how something can jump between discrete states.
>b-b-but the reals are continuous!
Then you're admitting that Parmenides was right and that we do not live in a universe made up of discrete units but rather one of pure, infinitely divisible, continuousness.
>Then you're admitting that Parmenides was right
Parmenides was arguing that motion and change didn't exist. Obviously moronic.
Right, because we live in a continuous world in which "motion" and "change" are just the internal rearrangements of one enormous continuous body. This is literally what I said in
, so I'm not sure why you decided to agree with me.
Thank you for the (you), though.
>Right, because we live in a continuous world in which "motion" and "change" are just the internal rearrangements of one enormous continuous body
So you admit the positions of Achilles and the Tortoise are rearranged at the time during the race predicted by calculus. Why did it take you so long to just admit you were wrong?
See
, this was already explained The paradox, like all of Zeno's Paradoxes, can be summed up as "what makes something move between two discrete states?".
It should be noted that the people Zeno was opposing would reject the idea of summing up an infinite series in the first place.
That might be true, but I don't want to talk about Greek philosophy, I want to talk about calculus.
you're in a greek philosophy thread autist
If that's the case, why did you choose to do this on /lit? Go make this thread on IQfy. If you hurry you'll get it up just in time for peak Americans-are-home-from-work hours and will be able to beat the seed oils and vaccines spam.
Because the accepted solution to Zeno's paradox is given by calculus. If you're obsessed with some culty shitskin gibberish like advaita it's easy to see why you would hate such a clearly logical refutation of similar beliefs
>Because the accepted solution to Zeno's paradox is given by calculus
No it isn't. See
. Calculus can't explain Zeno's Paradoxes because in order to do that it would have to demonstrate a world where calculus doesn't work. If you can sum up a series of infinite points, then you're saying that Zeno and Parmenides were right.
If you want to prove them wrong, then explain how you can move between discrete quantized states that do not have any continuity between them.
>If you can sum up a series of infinite points, then you're saying that Zeno and Parmenides were right.
>If you want to prove them wrong, then explain how you can move between discrete quantized states that do not have any continuity between them.
Bro I think you're kind of confused. I suggest going back and reading Zeno's paradox and going over some basic calculus.
Read the thread, this was already addressed in
oh the accepted solution, it's settled science!
So calculus solves Zeno's paradox which is exactly what I've been saying for multiple posts. Glad to hear you agree.
>It should be noted that the people Zeno was opposing would reject the idea of summing up an infinite series in the first place
No shit. Calculus would be invented for another 1500+ years.
how does calculus explain how you can move between two discrete states that cannot be further subdivided?
integer addition
so how do you add the integers?
the entire proof is 86 pages long, but you can find the whole hog in Principia Mathematica by Alfred North Whitehead and Bertrand Russell
Shorthand notes + "we'll define the process of addition in regards to motion later" = image attached
Yes, as a result of the nature of Being. I think the other anon is wrong to say that Parmenides posited infinite divisibility, but he's right in terms of purity and continuity. There are other details, too, for as the goddess says the signs regarding the nature of Being are many.
And this is patently moronic. Even the fact that you're replying to me shows you know it's moronic to because if there was no change there would be nothing to respond to. Every (you) you give shows how wrong you are. You sound like one of the advaita cranks who keep getting beat down here.
You just keep digging your hole. The Eleatics were right, Zeno successfully dealt with the ridiculous systems he encountered, and a mathcel like you should move on because you are incapable of considering the ramifications of this.
So you are an advaita crank lol. Called it lol. See this post
and feed me your (you)s
Never read advaita in my life. Keep seething, midwit.
>Never read advaita in my life. Keep seething, midwit.
According to you you've never read anything in your life since that would mean transitioning from not having read something to having read it. And you claim change doesn't exist.
>You just keep digging your hole.
Rofl what are you responding to? I thought change didn't exist? A response requires a change to respond to. You can't defend yourself without implicitly admitting you're wrong
Change doesn't exist as the targeted models/philosophers posit it. Same goes for multiplicity/division/independent existence. The Eleatics are putting forward an account of reality as a perfect whole. There is still a youth and a goddess, there is still a series of events that constitutes their conversation. Whatever account of "change" we posit will need to be relative/eternalist, for what-is cannot literally become something else/"what is not".
But that conversation is beyond you. You are a midwit because you cannot think contextually. You cannot think of any other system, you cannot process the ramifications of certain metaphysical truths and how they would play out, intellectually you are an npc and incapable of philosophy.
Again you respond. What are you responding to? It can't be to anything I wrote because then that would mean something has changed for you to respond to.
>you cannot process the ramifications of certain metaphysical truths and how they would play out
I can process it well enough to know how ridiculous it is. How can you type a response to me unless you admit something has changed to respond to? By even presenting your philosophy you've already disproven it to me since it's a change in my awareness
Listen to yourself. I said that I accept an eternalist account of change. I referenced Eleatic works to indicate that it should generally be acceptable given the characters and events described. And what do you? Prove that you cannot think contextually, you live a blinkered existence and will just continue down your lane. You'll forgive me if I leave it at that, you were never really part of this conversation.
>I said that I accept an eternalist account of change
Rofl. So you do believe in change. Calculus solves Zeno's paradox and the CHANGE of position of the individual racers. They change position in the same way you change your arguments in response to me.
very npc response, may as well be talking to chatgpt or reddit
If chatgpt is capable of pointing out a gaping logical flaw in someones argument it has some value after all.
that's a homosexual opinion
Dumb. The map is not the territory. Xeno has not uncovered a mystery of physics. He has simply described ordinary life in a way that is confusing to you. It’s a Chinese finger trap for the mind. Stop looking at it as a problem of space, and consider it in relationship to time. The trick works because Xeno keeps shrinking the time interval while your imagination is focused on the distance traveled.
Zeno was a student of the philosopher Parmenides. Parmenides held that reality was one giant continuous infinitely divisible mass. Some other philosophers disagreed, arguing that the world was made up of a large number of discrete states and things just jumped between these discrete states while spending no time in between them. Zeno created a series of situations that are, if you assume the world to be made up of discrete states, paradoxical. There's no paradox if you believe the world to be continuous and infinitely divisible, however, they're only paradoxical if you disagree with Zeno and Parmenides.
Yes, Achilles will obviously reach and surpass the tortoise, that's Zeno's argument for why we live in a continuous infinitely divisible world where all motion and change are just illusions caused by the huge mass of everything shifting around. If we didn't live in such a world, Zeno is arguing, Achilles would have to jump an infinite number of times between discrete states. Because there's an infinite number of states between start and finish, Achilles can never complete the action. Achilles can never complete "walk to where the tortoise was, then walk to where it was, then walk to where it was, then..." not because he can't run faster than the tortoise or because he has to move an infinite number of steps through a finite distance, but because he's moving through an infinite distance in an infinite number of steps. If you hold the world to be discrete, he can't actually do this, because eventually he and the tortoise will meet as they're both moving the minimum number of units.
Zeno DOES have another paradox, the Dichotomy Paradox, which is about summing up an a finite distance that is cut up infinitely, however.
You can just say "but asymptotes", but that's just saying that Zeno is right by admitting that reality is a smooth continuity and not made up of discrete units.
I’m familiar. You’re not. Motion and time are tied together. The seeming paradox only appears when you focus on the sequential changes of space. This is a distraction from the sequential change sin time. For each fractional movement, you are also observing a fraction of the time. What Xeno and Parmenides observe is not the infinitive divisibikity of reality, but the infinite divisibility of numbers. You can theoretically discuss the difference between 1/infinity inches and 1/(infinity plus 1) inches. But you must also remember to tie these theoretical distances with their partners in time. Obviously if you try to examine motion at 1 Infinitieth of a second, it will look like movement’s impossible. But all this really says is that motion is proportionate to time. It’s no paradox at all. It’s just common sense.
>What Xeno and Parmenides observe is not the infinitive divisibikity of reality, but the infinite divisibility of numbers
What's the difference, really? Are numbers not part of the fabric of reality?
>90 replies
The Greek homie just runs faster than the reptile homie and eventually passes him.
7th day of rest
Objects aren't points. Try this in real life, and the man will get so close to the tortoise that his body will at some times be ahead of the other.
Sorted.
We cannot hope to disprove Zeno if we can't even disprove 0.999... = 1.
>We cannot hope to disprove Zeno if we can't even disprove 0.999... = 1.
Rofl I can't wait to hear the morons who hate calculus have to say about 0.999...=1. It's going to be like every internet forum full of 12 years except they're all going to think they are philosophically brilliant.
Zeno's paradox is irrelevant; therefore there is no need to disprove it.
humans can catch turtles in real life, so I don't see how this scenario is realistic.
Who gives a flying frick my homie. Imma bend you over and Xeno my paradox into your tight butthole. Disprove that.
>numbers can be halved infinitely therefore motion is impossible
more like
>points on a plot I place on a piece of paper after some movement has occurred have the effect of reaching back into time and applying a force to the moving object stopping it until I place the next dot.
math so powerful!
either the universe has a discrete "bottom" in which further subdivision is impossible, or it is possible to cross infinite point in finite time
Movement goes from a place to another, in a discontinuous fashion. Then, you can always decompose the distance between those two places.
Anyway, with Zeno's method, you can also show that Achilles never reaches the end of its first step, because he should first reach half of it, then half of the remaining distance etc.
Every successive step takes exponentially less time and time is passing steadily so the two will meet. The idea of needing infinite steps is poor framing by the human but an error in the universe. The steps are nothing more than arbitrary distinctions in the mind.
>walks past you
>le electrons in discrete states
>le quantum granularity
Its sophomore calculation of limits you pseuds.
The infinite divisibility of space is actually necessary if there is to be any motion at all, because it means that after each division you still have a finite number of "parts". The real problem would be if the turtle had to go through an infinite series of infinitely small parts.
How the frick is it a paradox? It's an illustration of a simple as frick mathematical concept. The racers could be anything.
>duh if da race car never passes da earfworm, it will nevuh be in da first place uh durrrrrrrr
1. Pick reference frame that of a tortoise(I.e. he will be standing still in ~~*this*~~ reference frame
2. Subtract tortoise speed from that of a bozos' and you'll get his relative speed in specified reference frame.
3. Just divide handicap distance with aforementioned speed and you'll get time in which handicapped distance is reached by achilles in the ~~*relative motion frame*~~
4. Profit idk
>le infinitesimal calculus
le Occam's razor b***hes
It is only a paradox BECAUSE it is disproven every single day by everything that moves. Because there are particles which are "as small as is physically possible," and all matter is made up of such, the movement of such a particle must have a "smallest possible distance" which would constitute movement.
Some infinities are bigger than others. Simple as.
Achille's steps can't be infinitely small. Qed
What refrains you from choosing a reference frame witch moves with a speed that of a tortoise? That makes the tortoise to be standing still while Achilles covers the distance in between them in a single iteration.
P.s. let me remind you that for even such a simple problem there can be invented infinite amount of solutions with infinite levels of complexity but this is why Occam's razor exists to cut off that lard of extra complexity whenever possible.
This paradox assumes no other points in existence, and works only in a two dimensional plane deviod of time where the speeds of each entity are related to each other as their only point of reference. If speeds are held constant the paradox doesn't arrise, as it would only take time for the faster entity to gain the lead.
>If speeds are held constant the paradox doesn't arrise, as it would only take time for the faster entity to gain the lead.
Yes, exactly. It’s entirely stupid.
Achilles would easily outrun the tortoise in real life. Also it presupposes that Achilles can only go twice as fast as the then current speed of the tortoise. This would mean his speed is actually incostitent to stay in tune with the tortoises.
Don't see the paradox, either distance and time are discrete quantities, or they are infinitely divisible.
In each case, there's no paradox.