What is Zeno's Dichotomy Paradox? - Colm Kelleher
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- Опубликовано: 6 июн 2024
- View full lesson: ed.ted.com/lessons/what-is-zen...
Can you ever travel from one place to another? Ancient Greek philosopher Zeno of Elea gave a convincing argument that all motion is impossible - but where's the flaw in his logic? Colm Kelleher illustrates how to resolve Zeno's Dichotomy Paradox.
Lesson by Colm Kelleher, animation by Buzzco Associates, inc.
This dude got tired of thinking so he decided to go for a walk and ended up thinking even more
Relate
Hahhaaaahaa
*THAT'S CALLED ANXIETY*
...and it's infinite,
...but still we can overcome it
@@cibo889 r/ihadastroke ?
😂😂😂😂😂😂😂😂
Late for a meeting:
Boss: "Why are you late?"
Me: "Let me tell you about a little something called Zenos paradox..."
@Mr. Gang Banger because he doesn't know about the paradox
that way, you would've never reached
So zeno was an useless man who used to day dream like me ,the difference being his thoughts were inspirations for others and mine are jokes 😭
😂😂😂
LMAO😂😂😂😂😂😂😂😂😂😂😂
Square: I'm gonna end this man's whole career
Square actually helped to get a finite answer
@@muhammadaizaz6194 that's what he said
At the 6 month of the comment, it has 666 likes 😫
As long as we always ignore the tiny piece of remaining white.
@@slobodanreka1088
Bah!
Not happening...it's dovled now...
Bcuz they screw the square up😂😂🤣
I'm afraid of this topic. I guess I have Zeno-phobia...
I see what you did up there.
ahhh hahahahahahahahhahaha
Ba dum tss 🥁
Zenophobia is fear of god
@@yashchoudhary3529 I believe Xenophobia is: fear of outsiders
i.e. fear of foreigners, aliens, also perhaps gods, etc
Dad: son I’m going to the store
Me: okay when will you be back
Dad: *infinity*
swagxd same
Bruh this is too dark
DARK WTF
😐
@@gohorarsen5938 it makes me think that the dad go to the store and never return....
I think Zeno really came up with this as an excuse for being late. Good job Zeno.
😂😂😂😂😂😂😂
I resident that!
This might be an excuse to be absent.
3D = 1D X 1D X 1D
Can you visualize 1D as a physical reality?
Thus, is the concept of 3D real?
Tim Countis It really could’ve happend just like that and we don’t know
Since he never arrives, infinity is correct. Infinity means never.
Thanks so much for explaining this paradox in a way that I can finally fully understand it. The animation is also pretty good.
Zeno certainly had a lot of time on his hands - to think. Lucky chap.
Actual excerpt of the "Supertask" Wikipedia page: "Most subsequent philosophers reject Zeno's bold conclusion in favor of common sense."
Legend says that Zeno is still traversing to the park.
He is dead
Gave me chills!
@@legitimate8463 no u x2
😂😂😂😂
Still walking...
Zeno sure likes to make his life harder
The funny thing is that he was on was way to clear hi mind.
+Jalal Gibson meow
+Katja Thesaurus ?
Xynic 😂 😂 😂 😂
Increased difficulty forges a better player
You can either find a good wife at your young age, or you can either become a philosopher.
- A philosopher
Ahhh, and thats Elemementry Watson...💡
Or become a rockstar and bang as many 10's per day as you want until that gets old and then find a good wife at an older age
-A rockstar
Socrates
@@shraman224 NOOOO, you don't say?????
Another relevant saying. Those who can, do. Those who cannot do, teach.
Motion does not somehow become a "paradox" simply because of some trivial unrelated, irrelevant mental exercise
There is no paradox
Im here trying to understand Gojo Saturo's ability Limitless.
Lol same
Same😂😂
same lmao jjk nerd squad
Lmao! I had the exact same thought!
Yes
In other more convincing words: The fact that the distance to the park can be divided in infinite parts , does not turn said distance itself in infinite.
Physical impossibilities. It's like dividing 2 by itself and dividing that by 2, repeatedly, forever. It will never get to 0 exactly, mathematically. However, physical limits do cause states. Eventually you are so close to 0, that 0 becomes true, but only in the physical sense.
The paradox was a distance/ time question not a part/distance question . So yes... but no: >
true but it's playing with the idea of infinity.
it's an infinite division of time
Infinity divisions = infinity = infinite time
THANK YOU that's so much simpler.
That's like between any two number there are infinitely many numbers,
Say between 3 and 4, there are infinitely many real numbers....
When Diogenes heard a similar argument, he just walked away, proving that motion is possible.
Makson #00
According to Zeno's theory motion is actually possible and even progressive(depends on how u define progressive) however, it's the "reaching the destination" part with motion that is impossible.
(basically: Diogenes could walk away, but he'd be walking away for all eternity)
He was down to earth what can you say
What a badass
@@wolfblades90 You really are primal aren't you ?
Zeno's paradox is a famous paradox in Greek history and mathematics. The Achilles and tortoise race is one of the 8 most famous Zeno paradoxes. Famous for the Greeks failing to explain this paradox. Although now impressed not too difficult, but it took thousands of years before mathematicians can explain it.
when math seems more like meth
@@OHYS Wait, wtf.
@@OHYS Have u tried one?
We are in the Father, and the Father is in us. We are in the universe, and the universe is in us. God goes with us wherever we go, because we live and move in him. Our minds are part of God's mind, which makes us very holy. We are the light of the world (Jesus said so), and FORGIVENESS is our function as the light of the world. Love holds no grievances, so naturally, FORGIVENESS is the key to happiness ♥
@@bullpuppy7455 i don't believe in your jesus
Edit : this Christianary missionary IT cell guy lost in debate with me. Hence proved his God is fake.❤
@@Desi.Superman I don't believe you:)
Zeno: the world's first practitioner of Troll Physics.
Treblaine JAJAJAJ siii
😂 lol
but he opened a fundamental question of the universe, what is the smallest unit of distance in this world? what if a Planck's length is divided by 2 indefinitely...
If he moved at a constant speed then 1mph will be exactly one hour but if he were to stop every time he reaches the half way mark he will never make it.
Zeno had way too much time on his hands.
That was incredibly brilliant
+RFE Zeno was a lonely man that had no wife. . .
+RFE and space too...lol
+Antoine Rashad How do you know he was lonely? We basically know nothing of him.
+RFE Are you Karl Pilkington?
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
As I went to leave for errands, my spouse asked me, “How long will you be gone?” I replied, “The entire time.”
A group of mathematicians walk into a bar, the bartender asks, "what can I get you guys?"
The first mathematician replies, "I'll have a beer."
The second mathematician replies, "I'll have a half of a beer."
The third replies, "I'll have a fourth of a beer."
The fourth replies, "I'll have an eighth of a beer."
And so on...
The bartender returns with two beers.
Outraged, one mathematician demands to the bartender, "how do you expect us to all get drunk off of two beers!"
The bartender replies, "you guys should really know your limits!"
Special EDy, excellent 👍🏼
CyberKant both imply "from", though "upon" may be a more formal option. "Drunk from" and "drunk off of" sound like there is a subtraction of the alcohol, while "drunk upon" or "drunk on" suggest an addition of alcohol. You could even drop the redundant "of" and just say "drunk off"
I'm from Texas and hardly speak proper English in most circumstances, somehow "off of" seems more proper if less formal in this instance. Either way, we'll understand them. I think it's very true that Americans adore foreign accents, and we usually appreciate the variety that people can bring to the language. It won't sound wrong, it will just sound trendy.
I love puns😂
I'm dum. Plz explain
Armando Martinez
Half a beer, quarter of a beer, and so on added til infinity gives 1 beer. This, plus the first mathematician's 1 beer makes 2 beers.
this is a good excuse for being late to a math class
Uses math to get out of math class?
Awww yeah
+Webb Surfer LOL
+Webb Surfer
Not really. You would have to know the universe is not finite.
+ThinkTank255
It's both finite and infinite, but that's besides the point. Don't be so serious and have a merry Christmas!
+Webb Surfer "It's both finite and infinite..." Well, that's just nonsense. Happy New Year!
I remember this same idea occurring to me when I was about 10 years old (51 years ago). If I walk towards my bedroom wall at an ever decreasing speed I could keep moving for eternity but never reach the wall. My friends didn't think this idea was interesting but it blow my little mind at the time. Maybe I should have majored in math.
What a strange way to explain this problem.
The problem: "I have one mile that I subdivide infinitely many times". Explanation: "Take a square and subdivide it infinitely many times". xD
You still have a square. Lol
@@bern9642 The same way you will still have a mile, after infinitely dividing it :)
@@dhruv3726 yeah nothing changes. Regardless of how you divide it, it's still a mile.
Yeah, it added complexity without actually explaining anything. Maybe it helps spatial thinkers to add a dimension?
Exactly, they didn't explain anything! Still the square is a sum of infinity of half squares. So why the sum of infinity is 1 square meter??
Zeno'x paradox is pirate downloading a movie, but downloading stops at 99%...LOL
The accuracy of this statement 🤣🤣🤣🤣🤣🤣
DC++ was (is?) a downloading program where one could use the incomplete files...after all, how should the program (VLC Media Player) know what is complete and what is not?...:)
Finally someone with a common sense.
Ow cant believe you just summed up like that and it works
No. It really isn't.
That is great Colm, I am really impressed by the quality. Hope you are well!
3:31 "The entire square becomes covered with blue."
Nope, there will always be a tiny piece of white.
Exactly. Maybe visibly, but if you're only ever covering half of the remainder, you will never completely cover the square.
It will get completely covered up once you reach infinity. That is what calculus is based off of.
@@garrettcasey1452 no,if you zoom in more,there will be white portions
@@masakatvpacific but when it comes to a size of atom, won't the atom be split into half??
@@usmanabdullah6551we believe that when a substance is at the size of a quark, it can not be divided and it's the building block of everything, so it's not made up of anything
Walk a little faster Zeno.
But he will get there in just one hour.
Or just run
ONE MILE PER HOUR
Are 3D objects real?
Is the physical existence of a 1D or 2D object logical?
Given that both 1D and 2D concepts are not reasonably possible, are 3D calculations real?
I've talked a lot about this with my friends. We've concluded that the point was to show that logic is not rational on its own. The premise matters, thus, logic is dependent. You can use Logic to prove illogical things as Zeno points out.
Did they teach you calculus at school?
@@generalginger7804 Did they teach it? Yes, but are you meaning to ask me if I attended the class?
@@platoniczombie From where I am from, you have to attend all classes taught in scholl.
@@platoniczombie So yeah.
But he didnt prove an illogical thing, thats the whole point.
The sum doesnt equal infinity as he tried to argue.
i actually admire how he created a problem from nothing ... really , i felt distracted from common sense into the complex world of maths that i neglected the logical answer :/ this is more psychology than math and i still admire it
Great educators and animators , and great narrators to .
"How can mirrors be real if our eyes aren't real?" - Zeno
Zeno was Jaden Smith confirmed
Was Zeno trying to figure out the physics of optics or something?
But eyes are real ...rihht?
@@harshchauhan9746 Have you ever seen your own eyes?
MinishMoosen never see something doesnt mean it doesnt exist, if you want to prove your eyes are real, then touch it.. if it hurts then it’s real.
Something finite, can be divided into an infinite number of pieces. That in itself is pretty mind bending.
cannot be done with physical objects
This actually made a lot of sense to me because all of the halves are part of the whole, which we already know. Basically, Zeno had the answer the whole time.
This really shows how interesting math, understood as a language, is
let x = 1/2 + 1/4 + 1/8.....
Multiply the equation by 2
2x = 1 + 1/2 + 1/4 + 1/8 .....
2x = 1 + (1/2 + 1/4 + 1/8....)
2x = 1 + x [ because x = (1/2 + 1/4 + 1/8....) ]
2x - x = 1
x = 1
Hence total distance travelled = 1 miles
:)
Nice one.
Arya Ajgaonkar Well done!
Arya Ajgaonkar But doesn't this already assume that x = 1 from the beginning?
No.. We do not have the end sum of 1/2,1/4,1/8..... Etc. We are labelling it as x.
Arya Ajgaonkar sorry, it was the *1 +" part that made be confused.
1:52 gawDAMN some one hasn't been skipping leg day
John Doe lol😂
Dat Thigh.
THICC
😂😂😂😂
Thicccccccccccc
3:55, Yes, That's the stuff Zeno smoked before coming up with this Paradox.
I do this in the gym on the treadmill, splitting my workout time into several halves. Wow I didn't know zeno already thought way. Thanks Ted ed for making my day!
In comes quantum mechanics, where Zeno has already arrived at the park, while he's still at home too, depending on the observer. :P
@@_TG Hhahahahah
And Zeno is dead and alive at the same time
Schrodi
@@_TG I don't understand this reference, can you please explain it to me😌...
Schrodinger's cat. Google it.
I put a cat in a box and close the lid. I walk away and come back in a few minutes. When I return, I can say that the cat is indeed inside and not inside the box at the same time because it is both in an not in the box, the lid is on and therefore you dont really know and cant prove one way or the other if the cat is in the box or not In the box without looking so therefore it's both. It's called schrodinger's cat theory.
The real explanation is that any finite measurement can be divided infinitely into arbitrarily smaller parts, but the finite amount is still the same. Zeno chose to divide his journey into infinite halves while most ppl choose to use finite measurements.
This.
Well said that. It is all about the matter of perspective!
Yeah, Zeno stars without "1" mile as the total set/ identity of the "x" he has to traverse. And starting from zero he begins to add particulars to see if the total is simply the sum of its parts. He finds that you cannot ever reach the place. If you begin from the set equaling 1 mile then you may begin to add the necessary amount of discrete units that would add up to this already defined set. But Newton stumbled upon Zeno´s paradox again, and noticed that the best solution was to get infinitely close to the limit, but never reaching it. Zeno´s paradox is similar to the Greek paradox of identity, and the grains of sand. It is a paradox that shows, in a sense, that uniform motion never ends. That things in motion remain in motion.
maths before:
2+5=7
Maths now:
John has 3 apples , the wind is moving at 14m/ph now find the mass of the sun.
Okay reasonable but I'm pretty sure I haven't heard a thing times 10 to 50 kg 😂
That would be physics actually
But when do the two trains pass each other?
A must for every student to realize how important the geometric series is.
Fun Fact: The park Zeno was trying to reach is the same park where the apple fell on Newtons head. Had Zeno actually made it to the park and eaten the apple, Newton would never have invented gravity.
That's the stupidest and funniest thing I have ever read xD
+antreas antrikos please do not mock him teach him instead he is here to learn, BTW sir +jay pee gravity was not invented it was discovered since it already existed before
+MrKrinkelz No, Newton invented gravity during the early Renaissance. Read your history. That information was downloaded on to ancient tablets.
+jay pee
Seriously, you are the dumbest asshat I have ever seen or the greatest troll.
+Gold Logic evident troll. Poor fellow had to make it obvious - the ancient tablets part.
It's great to sit in the park after a wonderful conclusion!!
There was no error in the logic. The clear take away is that any section of time can last forever. Consider this : What if Zeno's mind could perceive each consecutive segment of time in the scenario as equals. Then Zeno will live forever between two time stamps.
Mmm. 4 minutes and 11 seconds of my finite lifetime spent for someone to tell me an hour long journey takes an hour. Great😵
Yep that's the math for you
You are probably still watching this according to zeno's paradox.
@Alonzo Tovanche A true classic. You should have more likes for that.
But what if it takes half the time to cover half the distance and half the time to cover half of that and so on and so forth, how much time would it take then?
This stuff is about limits in calculus. Very important stuff for weapons and such.
This is a good example of where math and physics diverge into different realms of thought. Physics is a strict representation of reality whereas math is free to theorize into to the abstract.
If you take a number and divide it by half, you can continue to do so an infinite amount of times. But if you take an actual rock and break it into halves over and over again, eventually you will have to stop at the singular atom. The same principle can be applied to physical distances such as the paradox in this video. On earth, there is a finite amount of anything you measure so it doesn't make sense to think about these kinds of hypotheticals.
Benzene eventually what?????????
TheGulumba hit "show more" dummy
Benzene you can split it more, quarks and whatnot
TheBestThereis... No, actually it is not accurate to say that "half an atom" can be represented by separating the protons and neutrons from each other. At that level, many other factors come into play with respect to what "makes" an atom. That is why quantum mechanics exists.
en.wikipedia.org/wiki/Muon
en.wikipedia.org/wiki/Quark, here don't refer to quantum physics if you don't know about it, you can always divide, don't assume something isn't possible because you don't understand it, or assume you know more than you do
Legends has it that TED ED is still counting from 1/2, 1/4 until 1/373949482929383832
Zeno’s dichotomy paradox breaks down when you have a minimum distance you can travel in a step. If we have a ratio of time and distance, as long as there is no minimum distance we can travel Zeno’s paradox is indeed paradoxical. Let’s assume though that the smallest distance we can travel is a step. We can take one step per second. This means that we can travel 3600 steps per hour. If the distance to the park is 1800 steps, we can use the ratio to figure out it will take 1800 seconds to get there too. But if we assume that this can keep going, like how far we can travel in half a second, the answer is zero steps, because it takes us one second to take the step and we can’t go any lower in distance travelled by us than a step. In reality there is such a limit. The Planck distance. Therefore at some point, even if we continuously move, eventually his paradox breaks down. I’m thirteen btw.
Dude, you're grasping things much faster for a 13 year old
I got to know this concept at 23 I am a physics major lol
Good for u buddy but the Planck length is not the ultimate length I guess
It's the length predicted by our current theory
If theory breaks down the entire notion breaks down
it may take a while but he will eventually get there
+Jackie Murphy Nope he would never get there since it's an infinite amount of divisions in half..it never ends so he would never get there
+Shinigami Bella Did you even watch the video?
+Shinigami Bella look up supertasks by vsauce
+Jackie Murphy fail
This is possible. After some iteration, Zeno stopped walking as with his leg he couldnt cover the smallest half. So, he stayed there..lolz
You are genius bro
I feel so smart because I've had this paradox in my head my entire life, and I've been trying to find a video on it!
I've watched the entire video and now I feel not so smart.
Just doesn't make sense that there's infinite space in a finite space... or infinite time in a finite amount of time...
That's actually very smart. You have discord?
@@thesmartnerd732 lol
@@bussycat3468 lol
Watching Zeno’s walk to the park is like watching my husband start his portion of the house chores.
Never again will I be able to dismiss something as easy by describing it as "Just a walk in the park"
So...Zeno was trolling everyone then??
I think he was just pointing out that the obvious answer isn't always the one traditional logic arrives at. He is well known for his paradoxes probably because he liked thinking of them.
He could also just walk until he gets there...
Darlaimerner Paradox=Puzzle not No Answe
@@archived-iron2343 But movement is impossible. Look up Zeno's feelings on arrows.
Imagine what would happen if a history teacher asked this guy a question and he says:" I am thinking... "
Just finished my Real Analysis unit on convergence. Finally was able to figure out one of these before the video explained it for me
Go home Zeno, you're drunk.
Arkham Sans /+
Yes but it would take him infinite amount of time to get home
This paradox was disproved a long time ago when the planck was introduced. It is the smallest unit of measurement out there. Anything smaller than a planck doesn’t make physical sense
Ah, that's good because this paradox makes absolutely no sense to me at all.
Well 'making sense' is a relative term/concept. The quantum physics doesn't make logical sense too! So, here we see the 'gap/possible contradiction' between logics (philosophical approach) and mathematics (physics approach), both of which could be correct and incorrect simultaneously (another quantum feature). And they both are the primary processing tools of our brain to explain different aspects of nature)
That's untrue. It's not that it doesn't make physical sense, it's that, theoretically it doesn't. Our computers can't compute it based on our number system.
We've never actually physical generated the heat of a Kugelblitz to know that planck length can't get any smaller in real life.
@@tprime2702 my question from you is that: Is anything our computers can do, a correct representation of what theory is to human brain?
@@tprime2702 I mean do u think our thoughts are also binary in their essence?!
this new way of looking at things encouraged me to find the sum of infinite series I always wanted to find
Him-- "Why did you never show up to our wedding?"
Me-- _explains Zeno's dichotomy paradox_
My walks to the park will never be the same.
This is a perfect example of how "logic" is not always reality.
Whenever you move you are basically moving an infinite distance in a weird way
3:12 But if all the progressive square/rectangles are a half of the other,it’ll never become a complete square right.There is always a small portion left.Same problem with the walking part
Well, I guess he kinda says that 1/2+1/4+....(whatever)=1
So then it really doesn't matter how much of "whatever" is there, it'll be finite.
But what you argue means that the area of the square will always be slightly less than one. Still not infinity, like what Zeno concluded.
Onaji Deshou infinity here is the number of times we can progress in the series,meaning we can divide the square/rectangle infinitely many times.The size will be less than one at some point,evidently
this kind of problem is called a supertask, doing an infinitely many amount of things in a finite amount of time.
Incise Infinity yeah,just like Gabriel’s cake
Both measured time and infinity are illusions. They are the limitations of human understanding.
Reminds me of William Blake’s “eternity in an hour”
Infinity is quite easy to understand once you stop thinking of it as a real number.
1/infinity still does not really solve the paradox. If you have to pass through an infinite number of ever decreasing half way points, then how do you ever truly reach your destination? The paradox is not just about time but about idea that a line has an infinite number of points.
+Nymeria Meliae
Mathematically, the distance (sum of infinite number of points in a certain interval) left after each interval would be (1_unit_distance)*0.5^N, or 1/(2^N). If we say N, the number of intervals, is infinite, then on the infinite-th interval, the distance would be 1/infinity, which according to mathematics is simply zero. Therefore, if you were to go on for infinite intervals, the distance left would eventually become zero, and at that point, you would have arrived at your destination. Similarly, the length of time and effort necessary to cross each interval would decrease by half until it reaches 1/infinity = 0, and you can travel through infinite number of points in a finite amount of time and effort.
This could also be represented through mathematical geometric series summation. According to calculus, the sum of infinite geometric series, which is in a form of a*(r^N), where -1< r
Albert Kim
I understand that and it is a great explanation but the reality is that 1/infinity is never truly zero. It might be as close to zero as to make no difference but there will always be 0.something. There will always be 0.0000......00001
+Nymeria Meliae You are right that 1/infinity isn't physically zero, but a time interval and effort of 1/infinity unit is so small, it is not noticeable. And we can certainly say that crossing a single point with unnoticeable effort is highly possible. And within the motion of crossing the given distance of 1, we simply repeat that unnoticeable effort and time infinite times. This, mathematically, is 1/infinite effort times infinity, which results in 1.
This is possible because the distance, time, and effort were all divided by a same constant called infinity, meaning the ratio of the distance of 1 by 1 unit of time and effort is equal to ratio of distance of 1/infinity by 1/infi
unit of time and effort.
Now, if the above condition is true, which I've proved above, since crossing a single point, a 1/infinite piece of the distance, is both feasible and easily done with 1/infinite bit of time and effort, by the identity of the ratio, crossing the distance, the multiple of infinite points, is both feasible and easily achievable with 1 unit of tome and effort, which is an infinite multiple of 1/infinite piece of the total.
+Nymeria Meliae infinity cannot be put into a math problem like any other finite number. 1/infinity is strange sounding
This is also different from the original story where Achilles is trying to race a turtle. Unlike the stationary trees here, the turtle is always moving, and therefore, Achilles can never catch up to him. I don't think they properly represented the dilemma in this video.
The area/distance chosen is finite.
So even with infinite addition.. The answer is bound to come finite.
As a kid, instead of paying attention in class, I used to wonder about things like this. I used to wonder how things ever touched. Doesn’t it just keep getting closer and closer without ever really touching. Then Sister Perpetua would smack me on the head and I’d think “Oh, now I get it.” Something else I wondered about was that until I learned about something, it never happened. In my world it never existed until I was made aware of it and if I was never made aware of it then it never happened. Absurd, I know. But I hated math class and my mind would wander. I also used to draw perpetual motion machines in my copybook. It was always steel balls on various ramps. That’s when I learned about friction.
Wtf! What a cliffhanger, tell us more
This seems like a stoner thought. He probably smoked a bowl and left his house to let it air out when he wondered how long the walk was and was like "woah.....*_*"
damn, I thought I was the first to realize this paradox
Zeno owned you
by thousands of years
I truthfully thought of this paradox as well but with atoms getting closer and closer before they repelled
Colby Fritz A couple of thousand earlier, and you would've been remembered forever.
I still dont get this, how can the travel time be 1 hour? I mean by this, reaching 75% of the travel alone is already one hour and he yet to arrive
Three things about this:
1 - One can use calculus to solve this.
2 - One can use Planck's Constant to solve this.
3 - One can double the time of step #1 to solve this.
This riddle relies on mathematical ignorance to work. It doesn't rely on reality. If "science" tells you something which just ain't so... then science is wrong.
Can any of these solutions be applied to time?
I mean - is time infinite?
Is the universe infinitely old? Is that mathemtically possible?
Can an action take an infinite amount of time like a distance could? It cant, but is there a way to use math to prove it? Because we cant divide an unknown amount of time into 2 and then multiply the firrt part....
I don't know. To balance the equation, you only need an inverse-infinite on the other side. Since the ability to cut physical space/distance has a finite limit, you'll only find solace in the infinite slowing time component.
-
I don't know.
-
I'm applying Newtonian physics and algebra to to situation that probably needs quantum and calculus -- and I barely know squat about calculus, and I've watched a few RUclips videos on quantum, so I know nothing -- and possibly less than nothing -- on quantum.
@@TROOPERfarcry i appreciate your honesty :)
Thank you for that answer :)
It's similar to the paradox of Achilles and the tortoise, where Achilles can 'never overtake the tortoise', because every time he reaches the point where the tortoise was, it has moved forward a little in the time Achilles took to reach it.
Damn Greeks...nothing is ever straightforward.
That's why they loved it from behind
Their level of intelligence was extremely high for a simple man to understand it.
@@ArthurKnight1899 thats your conclusion with your limited brain and your poor barbaric language .
and we are sure they "loved" it less than you :p
@@ArthurKnight1899 what is your mama has to say ...did she liked it??
This pisses me off, because this does not resolve the contradiction. You have merely dismissed it as a "paradox". The point is not the "time" it takes. It is the NUMBER of parts that must be traversed. Physicists use the same argument today to reject the idea of a completed "infinity". Zeno's contradiction (as it should be called) is correct.
The REAL contradiction is in the definition of "infinity" itself, which is meaningless and circular.
Totally agreee !
That depends. Math itself is circular. Infinity is a mathematical concept. We don't know how the real world works - recently some evidence was found that the world has a "resolution" in a way making this problem have a finite amount of steps.
"Math itself is circular."
Not true. That is the opinion of a naive high school graduate. You will not hear that from an honest mathematician.
ThinkTank255 Math is based on a few axioms from which everything is deduced - most often based on circular proofs such as induction. Mathematics depend on the fundamental assumed axioms, which are undefined (primitive notions), which makes math circular in nature.
Now the problem I see here is that you call the definition of infinity circular while math itself is based on circular, yet valid, logic.
How about you define what you mean by the definition of infinity being circular? Since that is what you are criticizing.
"Math is based on a few axioms from which everything is deduced - most often based on circular proofs such as induction."
Induction is not circular if it has a proper base case, as all induction should. Also, in many cases the base case is improperly dropped, allowing an arbitrary set to defined the base case, hence your confusion. For example, it is perfectly valid to choose {1,2 3} as the positive natural numbers. The definition explicitly allows the arbitrary choice of the positive natural. The set {1,2,3,...} is actually not a properly defined set. It is a SELECTION from a collection of sets each of which is finite. Yet, this type of mathematical ambiguity is frequently allowed, even though, technically incorrect.
"Mathematics depend on the fundamental assumed axioms, which are undefined (primitive notions), which makes math circular in nature."
Wrong. Just completely wrong. We MUST get rid of this incorrect understanding of mathematics. Contrary to your assertion, axioms ARE ALWAYS non-circularly defined syntactically. Semantic interpretations are, technically, not even necessary. For any syntactic formalism there exists an infinite number of semantic interpretations. Who is to say which one is "right"??? That is up to the person reading and interpreting the maths.
Thank for your beautiful video! I learnt limit at high school.
Woah what a very nice video, It taught me something and nothing at the same time
The statement combines mathematical logic and physical logic, which is why there's a paradox. Dividing by two forever is only possible in the abstract mathematical world. In the physical world, everything is made of elementary particles that would one day stop you from dividing (and thus make it possible for you to travel 1 mile in a finite amount of time).
+Mehdi Moussaoui It's a paradox because Zeno didn't have the math required to solve it. An infinite sum resolves the problem fine because Zeno literally defined the problem in such a way that the sum of the infinite terms would be finite. No need to talk about elementary particles or anything like that, this is a math problem.
The same thing can be done with time, i.e. one hour can be divided into an infinite amount of smaller pieces. In a way, it is both finite (one hour) and infinite (the number of possible divisions of that time).
Zeno : you can't move
Gojo satoru : yeah that's what I said
Zeno forgot about acceleration and deceleration. If he walks exactly 1 mile he has to accelerate to walking speed and when he gets approximately close to his destination, he must decelerate. But if he only cuts his speed by half each step, he will never come to a complete halt. So he will keep traveling forever but never get where he is going. The more you near your destination, the more you keep slip sliding away.
walking to the park for 1 hour? fuck dat
Walking at 1Mph
Fuck that haha, might as well crawl.
Zeno went to the park to smoke some herbs & tripped about his journey then thought it was a good paradox XD
yours is the most plausible solution of them all. blaze on, brother!
This video finished zeno's journey
I like explaining it in this method:
n = 1/2 + 1/4 + 1/8 + 1/16...,
multiply 2 to both sides,
2n = 2/2 + 2/4 + 2/8 + 2/16 + ...
2n = 1 + (1/2 + 1/4 + 1/8 +... )
substitute n in on the right-hand side of the equation where the brackets are shown
2n = 1+n
minus n to both sides,
n = 1
finally something i can apply from my math class in high school -_-
since sum to infinity of a geometrical sequence = a / (1 - r) where a is the first term and r is the common ratio as long as the range is -1/2 < r < 1/2
so it's just 1/2 + 1/4 + 1/8 + .... = (1/2) / (1 - (1/2) ) = 1
my man
You're absolutely right but that not the point of Zenone, he made up this paradox to contradict the point of the Pitagora who said that all the matter and time is infinite. So Zenone used his hypothesis in a wait to contradict Pitagora, and that only one of the four paradox that Zenone used.
Zeno out here discovering Planck length in Ancient Greece
It is so mesmerizing that infinite numbers can add up to a finite number.
Also, another thing: Electrons can teleport, and atoms vibrate so fast that they practically teleport. So in reality, you're teleporting back and forth an atom distance.
My hand is shaking violently, is this normal?
I really need to write a sci-fi book now, and coin the term 'reality limit'. The 'reality limit' is what is achievable vs. what is conceivable. When you get close to the 'reality limit', the margin for improvement gets so small that the overall effort to overcome a previous best becomes so exorbitant that it effectively becomes impossible. This means if an organic reaches a combat capability that is really, really close to the 'reality limit', it matters not how many fighters you send or how close they are in combat skill to them, or even if they are an infinitely respawning machine that learns from every encounter. They will always lose, because of the exponential increase in the amount of effort it takes to overcome someone approaching the 'reality limit'. And of course, every time the challenge gets harder, the organic in question is pushed even closer to the 'reality limit'.
@@TarsonTalon g
Forgive my ignorance, but, what is the point of this and this theory?
Zeno was a follower of Parmenides. Parmenides was the founder of the Eleatic school of philosophy (although he was very much influenced by Xenophanes). Parmenides main point of philosophy was that there can be no 'becoming', there is only 'being' (as in a state of being) or non-being. Motion constitutes change which equates to becoming. Zeno's paradoxes, of which there are many, were aims at disproving the logic behind motion/becoming.
Ok. Thank you very much.
In my opinion, which I have held for decades, the point is that Zeno was a jackass.
Ao Chen I don't think calculus is based on limits. Limits are just an easy way to fundamentally and intuitively calculate derivatives, which proves that Newton's theories of differential calculus are correct. Integral calculus is proven by differential calculus.
The area under a curve can be broken into a stairstep with 90° steps, these can easily be measured to find the area of each step. The total area under the curve(the differential of the function) is the sum of the area of the steps, when the number of steps approaches infinity, or inversely, when the width of each step approaches zero. This is differential calculus using a limit equation, but it's much easier to just assume that the rules of differential calculus are correct and utilize its shortcuts.
I remember my teacher once told me about this but it wasn't related to time and distance, but, it was related to the number line. i.e. there are infinitely many numbers between any two integers and if there are infinitely many numbers between 2 integers then how do you proceed from one to the next.
Love the graphics.
Interesting sir, and its solution
I thought of this when I was about 9 years old and had been trying to explain it to others ever since.
Now in my forties, I find out it has a name and a solution!
I have a simpler solution/proof: Just double the distance and see how long it takes to reach half-way.
O_O
I don't understand how someone could think it would be infinite: the infinite number of values are real numbers, but they are 1/2 of the previous value, reaching towards a value of 0. As such, the values cannot exceed any value before it, and thus cannot exceed the original value.
+SirRandomMonkey Yeah, I didn't see the paradox either. It's a purely mathematical issue, where each fraction is counted as a whole number. If the total distance is represented in halves and each half is a solid number the result is infinity. Just psychological bullshit. It's simply wanting to find the answer to something from a different perspective
the value is actually equal to 1. I hope that help because this is really easy to understand
Jank s Which means it cannot exceed 1. If he stopped part way, let's say after 10 dichotomies, his covered distance wouldn't exceed 1. Don't see how I was wrong...
+SirRandomMonkey Sorry, "Sir", but infinitesimal calculus weren't available in ancient greece. This video sucks because it doesn't present the real argue of Zeno to the pitagorich school about the incomesurable problem. In that time, they hadn't irrational numbers and rational numbers were an exoticity.
SirRandomMonkey it because he's traveling the distance so u add them up. so 1/2 + 1/4 + 1/8 + 1/16 ...
i think u do understand but we weren't on the same page lol
I am convinced he came up with this while he was high.
Here for Gojou’s infinity
I thought of another way to sidestep this paradox...
Lets say Zeno's argument is true. The first step of travelling a distance d is to travel d/2. The next step is to travel d/4. Then d/8. Or, the nth step is to travel d/2^n. It takes an infinite number of steps to reach distance d, so he argues you can't travel distance d.
However, he also says that travelling d/2 takes just one step. How should I travel d? Simple; overshoot. I'll instead attempt to travel 2d. The first step in travelling 2d is to travel d. But, wait a sec, I just traveled d, so I'm where I want to be, so I just stop. Infinity crisis averted.
+Manabender The purpose of the paradox is to understand the flaw in the logic. You can't do this by simply posing a different problem and solving that one instead. Anyway, Zeno had several paradoxes of motion. Another says this: If zeno starts a journey, first he must complete half that journey. But before he can complete *that* distance, he has to get half way there... and before he can get to there he has to complete half of that journey and so on and on again until Zeno never makes any progress at all. Your variation doesn't solve that one.
+Frank Cappar I agree. Why do they bring time into it when we cannot logically solve the position paradox.
+Manabender You are fundamentally misunderstanding the problem. He is saying regardless of what d you choose, this will still be a problem. So, if you want to travel a distance of 2d, you have to travel a distance of d first, if you want to travel a distance of d, you have to travel a distance of d/2 first, etc.... It is the exact same problem, all you have done is show the contradiction holds for both d and 2d. Indeed, his logic holds for any D. This is why continuity is so absurd. The essential "solution" of modern mathematicians is just to say when things get really tiny we can forget there is a problem at all (and "jump" that tiny step), because humans really do not care about things that tiny. It is not really a solution, they are just dismissing the contradiction out of pragmatism.
+Manabender Ya lost me the moment you tried to put it in math.
its simply about the steps----the lenght of a step cant be variable