Zeno's Paradox - Achilles And The Tortoise
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- Опубліковано 26 сер 2024
- In the first of a series on paradoxes, we take a look at Zeno's famous paradox of motion. Zeno argues that the Greek hero Achilles could never catch a tortoise in a race, as long as the tortoise is given a head start.
Many solutions have been given to Zeno's paradox, but are you convinced by the Standard Solution?
Music:
"Kool Kats"
Kevin MacLeod (incompetech.com)
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During the debates, this would have been solved easily by punching Zeno in the face. Then claiming that if motion is not possible, he would not have been hit.
To that, he would say that his senses fail him.
You that's LITERALLY what happened!! 😂 Now I can't remember if it was Zeno or his master Parmenides, but I'm sure someone did exactly what you said...
LMFAO!!
That is what makes it a paradox...
You sir are a genius!!
Teacher: Why are you late?
Me: _explains Zeno's paradox_
Troodon formosus hahaha. The most useful application of Zeno’s paradox I can think of
😂😂😂
Would that not be "How are you here?"
Genius
Girl: Come over I m home alone.
Zeno: I can't
Girl: Why?
Zeno: Because Motion is Impossible.
It sounds like Chris Hansen would be there waiting for him anyway
Girl: My parents have gone away for the entire weekend.
Zeno: Be right there!
😂🤣🤣🤣🤣🤣🤣🤣🤣
i dont even know what the paradox is... did this video accurately describe it?
@@ededd3175 no. it didnt not... Einsteins 1906 paper was provent that motion and existence are incompatable.. the race is meaningless as there are in differnet lanes. Zero i 500 bc had notions we are just starting to realized are useful.. The dispele "paradoxes" in modern phyisics.
Zeno: "So what did you do this afternoon?"
Socrates: "I went on a stroll."
Zeno: "Impossible."
Lol according to legend when Zeno told a bunch of philosophers about this “paradox” one of them got up and walked across the room.
Zeno: why are you lying to me
Samuel Willis 😂😂 Good one
@@BoxStudioExecutive 🤣
i dont even know what the paradox is... did this video accurately describe it?
Zeno was an idiot. That's why he's dead. Otherwise, he'd still be halfway to his dying breath, but never reach it.
Made my day, thanks
Zeno's paradox gets rekt by hxhdfj ifzir st c paradox
He'll never reach the truth of his death... that is the power of Gold Experience Requiem...
I think he was a prankster.
Well....brilliant.
That running animation tho. 😂
He's speedwalking....
Never skip leg day
No wonder he can't catch the tortoise running like that.
Well his heel was always his weakness. Good thing the tortoise didn't challenge him to sword fight.
Shimmy shimmy shimmy...
Swalla la la!!
Trolling existed already in -500
Hah yes
@@ricobrawlstars4880 Which could have stayed alive until Sir Isaac Newton was the one that killed that troll using a weapon he created called "Fluxions".
ahh so Gojo's power is just making this paradox real
yes
Sounds like non sense,his ability doesn’t make any real sense cause if it were real then he himself wouldn’t be able to move nor anyone in his verse cause motion wouldn’t exist
@@deonte8355 you lost me at “if it were real”
@@zejuicecalibur2255 im mean real inside his verse,not in real life bud
@@deonte8355 you do know he has the ability to control it right? Meaning he can allow things to touch him and affect the range of the infinity that exists between him and an individual/object. Also the infinity doesn't affect him, it's mainly applied to others/objects.
It's ideas like this that make me think alot ancient philosophers were just really bored.
It's the idea like this make you an arrogant modern man
@@user-td3ut4tg3v it's replies like this that make me think a lot of people don't understand humor
@@michaeledmunds7266 😕how is that even humorous
@@user-td3ut4tg3v humor is subjective
@@user-td3ut4tg3v Do you feel like a smarty pants now that you needlessly insulted them?
It looks like English isn't your first language so try not starting shit with people in that case
"Awe crap! Zeno didn't show up for work again."
"What was his excuse this time?"
I hope I'm not the only one here from Jujutsu Kaisen
You aren't alone, my friend.
@@abhineetkunne6172 Manga readers rise up
The infinity
🙋♀️
Meeeee
"read a book, your stupid is showing" is what got me here HAHA
I thought the answer is the tortoise bites Achilles’ heel and the tortoise wins the race.
Damn I wish
😂😂
200 IQ
@@photonx3513 200 iq play
"Sum of infinite finite values is finite".
Thank god for this... otherwise I'd never be able to get to the bathroom in time.
Shahbaz Sheikh It would always be a halfways away.
I didn't get to that part of the video in time so I shat myself.
It has to do with convergence.
Say I want to walk 2 meters. I can walk 1 meter per second.
In one interval, I walk 1 meter in 1 second. In the next, I walk 1/2 meters in 1/2 seconds.
1/4 m per 1/4 s, ... so on and so forth.
I have an infinite number of intervals, yet I have still walked 2 meters in 2 seconds.
Zenos was the 1st to prove space and time are not absolute unless you atribute values to it.
Actually couldn’t you argue that you don’t even have an infinite number of intervals because the Planck length is the smallest distance possible. You can’t divide 2 by 0 but instead should divide 2 by Planck’s length to get the number of intervals
@@illusion116 Well, not exactly. As others have already pointed out, Planck length isn't 'the smallest distance possible' but rather the length at which our understanding of a different position between two objects at a quantum level breaks down.
Besides that, we can't divide 2 by 0, but we can use limit notation to say LIM n->∞ [SUM(1/(2^i), i=0, n)] = 2
Now I understood why I cannot reach my classes on time 🙄🙄🤔
Lol
😆🤣🤣
"Sorry I'm late. Zeno's paradox got me."
Its more a demonstration on our limited understanding on maths
patrick hinge most of these paradoxes are most likely not actual issues but simply beyond human understanding.
@@Valyssi yeah, thats how math solves this problem
But its space itself continuos or discret?
not a limited understanding the guy who made this is just a misunderstanding completely. the man and the turtle are separate entities. the man goes a certain mph and the turtle goes a certain mph. the distance from point a to point b is it’s own entity too. how fast the man goes from point a to point b does not need to be dependent on the turtle. the person who made this theory is just overthinking and coming up with something that’s not right because of it
@@Valyssi this is a well perpetuated story among some philosophers and mathematician but misses zeno's point entirely. Zeno is proving not just merely that motion is impossible but that SPACE is inherently contradictory when taken as an independent existence. (Zeno is arguing inversely for Parmenide's own premise), explaining movement as a convergent series explains one part of the paradox which is how seemingly infinite points exist between finite distance but it DOESNT explain how for any given space, its Quanta is both discrete or continuous, observation merely assumes it to be.
To put it another way, if for any and all space coordinates, if from any point from A to be B you have both quanta (points A and B) and Continuity (length AB), you have a contradiction. Either, A and B are substantial and length AB is composite, or the other way around. the contradiction of space is precisely to shift from one stance to the other when convenient without realizing that Space on its own cannot be both at once. Space either becomes one discreteless infinite space (Parmenides) or space becomes a construction from non-space parts (Leibniz)
This is why all the top metaphysicians of the late 19th and 20th century had different responses. Bradley bit the bulet and deemed Space unreal and only the One (the Absolute ) exists, Alexander alsoo deemed space unreal but added that you only need to add the 2nd half, time to resolve the contradiction. Whitehead deemed that reality is fundamentally discrete but these discrete units, the actual occasions through relations have infinite capacity for summation and divisibility. (divisible but dont exist divided is Whitehead's motto).
www.quora.com/Why-cant-mathematics-explain-Zenos-Paradox/answer/Miguel-Fonseca-15
the sparknotes version, the idea that calculus solves Zeno's paradox by introducing the convergent series confuses a mathematical apparatus for conceptualization with the metaphysical conundrum. To say, space just happens to be both discrete and continous without problems a priori is no different than saying movement just happens because we see it.
Our philosophy teacher once asked us this question and perfectly portrayed Zeno by staying oblivious to our down to earth reasoning. Here's my take.
From Zeno's POV, in order to move from point A to point B you would travel an infinite amount of distances, since before reaching the first step you need to reach half of that step, and so on. BUT since the time it takes to travel also gets infinitely small, smaller increments of distance become cancelled out with how little time they require and thus, motion is possible.
Later on, physics teaches that v = dx/dt, which is pretty much spot on
i dont even know what the paradox is... did this video accurately describe it?
Yeah Aristotle wrote that in physics lol
??? "smaller increments of distance become cancelled out with how little time they require" they go hand in hand the smaller the increments the smaller the time. Both just continue to infinitely get smaller. Obviously the distance isn't infinite yet we don't have an answer as to "why". I'ts a self-contradictory statement the logic used cant be called wrong yet its wrong. A paradox
it did@@ededd3175
Gojo satorou asked me to study more
Same, I was like what the hell is he tailing about.
@@Thisisjustname yeah 😅
I came here because jujutsu kaisen.
satoru OP
Haha me too! No...3...thank you Akutami-sensei!
Eh? How?
@@d.a.r.n1869 zeno paradox is one of gojo satoru power
@@kyoshuko20 The control of space..... yeah now that I think about it, it is.
So in other words, the Tortoise said “Nah I’d win”, and then he lost 🤔
Quantum physics actually fixes this problem. There is a smallest unit of distance possible that they could travel in the smallest unit of time possible, and eventually the distance left between Achilles and the tortoise would drop below that threshold. When that happens, during the next unit of time, Achilles would either have to stop, or immediately catch up. And since he doesn't stop, he catches up. He can only go either at least that unit of distance, or no distance.
It's impressive that people were thinking about covergence of infinite series so long ago. An easy example is the decimal version of 1/3. If you write 0.333 that's close, but to be totally accurate you need 0.333333333 recurring, which is an infinite series. If you truncate the decimal you don't quite get to 1/3, much like Achilles never catches the tortoise if you truncate the series.
Is anyone else here to understand how Gojo’s powers work?
Jujutsu nerds assemble
Every time that Achilles moves forward the increments get exponentially smaller but so does the times that it takes him to pass the turtle. Say he has to run 10 meters to pass the turtle and it takes him 10 seconds to do so. If you keep making the distance increments smaller you’re also making the time increments smaller and then time also doesn’t exist??? This is because space and time are relative to each other. You can’t have one without the other.
What do you expect from a person who was born 2500 years ago 🤣
"If time exist then explain why I got rejected infinite amount of times"
-Caleb Cantroast
Sure but that dosent solve the paradox both time and space get smaller but that's just it. It will forever continue to get smaller and it doesn't matter how small the numbers get if they never reach zero. It's a paradox for a reason we know its not possible for the distance to be infinite yet we cant prove why and until someone does prove why it will remain a paradox
This paradox is like "why water is wet?" question
Gege Akutami sent me here
This is a logical fallacy not a paradox.
It's not so much a logical fallacy but an interesting thought experiment that can directly be explained by calculus, but that wouldn't be formally invented for hundreds and hundreds of years. You're not giving his intelligence the credit it's due because you don't understand.
Not understanding something and being smug about that lack of understanding is basically UA-cam comments in a nutshell.
@@Oneiroclast it's just simply another testament to his intelligence -- the fact that he understood the importance of this concept that long ago, when people today dont even get it when its directly explained to them.
@@bjordsvennson2726 You don't need calculus to understand the fault with this paradox.
@@ihsahnakerfeldt9280 understanding and proving are two different things
Satoru Gojo Reference
All y’all solving the paradox thingy
Me: wtf a talking tortoise
Lol me
1.6 *10^(-35) is Planck length i.e. the smallest length possible between any 2 object in the universe....... After this Discovery it doesn't seems to be a paradox anymore
Except that is not at all what the Planck length is. It is merely the point at which it is thought our understanding of quantum mechanics breaks down because quantum gravity becomes dominant. There is zero evidence that the Planck length (or Planck time) shows that space (or time) is granular.
Yeah, I thought it was impossible to move, I ha ether theory for ages, but then I learnt about Planck length and everything made sense
By discovering that length, discovering will be stopped?
@@camerongray7767 😂😂😂
have you been there?
Gojo Satorou anyone?
This is a paradox I pondered a lot about as a child. I wasn't aware there was a Greek tale about it or that it was even something other people had ever considered. I just thought I was being stupid. Glad to know I'm not the only one out there.
Honestly this paradox describes exactly what life feels like to me, and always has. No matter what or how much I do, it's never enough. The goalposts always get moved and the work required to reach them proportionately doubled.
who's here after seeing episode 2 of Jujutsu Kaisen lol , Gojo Told me to Study i came to study .
The whole gang is here
This is the Green Baby's Stand in JoJo Part 6, basically.
Michael Scott: Now explain it to me like I am 5
Me: I agree
Gojo brought me here
this has an incredibly simple solution with "smallest units", basically, 1 step will always claim a (roughly) same distance so you will reach a point when a single step will be bigger than the gap.
i dont even know what the paradox is... did this video accurately describe it?
@@ededd3175 A paradox is something that seems contradictory but turns out to be true. How can we reach the end of this race course if we have to cover an infinite number of points? We should NOT be able to travel an infinite distance. But we know that we actually can reach the end of the race course, although it might sound like we shouldn't be able to.
This dude was 2500 years ahead of his time, can you imagine that, it gives you the shivers when you actually think about it! Nobody will be as gifted and clever like this ever again Zeno Heraclitus these men were something else.
Really? What did he do exactly, other than ask an unecessary question to an unecessary topic that doesn't happen?
Because to me, the only thing this dude was, was being extra.
@@MatBaconMC He asked questions thought provoking questions in the form of paradoxes that made every mathematician, physicist body rage with warm blood in trying to solve it
@@SDSen And for what? Movement exists and you can overtake a tortoise without breaking a sweat, so what was the point really?
But i do agree with you on the part about making mathematicians' and physicists' bloods boil. Must've been fun to watch them freak out at the time.
@@MatBaconMC Agreed movement exists, I back the Heraclitus POV. But this paradox isn't so simplistic, a great deal of Quantam mechanics and Mathematics have been used to sort this paradox. If you just think about the fact that this was by a man who lived over 2500 years ago. It's an incredible paradox to create
You are really cutting yourself short man.
It is interesting to note that every culture throughout history has had some variation on a Tortoise racing against a much faster opponent as part of their mythology. Like the great flood it seems almost impossible that it was not based on some event deep in humanity’s shared ancestry. Even the nomadic Glangle people of the fearsome Dyk hinterlands have a variation, where a slow moving creature with a shell on its back challenges the fastest cat in the kingdom to a race and by winning, wins the heart of the queen.
The moment Achilles is one plank length away from tortoise, the next moment he has to be with the tortoise and the next momen after he will overtake.
As Achilles is closing in, the toirtoise is always moving a little bit forward, therefore always stayint ahead of Achilles... I dont see why this assumption excludes bypassing? :)
The fact that you can cut the distance between the 2 to an infinite amount of points, does not mean Achilles cannot bypass.
I remember reading about this theory in a book when I was a kid and it really messed with me. The situation in the story I had read went along the lines of "A hungry man is running to reach a boar. As he runs, he first reaches the halfway point to the boar, and the second time he runs, he only reaches 3/4 of the way to the boar. If each time he moves towards the boar, he only moves half the distance of his previous movement, he will never reach the boar, as the closer he gets, the further away the boar appears to become from his motion, even when he is nanometers away from the boar, the distance he has left to travel is infinite.
i dont even know what the paradox is... i dont know why i can't follow it... did this video accurately describe it?
This is something that makes total sense in theory but would never work if actually carried out
I think gojo satoru power is similar to this
really interesting thought but reality looks kinda different
in this example archi gets slower while the turtle holds it's speed
and that is why most mathematicians suck at sports
You totally missed the point of the Zeno's argument. 🤦
@@AashishVishwakarma
I get the math and philosophical stuff, just saying these are fundamentally different from reality
@@AashishVishwakarma , Zeno's argument honestly doesn't even matter when he is coming to such a ridiculous conclusion. Just by looking at his conclusion, you know his argument is flawed, the same way there's no real reason to entertain the argument of someone explaining to you why bees can't fly or why the Earth is flat. Zeno says movement is impossible, and he is dead wrong.
Besides, Mirco is actually explaining the only way Zeno's turtle example works. For the runner to never catch up, he must cut his speed at every mark. If the runner maintains his speed, it is impossible for him not to surpass the turtle (given that any amount of distance was closed between them once the runner started).
@@SgtSupaman The way he is slowed down represents the arbitrary scaling down and choosing of time intervals so that Achilles is always behind.
Achilles wasn't slowing down, the increment which was being measured was decreasing.
Let's say he was 10x faster than the tortoise, and the headstart is 10m. When he travels 10m the tortoise will travel 1m. Then when he moves 1m the tortoise moves 0.1m. Neither is slowing down or speeding up, the ratio between the speed of the two is still 10 to 1, it's just that Zeno failed to realise that 10+1+0.1+0.01+...-is a converging series, but even that knowledge will only tell us that Achilles passes the tortoise at 11.111...m, not why/how. That's what the paradox is asking about. So as Aashis said, you completely missed the point.
So... basically he's saying there's an infinite amount of points in a straight line and if the tortoise was given a head start on every single point then the tortoise wins? I wish you could have just explained it like that. Not to mention Zeno must not watch races often to come up with this.
If the tortoise had a head start on every single point then he'd be starting at the finish line, so yes, he would "win".
He’s wrong, in real life there’s a smallest possible distance, so any distance is composed of X amount of that distance, look up planks constant, if things could get infinitely small then motion would be in fact impossible
@B Ball Look at all the famous philosophers, almost all of them drank quite a lot.
Before watching the video, This isn't a paradox. It takes standard math's and changes it to calculus.
That is to say. You don't need to decrease the distance by half until it reaches an infinitesimal. You continue at a velocity until the full distance is reached and you can absolutely keep going past that set distance
This paradox only makes sense if we assume that both Achilles and the turtle run at the same speed which is most likely not the case
No. The paradox very much relies on the tortoise being slower. That's why the gap shrinks every time. The whole paradox wouldn't exist if they were moving at the same speed. Of course Achilles would never overtake the tortoise if they're going the same speed
@@reuben3588 Then that's even worse because if the tortoise is slower then Achilles will 100% catch it the gap becoming smaller and smaller with Achilles never being able to catch it is pure bs
Philosophy(noun). The art of explaining why you're late.
People here for Gojo. Do you think the Flash could touch Gojo?
no
I recognized and contemplated this paradox before I realized it was a paradox.. I was only 12 yrs old and I was thinking how if I kept only walking half the distance of my previous distance then I couldn't make it to my porch and I wouldn't have to go inside for chores. However I knew I definitely could walk to the porch despite the infinite distance between the porch and me since I've entered my house plenty of times. I have pondered an answer to the seemingly unanswerable questions of why and how until today
what
think about this, someone jumps 8 meters, then he keeps jumping half his distance, example: 8 4 2 1 1/2 and so on, how mamy jumps will it take to get to 16 meters total? 8+4+2+1/2 and keep adding until its 16
This argument is based on the assumption that space and time can be infinitely divided. This paradox (and others by Zeno as well) is one of the firsts hints we find that suggest the contrary. It would take 2400 years for quantum physics to come up with a theoretical framework to support this.
exacltry.. .he had idea Quantum Gravity before we have the math or no what to call it Quantum Field Theory? well its not a field thery becasuse its more logical to pursue lattice or matrix theory now. There are no machine representations of real numbers either. They can't be communicated withtout error. So now we are using posit, n bit integers.. We haven't caught up to Zenos "paradoxes" and never will because time is an illusion.. All proven in the last 100 years.. Of course Zeno had a 2500 year "head start so its not quite fair " lol
Sometimes I also have these kind of illogical doubts which seems to be logical, just like Paradoxes of Zeno, but I used to not think much about it as no one gives it importance saying that it is illogical and has an obvious answer. But now Zeno gave me MOTIVATION to think more and have these kind of confusing doubts, or to be precise, Paradoxes
Anyone here to understand how gojo satoru’s infinity works?
Planck's mesaure:
I'm about to end this man's whole paradox
That's not how reality works. If something has space, It's infinitely divisible - no matter how smaller and smaller particles you find.
@@Robobotic
"That's not how reality works. If something has space, It's infinitely divisible"
Are you sure about that? Can you prove it? What instruments would you use to measure a space of a smaller diameter than a Planck Length? Or an interval of time shorter than Planck Time?
Also, is there any currently accepted theory of physics that fundamentally requires the existence of a smaller space than Planck length or a smaller interval of time than Planck time? Especially since most (if not all) current physics models start to break at around such tiny units?
@@roadent217 Something has length regardless if measurable. That which has length has length within itself. That's just logic.
@@Robobotic
"That's just logic."
Wrong. We're talking about physical measurements here. Pure theoretical logic does not allow us to have any direct insight into physics.
"That which has length has length within itself."
You can only say that, logically, if distance were a continuum, all points in said one-dimensional distance would aggregate into an uncountably infinite set, such that, between any two given points, one could always find an another point.
However, right now the premise itself - that distance is a continuum - is called into question. If you have evidence why, say, Einstein's General Theory of Relativity breaks down if space is discrete, feel free to share.
@@roadent217
Theoretical already implies universal abstract categories which are not physical.
Is there even any insight into physics?
What do you mean by distance being a continuum?
The paradoxes both stem in space and time. There is no need for space to be discrete.
You have really great videos, you are surely going to hit millions, just never give up and keep doing your best.
The real issue with this whole paradox is that it never takes speed Into account speed time and distance are woven Into the fabric of space they all coexist with in a Trinity ..... He's saying that u can forever cut the distance in half yes that's true. But when u account for speed the product and sum of all three will always arrive at a definitive number .. this theory is basically saying if I take 100 steps for every 50 u take u will never catch me and that is true. Notice in this race he never mentions a distance in which the race ends therefore the position of the turtle is the end point which at this point means no he will never catch the turtle because he is a continually at half . Not until u add speed can u say he will definitively over take turtle
But that's not the point the point is to prouve that a 2 m distance can become infinit with 1 + 1/2 + 1/4 ...
This would only work if the person is marking the point where the turtle currently is, walk to that point, then check the position of the turtle and repeat.
This is coincidencially how a "classical" computer works
Zeno is your obnoxious friend after 2 a.m. at a party, zapping your last remaining energy by forcing you to try to prove that motion is truly possible.
A finite line can be divided infinitely
To the people who are saying this isn't a paradox because you think you understand it I would highly recommend Vsauce video on paradoxes I believe they use this very example in short something does not stop being a paradox once we understand it it just becomes a different kind of paradox a paradoxes real purpose is to highlight the limits of our understanding paradoxes are not unanswerable just because you know the answer does not mean it no longer has anything to teach
vsauce is worse
Can you use periods? i got a head ache from reading that.
@@wesleyge1
No
MrElionor The real paradox here is how you know so much about paradoxes but nothing of basic grammar.
@@tap1983
How is that a paradox?
here from jujutsu kaisen :D
yeaaah, me 2
This makes my brain hurt so badly
You just presented me with an issue i didn't know about then fixed the issue immediately
Talks about how Achilles never catching up but shows Achilles running slower. Lame
😂😂🤣
Here before the satoru gojo stans
Oh shit, this is how the Green Baby's stand works. I had never heard of this paradox until now.
Based on this paradox, humanity can never go extinct with a TFR of 1.0
Nice dude! I understand the differing nature of infinities now a bit better now!
Gojo Satoru from jujutsu Kaisen
I actually kinda do this paradox in my head when I try push my limits durning long distance runs
I liked the supertask solution, where you move 50m in 1minute, then 25m in half a minute, then 12.5m in a quarter minute then by the end you will have moved 100m doing an infinite number of steps in a finite amount of time
the way that I understand it is that distance is only infinite in the sense that it can be divided any number of times. However, there seems to be a difference between functional infinity and theoretical infinity. Theoretically, you can divide any space to any degree you wish however functionally the numbers become so astronomically small that there is no real effect hence the law of improbability. This is why even though every atom has a gravitational effect on every other atom you aren't being pulled into space or why we cant feel the earth's magnetic field. The values represented are so functionally small there is no tangible effect. Any thoughts? or did I completely miss the mark here?
Came here because of Jujutsu Kaisen😆
The observation that the runner overtakes tortoise proves convergence of infinite series
Other person: This paradox makes no sense
Gojo and Green Baby: That's how our powers work.
Zeno was the most "Brilliant" scholar of his time... Still none of his theories make any sense...
Joe Biden never makes any sense, but democrats still think he's brilliant...just goes to show there are stupid people in every timeline 😂
Absolutely
achilles and the tortoise
achilles has a speed bonus so he will always pass the tortoise no matter the headstart
second paradox by 224 steps [or i remember by memory] he would had reached a distance 3 times the destination
??? I think your missing the point
what if the tortoise gets a head start to finish line first before achilles can move
This is how Gojo's power works.
ALL of existence is a paradox, so with that understanding, this makes total sense.
Due to something called the "Big Bang Theory".
Limitless technique. Infinity
Yup lol
Sure, if you assume that time infinitely regresses to zero, then this makes sense. Since reality doesn't work like that, we're good.
BS. Our models of reality are limited at Plank time but we don’t know if time and/or space is continuous or discrete.
Basically paradox word is coined from two latin words para and doxa which is commonly translated as beyond opinion or let's say against popular beliefs. Human mind can operate only within certain limits and it's thinking is limited to certain "dimensions" of time and space. In Greek word mind's thinking at the basest levels of it's operation was denoted as doxa - every human mind has it's opinions and all the mind can do is think within this limits, always swaying between two extremes which limit it and always changing it's opinions. The opposite words of doxa are episteme and gnosis which are not opinions but different kinds of advanced "knowledge". What Zeno was trying to say with his paradoxes is that you can not reach into "metaphysical dimensions of absolute truth which are beyond the mind" with the mind which is limited and operates in time. If you try too much you will break the mechanism of the mind and go mad. So this paradox is actually description of a fractal (tortoise shell is beautiful representation of a fractal i.pinimg.com/originals/3b/cf/18/3bcf18cabe462310f5d4e97e9e6aceb8.jpg) which is infinite and never converges and Achilles is human mind - hero with a sword (mind is a mechanism like a sword it always cuts the physical reality in half with it's minding and makes parts from the whole). Humanity is always trying with it's limited mind to limit the unlimited, because it is not aware of it. But this is not possible of course. The only possible solution is that the mind surrenders to the realitiy which is beyond it. Absolute truth is always a paradox (beyond mind), but not every paradox is truth. But Zeno was The man and his paradoxes are a little Zen koan gems :)) and not so much mathematical enigmas.
It feels like a urban legend not a paradox
Jujutsu Kaisen brought me here....
Zeno was correct. If space were infinitely divisible no first step could be taken.
The sum of steps argument is incorrect because that sun is never realised in an infinitely divisible universe.
The reason movement does occur is that space is not infinitely divisible- it’s quantised.
think about this, someone jumps 8 meters, then he keeps jumping half his distance, example: 8 4 2 1 1/2 and so on, how mamy jumps will it take to get to 16 meters total? 8+4+2+1/2 and keep adding until its 16
Another Zeno Paradox: If things are infinitely divisible , then how can it make up objects that are finite in size.
bro, all those infinite points will equal a finite number, take a calculus class and you'll find that out for yourself, this is a flasidical
@@potassium8759 yes everyone knows that in calculus it will eventually be equal to 1 or more. The problem is how do you reach infinity in the first place?
THATS WHY WE USE LIMITS
Oh correct, there was another Greek philosopher, the man who named the "atom" or gave it its meaning as he was contemplating the smallest particle of a "thing:" i.e. if you cut a loaf of bread in half and repeat the step, you will go from a half loaf, to a slice, to half a slice, to one quarter and so on ... the idea being: as long as you cut something in half and throw one side away, you will always have the other side to continue cutting. In modern day physics, this process would stop when the matter or thing would become so tiny that it would lose "locality" and start zipping around all over the place and exhibiting sub atomic behaviors. For the item or thing to continue being split in half at that point ... well, what WOULD be the point ? Cool vid. Thumbs up. FUN FACT RELATED TO FRACTAL SIZES SUCH AS THIS: how far into a forest can you walk ? Answer: only half way ... the other half, you're walking out ! END
Also, not to mention that before Democritus, there was another Greek philosopher that believed that everything was made up by the 4 elements, which are earth, wind, water, and fire. He also came up with a 5th element that was only used by the gods, and it acted like a "bridge" linking Earth and heaven. This is because he knew there are 5 Platonic solids, and each of the terrestrial elements are made up of tetrahedra, cubes (hexahedra), octahedra, and icosahedra. The dodecahedron represented the "5th element", and also, Frozen 2 is a movie that brings those thoughts to life with the elements representing a "spirit", and even emphasized the 5th spirit being a "bridge" between the gods and the people.
@@AlbertTheGamer-gk7sn the 5th element is Ether but I believe what the ancient were describing in our modern age would be "gravity" or the "thing that brings things together." On the other side of these "ten" dimensions it would be the proof of a Creator Supreme Being; much as Alan Watts explains, but not in these words: The Creator Supreme Being is infinitely large, that is why He can only be perceived as an avatar or a representative, in religion the Son or in mysticism the Sun. However, as watts says; Like an inflatable raft if God were to appear he would consume all space and time ... He'd be so in your face you couldn't see Him ! there for when god steps away we "see" trees and water and life ... other wise there'd be nothing to see but GOD !How dreadful might that be ?" [classic alan watts chuckle]. By stepping away a vaccuum is created .. that's why there's gravity. The rebuttal to that is a computer with programming, or just energy .. no personality. Personality gives intention, wants and desire ... kinda like ... mankind, and womankind .. but not humankind, I think that means "man beast". still researching. Stay tough. "it's a wilderness out there." -- Tommy Lee Jones The Hunted.
jjk fans????
Just pass the turtle this doesnt solve my jjk stuff
so zeno was just high???
Its funny how people confuse quantity with value.. for example; 4/3 has a definite value which is 1.333333..... with 1.3 being its base value repeated by 3s after .3... but the quantity of 3 after the decimal point is infinity.. so what i am trying to say is the quantity of halves of the distance is infinite which goes through an infinite sequence but its base value is always definite which is 10..
someone never taught this man acceleration or velocity. and yeah the distance seems infinite but in that way we are infinite beings (just a smaller infinity)
It's not a paradox, it just leaves out information to make the theory work.
Every step achilles takes crosses a minimal and maximal distance.
For the first part, achilles takes for example 10 steps before he is where he tortoise was. He then only needs two more steps. Hots thirteenth step passes the tortoisr and then it's of to the finish.
This paradox only works if achilles isn't taking steps but is instead sliding like a statue. But even then it still wouldn't be a paradox
It was a paradox at the time the concept was realized. Calculus hadn't been invented yet.
@@jakerittlinger440 His comment isn't based on calculus.
I feel like argument only works if it's a very short distance because it takes him a quicker and quicker time to get to the last point that the tortoise has moved until that time is unrecognizable and the tortoise is passed
Is this the paradox? I always thought the paradox was "if you always travel half the distance toward your destination, you will always be moving forward, but never reach that destination". The paradox being that you can move forward infinitely without ever reaching the destination no matter how close you may get.
Seems like your explanation may have been his humorous way of expressing the actual paradox.
Gojo Satoru