Achilles and the Tortoise - 60-Second Adventures in Thought (1/6)

[@joejames1794]

I can’t be the only Jujutsu Kaisen fan in these comments. Gojo Satoru techniques can be complicated.

[@richoleeplazo5755]

nah mate

[@swiftDKB]

Im reading that chapter right now lol

[@tylerchampion9356]

HAHAHAHAHA

[@gamec12]

I felt this comment XD

[@Vanziethel]

Didn't expect this to be the first comment, but it's why I'm here. Funnily enough, I had already heard of this, but I forgot that it was called achilles and the tortoise.

[@Insectist]

The manga called Jujutsu Kaisen brought me here! Cant wait to revisit this when the anime comes out!

[@sfwreaths1]

No

[@my0sca43]

goddamn im the same

[@demonio_fleur]

Yeah jujutsu kaisen brought me here too

[@jacobvilleneuve3934]

same

[@sbababaplua]

Omg it's not just me

[@stephanevermette145]

The Tortoise and Achilles is not a paradox when you realize you're only observing a diminishing slice of time at every pass. You're only comparing the distances within an ever-decreasing delta t until Achilles asymptotically reaches the tortoise. Assuming Achilles is running at a constant speed, if your time scale is constant, and not logarithmic like it is in the "paradox", Achilles will obviously pass the tortoise.

[@occamsrazor1285]

Bingo. It assumes a reduction in timeframe. Distance = speed x time. In order to maintain the timeframe (time a constant rather than a variable, as this story requires since it assumes time is the constant of infinite), it requires speed is reduced inversely to time. Put simply; the story requires you to attempt to place a non-real restriction on the real world. You end up flip-flopping between a state of "what if" and your mind "know" the real world doesn't work like this; essentially attempting to apply the rules of an abstract universe onto the framework of the real universe. This story is more a trick of language than it is a trick of maths. Forgive me if I misused any terminology, I'm not classically trained in maths.

[@jayanthiiyengar9251]

stephan, I don't think that is the point here. Achilles will obviously pass the tortoise but the paradox here is that even a finite thing can be infinite. take for example the numbers between 1 and 2. one would say they're only 2 numbers but , there can be an infinite number of number between 1 and 2 like 1.1, 1.2, 1.01, 1.001 etc.

[@stephanevermette145]

Yes, while it is understood that this can be used as the basis for teaching asymptotes and the like, great care must be taken in not saying specifically that Achilles will never pass the tortoise. Such a claim is false, unless the tortoise actually arrived at the finish line first.

[@Raphe9000]

i thought i was the only one who thought that the reason the paradox does not work is because it is being showed the wrong way. My thought train went almost exactly like urs. I also solve that hand 1 2 different ways but this is a comment from 1 month ago before i solved it the second way which is your hand flat, therefore you have half the distance so many time until the hands come in contact, therefore you can solve it by counting the bumps and free space so only the main part of the hand is considered the distance halved making it where the bumps will touch being counted as free space after so many halves (plus an infinity cycle cant be stopped or it wouldnt be callied infinity): "i just solved the the tortoise one and the hand one. THE HAND ONE ISN'T AN INFINITY CYCLE BECAUSE INFINITY IS GOING ON FOREVER AND U NEED TO KNOW YOU CANNOT TOUCH ANYTHING You Can't Touch Anything k so how did i solve the hand one you might be asking. after u half the distance so many times, you are at that barrier where you cannot continue to move your hand. u just halved the distance so many times to where you cannot move further. your hands not making cont act makes this possible. you can still half the distance because you are not touching your hand, but you cannot move your hand further. now with the tortoise one, EVERYONE SHOWS IT WRONG! IF HE IS 1 METER BEHIND THE TORTOISE HE CAN SPRINT ANOTHER 100 METERS! IF THE TORTOISE MOVES 10 METER IN THAT TIME LIKE IT DID AT THE BEGINNING OF THE RACE, HE JUST GOT AHEAD! SHOW IT IN A DIFFERENT WAY! I'M SURE HE ISN'T TOO TIRED TO SPRINT LESS THAN A METER IF U KEEP THE CYCLE GOING FOR A LONG TIME! THAT IS HOW HE WINS! also pls do not steal what i said and claim it as your own. you can always see my comment has the 1st date AND you can copy and paste this comment as long as you say I SOLVED IT(even though I bet I am not the 1st one to solve it, i thought of this my own)! as the video says, the hand paradox has been solved, but i solved it differently. now i am a great fan of Numberphile, and i wanna say this: You guys inspired me to solve it. I give credit of the video You Can't Touch Anything to Vsauce and am using it as proof." I'm happy someone has the inelegance to find this flaw with a giant circle around it saying look at me which doesn't need a high IQ to find out. JUST THINK OF IT IN A SIMPLE WAY PPL! ok i am done and thx for being another paradox impersonator catcher. wait i wanna say how i solved that paradox about a rock and god LOL! The paradox is that if god has infinity power, he can create a rock he cannot pick up, but if he has infinity power, he can pick up that rock. Proof it aint no paradox in ma book: You think of it as a no brainer (like i did after i solved it the more complicated way) and say "God doesn't need physics and we only think about things with physics but if god can do anything he can make a rock he cannot pick up then pick it up cus he don't need physics," or think of it as if god has infinity power, he can limit his power from all-none from a negative amount of years, to forever therefore only have a limit of strength or power, then create a rock he cannot pick up. once he got infinity power again, he could pick it up again, but there was a time when he couldn't, so i solved a paradox. but i don;t study these paradoxes in a lab or anything crazy, i tell my friends about them at school, them come up with a solution (insulting my intelligence cus i was thinking of how hard it was tho it was actually easier than pi yes the number pi).

[@stephanevermette145]

Your God-and-rock paradox is interesting. But for God (a spiritual being) to create a rock (a physical object) that he himself cannot pick up, he would have to manifest himself as a physical being and would thus be subject to the same physical laws as the rest of the universe which He has created.

[@MochaPhilanthropist]

If Gojou Satoru brought you Here Take this W

[@_rinnegan3]

W twin

[@itoldyouthat1049]

yep

[@samaraoliveira3400]

thanks

[@TheGr8one1022]

Grow up, loser.

[@jeff_shady3571]

Same

[@lexxx89]

so that’s how gojo satorou’s power works....

[@Mimi-mq2wj]

STOP IM DEAD THIS US WHY I AM HERE

[@SuperRONDALE]

The his is why I am here and I’m still a bit lost. But not as much. His power works the same way that haunted house works but for cursed energy instead of space, which is ridiculously broken

[@JustAGuy8541]

​@@SuperRONDALENow I see why people think he can Solo all of Shonen i mean he doesn't He loses

[@SuperRONDALE]

@@JustAGuy8541 He basically has the same (plot)power of Goku or Superman.

[@jasondobbins9735]

@@SuperRONDALE what haunted house are you talking about?

[@CertifiedZoony]

i guess when gojo said "its important to study more" it resonated with the entire comment section💀💀💀

[@willadams2937]

My favourite part is when suddenly time slows down only for Achilles.

[@boomynote]

Gojo satoru moment

[@Rivergirl2878]

Everyone asks, who will win? But the question we should be asking is, Where is the finish line?

[@Ajaxlancer]

***** ha. ha. ha.

[@Profalactics]

+RiverGirl Bloody Finns helpin g the Nazis in WW2

[@isak098]

+Profalactics More like Nazis helping the Finns.

[@Moon-sr7zd]

Does it matter tho? Theoretically wouldn’t the tortoise reach the finish line before Achilles does?

[@IXI-cy3nj]

but i thought the mitochondria was the powerhouse of the cell

[@MoxieAwesome]

The point of this paradox was not to make a mathematically sound assertion, nor to suggest that in our phenomenally experienced reality, the tortoise would actually beat Achilles. You have to comprehend the historical context. The purpose of this paradox is to 1.) support metaphysical claims of an unchanging arche made by Parmenides (Zeno's teacher), and 2.) demonstrate the difference between knowledge acquired through the senses, and knowledge derived from pure reason alone (the latter being the conclusion of this paradox). It is a parable meant to illustrate the metaphysical claim that an infinite imperishable substance provides the foundation and origin of the universe (a condition in which change, transition, or "movement" are merely phenomenal illusions rather than metaphysical truths).

[@metatron4890]

The problem is that Zeon's argument although apriori in nature is not sound and the mathematical objection is why Zeno was wrong. If change is indeed impossible, it is not going to be proven by pure reason alone since there is no logical incoherence from the very notion of change being a real feature of the world.

[@anthonypopescu5109]

I just don’t understand the rules of the paradox if you can elaborate. Why in the paradox is Achilles assumed to be as fast as the tortoise. We know in the real world, he would clear the tortoise. Why does the paradox acknowledge that by the time he has reached the tortoises initial position, Achilles was fast enough to shorten the gap but not completely cover it and catch up. It feels this paradox only works if achillies is .0000000001% faster than the tortoise. Sorry for all the questions but you seem to have a good grasp and I can’t find the answers I need to understand this anywhere else

[@supercat5meow864]

@@anthonypopescu5109i think its not practical in real life because obviously achilles would win but its basically saying that, from the headstart, tortoise travels from A to B. Achilles therefore travels the same distance, yet tortoise has gone to C whilst achilles was getting to B Now achilles has to get from B to C, but by the time he gets to C, tortoise would have travelled to D. And so on. The distance gets smaller each time but assuming that chain of thinking, achilles would technically never reach the tortoise, just get much and much closer. In real life, the tortoise would lose of course.

[@davidroddick91]

The issue with this "paradox" is that it assumes that the distance Achilles travels is a function of the distance between him and the tortoise, and not a separate value unto itself.

[@charlesthompson5645]

It’s why this is an infinite loop thought. Prob why they call Gojo ability infinity

[@Omeniser]

Precisely.

[@normalizekickingchildren5594]

Thanks. I thought this paradox was silly💀

[@sandyzamudio7574]

I'm here from the Jujustu Kaisen manga lol

[@chilldwill7179]

Im reading Jujutsu Kaisen right now and I'm trying to understand Gojo's technique. I understand it now.

[@raizel-cadis]

I don't pls help

[@zhangbill1194]

@@raizel-cadis There's nothing to understand, it's a stupid paradox based on baseless things. This paradox basically says is that archllies.will run closer and closer to the turtle until he eventually catches up. Which isn't a paradox at all, it's just facts.

[@samaraoliveira3400]

@@raizel-cadis so i read this in another video's comment once and i think its a good way to explain you know the sequence of numbers right? so, its 0, 1, 2 3, 4, 5... and it goes on in this sequence there is no number between 0 and 1, however you can also say that 0.5 is between it just as it is 0.05, 0.005, 0.00005... and like this you can say there is a infinite amount of numbers between 1 and 0, because you can never reach total zero if you just keep dividing them like that so gojo's ability just takes this infinite and turns it into a real thing so nothing can touch him

[@CDPRR]

Gojo's Infinity isn't always passive and he had to focus this on. To overcome the infinity, a battle with a dense domain(stronger or polished) will always hit their target, or a weapon imbued with cursed energy that nullified all cursed techniques.

[@l.lawliet2222]

His ability is passive

[@shalahudin_ayubi2252]

@@l.lawliet2222 before awakening gojo need to manually active his infinity

[@AldenRogers]

It's easy to have unsolvable problems if you don't include all of the variables.

[@TheBUDR]

Its not an unsolvable problem

[@hawks7111]

@@TheBUDR It's literally called the achilles *paradox*

[@MisterVercetti]

I think the fatal flaw of this experiment is that it doesn't take into account the fact that, as the time frame measured gets smaller and smaller, the difference in speed between the two means that, eventually, a point in time will occur in which the tortoise does not move, but Achilles does. This is the point in which Achilles officially passes the tortoise, at which point everything else is a moot point. In a way, this flaw ends up disproving the very concept Xeno was trying to demonstrate; there are things that can't be divided infinitely under certain circumstances.

[@MisterVercetti]

To clarify what I mean, let's use something with a definite point of measure; in this case, a video game. Let's suppose you've programmed the tortoise to move one pixel every two frames, and Achilles to move one pixel per frame. If you give the tortoise a head start, assuming a 60fps frame rate, the tortoise will have traveled 300 pixels during that time. When Achilles starts, it will take him only five seconds to cover that same distance, at which point the tortoise will have traveled another 150 pixels. Achilles travels that far in 2.5 seconds, during which the tortoise has traveled another 75. You keep dividing the time frame in half until eventually the time span you're dealing with is individual frames. So, let's say you have pixels 1-5. At the point we're about to discuss, Achilles occupies pixel 1, whereas the tortoise occupies pixel 2. Only Achilles moved the previous frame, so on our first hypothetical frame here, both Achilles and the tortoise move, meaning A now occupies pixel 2 and T occupies pixel 3. On the next frame, only A moves, so now they both occupy pixel 3. On the next frame, they both move again, meaning they both occupy pixel 4. On the next frame, A moves while T does not, meaning A occupies pixel 5 while T is still stuck on pixel 4. Achilles has now officially overtaken the tortoise.

[@johnwickv9852]

I actually understood your explanation and i think the speed difference between Achilles and the tortoise is so huge that even with the head start Achilles can catch up to it at one point and surpass it

[@SoapSou]

​3 years old but I just wanted to say this is one of the best explanations I've seen on this topic.

[@BB-pc8vc]

@@SoapSou it doesn't make any sense to me at all.

[@youngknowledgeseeker]

So Zeno is trying to show there is an infinity between their two locations while in motion, because in his mind the distance between where the Tortoise is and Achiles reaching it can be "infinitely" smaller and never reaching. However your saying, eventually, he will catch up to the spot because he's moving at a faster pace. This is really hard to think about lol, but it feels like it shouldn't be 💀.

[@lazynomad1356]

This paradox points to the fact that real physics time can not be divided infinitely. There must exist an undividable quant of time, in which Achilles would sort of teleport and catches up with the turtle.

[@Rhishisc]

Planks constant

[@lanchanoinguyen2914]

you guy had talked about my interesting subject.i also want to talk about planck length.if the time is divides by planck length,the time is not existing.Because the object can't move when its time line doesn't seamless,also meaning the object really static,and another version of it or some new universe which not connected with the old object will take it position,and the new people will don't know who are achilles and zeno.However,the new people might still behaving their thinking that every things are all moving by comparing with their memory.but the memory in here is absolutely not meaning the memories,it's just the place to contain some value.And then,the time doesn't exist,and achilles don't win the turtle,but "he" could in the front or the backward position to the turtle in some universe that we can't see.

[@rperalta071]

it just puts the race on replay.. nobody wins, but nobody loses either

[@PinkyPieVidz]

I've watched this multiple times to understand it.

[@frosty98-t9h]

Hey man are you alive ?

[@tesnaibs]

@@frosty98-t9h it's probably his 284th birthday

[@frosty98-t9h]

@@tesnaibs XD

[@technos_orphan_obliterator]

We all know you're here after either reading the manga or watching the latest episode of JJK. And yea, this is the paradox Gege Akutami based Gojo's powers on. He even got a mathematician to double check wether he crossed the boards or not(he didn't get alot of it right).

[@marcusqwj]

The way i try to understand is that when Archilles reaches the point where the tortoise was orginally at, they 'shrink', Archilles is far behind the tortoise again, and the cycle repeats infinitely. But this can't be a reality haha.

[@rperalta071]

It's a geometric technique

[@rperalta071]

I'm glad I'm not the only human fascinated by this type of stuff

[@rperalta071]

It's weird because your not really scaping or winning, you just access a fresh timer to repeat...

[@rperalta071]

Like you mentioned, it can't be reality, but i think more of a game changing tool...

[@DreamPen]

I never liked this paradox. If the insight here is how we can divide things infinitely, I'm cool with that. But literally- PRACTICALLY- speaking, it's nonsense. We don't move in fractions and proportions to anything, whether in a race or towards static objects. Our movement is not measured in divided portions. Rather, we move in increments: I don't traverse distances 50% by 50% over time but, say a kilometer per 12 minutes. Enough time passes and the kilometer runs out. Eventually- and realistically- Achilles does catch up and pass the tortoise. But at that point, it's because we realize that Achilles is actually moving more than a 100% of the tortoise's speed. Of course he's going to cover an even greater distance than the tortoise did in the entire race.

[@footballfan3991]

don't care virgin

[@cookiedough5055]

@@footballfan3991 please don't

[@xs3gfault]

To me, the easiest way to see through this paradox, is that to tortoise also takes time to gain distance. there has to be at least x amount of time for the tortoise to gain any distance. Once the amount of time that it takes Achilles to close the gap is less than that what the tortoise needs to gain distance, he will catch up and then pass.

[@rperalta071]

The whole thing is a loop. over and over... nobody wins or lose

[@compoundtings8490]

Ah yes, but you see, as these gaps become continually smaller, the man would have to slow down in order to never catch up with the turtle. If he maintained his current speed, it would have constantly divided the fractions like half and half until a whole was made, but in this instance the fractions are going half, quarter, eight, which means the human is running slower constantly as well, never-ending.How have I broken the paradox you may wonder? They call me Nightingale...

[@kushalreddy9830]

who is here after getting recommended by Gojo Sensei

[@brendanwoods7278]

This paradox always makes me infuriated; its one that sounds good on paper until you realize that in a physical plane, this is silly. Unless Achilles is letting the turtle always stay ahead, he would win the race.

[@nmim4994]

nO he wouldn't.

[@Morfe02]

Unless Achilles Is tired of the first distance

[@thedancinggymnast]

It is possible for the tortoise to win, but only over a finite distance with a large enough head start. As soon as the distance is infinite there is sufficient time for Achilles to pass, even if he is only travelling a fraction faster than the tortoise.

[@rperalta071]

Is not about winning or losing.. it's a endless loop

[@raider360X_sot]

The problem is that it simply isn't an infinite loop. Eventually the value you're dividing (the amount of time the tortoise has to move before Achilles catches up) becomes so small that the tortoise simply won't be able to move enough to outrun Achilles, who will overtake him and win the race.

[@mesbahessa8745]

the paradox is only possible if both the turtle and Achillies move at a constant speed

[@eddyvideostar]

Mesbah: *Thank you.* This is wise, logical and true.

[@mrhoustonn]

No, it isn't. Velocity or acceleration make no diffence in the scenario, it's sad the number of upvotes this comment got, people are so lazy to think. Achilles passes the tortoise because spacetime is quantized; have a minimum "block" that can't be divided anymore, possibly plank's lenth and time. Proving movement is actually a series of "teleportations" between one "block" of spacetime to another.

[@trevorallen3212]

That logic is very absurd, yet even if this was true when will the final sequence end?

[@tesnaibs]

no it doesn't matter

[@Gojo-jg2zs]

"Welcome to infinity" - Gojo Satoru

[@gerbertela]

I came across this after reading Borges' short story entitled, "The Lottery". The concept of time being endlessly divisible and subdivisible got stuck in my head for days, and it still is.

[@jashshah200]

Zeno- at's a clever guy who put everyone into thinking. I actually came across this on reading mention of the tortoise paradox in a book. Of course, reality and inherent representations of an object are two polar concepts; but it was witty to think of such a 'paradox'. And of course, as Georg Cantor points out; Some Infinities Are Bigger Than Other Infinities. ❤

[@afroslacker7383]

Gojou: “Read a book” Me:

[@gajendrabora]

Just because you are incrementing time by delta it does not mean you are following the race for a longer time. In this case each time delta T will decrease by geometric progression and no matter how many times you calculate total time will always be bounded by a limit. like if you add 1 + 1/2 + 1/4..... infinity it will always be lesser than or equal to 2. In this way total race time calculated by above logic will always be bounded by the time till tortoise is in lead (like 1+1/2+1/4... is bounded by 2).

[@snoopster77]

This is the answer folks. Nothing to do with differing speeds.

[@KaneinEncanto]

Missing component, each decreasing segment of distance also represents a reduced timeframe during which the distances are covered. At some point the paradox would bump up against Plank Length for either physical length, or minimum length of time.

[@douglasphillips5870]

Zemo is looking at the question wrong for determining a winner. You need to compare the relative speeds plus the head start to the length of the race. By leaving these details out Zeno limits the ability to examine the question fully, so he can force the answer he wants. It's more about deception than reason.

[@DiscoticUK]

+Douglas Phillips Anyone else read that in Scruffy's voice?

[@kzv5468]

Lmao literally everyone is here cause of Gojo! Well glad that we're all idiots and not just me lol

[@HugaHoodie95]

The paradox is that you can split a finite number into an infinite amount of points. e.g Achilles is running round a race track of length 400m. But as you know, before he passes the 400m mark, he must pass the 200m mark; before he passes the 200m mark he must pass the 100m mark, and before this the 50m mark, 25m mark and so on. it gets to the point where before the 1/10000 mark he must pass the 1/20000 mark and as there is no maximum limit for the denominator, this continues ad infinitum

[@GroovingPict]

Narrated by David Mitchell?

[@MrKohlenstoff]

It appears so. Or somebody with the exactly same voice.

[@GroovingPict]

MrKohlenstoff so either David Mitchell or Rob Brydon doing his impression of him then ;)

[@davidseaton4351]

that's what i was thinking!!

[@wtfduud]

Being a mathematician must have been so easy before the invention of calculus.

[@YesNO-bn3pq]

0:42 This gap became shorter than Achilles’s STRIDE this is not a paradox It’s a crazy idea

[@TamySmart]

You have many other factors to consider such as speed and ones velocity. If Achilles happens to be moving at say 100 meters a second, while the tortoise only travels 2 meters an hour(two different time units) Achilles velocity and acceleration would be greater to that of the tortoise, and eventually upon catching up, he will be able to travel farther than the tortoise. And even if they happened to somehow have the same speed although unlikely, this does not disprove an objects motion. Considering our earth is rotating around its axis, and revolving around the sun, and the sun is floating about in the Milky Way, which is going about through our galaxy which is constantly changing, motion is indeed possible and occurs every second of everyday! So no, I do not consider this a paradox.

[@laurachagam1460]

LOLOL omg Tamar. ily.

[@sumantpottepalem8729]

But they said the paradox was false. Also the Earth rotating and the Milky Way have nothing to do with the distance.

[@TamySmart]

Sumant Daequan Dwyane James Jones III I know it does not involve distance, but it involves motion.

[@arhalts]

(acceleration need not be examined for this (nor would it always be greater than the tortoise ) 1. Zeno knew that motion happened. 2 Zeno believed his reasoning that you could divide space into an infinite number of sub intervals was correct. ( he was infarct correct here) . Due to the fact that he did not have the tools to address how infinite series behave, and that is part of where this solved paradox originates from. Zeno incorrectly assumed that an infinite series of numbers added together must be infinite eg 1+1/2+1/4+1/8+....+1/2n+1/n = infinite when in fact Taylors series show that 1+1/2+1/4+1/8+....+1/2n+1/n = 2 This is where the majority of the paradox originates from. The second part is improperly dealing with the time domain. As the distance halves so does the time it takes to cross that distance at any velocity. resulting in a similar Taylor series for the time it takes to catch up to the tortoise. You can't really blame Zeno for not knowing how to deal with infinite series, inf act it would be centuries until anyone could. Nor was Zeno an idiot. He knew things could move and pass each other, That is why it was a paradox, but in reality a better understanding of reality was able to address this problem. ( think about that when you think of other paradoxes) Also you point out the motions of the cosmos. Zeno lived in a time that predates physics as we know it (at the time they believed heavier objects fall faster and the world was made fire , rock, water and air. and that the sun was the center of the universe, give the man a break his paradox was actually a useful for helping people understand that not all infinites are equal.

[@sumantpottepalem8729]

^^^ Swag

[@artuigi1241]

No one's mentioning its in Jojo too with the Green Baby's Stand in part 6

[@WilliamLetzkus]

Excellent site for learning about paradox!!! Dr. Why

[@eidolonvector4844]

I've seen this mentioned a few places and I won't ever understand it. For this to make sense, Achilles would have to stop at each point, giving the tortoise continual head starts. No one seems to mention the subsequent head starts though. Only the original.

[@MarkSamurai5]

+eidolon vector I think the fable, "The Tortoise and the Hare" by Aesop would explain it.

[@mohammadsultan639]

No he doesn't need to wait because whilst achilles is catching up to him, he's using that to get another headstart. By the time he catches up to that headstart, the tortoise will have moved a bit further thus giving him another headstart and so on.

[@mtubeme]

the problem with this as stated is that there is no limitation put on achilles. so if he is indeed moving at a consistent speed and that speed is faster than the tortoise's speed then he will overtake the tortoise at some point. yes, there is a race that the tortoise would win, depending on their speeds. the length of that race is the longest race the tortoise can win. in the next moment achilles catches, and then passes, the tortoise.

[@ludovert]

The distance of one is not in relation to the distance of the other... after 10 seconds, the tortoise has taken 10 steps. In 1 step, Achilles moves the equivalent of 2.5 tortoise steps. this means that after 15 seconds, the tortoise is at 15 steps and Achilles at 25 tortoise steps. This also means that the meeting point between both contestants is precisely calculatable...

[@wolfson109]

The calculation for the time taken for Achilles to catch up to the turtle is an infinite sum. However, since each term in the infinite sum describes the function over an period of time which is decreasing as n/2 (where n is the number of the term) and since we are measuring time with a clock (which must have an associated statistical error), we define the mth term such that the time described by all subsequent terms is less than the error in the clock allowing us to truncate the series.

[@VOLKHVORONOVICH]

This was recognized as a false paradox a long time ago. It seems to make sense: Achilles travels 1000 feet, the tortoise travels 100; Achilles travels 100 feet, the tortoise travels 10; Achilles travels 10 feet, the tortoise travels 1; Achilles travels 1 foot, the tortoise travels 1/10 of a foot. But this would only work if Achilles and the tortoise would shrink in size, keeping the same proportions relative to each other. Then it would be impossible for Achilles ever to catch up because the relative distance between the two of them would be continually increasing. Achilles feet always remain the same size, however. You can imagine that by the time the tortoise has covered 1/100 of a foot, Achilles, who has just traveled 1/10 of a foot would pass the tortoise. The numbers might be steadily decreasing, but Achilles' feet do not. This is the flaw of confusing ideal, abstract mathematics with the functioning of the real physical world.

[@sciguy1893]

All you need is a brain to understand that achilles would eventually surpass the turtle quite quickly. I find it weird that a learned man would confuse abstract maths with testable physics in the real world, that you can test with just your eyes even.

[@sciguy1893]

To me the most logical model of thinking is observing reality and creating a testable hypothesis on it and creating your maths around it. Not creating your reality with your maths.

[@VOLKHVORONOVICH]

YES! I figured out the same thing myself. The flaw in the paradox is that it presents physical reality as a mathematical abstraction. You can keep on reducing the size infinitely, the proportions would always remain the same. But the physical dimensions of Achilles and the tortoise remain the same.

[@thedancinggymnast]

@@sciguy1893 exactly. If this was true, no predator would ever catch its prey. Babies would be infinitely crawling away from their parents, frantically running after them etc. Lol

[@man-batiszkokabatsow4153]

Now imagine tortois racing certain Green Baby

[@Glatier]

That's exactly what I was thinking when I learnt about Limitless lmao

[@fredericgourdeau4583]

Excellent and short. Thanks!

[@MySerpentine]

This sort of thing is why I don't trust math to properly reflect reality.

[@Mrjrmagician]

Time slows down for this to be possible, Achilles closeness to the turtle is always going up while time is always slowing down.

[@RohithBasu]

this is kinda like a speed of light approach but never catch up with light type of paradox

[@arvd227]

WHOS HERE AFTER S2E2?

[@anasarkawi4331]

My mind is blown up

[@faisalalialazmy9920]

Wow me too

[@danthemango]

thanks for the link in the description!

[@SanaOvaisKhan]

just because a pie is cut into a million pieces, doesnt mean it takes longer to eat, or that it can never fully be eaten.

[@EtaiOren]

This paradox presumes that they are going at a certain speed. otherwise explain how can one car can be overrun by another car on a flat, straight road, given that they are going the same direction on the same road?

[@mookerz1383]

Thinking of it in this way debunks the idea of it being a paradox, as there is a span of time when the slower moving object is not changing position, while within that span of time the faster moving object is changing position, thus Achilles eventually overtaking the Tortoise.

[@mehcaca]

While that's true, this is still not a paradox. All they're doing is making each subsequent increment of time smaller and smaller, and knowing the nature of numbers, you could continue to cut each increment in half forever. But in reality, time flows in equal increments, so this isn't a paradoxical dilemma.

[@KhanggiTanka]

Just one word to explain it: Philosophy

[@alextroch]

this is like a riddle I've heard " if a frog starts out 2 feet from a wall and hops half the distance of where it was to the wall, how many hops will it take for him to reach the wall" the answer is clearly that he will never reach the wall and his hops will get infinitely smaller

[@propstoyomother]

This Video is true if and only if Achilles slows down each time he reaches the tortoise's new destination.

[@mookerz1383]

I like to think of it this way. Consider Achilles and the Tortoise as points, but not just any points, their placement along the racetrack being represented by the point on their body closest to the finish line. Imagine a very slow runner instead of a tortoise. When its right foot is extended, the tip of its right foot is the closest to the finish line, but when its right foot is planted and its left foot is moving forward, there is a period of time where its position isn't changing.

[@kingkrazy0wns]

The Achilles and the tortoise paradox is not a literal problem to be solved. Rather, it is a thought experiment. If we apply modern physics as you suggested, then yes, the solution is quite obvious - Achilles beats the tortoise in the race. Zeno and the other Greek philosophers knew this as well, but they approached the problem from a different, metaphysical angle in order to provoke discussion and create a seemingly logical paradox.

[@suerhea4400]

I know what the paradox means but if achillies is faster or accelerating at a faster pace wouldnt he just surpass the tortoise?

[@ndbass09]

I like this. It makes you THINK.

[@rperalta071]

Its similar to cutting your entire mass in half, repeat as many times as needed, just to gain distance from a near by or invading object... but his technique cuts or expand time and space... is interesting

[@TheSterlingArcher16]

The example is suggesting that Achilles would be covering shorter and and shorter distances while catching up to the hair, meaning Achilles would be running slower and slower as he approached the tortoise. In actuality Achilles wouldn't be slowing down to cover the tortoises distance, making this not a paradox

[@tesnaibs]

it's not about slowing down because the time delta and the moving distance of both achilles and the turtle is getting divided by the same amount, which makes it the same velocity

[@tesnaibs]

says 12-year-old

[@tesnaibs]

it'd be cool if you reply to this

[@TheSterlingArcher16]

@@tesnaibsI don’t recall this comment but intuitively for any time period where the tortoise advances, Achilles advances a greater distance. Doesn’t seem like much of a paradox.

[@tesnaibs]

@@TheSterlingArcher16 U replied 💀💀💀

[@WDeeGee1]

This just shows that human logic is too small a box to fully grasp reality.

[@Aristocles22]

The lesson is that you cannot keep dividing time and space into ever-smaller pieces. Eventually, something must give.

[@Xzalander]

@Rexorsist See Top Comment #1. Zeno's Theory was ignoring the factor of time. Hence the video mentions that while the original purpose of it was kind of nonsense (Achilles can never pass the tortoise -until- the moment at which Achilles passes the tortoise.) and merely states something is behind until it overtakes, it did give birth to dividing finites by infinites.

[@chriscrumly]

Is this why however much my running slows down to tortoise pace - that Achilles pain is always there and just won't pass?!

[@Aislinsweetdreams]

What stops achilles from running faster?

[@freeflaminginfinite917]

Surely this is only possible if you were to assume that both of their speeds were equal, meaning that Achilles would never catch up (One damn speedy tortoise). If his speed was even 1/1000000 faster than that of the tortoise he would eventually pass it, given that the finish line is far enough away.

[@m4173_]

@mtubeme Nice explanation, got it now :-) But why didn't Zeno take this into consideration?

[@MitrasMeditation]

When people try to solve the question with comon mathematical solutions, they only show that they didnt understand the Question. Its a quantum problem, not solveble with common math.

[@ozgurtufekci6837]

The gap between them will be smaller and smaller. (gap/2,gap/4,gap/8,gap/16 .... gap/2^n) Achilles catches the turtle when that gap becomes less than the width of Achilles

[@nmmeswey3584]

Ozgur Tufekci No, because "acheles" is where the tip of his foot is

[@themaddoofer2417]

Roque Moreno pretty sure acheles is at the back of the foot, not the tip

[@magnxs]

if the turtle starts 10 meters in front of achilles and he runs 10 times faster, he will catch up with him super fast this doesnt make any sense

[@kartikwaghmare2867]

More 60 second Adventures!!!!!!!

[@kal1589]

JJK chapter 69 page 14. Someone told me that studying was important

[@ardashk]

Here's a simple explanation: The way the paradox is described is not how the race actually happens. It's how you look at it. It's as if you're watching it in slow motion, and slowing it further and further so that the actual time at which Achilles passes the tortoise, takes infinite steps to reach. It's wrong to say "Achilles will NEVER pass the tortoise", when you are not allowing time to flow normally. More details: clickexist-dot-com/2013/05/25/achilles-tortoise-paradox/

[@sulitjc5yearsago421]

this is what it feels like to catch up with your friend when your running

[@MartinFaulks]

This is great!

[@Im_crybilon]

Came here from D.I.C.E. The Cube that Changes Everything!

[@jmanjumpman]

I don't think this paradox properly accounts for velocity and acceleration. Or am I looking at it wrong?

[@christinecarpediem1512]

infinity means inability of measurement.. eg between 1 and 2 are infinite numbers but it still occupies certain space on a diagram

[@vaibhavsrivastva1253]

This paradox was mentioned in the Class XI (Eleventh Standard/Grade/Year) Physics textbook of the CBSE (Central Board of Secondary Education), published by the NCERT (National Council for Educational Reasearch and Training).

[@johntrex1742]

Exactly how far would the turtle be from Achilles for a head-start?

[@Im_crybilon]

It doesn't matter, really.

[@mehcaca]

What if the tortoise stood still? By the time Achilles is an inch from the tortoise, the tortoise is still in its spot. By the time Achilles is one billionths of a micrometer from the tortoise, it's still in the same spot. If I change time and speed, I can make the distance between Achilles and the tortoise infinitesimally small, regardless of whether the tortoise is moving or not. The tortoise has effectively become the finish line for Achilles. See my point? This ain't no paradox.

[@vroom28]

is this david mitchell?

[@sunshineforyou90]

Yes. Yes it is

[@johnnye87]

An infinite number of points which rapidly tend towards being infinitely close together. Infinity divided by infinity.

[@TipsyTulia]

It is based on the assumption that Achilles runs to get to where the tortoise was when he started running. It does not contemplate that Aquilles does not run to catch up, but to pass the tortoise.

[@CosmoShidan]

Interestingly, Zeno's paradoxes would later influence Lucippus and Democritus to formulate the prototype of the atomic theory, unless you count Kanada as being the first atomist by 100 years before the former.

[@Fl4dd3rm0uz]

if both always move at equal speed...?

[@5minshandcraft123]

This is actually Convergent Time series..... If you sum up the time up till it approaches infinity. You get the exact time where Achilles does pass the tortoise......

[@StillTryingMyBest]

I'd like to challenge that by saying the tortoise only needs an infinitesimal amount of time to gain distance. He is constantly gaining distance and so the time it takes for Achillies to close the gap will always allow the tortoise to have moved even barely.

[@jaykay3512]

I haven't read the manga but I'm guessing Gogo and Geto are not just strong but have extremely high IQ's to understand the depth of their curse powers.

[@GimmethatChimy]

This is a great animation :)

[@user-mn3tr7zr3p]

If the tortoise bites his heel, the tortoise would definitely win 😏

[@StillTryingMyBest]

The speed they are moving would not affect it in any way. Try watching again:D

[@sayanbhadra2371]

Someone told me to study more, that's why I'm here

[@avu2888]

If the gap is getting smaller, that means that Achilles is running faster than the tortoise is walking. Which mean that if given enough time, Achilles will eventually bypass the tortoise... no?

[@ewilliams685]

The root of this problem isn't the speed but rather the distance. If Achilles can only cover thr distance the tortoise last covered, he'd always lose as he'd never catch him. It isn't depicting an actual race. What it is saying in theory is that the distance between two objects in both infinite and finite as you can infinitely divide the distance from point A and B. But yes in real life the logic wouldn't work.

[@avu2888]

@@ewilliams685 my brain hurt from that but it made it make sense, thanks for explaining :)