Something I decided to not include in the video, but might interest some of you: I find it interesting how the way that "individual points on an object" act in this question is a bit similar to how "individual moments in time" act in Zeno's arrow paradox -- where, if you shoot an arrow from a bow, and look at any individual moment after that, the airborne arrow will not be moving. Yet if you stack moment after moment, one after another, in quick succession, the same way that moving time works, the arrow WILL be moving -- which should be impossible, if it isn't moving in any one of those moments which make up time. Basically, thinking about an individual point is similar to thinking about an individual moment. Reality isn't built to account for those concepts. Which might imply there is no such thing as a point or a moment, the smallest measurements of space and time. Absurd. (also -- in case you missed the community post, the new profile picture is the very generous artwork of @SovietGirlReal. It is masterful.)
You've fuckin' cracked, Chimmaney. This proves it. You've finally lost it. First the schedule, now your mind. WHAT IS HAPPENING TO YOU?! Nah, jk, good video.
Relativity is a common problem in math; From your perspective there is no motion in a boat, and you can't feel the curve of Earth as you travel into the horizon. And despite this probably being the intro of your 5-6th grade physics class, your entire video (and this comment) acts as if you made a new math discovery. So yes, the "point of rotation", for all intents and purposes, rotates. After all, rotation is a type of transformation over an entire lattice: If that transformation doesn't change a state of a single point, it doesn't mean that transformation of the lattice didn't occur. Think of moving the letters of "POO" once to the right with wrap-around: "OPO", there was a transformation and movement, even if from the perspective of the last letter, nothing changed. Zeno's arrow paradox is not even a paradox: Velocity = distance * time. If you remove the time and just take a picture of space (distance), then obviously there is no velocity. This is 3rd grade math, come on. At the end of the day, your use of "Zeno's paradox" shows that a lack of understanding of math, at the same level as quantum mystics who believe they can affect reality by closing their eyes (and therefore not observing particles): Reality does have a single point and single moment. All types of math work with them. If they don't work in yours, it's probably sign that you did something wrong, not that you proved a new theory. TL;DR: You are wrong. Your example of a circle made up of points is a lattice. If we think of the points as atoms or even quarks, they would all have some type of connection to each other. Those connections do rotate as the lattice does, even if the central "point" cannot be shown to rotate by your math.
@@benshulz4179 You have fundamentally misunderstood so many things about this video that I don't even know where to start with this comment, which is at the very least somewhat less rude than the others you have left across this entire comment section. Of course individual moments and points do exist. My comment saying that something "might imply there is no such thing as a point or a moment" was so clearly framed as an "even though we know that can't possibly be the case". And given that moments DO exist, and time is a collection of individual moments, Zeno's arrow paradox in no way "removes the time" from the velocity equation. That's like saying that measuring one second of the arrow's travel is removing the time from the velocity equation. The paradox is saying that, if time is made up of infinite, infinitely small moments, during each of which the arrow is not moving, then how can it be moving when you put the moments together, unless there is some time happening between the moments? The answer to the paradox isn't that moments can't exist, or that nothing can ever move, it's that the way humans think about infinity is flawed. We imagine a world where you can see from one moment to the moment directly beside it, because we're used to working in fields next to infinity -- but this is not the case. In the same way that you cannot see the number just before or after infinity, or the decimal just before 0.3 recurring. The same is true of points. Of course points exist, nobody here ever suggested that points not existing was a real possibility. But they are so infinitely small that humans have trouble thinking in terms of them. Which is what you've done here as well. A point is not like an object. An object can spin. When an object is upside-down, you can measure each of its points top-to-bottom, and read them in the order of ABC. Then you can spin it rightside up, and those same points will read as CBA. But a point is like a moment. Just like humans imagine that there must be something "between" moments, people imagine that a point must itself have points. But it does not. A point can never itself be upside-down, or sideways, or at an angle. It has no top half to compare to a bottom half. It is infinitely small. A rotating object has its parts, its points, relocating themselves along a circular path. Every measurement you take down to the level of "point" will be rotating too -- each cubic millimetre, each atom. But each of those points on the object are doing nothing more than tracing that circular path, relocating themselves. When they spin from the top half to the bottom, they do not themselves end up upside-down compared to their starting position, even though intuition tells us they should be. A point cannot rotate. And the point in the middle, which doesn't even trace a circular path, highlights this perfectly. It's not that we can't "see" the point rotating, or that we can't "feel" the point rotating, and because of that I'm claiming that means it isn't rotating. It's that, if you did rotate a stationary point, you wouldn't be doing anything. Nothing happens to it. It's not that it looks, feels, or acts identical after rotating 180 and staying stationary -- it's that is IS completely identical in every single way. A single stationary point cannot spin. The fact that the default human position, before thinking about this, is "but it has to spin", is the very reason I made this video. Because I found the idea interesting. How it's contrary to what we "feel" should be right. We compare it to what we know, with spinning objects, spinning atoms, so on. We go as small down as we can comprehend. But we still have difficulty understanding that a point cannot spin, because it's not like any larger measurement. We still have difficulty understanding that you can never see the moment immediately after another moment, because it's not like any larger measurement. Because we weren't built to imagine infinity.
@@Chimmaney Oh, I see. "A rotating object has its parts, its points, relocating themselves along a circular path" That's a weird misunderstanding. Rotation isn't defined as "movement in a circular path" Rotation is a property of a manifold. Best exemplified in a simple example you can do on pen and paper: Move a manifold across a mobius strip. When it reaches the starting point, it has rotated 180 degrees. This is true of every manifold. This is your logical fallacy: "A point cannot rotate." If this was true, you wouldn't be able to move a point across a mobius strip. Now, you might already have a thought in mind. "But a point in space has no defined rotation, only location." I will shut this down by mentioning that in the video, you said: "points at the edge of the circle rotate". This is important wording: You are saying that points can be rotated: That they have the property of orientation. And that makes perfect sense: Your example is a circle, so the points are not simply orbiting a center, like stirring a pot: By your own words, these points are part of a "spinning circle", a lattice. The lattice is an important part: If a translation is applied to a lattice, every point in the lattice is affected . And because you stated that the "circle rotates", the center's orientation has been changed, albeit without any movement. Yes, you cannot draw the "point's rotation". Completely true. But you also cannot draw it's location, or draw the time that it existed in. But the math still holds up, and your own wording, where we construct a lattice of points, which each have the property of rotation (as some points can be rotated, by your own words), means the math would still hold up. "it's that is IS completely identical in every single way." It is not. It's orientation has changed. "A single stationary point cannot spin."" Why not? Can a orientationless point move? What's this relationship between orientation and movement that you've come up with, and why does it seem arbitary? "Because I found the idea interesting. How it's contrary to what we "feel" should be right." This is because you made a mistake. "Points have no orientation" isn't that interesting of a discovery, especially not when your video starts by claiming that some points in a circle are rotating because they are... moving in a circle (which isn't the same thing?)
@@benshulz4179 To clarify, the speech used in this video was not meant to be taken as precise gospel. I call the disc a circle, and I say that the points rotate, because I want to easily communicate my ideas. I don't want to bog down a youtube video, which is not a mathematical paper, by adding clarifying statements to every word I use -- especially when most people understood my meaning just fine. When the disc/circle rotates, it relocates its points in the traditional way we think of rotation. Yes, rotation isn't defined as "movement along a circular path", but that is exactly what happens to the points of a rotating object -- the points I was clearly talking about when I said that. I agree, that isn't what happens to the object as a whole, just its points. Yes, I am claiming that points have no orientation, because a point that is at a different orientation is identical not just to our senses, but in every possible way. While a symmetrical object that is rotated may look identical while it is not, because the points along it are in different positions, a point that is rotated IS identical. You still seem to misunderstand the infinite smallness of a point, and why it is that I believe they cannot have orientation. I'm happy to be proven wrong here, by somebody seeking discussion coming in with good reasoning, but your only reason against this is that it feels wrong. That's a notion that I agree with, but it is not meaningful beyond friendly conversation. My imprecise wording, intended for ease of communication in a short youtube video, does not give points the ability to face a different way. I'm sure you understood that, given that you seem to understand what I'm saying with points having no orientation. It feels very bad faith to say that, because I said "the points rotate" early in the video before revealing my conclusions, I am contradicting what you clearly do understand me to mean. "A single stationary point cannot spin" was meant to seperate the two possible definitions of spin. Yes, I believe that none of the points on the circle are changing orientation, but they are still moving around in a circle, in a manner commonly identified in language as spinning. People point at a spinning circle, and define that motion as spinning -- because of how words work, they are correct, even if the points on it are not changing orientation. If you don't think any of this is interesting, that is entirely legal, and has been the whole time. I do think it is interesting, and other people clearly do as well, but not everybody will. I feel like we're not even talking to each other, and I don't feel like you're coming from a place of good faith or discussion, so I'm happy to leave this here. Sorry that this video wasn't for you, I hope your next one hits the spot.
It’s so cool that you played with this. I think brouwer’s fixed point theorem proves your conjectures. Both rotation and translation are continuous linear transformations so there must always be a point in a bounded area with no holes that never changes for either transformation. Vsauce did a video on something like this a while back, look up ‘fixed points’
Thanks! I'll definitely take a look at that theorem and that video. I'm glad that you could link this to other stuff you know about, that's super cool.
You're not asking if a spinning circle spins, you're asking if the central point on a spinning circle is spinning. The circle is spinning, That's provable. But the point can't spin. Rotation, by definition, is moving AROUND something else. Now, if we delve in quantum physics, that answer gets a bit murkier.
An interesting extension: If you warp a circle in some way so that it appears the same, there will always be at least one point that did not move. This works for any finite closed and connected region of points, too.
That does sound interesting! Can you explain what you mean by "warp a circle in some way so that it appears the same"? Do you mean like rotating around the centre, flipping horizontally/vertically around the centre, etc.?
As in, the point of rotation of any object will always be an empty space? That's an interesting thought. In that case, the point of rotation could never be a part of the object, and so every point ON the object would be moving in a circle in the way our brains naturally tell us they should be. Spinning any circle is like spinning a donut around the middle of its donut hole, just on a much smaller scale. That's actually a very interesting "solve" for this question. And given how small-scale everything we're talking about here is, it would be impossible to notice if everything COULD only move around those "gaps", and never around an actual physical component. You wouldn't feel the slight "magnetic" adjustment to make the nearest gap the point of rotation, as the object snaps into place to make it so. Might be near-impossible to prove either way, but definitely a very interesting idea.
@@Chimmaney With a point having literally no length, it seemed to make sense. My next guess would be that after you hit the point where matter expands(?) into wave functions, like the electron experiments, maybe rotation just isn't really a thing anymore.
my thesis is this: Let a circle with center C be defined as a set of points S such that for each point in S, its distance to C is less than or equal to some number r, namely the radius. (Mathematically this shape would be called a disk, as opposed to the circle which only consists of the outer rim of the disk; however, I'm conflating the definition here as it appears to be done so in the video.) Let a rotation of angle θ around a pivot P acting on a point A result in another point A' such that the angle APA' is of magnitude θ when going counterclockwise from line segment AP to line segment A'P. Let two shapes S and T be equal if and only if, for every point P within S, there exists exactly one point P' in T such that P=P'. Let two points P and Q be equal if and only if, for every possible coordinate system they have the same coordinate. Now we rotate circle S around its center C. Note that for every angle θ, for every point P on the circle S, there was exactly one point P' such that P is P' rotated an angle θ around the center C. Thus, we satisfy shape equality, and we conclude that a circle rotated around its center is the exact same circle. In more concise mathematical symbols: circle(C, r):={P|d(P,C)≤r} rot(A,P,θ)=((A₁-P₁)𝖼𝗈𝗌(θ)+(A₂-P₂)𝗌𝗂𝗇(θ)+P₁,(A₁-P₁)sin(θ)-(A₂-P₂)cos(θ)+P₂); note ∀θ∈ℝ:d(A, P)=d(rot(A,P,θ),P) (Shape:={X|∀P∈X:P∈ℝⁿ}) ∀A∈Shape∀B∈Shape:A=B:=∀P∈A∃!P'∈B:P=P' ∀n∈ℕ∀A∈ℝⁿ∀B∈ℝⁿ:A=B:=∀k∈{1,...,n}:Aₖ=Bₖ Theorem: ∀C∈ℝ²∀r∈ℝ⁺∀θ∈ℝ:circle(C, r)={P|∃!P'∈circle(C, r):P'=rot(P', C, θ)} Proof: By definition, ∀P∈{P|∃!P'∈circle(C, r):P'=rot(P', C, θ)}∃!P'∈circle(C, r) ■ Q.E.D. in actual english: A circle rotating around its center cannot be said to be rotating at all because when it rotates it doesn't change
Well actually, an electron is a point particle. It's not a "ball" like many depict it as. An Electron's spin is not rotation. It just has many aspects similar macroscopic spin that we use the term. There's a common meme about explaining quantum spin: imagine a ball that's rotating, except it's not a ball and it's not rotating. That's an electron spinning. It's just an intrinsic property of the electron that we understand through macroscopic analogues.
I don't know anything about that, but it sounds very interesting. Gonna have to do some reading. I was just using an electron as an example of "small object is still infinitely larger than a point, so it can rotate".
Rotation is a form of movement. Movement is inherently relative. You can not, by definition, move something relative to itself. It has nothing to do with the homogeneity of a point. The problem lies in the fact that you're trying to move an object relative to itself.
That's a good explanation for what is happening here, but it doesn't disagree with the point in the video -- the "objects" around the point of rotation move, while the point of rotation does not. The fact that it isn't moving because it CAN'T move relative to itself still results in the weird case of "everything is spinning around this point and this point is not spinning".
In this simulation you cant tell if it's spinning just by looking at it. but if you had a perfect circle spinning in real life you could feel if it is spinning just by touching it
Absolutely correct. To be clear, the thing of "you can't tell this circle is spinning until I add dots" is meant to set up the later "this point is not spinning", I was in no way trying to imply that the circle was not spinning before the dots, or that it can only be spinning if you can see that it is.
Hello Mr Chimmaney I would like to humble request a darkest dungeon 2 100 weeks series I just completed the darkest dungeon 1 100 weeks and need more. Humble request Adamski234
But can a stationary point spin? Can a single point ever be sideways, or upside down? I kind of feel like a stationary point can never be spinning, because nothing is happening to it.
@@Chimmaney The thing that confuses me is that, is the point causing what’s around it to rotate? Then wouldn’t that mean it’s rotating? Cause if it’s not rotating, isn’t everything just sliding around the center point?
@@themaydayman That's the idea that got me wanting to make this video. I think that's exactly what is happening, with everything sliding around the point of rotation, even though it is a WEIRD AS HELL thing to claim. It's one of those things that feels like it can't possibly be true, but the more you think about it, the more you realise you've found 4 reasons it is true and 0 reasons it isn't besides "feeling wrong". Very strange.
@@Chimmaney The only reason I can think of it being wrong is imagine three balls with a pole stuck through them, rotating around the middle ball… the middle ball has to rotate the pole (connection between things) to move the other balls
I think it's examples like that (which you're correct about, the pole would rotate) that make us feel like this is wrong. But the thing is, that pole's molecules would all be rotating around its centre, tracing a circular path -- but the point of rotation in the middle of the pole would still be stationary. What this boils down to, is whether or not a stationary point can rotate. Because a single point is a single point, it can't ever really be upside down, or sideways. The only real way to identify rotation is by following the path something traces as it moves around in a circle -- and when you zoom in to a rotating object, ALMOST everything will be doing that. The atom in the centre will have its parts moving around in a circle, the neutron in the middle of that atom will have its parts moving around in the circle -- but the point of rotation in the middle has no parts, and it will not be tracing any path at all. It will be entirely stationary and motionless, and in my opinion, not even rotating. It's definitely a weird idea and super interesting to talk about, at least for me. Thanks for engaging with the question enough to talk about it!
Rotation and movement are not the same. You can't just say the point isn't rotating because it's not moving. If you could, then whenever you move the circle in a circle, all points in it would be rotating. And that would extend to any movement also being rotation.
Rotation and movement are not the same, you're right, but it's different when we're talking about points. A point has no top or bottom or sides -- it has no parts. A purple circle on a screen that rotates is constantly replacing its purple pixels with visually-identical purple pixels -- a stationary point that "should be" rotating is constantly replacing itself with itself. It doesn't just look identical, or act identical. It is identical. A point is so infinitely small, that rotation as a concept is completely removed from it. A point has no rightside up, or upside down, or sideways. It is wholly and truly 100% identical at every moment where it "should be" spinning, even though the same is not true of larger objects. Because of how infinitely small a point is, it's difficult to visualise this, which is why I found the topic interesting enough to make a video on.
@@Chimmaney Your video claimed that some points in a circle rotated (not orbited), implying the existence of a point's orientation. In this universe, points have orientation. When a "circle rotates", each point of the circle changes orientation, including the center point. "A point is so infinitely small, that rotation as a concept is completely removed from it." In this universe, points have no orientation. No part of the circle can rotate. Rotation doesn't exist anywhere, there is only circular motion: A circle cannot spin. These two universes cannot coexist. Your original video stated that you believe in the first universe. This comment seems to imply you believe in the second.
@@benshulz4179 I used the word "rotated" for ease of communication and to set up the video's conclusion reveal, like how I used the word "circle" instead of "disc" for ease of communication. Yes, I believe points have no orientation. Me using the word "rotate" in a youtube video intended to be accessible does not change this. You seem to understand my meaning, but still act as if you do not. My video quite clearly agrees with the stance I have in these comments, and a choice of wording at the opening of a video does not contradict this. Objects can change orientation, as their points shift position, so rotation still exists. Just not on the micro scale of infinitely small points. A circle can rotate, a fingernail can rotate, an atom can rotate, everything larger than a point can rotate -- a point can not. If you disagree with this, that is fine. I would be genuinely interested to hear why and how someone might argue that a point can have orientation, because I like to learn things from people who can competently discuss a topic, but your strange behaviour and rude attitude makes me doubt that I'm going to get that here. Even if you really have been holding back the answer to how a point can have orientation through all of your comments across this video's comment section, I don't expect to receive it in a good faith way intended to share knowledge for the joy of it. So I'm happy to leave this reply thread here. Best wishes to ya mate.
@@Chimmaney "how a point can have orientation" Geometry has property inheritance: If a manifold has a global property like orientation, all manifolds making it up (including points) also must also have that property. "Objects can change orientation, as their points shift position" This is saying that orientation isn't a property. There's 3 types of transformations: Translation, rotation and reflection (and scaling, depending on who you ask) If "rotation" now just means "circular translations", a lot of weird things happen. Moving fully across mobius strip wouldn't be rotation by this definition, while the Earth would "rotate" around the Sun, as each point of Earth is moving in a circular path. This statement cannot be true. Orientation must exist as a property of manifolds. Saying otherwise simply doesn't work: We could turn objects into their pure rotational symmetric counterparts without rotations. In the future, when you come up with a new idea, try to think it through to the end, and look at what simple facts of reality are broken if you are correct. Circle's center doesn't rotate because points have no orientation? Oops, now geometry is broken. :( That's hard to believe, don't you think?
Something I decided to not include in the video, but might interest some of you:
I find it interesting how the way that "individual points on an object" act in this question is a bit similar to how "individual moments in time" act in Zeno's arrow paradox -- where, if you shoot an arrow from a bow, and look at any individual moment after that, the airborne arrow will not be moving. Yet if you stack moment after moment, one after another, in quick succession, the same way that moving time works, the arrow WILL be moving -- which should be impossible, if it isn't moving in any one of those moments which make up time.
Basically, thinking about an individual point is similar to thinking about an individual moment. Reality isn't built to account for those concepts. Which might imply there is no such thing as a point or a moment, the smallest measurements of space and time. Absurd.
(also -- in case you missed the community post, the new profile picture is the very generous artwork of @SovietGirlReal. It is masterful.)
You've fuckin' cracked, Chimmaney. This proves it. You've finally lost it. First the schedule, now your mind. WHAT IS HAPPENING TO YOU?!
Nah, jk, good video.
Relativity is a common problem in math; From your perspective there is no motion in a boat, and you can't feel the curve of Earth as you travel into the horizon. And despite this probably being the intro of your 5-6th grade physics class, your entire video (and this comment) acts as if you made a new math discovery.
So yes, the "point of rotation", for all intents and purposes, rotates. After all, rotation is a type of transformation over an entire lattice: If that transformation doesn't change a state of a single point, it doesn't mean that transformation of the lattice didn't occur. Think of moving the letters of "POO" once to the right with wrap-around: "OPO", there was a transformation and movement, even if from the perspective of the last letter, nothing changed.
Zeno's arrow paradox is not even a paradox: Velocity = distance * time. If you remove the time and just take a picture of space (distance), then obviously there is no velocity. This is 3rd grade math, come on.
At the end of the day, your use of "Zeno's paradox" shows that a lack of understanding of math, at the same level as quantum mystics who believe they can affect reality by closing their eyes (and therefore not observing particles): Reality does have a single point and single moment. All types of math work with them. If they don't work in yours, it's probably sign that you did something wrong, not that you proved a new theory.
TL;DR: You are wrong. Your example of a circle made up of points is a lattice. If we think of the points as atoms or even quarks, they would all have some type of connection to each other. Those connections do rotate as the lattice does, even if the central "point" cannot be shown to rotate by your math.
@@benshulz4179 You have fundamentally misunderstood so many things about this video that I don't even know where to start with this comment, which is at the very least somewhat less rude than the others you have left across this entire comment section.
Of course individual moments and points do exist. My comment saying that something "might imply there is no such thing as a point or a moment" was so clearly framed as an "even though we know that can't possibly be the case".
And given that moments DO exist, and time is a collection of individual moments, Zeno's arrow paradox in no way "removes the time" from the velocity equation. That's like saying that measuring one second of the arrow's travel is removing the time from the velocity equation. The paradox is saying that, if time is made up of infinite, infinitely small moments, during each of which the arrow is not moving, then how can it be moving when you put the moments together, unless there is some time happening between the moments? The answer to the paradox isn't that moments can't exist, or that nothing can ever move, it's that the way humans think about infinity is flawed. We imagine a world where you can see from one moment to the moment directly beside it, because we're used to working in fields next to infinity -- but this is not the case. In the same way that you cannot see the number just before or after infinity, or the decimal just before 0.3 recurring.
The same is true of points. Of course points exist, nobody here ever suggested that points not existing was a real possibility. But they are so infinitely small that humans have trouble thinking in terms of them. Which is what you've done here as well.
A point is not like an object. An object can spin. When an object is upside-down, you can measure each of its points top-to-bottom, and read them in the order of ABC. Then you can spin it rightside up, and those same points will read as CBA.
But a point is like a moment. Just like humans imagine that there must be something "between" moments, people imagine that a point must itself have points. But it does not. A point can never itself be upside-down, or sideways, or at an angle. It has no top half to compare to a bottom half. It is infinitely small.
A rotating object has its parts, its points, relocating themselves along a circular path. Every measurement you take down to the level of "point" will be rotating too -- each cubic millimetre, each atom. But each of those points on the object are doing nothing more than tracing that circular path, relocating themselves. When they spin from the top half to the bottom, they do not themselves end up upside-down compared to their starting position, even though intuition tells us they should be. A point cannot rotate. And the point in the middle, which doesn't even trace a circular path, highlights this perfectly.
It's not that we can't "see" the point rotating, or that we can't "feel" the point rotating, and because of that I'm claiming that means it isn't rotating. It's that, if you did rotate a stationary point, you wouldn't be doing anything. Nothing happens to it. It's not that it looks, feels, or acts identical after rotating 180 and staying stationary -- it's that is IS completely identical in every single way. A single stationary point cannot spin.
The fact that the default human position, before thinking about this, is "but it has to spin", is the very reason I made this video. Because I found the idea interesting. How it's contrary to what we "feel" should be right. We compare it to what we know, with spinning objects, spinning atoms, so on. We go as small down as we can comprehend. But we still have difficulty understanding that a point cannot spin, because it's not like any larger measurement. We still have difficulty understanding that you can never see the moment immediately after another moment, because it's not like any larger measurement. Because we weren't built to imagine infinity.
@@Chimmaney Oh, I see.
"A rotating object has its parts, its points, relocating themselves along a circular path"
That's a weird misunderstanding. Rotation isn't defined as "movement in a circular path" Rotation is a property of a manifold. Best exemplified in a simple example you can do on pen and paper: Move a manifold across a mobius strip. When it reaches the starting point, it has rotated 180 degrees. This is true of every manifold.
This is your logical fallacy: "A point cannot rotate."
If this was true, you wouldn't be able to move a point across a mobius strip.
Now, you might already have a thought in mind. "But a point in space has no defined rotation, only location." I will shut this down by mentioning that in the video, you said: "points at the edge of the circle rotate".
This is important wording: You are saying that points can be rotated: That they have the property of orientation. And that makes perfect sense: Your example is a circle, so the points are not simply orbiting a center, like stirring a pot: By your own words, these points are part of a "spinning circle", a lattice.
The lattice is an important part: If a translation is applied to a lattice, every point in the lattice is affected . And because you stated that the "circle rotates", the center's orientation has been changed, albeit without any movement.
Yes, you cannot draw the "point's rotation". Completely true. But you also cannot draw it's location, or draw the time that it existed in. But the math still holds up, and your own wording, where we construct a lattice of points, which each have the property of rotation (as some points can be rotated, by your own words), means the math would still hold up.
"it's that is IS completely identical in every single way."
It is not. It's orientation has changed.
"A single stationary point cannot spin.""
Why not? Can a orientationless point move? What's this relationship between orientation and movement that you've come up with, and why does it seem arbitary?
"Because I found the idea interesting. How it's contrary to what we "feel" should be right."
This is because you made a mistake. "Points have no orientation" isn't that interesting of a discovery, especially not when your video starts by claiming that some points in a circle are rotating because they are... moving in a circle (which isn't the same thing?)
@@benshulz4179 To clarify, the speech used in this video was not meant to be taken as precise gospel. I call the disc a circle, and I say that the points rotate, because I want to easily communicate my ideas. I don't want to bog down a youtube video, which is not a mathematical paper, by adding clarifying statements to every word I use -- especially when most people understood my meaning just fine.
When the disc/circle rotates, it relocates its points in the traditional way we think of rotation. Yes, rotation isn't defined as "movement along a circular path", but that is exactly what happens to the points of a rotating object -- the points I was clearly talking about when I said that. I agree, that isn't what happens to the object as a whole, just its points. Yes, I am claiming that points have no orientation, because a point that is at a different orientation is identical not just to our senses, but in every possible way. While a symmetrical object that is rotated may look identical while it is not, because the points along it are in different positions, a point that is rotated IS identical.
You still seem to misunderstand the infinite smallness of a point, and why it is that I believe they cannot have orientation. I'm happy to be proven wrong here, by somebody seeking discussion coming in with good reasoning, but your only reason against this is that it feels wrong. That's a notion that I agree with, but it is not meaningful beyond friendly conversation. My imprecise wording, intended for ease of communication in a short youtube video, does not give points the ability to face a different way. I'm sure you understood that, given that you seem to understand what I'm saying with points having no orientation. It feels very bad faith to say that, because I said "the points rotate" early in the video before revealing my conclusions, I am contradicting what you clearly do understand me to mean.
"A single stationary point cannot spin" was meant to seperate the two possible definitions of spin. Yes, I believe that none of the points on the circle are changing orientation, but they are still moving around in a circle, in a manner commonly identified in language as spinning. People point at a spinning circle, and define that motion as spinning -- because of how words work, they are correct, even if the points on it are not changing orientation.
If you don't think any of this is interesting, that is entirely legal, and has been the whole time. I do think it is interesting, and other people clearly do as well, but not everybody will.
I feel like we're not even talking to each other, and I don't feel like you're coming from a place of good faith or discussion, so I'm happy to leave this here. Sorry that this video wasn't for you, I hope your next one hits the spot.
It’s so cool that you played with this. I think brouwer’s fixed point theorem proves your conjectures. Both rotation and translation are continuous linear transformations so there must always be a point in a bounded area with no holes that never changes for either transformation. Vsauce did a video on something like this a while back, look up ‘fixed points’
Thanks! I'll definitely take a look at that theorem and that video. I'm glad that you could link this to other stuff you know about, that's super cool.
Careful, questions like this will get you thinking about black holes!
Can a circle spin?
Yes.
*clicks off*
Wait come back I have some other questions I want your help with. Can a match box?
@@Chimmaney no but an aluminium can
You're not asking if a spinning circle spins, you're asking if the central point on a spinning circle is spinning. The circle is spinning, That's provable. But the point can't spin. Rotation, by definition, is moving AROUND something else. Now, if we delve in quantum physics, that answer gets a bit murkier.
if Chimmaney had cliffnotes
Rotation isn't defined as movement, what are you on about? Rotation can cause movement, but they are not the same thing.
this video is making my brain hurty
Chimmaney thinking of circles spinnng so much he stumbles into quantum uncertainty principles. lol
just wait until someone tells you about electron spin
An interesting extension: If you warp a circle in some way so that it appears the same, there will always be at least one point that did not move. This works for any finite closed and connected region of points, too.
That does sound interesting!
Can you explain what you mean by "warp a circle in some way so that it appears the same"? Do you mean like rotating around the centre, flipping horizontally/vertically around the centre, etc.?
Zeroeth dimensional shenanigans, huh?
All things considered, I imagine true 0 would ultimately be an empty space between what makes up matter.
As in, the point of rotation of any object will always be an empty space? That's an interesting thought.
In that case, the point of rotation could never be a part of the object, and so every point ON the object would be moving in a circle in the way our brains naturally tell us they should be. Spinning any circle is like spinning a donut around the middle of its donut hole, just on a much smaller scale.
That's actually a very interesting "solve" for this question. And given how small-scale everything we're talking about here is, it would be impossible to notice if everything COULD only move around those "gaps", and never around an actual physical component. You wouldn't feel the slight "magnetic" adjustment to make the nearest gap the point of rotation, as the object snaps into place to make it so.
Might be near-impossible to prove either way, but definitely a very interesting idea.
@@Chimmaney With a point having literally no length, it seemed to make sense.
My next guess would be that after you hit the point where matter expands(?) into wave functions, like the electron experiments, maybe rotation just isn't really a thing anymore.
Once again, my man cooked.
This is some greek philosopher level cooking right there!
The ancient greeks cooked quail eggs I think.
Hey, I like a video that not only makes me chuckle, but also think, great one!
Thank you!
my thesis is this:
Let a circle with center C be defined as a set of points S such that for each point in S, its distance to C is less than or equal to some number r, namely the radius. (Mathematically this shape would be called a disk, as opposed to the circle which only consists of the outer rim of the disk; however, I'm conflating the definition here as it appears to be done so in the video.)
Let a rotation of angle θ around a pivot P acting on a point A result in another point A' such that the angle APA' is of magnitude θ when going counterclockwise from line segment AP to line segment A'P.
Let two shapes S and T be equal if and only if, for every point P within S, there exists exactly one point P' in T such that P=P'.
Let two points P and Q be equal if and only if, for every possible coordinate system they have the same coordinate.
Now we rotate circle S around its center C.
Note that for every angle θ, for every point P on the circle S, there was exactly one point P' such that P is P' rotated an angle θ around the center C.
Thus, we satisfy shape equality, and we conclude that a circle rotated around its center is the exact same circle.
In more concise mathematical symbols:
circle(C, r):={P|d(P,C)≤r}
rot(A,P,θ)=((A₁-P₁)𝖼𝗈𝗌(θ)+(A₂-P₂)𝗌𝗂𝗇(θ)+P₁,(A₁-P₁)sin(θ)-(A₂-P₂)cos(θ)+P₂); note ∀θ∈ℝ:d(A, P)=d(rot(A,P,θ),P)
(Shape:={X|∀P∈X:P∈ℝⁿ})
∀A∈Shape∀B∈Shape:A=B:=∀P∈A∃!P'∈B:P=P'
∀n∈ℕ∀A∈ℝⁿ∀B∈ℝⁿ:A=B:=∀k∈{1,...,n}:Aₖ=Bₖ
Theorem: ∀C∈ℝ²∀r∈ℝ⁺∀θ∈ℝ:circle(C, r)={P|∃!P'∈circle(C, r):P'=rot(P', C, θ)}
Proof: By definition, ∀P∈{P|∃!P'∈circle(C, r):P'=rot(P', C, θ)}∃!P'∈circle(C, r) ■ Q.E.D.
in actual english:
A circle rotating around its center cannot be said to be rotating at all because when it rotates it doesn't change
That is something I never thought about but is extremely intriguing. Also love the editing
Thanks!
Well actually, an electron is a point particle. It's not a "ball" like many depict it as. An Electron's spin is not rotation. It just has many aspects similar macroscopic spin that we use the term. There's a common meme about explaining quantum spin: imagine a ball that's rotating, except it's not a ball and it's not rotating. That's an electron spinning. It's just an intrinsic property of the electron that we understand through macroscopic analogues.
I don't know anything about that, but it sounds very interesting. Gonna have to do some reading. I was just using an electron as an example of "small object is still infinitely larger than a point, so it can rotate".
Rotation is a form of movement. Movement is inherently relative. You can not, by definition, move something relative to itself. It has nothing to do with the
homogeneity of a point. The problem lies in the fact that you're trying to move an object relative to itself.
That's a good explanation for what is happening here, but it doesn't disagree with the point in the video -- the "objects" around the point of rotation move, while the point of rotation does not. The fact that it isn't moving because it CAN'T move relative to itself still results in the weird case of "everything is spinning around this point and this point is not spinning".
@@Chimmaney Absolutely.
The central point does rotate from the point of view of any other point. The circle is a lie we all tell ourselves.
They can write, edit AND science?? What will Chimmaney do next
parking violation
In this simulation you cant tell if it's spinning just by looking at it. but if you had a perfect circle spinning in real life you could feel if it is spinning just by touching it
Absolutely correct. To be clear, the thing of "you can't tell this circle is spinning until I add dots" is meant to set up the later "this point is not spinning", I was in no way trying to imply that the circle was not spinning before the dots, or that it can only be spinning if you can see that it is.
Hello Mr Chimmaney I would like to humble request a darkest dungeon 2 100 weeks series I just completed the darkest dungeon 1 100 weeks and need more.
Humble request Adamski234
rotation doesnt exist its just movement influenced by external angular momentum to where humans perceive it as rotation
Cats don't exist they're just furry mammals made up of molecules to where humans perceive them as cats
But points cant rotate
no multivariable calculus smh
cool what if there's connections to the center point? doesn't that mean the center point is spinning?
But can a stationary point spin? Can a single point ever be sideways, or upside down? I kind of feel like a stationary point can never be spinning, because nothing is happening to it.
@@Chimmaney The thing that confuses me is that, is the point causing what’s around it to rotate? Then wouldn’t that mean it’s rotating? Cause if it’s not rotating, isn’t everything just sliding around the center point?
@@themaydayman That's the idea that got me wanting to make this video. I think that's exactly what is happening, with everything sliding around the point of rotation, even though it is a WEIRD AS HELL thing to claim.
It's one of those things that feels like it can't possibly be true, but the more you think about it, the more you realise you've found 4 reasons it is true and 0 reasons it isn't besides "feeling wrong". Very strange.
@@Chimmaney The only reason I can think of it being wrong is imagine three balls with a pole stuck through them, rotating around the middle ball… the middle ball has to rotate the pole (connection between things) to move the other balls
I think it's examples like that (which you're correct about, the pole would rotate) that make us feel like this is wrong. But the thing is, that pole's molecules would all be rotating around its centre, tracing a circular path -- but the point of rotation in the middle of the pole would still be stationary.
What this boils down to, is whether or not a stationary point can rotate. Because a single point is a single point, it can't ever really be upside down, or sideways. The only real way to identify rotation is by following the path something traces as it moves around in a circle -- and when you zoom in to a rotating object, ALMOST everything will be doing that. The atom in the centre will have its parts moving around in a circle, the neutron in the middle of that atom will have its parts moving around in the circle -- but the point of rotation in the middle has no parts, and it will not be tracing any path at all. It will be entirely stationary and motionless, and in my opinion, not even rotating.
It's definitely a weird idea and super interesting to talk about, at least for me. Thanks for engaging with the question enough to talk about it!
6 minutes wasted
The world will go on turning. Most of it. Uhhh, get back to me.
Rotation and movement are not the same.
You can't just say the point isn't rotating because it's not moving. If you could, then whenever you move the circle in a circle, all points in it would be rotating. And that would extend to any movement also being rotation.
Rotation and movement are not the same, you're right, but it's different when we're talking about points.
A point has no top or bottom or sides -- it has no parts. A purple circle on a screen that rotates is constantly replacing its purple pixels with visually-identical purple pixels -- a stationary point that "should be" rotating is constantly replacing itself with itself. It doesn't just look identical, or act identical. It is identical. A point is so infinitely small, that rotation as a concept is completely removed from it.
A point has no rightside up, or upside down, or sideways. It is wholly and truly 100% identical at every moment where it "should be" spinning, even though the same is not true of larger objects. Because of how infinitely small a point is, it's difficult to visualise this, which is why I found the topic interesting enough to make a video on.
@@Chimmaney Your video claimed that some points in a circle rotated (not orbited), implying the existence of a point's orientation.
In this universe, points have orientation. When a "circle rotates", each point of the circle changes orientation, including the center point.
"A point is so infinitely small, that rotation as a concept is completely removed from it."
In this universe, points have no orientation. No part of the circle can rotate. Rotation doesn't exist anywhere, there is only circular motion: A circle cannot spin.
These two universes cannot coexist. Your original video stated that you believe in the first universe. This comment seems to imply you believe in the second.
@@benshulz4179 I used the word "rotated" for ease of communication and to set up the video's conclusion reveal, like how I used the word "circle" instead of "disc" for ease of communication.
Yes, I believe points have no orientation. Me using the word "rotate" in a youtube video intended to be accessible does not change this. You seem to understand my meaning, but still act as if you do not. My video quite clearly agrees with the stance I have in these comments, and a choice of wording at the opening of a video does not contradict this.
Objects can change orientation, as their points shift position, so rotation still exists. Just not on the micro scale of infinitely small points. A circle can rotate, a fingernail can rotate, an atom can rotate, everything larger than a point can rotate -- a point can not.
If you disagree with this, that is fine. I would be genuinely interested to hear why and how someone might argue that a point can have orientation, because I like to learn things from people who can competently discuss a topic, but your strange behaviour and rude attitude makes me doubt that I'm going to get that here. Even if you really have been holding back the answer to how a point can have orientation through all of your comments across this video's comment section, I don't expect to receive it in a good faith way intended to share knowledge for the joy of it. So I'm happy to leave this reply thread here.
Best wishes to ya mate.
@@Chimmaney
"how a point can have orientation"
Geometry has property inheritance: If a manifold has a global property like orientation, all manifolds making it up (including points) also must also have that property.
"Objects can change orientation, as their points shift position"
This is saying that orientation isn't a property. There's 3 types of transformations: Translation, rotation and reflection (and scaling, depending on who you ask)
If "rotation" now just means "circular translations", a lot of weird things happen. Moving fully across mobius strip wouldn't be rotation by this definition, while the Earth would "rotate" around the Sun, as each point of Earth is moving in a circular path.
This statement cannot be true. Orientation must exist as a property of manifolds. Saying otherwise simply doesn't work: We could turn objects into their pure rotational symmetric counterparts without rotations.
In the future, when you come up with a new idea, try to think it through to the end, and look at what simple facts of reality are broken if you are correct. Circle's center doesn't rotate because points have no orientation? Oops, now geometry is broken. :( That's hard to believe, don't you think?