Zeno's Paradox and the Planck Length | Answers With Joe

[@curiosity_saved_the_cat]

"If there is anything that makes us human, it's our ability to make up problems that don't really exist" amen!

[@stephenblessed92]

See politics.

[@sinistersparky9657]

Side note: see capitalism for solutions to problems you didn’t know you had but found the solution to them on TV / YT

[@edgardogiudice5135]

@@sinistersparky9657 This is a very interesting math problem. It had been a riddle for ages.

[@veralenora4033]

So Xeno studied a school of philosophy that said our senses cannot be trusted, only logic. Then Galileo comes along and states that all logic must be checked against reality. And it's Galileo's conclusion, formalized by Roger Bacon the "first scientist" which works. Retired librarian

[@edgardogiudice5135]

@@veralenora4033 This issue is about Matematics, not Philosophy

[@tnvmadhav2442]

A infinite number of mathematicians walk into a bar. The first one asks for a pint. The second asks for half a pint. The third asks for a quarter pint. The bartender stops them and pours 2 pints and says "Know your limits"

[@bar7381]

Master Wayne" "Batman has no limits" "Well you certainty do sir"

[@jamesleblanc6948]

Commenting just to say that this made me chuckle

[@lonestarr1490]

4 logicians walk into a bar. The bartender aks, "So, 4 pints of beer?" The first one, "I don't know." The second one, "I don't know." The third one, "I don't know." The forth one, "Yes."

[@gkess7106]

The 5th one is shot before he can ask, then time stopped.

[@tnvmadhav2442]

@@gkess7106 Entropy was levelled. There was a spark and then a bang

[@lishlash3749]

An intuitive way to resolve Zeno's paradox: Just as you cut the distance in half with each step, you likewise cut the time it takes to make each step in half. And while it does take an infinite number of steps to reach your destination, the time it takes to make those steps becomes infinitessimally short. As for the Planck length, it is NOT "the smallest element of space", it is the shortest length (or time interval) that can be MEASURED. There is no evidence whatsoever that there is in fact "a smallest indivisible unit of space and time", and if there were, what Planck actually demonstrated was that we would not be able to measure it, no matter how precise our technology. The reason why it cannot be done is because the shorter the distance you try to measure (e.g. using a beam of light), the larger that light beam's momentum will become (due to Heisenberg's Uncertainty Principle). To reach down to the Planck scale would require so much energy to be concentrated in such a small space that it would create a black hole (with an event horizon the size of the Planck length). Concentrating the energy even higher would just create a larger black hole.

[@baudelaireaugustin6480]

Thanks. This makes thing a lot clearer.

[@matthm4137]

That's really interesting

[@VallenChaosValiant]

If you can't measure something smaller, then it might as well be the smallest unit. Functionally a unit is only useful if it could be differentiated. So if we could measure planck length but not smaller, then for all intent and purposes it is the smallest unit that MATTER for practical purposes. it's like how a painting is judged by what it looks like in the human visible spectrum. It doesn't matter that other wavelengths exist, the visible colours is what matters. In the same way we don't need to worry about levels of precision that can't be detected; by definition if the difference is undetectable then it doesn't exist and has no effect. On the other hand, if something that is different by less than a planck length mattered and has an effect, we would have detected the undetectable and broke the rule. QED unit differences only matter if they are detectable.

[@singh2702]

Its not a paradox when you consider that time flows(without pausing) , by you chopping each time and distance into smaller and smaller segments( time and distance have a one to one correspondence ) means nothing but showing that infinity exists in a finite value, which Cantor already did more than a 100 years ago. As an object moves through space over a distance at a certain speed , since flow of time is constant , as you get closer to the end of distance the frequency at which you will be getting a new value will approach infinity.

[@chrisgarcia6098]

I've had one of the worst 3 days of my life , and your video helped keep my mind busy. You are the best Joe!

[@joescott]

Sorry to hear that! Hope the rest of you week goes better. The Joe wills it.

[@stephenanastasi748]

OK... but it must have seemed infinitely long.

[@cocoa1996]

Actually, calculus _used to_ use infinitesimals, but they were superseded by the idea of _limits_ But infinitesimals are still there, in their own number line, called the _hyperreals_ (there are also the _surreal numbers_ ) Also, _I love_ *markdown*

[@NowanIlfideme]

In the old days we were [b]awesome[/b] enough to use bbcode... :(

[@joescott]

I failed Pre-Cal in college and I'm pretty sure that shines through.

[@cocoa1996]

Joe Scott nah. this is a pretty common misconception. And I don't know how education was in America, but I can say with certainty that over here, education truly sucks. So not really your fault you failed.

[@davidfragoso6366]

lol, respect what he is doing, dont come with propaganda. please keep the channel politics free

[@cocoa1996]

Just saw this. I don't get it why political topics are like this. How about a civilised discussion on it? Wouldn't hurt anyone. It'll just be fun :)

[@ajjamwal]

How do I finish watching this video, it's infinitely long

[@KamZero]

Abhi Jamwal Just watch the first half, then half of the second half, then the next eighth, then the next sixteenth, etc

[@Pining_for_the_fjords]

Abhi Jamwal I just finished it. I must have unlimited bandwidth and infinite charge on my phone.

[@joescott]

It took an infinite number of times for me to get some of those lines out.

[@poneill65]

Au Contraire, the video is 7.086462259951e+45 Plank time units long! Pay Attention Dude!

[@Tethloach1]

Zenos paradox I did think of it once without ever knowing of zeno, what happens if you divde time and space, movement is possible how exactly time is possible how exactly, I can sympathize with zeno because that idea was very personal to me sorry, an insult to zenos idea is an insult to me because i take that personal because i like that way of thinking, divide time infinitely divide space infinetly, thats the kind of guy i am. anyone who is against philosphy is against me by defaul and knowledge and science and mathemeatics.

[@PhoenixNL72-DEGA-]

Hm, if you split a cake in half, and keep doing that eventually you create a nuclear explosion XD

[@stephenblessed92]

Cut the cake in half, eat half. cut remaining in half, eat that, repeat... Infinite cake!

[@MaxBrix]

@@stephenblessed92 Let's spit a cake. I only get the first three pieces. You get the rest which is infinite.

[@ForgeMasterXXL]

No, your partner just punches you in the face for ruining the cake they just made...

[@Rampart.X]

Is the cake yellow?

[@lizard9159]

Zeno : creates a bunch of paradoxes Calculus : *AM I A JOKE TO YOU*

[@sovietsandvich8443]

This is a channel. Calculus is completely hypothetical and only approximates the real world. Every mathematician recognizies that the “continuous change” in calculus does not perfectly represent the real world.

[@veralenora4033]

@@sovietsandvich8443 But calculus WORKS. It allows us to create ideas which can be converted to engineering. That passes the test from science theory to science law. (I know Joe uses the word theory as a final conclusion, but he's wrong. Einstein's work is no longer the theory of relativity, its' accepted as the Law of Relativity.)

[@sovietsandvich8443]

Vera Lenora but the measurements and calculations of calculus can only be approximated. The concept of planck length and Planck time should be enough to show that “continuous change” cannot really exist. It’s similar to how 2*pi*r is the circumference of a perfect circle, but no real perfect circle can exist.

[@sovietsandvich8443]

Vera Lenora obviously speedometers work based on calculus, but the measurements will never truly be exact. The whole concept of a limit is that you continuously approach a given value. Derivatives and integrals are based off of limits, so they are approximations as well.

[@veralenora4033]

@@sovietsandvich8443 Thank you.

[@JKShred]

I love how you move around the screen with every edit cut. It breaks the monotony usually created by edit cuts.

[@NovaStrike118]

the "is the lamp at the end on or off" thing is kinda like asking whether infinite is an even or an odd number

[@lonestarr1490]

Basically, yes. And the answer is simple. Modulate the lamp by a function that is equal to 1, whenever the lamp is on, and equal to -1, whenever the lamp is off. Clearly, that function does not converge.

[@zetahurley7323]

@@lonestarr1490 well that just gives you "there is no answer" which Is hardly an answer, and if you treat the sequence of alternating 1 and -1 as if it's a convergent sum even though it's not, and you set it equal to a value, that value winds up being 0, which would indicate that the light wouldn't be in any state, but if you had to say it was, then it would be half on

[@tompayne3255]

I love this video, but you have got two of Zeno's paradoxes confused. The arrow paradox is the idea that at any one moment - assuming time is finite - the arrow cannot move as it is occupying a space its own size and cannot move in between the instants. The dichotomy paradox which you mention in this video works with the example of an arrow, but is a different paradox. Zeno uses the idea of an athlete running from one end of a stadium to another, and its often called the stadium paradox.

[@keaaudi6473]

exactly, well said

[@kecskemetib]

Indeed, and the irony is, that in the video he says "if there is really a smallest invisible space and time then Zeno's paradox is solved"... but this idea is exactly what the real Arrow Paradox objects to (no wonder the atomists had a hard time with Zeno).

[@pepperwood8811]

I admire you for having the courage to do a downward camera shot on the top of your head. If I were to do such a thing it would highlight my thinning hair. Not balding, just thinning.

[@jessstuart7495]

Zeno didn't understand that infinite sums can converge to finite values. If you sum the times the arrow takes to get to the next point half the distance to the target, you get a finite time equal to the distance divided by the speed. Zeno's "paradox" illustrates a really important point. Paradoxes arise because of our misconceptions (or assumptions) about nature. Nature always proceeds. You can't break nature, you can only break your understanding of it.

[@h1a8]

Jess Stuart That's not the problem. We know that an infinite number of things can equal to a finite amount of something. The problem is how do you reach infinity in the first place?

[@richardyoung3074]

Each increasingly small step towards the target takes a (proportionally) increasing small time. And just like the sum of the infinite series of distance slices sums to a finite number, the infinite series of time slices does too. 1/2+1/4+1/8...=1 this is true for distance and time (and apples and ...) Zeno paradox is not a paradox (mathematical or real), is the cleaver question from a deep thinker who did not know about infinite sums. His question was just a couple of 1000 years to early for the answer.

[@clarewulf2054]

The referenced Veritasium video explains this nicely.

[@trevorallen3212]

@@richardyoung3074 like h1a8 said how do you reach infinity in the first place if you're going only step by step without skipping a single step in the first place what is so hard to understand?!?

[@wizardtim8573]

@@trevorallen3212 You don't. Infinity itself is an illusion.

[@miovvv]

i spent my whole day reading about how time doesn't actually exist and i was like 100% convinced that it has to be true but now this video is giving me an existential crisis

[@YTjndallas]

I sooooo appreciate these videos as the way explained in a way that can be conceived.

[@matthewforsee5092]

"There's nothing more human than the ability to make up problems that don't exist" , amen bro.

[@keaaudi6473]

Great that you gave a brief overview of Zeno, but there is way more to this than you mentioned! Zeno's paradox of space and time can only be explained by quantum physics and Heisenberg's uncertainty principle which unfortunately you do not mention at all. There is an excellent book about this and I highly recommend it. Cheers

[@StanleyOrchard]

That needs to be a shirt... "Give them a Planck Length and They'll Take A Proton."

[@CreativeSingularity]

That is a really good shirt idea. Well played old chap, well played.

[@wild360]

I think Xeno's paradox demonstrates the absurdity of "infinity" in the real world. On that note, do a video on G64 and TREE(3) and explain how we know TREE(3) is larger than G64 when we can't calculate either. :)

[@70stunes71]

This is by far, my favorite video of all you have made.

[@draconyxRPG]

I think even in a continous universe, you solve the problem of zenos paradox by thinking that in each smaller path aquiles do in a small amount of time, due his constant speed, so in infinitesimals distances he does in infinitesimals amounts of time, and this sum of time converges to a finite time when he passes the turtle

[@stevenloudermilk7036]

"if there is anything we humans are good at...." great ending.

[@joescott]

I've got my cynical side. :)

[@pizzamaster355]

The answer to this question by the way is being stupid

[@alcoholandfun243]

Hey Joe, I watched half your video last night, and half of what was left tonight. I watch half of what remains tomorrow night, and so on. Can't wait to get to the end 🙂

[@mkvantassell]

You're really good at this. It's a nice summary of information

[@joescott]

Thanks!

[@azithro8]

Joe Scott vjop

[@alijoueizadeh8477]

Thank you Joe for sharing your version of thinking about Zeno's paradox.

[@hasanshirazi9535]

A simple mathematical solution to Zeno's paradox is that although arrow will have to travel infinitesimal number of fractions to reach its target which seems to be never ending, but the time taken to travel each successive fraction also decreases by half and hence the time taken to traverse the final infinite fraction will be infinitesimally small i.e. zero. Hence the arrow completes its flight as it covers the final infinitesimal fraction in zero time.

[@aodhanodonnell3681]

I like it, a finite distance in a finite time frame, discrepancy is nil,

[@zmeireles68]

Joe, your sense of humor is awesome.

[@spencerholmes8538]

A very simple answer to Zeno's paradox exists in basic math: When you halve the distance you also half the time it takes to travel that distance, keeping your time to travel any given slice of the movement at a constant rate. By the time you near (thought experiment) infinite points or slices, the time is reduced to an infinith (not a word...yet) amount of time. Voila! The turn is completed unhindered by the halving affect.

[@j-r-m7775]

Also without understanding this you wouldn't be able to explain how you halved the distance in the first place. To go 20 feet you first need to go ten feet. But how did you go ten feet if you first would need to go 5 feet.

[@mellissadalby1402]

Excellent video. The premise of an infinite number of decreasing values also agrees with my heretical assertion that x/x = 1 (where x is identically equal to x for all intermediate values) as x approaches (and reaches) 0, thus proving that 0/0 = 1

[@epen1898]

I once read that the smallest amount of time was the time between when the traffic light turns green and when the guy behind you honks his horn.

[@gobblinal]

Is that not a "New York second"?

[@zachnun7145]

This is my favorite episode from this channel

[@ezOqekuRitusohI]

I have seen many mathematicians struggle with this paradox, because they are so focused on mathematical equations that they cannot see the obvious answer: the space between two defined points is not actually infinite.

[@markmarco2880]

Joe, I never hardly ever comment, but I had to thank you for not mentioning Xenu, backwards and forwards, not, that was heart-warming-ly great.

[@EastNorthEast]

Please talk more about that mythical creature who brain washed souls! That sounds fascinating and I can’t find anything on the inter web about it

[@boony7544]

I never heard about this paradox. Really cool stuff.

[@judgeomega]

"if theres anything that makes us human, it's our ability to make up problems that dont exist" -Joe Scott

[@davidroddini1512]

Actually by switching the lamp on and off at an increasingly more rapid rate, at the end of the time period it is in a superposition of the on and off states; at least until the waveform collapses. Or until the switch wears out and breaks, in which case the lamp is off.

[@zbyszekz77]

Or the switch lever breaks in ON position, so the lamp is on. Result of the supertask is not the superposition though.

[@Nookerdog777]

It's both. Everett was right.

[@erinbaggarly900]

Max Planck's first dating attempt. " Hey there doll. Want to see the length of my plank"? Doll: 🤭Oh my. It's so tiny. Max: 😕....🤔.....😃... "To the chalk board"!!! My apologies. It's late and l was bored.

[@kendomyers]

This is a catastrophe that wouldnt occur if you were measuring a black body instead ... Eh? Eh? ...ill see myself out

[@whocares2214]

@@kendomyers noooooo🤣🤣🤣 that's a phallic fallacy!!

[@MarxWegener]

In Zeno's paradox we deal with speed (distance over time) and negate the time and only focus on distance. As the distance between Achilles and the tortuous approaches zero, so does the time frame. The reason he never get to the tortuous is the time has stopped.

[@jayraskin]

Great explanation. Thanks.

[@simewn]

Zeno's paradox is an infinite sum that converges, therefore we can have a finite result.

[@balazskecskemeti]

Faaaar from "resolved". Here is the real "arrow" paradox from Zeno: "If everything is either at rest or moving when it occupies a space equal to itself, while the object moved is always in the instant, a moving arrow is unmoved." So how does something move some planck lengths between planck instants, if it is standing still in every instant?

[@karldavis7392]

In pre-calculus we blew through this with a section called "growth rates of infinity", so basically infinity divided by infinity makes a finite number.

[@ImTabe]

A great video as always!

[@joescott]

Thanks!

[@dwolff4127]

Zeno's pardox is misrepresented often...and so is here. The function is an ever more accurate description of the moment before the defined ending moment. The hare passing the turtle. The arrow reaching the target or whatever you wish to use. The correct question is How do I describe the position/time just BEFORE completion with infinite accuracy. As the number of moments (or distances) necessary to complete any action increase to infinity, the time taken for each moment approaches zero with equal vengeance.

[@maxarmstrong885]

Thanks for another fun video! Don't know about everyone else though, but I'm struggling to see how these are paradoxical. Taking the arrow hitting the target example. If the arrow takes 1 second to go from the bow to the target, if you observed this for 1 second, you'd see the arrow hit the target. If you watch it for 0.5s. Then another 2.5s. Then another 1.25s etc you'd see the arrow get closer to the target in smaller and smaller frames. As such, if you continue to watch for smaller and smaller lengths of time, you'd see the arrow get to the target making smaller progress each time. Take this to infinity, you'd never see the arrow touch the target unless you had the full 1s of time watched. 0.99999... seconds wouldn't be long enough to see it hit. All I am seeing here is a Greek guy tell us that you can break things down into an infinite number of tiny pieces to describe the infinite lead up to an event happening. So to answer the question about whether the bulb would be on or off... It would never reach a point of fixed state. So it would be described as alternating between on and off at an increasing frequency. To oversimplify, if I told you it took 2 seconds to do something. At any point in time before 2 seconds that thing would not be done.

[@BrianDaleNeeley]

(5:45) That statement *ABSOLUTELY* needs to be on a T-shirt. Great, now I have to go and see if you have it on a shirt.

[@roxannc8333]

Thanks for breaking this theory down. I never heard it before

[@TK199999]

I have heard another version of Zeno's Paradox, does a Black Hole have a bottom. We call the point the singularity but that just means we have no idea what's past it. Though Planck again steps in, with some physicist saying that a Black Hole has bottom and its end point is not 0 or infinity. But that all the matter and energy inside is squeezed down to the Planck width. That a Black Hole is really a balance of forces, where it's the matter and energy falling in that keeps it going. But once that stops, like after the heat death of the universe, then the other fundamental forces start pushing back against the gravity and evaporation via Hawking Radiation is accelerated.

[@TheSkullReviews]

The Planck length does have very profound implications, it shows that the universe is finite in the small as in the large, meaning if you were to cut the smallest length in half (planck length) that item loses locality, meaning it is everywhere at once!!! I have an idea for a video to: ZPE zero point energy and the fact that their is more of it now than was in the past an how it effects time, electrons and also the speed of light, its truly mind blowing to consider the implications on how much it effects our perception of time and how it has shaped the very world and universe we live in:) If interested I can point you in the right direction for content.

[@joescott]

Yeah, please share. :)

[@zbyszekz77]

I'm just watching all of your videos and catching up. Supertask is to perform infinite number of steps in finite time. The second part of supertask definition is very important. But nevertheless the video is very cool and I would recommend to read about Oracle machine and Hypercomputation (like Turing machine orbiting black hole).

[@nicholasvanlandschoot]

The reason you can reach your end destination on the chair is because you do not halve two travel in halves;You may travel 1 whole, 3/4 ,16/27 18/19/ or 1/2 at a time.

[@devincahoon830]

Which brings up another question. “Has curiosity killed Schrödinger’s cat?”

[@simonmorgan225]

Yes and no?

[@shauryaster9180]

why don't you have a billion subs?

[@joescott]

Your expectations of my channel are a bit high...

[@chriscubbernuss3288]

He'd first need to get 500,000,000 subs. But before that, Joe would need to get 250,000,000 subs. But before that,... Hang in there, Joe. You'll get there someday.

[@alexgeisel2581]

His stomach is not that big.

[@daerdevvyl4314]

Shauryaster I have four goals in life: to have a lot of subs.

[@kgcolor]

@@alexgeisel2581 haha

[@miltosLaz]

That thought experiment with the light ball and the time it made me think of how the particles are in superposition, so the the light ball might be on and of at the same time when you go so small in time if that makes any sense.

[@Bodyknock]

The solution to Thompson's lamp paradox is just that the function O(t) which is 1 if the lamp is on and 0 if the lamp is off isn't defined for t > 1. The paradox only defines that function for 0

[@OceanBagel]

Assuming Planck was right about Planck length and Planck time, does that mean wavelengths of light can only take on discrete values that are multiples of the Planck length? How would redshift and relativistic effects affect this?

[@postmachine]

i am not very well educated on the subject but from my limited understanding, yes, the universe is discrete. energy can only be transferred in packets of energy (QUANTities) of a certain smallest amount. from this follows that measurement is dependent on those limitations, which makes the planck length the smallest measurable distance.

[@thstroyur]

But being 'measurable' and 'existent' are two different things; even though the uncertainty principle limits accuracy, that doesn't mean automatically that spacetime itself is discrete. Sure, assuming this may be practical for calculations (e.g., in lattice QCD), but it brings in difficulties of its own: for one, we're not allowed to use the differential machinery we're used to, as it is--a major shortcoming, IMO.

[@alijoueizadeh8477]

Good question

[@talltroll7092]

A photon would collapse into a black hole well before its' wavelength approached Planck length. We're going to need a much more sensitive method of measurement if we want to do actually useful work at that sort of scale

[@JoGaJungle]

with regards to zenos paradox, its depends on how you define “you” when calculating position. does “you” have a length or is “you” an infinitely small point somewhere in the center of the front of you and the back of you

[@veralenora4033]

Xeno's Paradox as stated considers a constant speed. Achilles is accelerating, speed considered over decreasing time. Time is the factor which solves the apparent paradox.

[@richarddeese1991]

I've read that most of these are just different versions of the same thing. Anyway, as far as Achilles & the tortoise, I always thought that maybe the rate at which he crosses succeeding half-distances actually reaches or exceeds infinity. Besides, in the Achilles & the tortoise paradox, Zeno seems to concede that they are in fact moving, so you could make the same assumption about the arrow & go, "In your face, Zeno!"

[@shauryaster9180]

Do a video on the Mandela Effect please. I have been doing my research and still haven't concluded between Psychology and Parallel Universes. It'll be awesome to hear your side of it.

[@joescott]

Browse my channel, it's one of my most popular videos.

[@lasttime500]

There's a limit of how much you can divide something. But what's interesting is that there seems to be no limit of how much you can multiply something. There's no theoretical limit of how big a volume can be as far as we currently know.

[@senselocke]

Zeno's Paradox has always seemed to me something that would be considered very profound by people who are very high.

[@aodhanodonnell3681]

Lol

[@pdougall1]

This is actually hugely consequential! Consider the that the quantized nature of everything is a necessity for our experience of reality at all (meaning we can move from one place to another). Someone designing our reality would have to produce this basic concept as a substrate to construct reality. I think it provides evidence that we are living in a simulation (though I'm having a little trouble building a formal argument).

[@SweetHyunho]

Are you assuming that time actually exists and flows? Can we really be sure causality is aligned with our arrow of time if we include quantum events?

[@pdougall1]

hm... So possibly the the concept of non-euclidian spacetime preempts zeno's paradox. Meaning it's only paradoxical because of the way we perceive spacetime? Trying to grok this video for inspiration kzbin.info/www/bejne/j6rGcq2aqbp8odE

[@mc101]

How about covering "The sum of all positive integers equals -1/12" or 1+2+3+4......= -1/12

[@aodhanodonnell3681]

Eh, that's the point,

[@baruchben-david4196]

Reductio ad absurdum doesn't always work. Schroedinger's Cat was an attempt to show that a quantum notion was absurd, and therefore incorrect...

[@nwmotog]

planck length. just another parameter of the simulation.

[@joescott]

The pixel of the universe?

[@nwmotog]

Joe Scott hahahahaha yes! 😂

[@h1a8]

IncognitoGambino Exactly!

[@gutspraygore]

Is our universe expanding because we're being upgraded? Are we DLC?

[@machielluchtmeijer7796]

@@gutspraygore worst DLC ever. 0/10 would not buy

[@LegionOfWeirdos]

Parmanides looks a lot like Epicurus. They could be brothers if they didn't live in different centuries. I thought at the end of the minute the lamp was both on AND off :/ "The ability to make up problems that don't really exist"... sounds a lot like some of my co-workers.

[@shruggzdastr8-facedclown]

You saved the best for last (@5:45)!

[@tarzanswe2901]

haha love you man, your funny and most of all interesting and educated. could have a long monologe like you but im lazy.. so just awsome have to sum it up!

[@gacoc]

Zeno was a monist. He put forward his paradoxes to demonstrate that if there is more than one thing, then any change in the relative position of those things (i.e. movement), leads inevitably to logical absurdity. Zeno's position is really a very subtle one. It isn't open to refutation by mathematical or physical argument. In modern day language he is saying that, ontologically, all we can say is that only one thing exists for certain, and that is the Absolute. Division or partition of the Absolute into discrete things is a mere social construct, a fiction to which we are habituated.

[@cafertaskran8180]

In fact, the zeno paradox is a matter of observation, indeed, someone who can observe the event in infinitely small time periods will observe that it is not possible to get from point A to point B.

[@atil4]

Would be awesome if Joe Scott, or anyone, can explain: 1) how Planck reached that conclusion of planck length (minimum length possible), and en even more, 2) why the other planck units are not minimum possible, like, planck mass, planck energy.... I really wondered this question for many years if any one can answer! Thank you.

[@joescott]

True story, I actually had a segment recorded that discusses that but it somehow didn't make it in the video. He came up with it by creating an equation that factored in 3 other constants, gravity, the speed of light, and Planck's constant. Not sure how he came up with the equation, though. en.wikipedia.org/wiki/Planck_length

[@NearlySurrounded]

Love the show, Joe!

[@umeshkhanna4896]

infiniteeeeeeeeeeeeeeeee thanks for the video Joe.

[@joescott]

You bet!

[@Retrodan680]

Hey I have always wanted to know what makes living things cells stay together and not just fall apart? please do a video on this.

[@Smingleflorp]

Semipermeable membranes.

[@aodhanodonnell3681]

Bill Morris the random field of quantum probabilities is adequate to maintain Newtonian physics, why? We'll have to wait for a theory of everything it can't be explained away by concepts of biology it is a reiteration of the question not an answer

[@StephenRansom47]

The reason why a 'Plank-like' measure is important is that it will be the 'line where the physical can no longer be measured because it is no longer an object. See: Cartography and the measure of coastlines.

[@larascott2146]

zenos arrow paradox is actually not another version of his dichotomy paradox but is an independent paradox. It states that in one instant an arrow that is flying cannot be moving but since time is made up of instants then motion must never happen. (Not saying this troll just wish to imform :) )

[@michaelcox5166]

The idea of a limit is by itself completely sufficient to explain Zeno's paradox, full stop. An infinite series of steps CAN add up to a finite number. 1/2 + 1/4 + 1/8... does IN FACT equal exactly one, not infinity. Though interesting, the Planck length discussion really doesn't have anything to do with the topic. You do a great job with these, even the difficult ones.

[@aodhanodonnell3681]

I disagree, conceptually the paradox is airtight in practical physics it is irrelavant, infinity is not made of the sum total of numbers approaching infinity, the minor discrepancy amounts to the same as a large discrepancy, however you represent it.

[@mikey_gc8]

Finally back in action, my man 🤙

[@joescott]

Got a little derailed for a couple of weeks. Don't call it a comeback... :)

[@Feroxing12]

wow. I dont want to play smart guy but I suggested this when I first heard about achilles and turtle.

[@ronisCR10]

Hola Joe! Could you make a video explaining why in "Zeno's Paradox and the Planck Length" you affirm that the Planck constant is the minimum unit? Saludos desde la soleada Costa Rica...

[@thequintessentialgamer7514]

Gorgeous hair good sir! (As I stare at the top down shot of Joe's head)

[@thecolorpixel9782]

Can you do a viedo explaining the fundamentals of quantum physics, like why are the numbers zero and one used? what do they stand for? please make it simple! thank you

[@chrishunt4211]

The first problem I see with Zeno's paradox is in the hypothesis itself. This exercise requires a known end point and therefore debunks itself. Without an end point there can be no halfway point. Even adding "time" to the math doesn't ruin logic. If you divide the distance by half of the previous distance then, assuming same rate of speed, the next duration is also halved (both distance and time). Since a halfway point requires an end point we already know the total distance and time. Zeno is just dividing by half and never reaching the end point, still not exceeding the total time.

[@KevinsDisobedience]

This was a good one, Joe. Perhaps our logic is not the logic of the universe, or at the very least not perfectly so.

[@joescott]

Thanks!

[@BardicInspiration]

Thanks for making this video, you made my day! And you even pronounced my last name right. You truly are a super genius Joe Scott!

[@joescott]

I like that your bar for super genius is so low. ;)

[@BardicInspiration]

Einstein, Hawking, Joe Scott :D

[@joescott]

That sounds right...

[@clarewulf2054]

Another great example of how we misunderstand infinity is the idea that in an infinite universe infinite things must happen. The number of rational numbers between 0 and 1 is infinite. The number 15 does not occur in there.

[@Mikeanglo]

You're telling me I could have infinite cake and nobody told me?!

[@jameswallace9906]

The lamp is off bc the starting point is that of an even iteration where beginning-and end are undefined. Thus if one continues infinitely, one leaves the lamp off to the conclusion the iteration, like wise if the lamp starts the iteration in the on position the end of each iteration would be off.

[@spiraldude]

Plot twist: Zeno makes a reappearence in both Black Hole Physics and Quantum Mechanics. So called "tortoise coordinates" may be used to get around the "mathematical singularity" that pops up at the event horizon of a BH. And then there is Zeno's paradox in QM that if you measure something in quick enough succession, the state seems frozen in time... so the particle doesn't, like, age.

[@vincentconti3633]

This has always disturbed me. I think of it when I am walking somewhere! And then there is the length of our lives! My halves are getting shorter! Yikes

[@ahlussunnahahlussunnah4262]

Tufrah of Nizam is an other solution to this problem. That is a body jumps/leaps from one point of space to another point of space without being on any one if the intermediate points of space b/w the two . This is in harmony and In conformance with Plank’s Solution. There must be a minimum dustance for Tufrah طفرة

[@aviraljanveja5155]

The number of Divisions keep going higher to supposedly infinity, but as the the number of Divisions go higher to infinity, the size of those divisions go down to zero. And when zero(nothing) and infinity (everything) collide. You get something. The limiting value. They are all around us. Everytime you go from a 0 to 1 or 1 to 2.

[@jtarrats100]

love ur channel cheers

[@abdusalam3ar]

My new favorite quote: "if there is anything that makes us human is our ability to make up problems when they don't really exist"

[@levipack3835]

I think Zeno's Paradox demonstrates the fact that things do not actually travel continuously. They travel discreetly. So on at least some sort of subatomic level, the atoms that make up our being have to disappear and reappear. So in a sense, we, on a very small scale, are teleporting across small distances. So we don't travel linearly... so there is no Paradox. But the Paradox does at least demonstrate that linear movement is not possible. Pretty insane when you think about this was thought up thousands of years ago. I think this is where quantum mechanics probably comes in to save the day.

[@thingthought9930]

yea!!, science video

[@Ramjamsarnie]

This is why I have always asserted that the fifth physical dimension is scale (relative to space time) We cannot travel in it (size or speed) beyond out very narrow limits and we cannot observe what is beyond our limits - so we assume that’s all there is. Just like a two dimensional being would imagine a three dimensional world!

[@oussamaabdelilahsofi2683]

We are so complicated that's why why we came up with more complicated things that we can't understand

[@joescott]

If only we could just stop thinking...

[@ofsinope]

"...calculus, which relies on infinitesimals..." *TRIGGERED IN MATHEMATICIAN*