Does the center of a disk exist?
Re: Does the center of a disk exist?
It's not very different to Zenon paradox.
I don't give too much think to it, but "center" is a mathematical function, and reality is... complex, as you probably know, irrational numbers are everywere, just as another example of the same.
I mean, we say the center of the disc asuming it's a perfect circle, like we say the center of the Earth asuming it is a sphere, but they aren't. There are probably no perfect circles (I mean things with that form) in the Universe, we just give a theoritical circle to the object o the position of objects.
If reality is a continuous for you, then, points and space are just relative positions, and, since you can't atach a completely accurate measure of position, no matter how good are your instruments, everything goes to theoretical things, and in theroreticaland, there can be things "wrong but simple enough", in fact, there can be no perfection, since we can't have the whole Universe in our head.
I don't know if I'm being clear for you XD.
I don't give too much think to it, but "center" is a mathematical function, and reality is... complex, as you probably know, irrational numbers are everywere, just as another example of the same.
I mean, we say the center of the disc asuming it's a perfect circle, like we say the center of the Earth asuming it is a sphere, but they aren't. There are probably no perfect circles (I mean things with that form) in the Universe, we just give a theoritical circle to the object o the position of objects.
If reality is a continuous for you, then, points and space are just relative positions, and, since you can't atach a completely accurate measure of position, no matter how good are your instruments, everything goes to theoretical things, and in theroreticaland, there can be things "wrong but simple enough", in fact, there can be no perfection, since we can't have the whole Universe in our head.
I don't know if I'm being clear for you XD.
Re: Does the center of a disk exist?
I challenge you to give a single example of an irrational number in reality, if by reality you mean the physical world. You can't just quote a physics formula involving pi, since that is a model of reality and not reality itself. You can't point to circles because there are no perfect circles.TSBU wrote: I don't give too much think to it, but "center" is a mathematical function, and reality is... complex, as you probably know, irrational numbers are everywere
Would you care to revise your remark?
Re: Does the center of a disk exist?
Can you read again what I wrote? Anyway, I challenge you to find a rational number in reality.wtf wrote:I challenge you to give a single example of an irrational number in reality, if by reality you mean the physical world. You can't just quote a physics formula involving pi, since that is a model of reality and not reality itself. You can't point to circles because there are no perfect circles.TSBU wrote: I don't give too much think to it, but "center" is a mathematical function, and reality is... complex, as you probably know, irrational numbers are everywere
Would you care to revise your remark?
Re: Does the center of a disk exist?
But I never claimed you could. You are the one who claims there are irrational numbers in reality. Perhaps you should read your own post.TSBU wrote: Can you read again what I wrote? Anyway, I challenge you to find a rational number in reality.
Re: Does the center of a disk exist?
I'm not good at English, and natural language is ambiguous. But...wtf wrote:But I never claimed you could. You are the one who claims there are irrational numbers in reality. Perhaps you should read your own post.TSBU wrote: Can you read again what I wrote? Anyway, I challenge you to find a rational number in reality.
I just said they are everywere, and they are everywere, in math, in our heads (also, everything you know, even the concept of reality, is in your head), they are not in reality. Also, the rest of the text is saying precisely what you what to teach, just read the second paragraph, where I say that perfect circles don't exist in reality.I don't give too much think to it, but "center" is a mathematical function, and reality is... complex, as you probably know, irrational numbers are everywere, just as another example of the same.
Thanks for the language lesson dude, maybe you should try to ask next time?
Re: Does the center of a disk exist?
This is why records suck. The last parts of a phonograph record, where the angular velocity is lowest, offer notably inferior sound compared to the first part.

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Re: Does the center of a disk exist?
Good question. I've thought of a similar one. But before I mention this, you say 'rotational speed' which is the same as the angular speed. As such, the center has the same rotational velocity. The arc distance traveled in constant units of time is what is smaller as you move towards the center. As such, that velocity is what is 'slowing down'. It can be zero given that interpretation but is still spinning at the same rate AT THE POINT. This is where you can interpret that what is 'lost' linearly is 'gained' in spin. If you imagine such a disk with an infinitely larger radius, the opposite is the case (if not in actual space): that the speed approaches infinity in a LINE!(??) This is one way you can LOGICALLY infer why there is an actual SPEED LIMIT.Philosophy Explorer wrote:When you spin the the disk, it moves in a rotational motion. The faster it spins, the faster it moves.
So far I must be boring you with those facts. But something else is happening (or not happening depending on your POV). As you're moving linearly towards the center of the disk, its motion is slowing down
(assuming the disk is maintaining the same rate of rotational speed). And as you keep moving towards the center, you're moving even more slower. Until you reach the exact center where the pattern shows you're not even moving at all! And it doesn't matter how fast that disk is spinning; its exact center never moves.
This seems to defy common sense. How could the entire disk spin while its (attached) exact center never moves? One way to resolve this apparent paradox is to deny the center.
For me it makes sense and I accept it as part of my reality even though it's theoretical. How about you?
PhilX
Then, knowing there is a speed limit logically, you have to go BACK to the thought experiment with this assumed. Then you treat the transfer of information maximum and fixed on its tangent velocity. This is what I was leading to my own inspection. If the tangent velocity is fixed, the closer to the center means that your angular velocity is increasing towards the center until you get an infinite spinning speed. The actual 'disc' would be warped as a spiral and the center would also be both not moving as is moving. For all cases, a logical center has no speed AT THE CENTER in neither angular nor tangential velocity.
Real objects actually DO warp when spun as a spiral and depends on HOW they initially accelerate to any speed. If begun at the center, a 'torque' force initiates the spin and makes the object, like a record, begin spinning from the center outwards AT THE SAME RATE in all radii out to the edge of the disc as an unperceivable spiral unless very large. A small disc like a record is just too small to notice. (Mind you, all records and CDs usually have nonexisting centers anyways! )

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Re: Does the center of a disk exist?
The physicists and math guys have an interesting way of looking at the center of a rotating disk.
First you can always choose a frame of reference in which the rotation goes away. That is interesting.
But assuming you don't do that then you can attach an arrow called a velocity vector to each point of the record. The length of the arrow is the speed of the record at that point, and the direction is the direction that point is moving in. They say its the instantaneous velocity vector of the point. These arrows form what is called a velocity field  its just vector or arrow at each point.
Now what is interesting is that if you take any closed curve  like a loop of string and lay it on a record and then add up the velocity vector along the direction of the string for the whole closed curve of the string you get zero for every curve that does not contain the center of the record!. This function is called the curl of the vector field and there is always one point on the surface of a rotating planar figure that will have this property...i.e. there is always one point for any planar figure that will have zero velocity and nonzero curl.
But it gets even more interesting for the number of points on a sphere that have nonzero curl is two! Not one! On the earth these are the north and south poles.
And it gets very interesting then for if you take any shape that can be made from a sphere by deforming it continuously  take a pyramid for example  and then you count the number of vertices, edges and faces and form the sum VE+F you find the number is always that same 2. So if you take all the facets of a diamond and count the edges and vertices then just like a pyramid it also will be two. And it doesn't matter how the diamond is cut!
But if you take a torus or a donnut shape you can have it rotate with zero "centers"! The rotation is up and out the middle then around the top and down the outside then back up the center for example. And there are no points like the poles on the earth or the center of the record. All points have nonzero velocity and zero curl!....and sure enough if you triangulate the torus and count the vertices, edges, and faces you get a zero!
This is called the Euler characteristic and it can be formed for any solid. You just imagine the wind blowing and and count the centers and you will know the number of vertices  the number of edges + the number of faces. Its very interesting.
First you can always choose a frame of reference in which the rotation goes away. That is interesting.
But assuming you don't do that then you can attach an arrow called a velocity vector to each point of the record. The length of the arrow is the speed of the record at that point, and the direction is the direction that point is moving in. They say its the instantaneous velocity vector of the point. These arrows form what is called a velocity field  its just vector or arrow at each point.
Now what is interesting is that if you take any closed curve  like a loop of string and lay it on a record and then add up the velocity vector along the direction of the string for the whole closed curve of the string you get zero for every curve that does not contain the center of the record!. This function is called the curl of the vector field and there is always one point on the surface of a rotating planar figure that will have this property...i.e. there is always one point for any planar figure that will have zero velocity and nonzero curl.
But it gets even more interesting for the number of points on a sphere that have nonzero curl is two! Not one! On the earth these are the north and south poles.
And it gets very interesting then for if you take any shape that can be made from a sphere by deforming it continuously  take a pyramid for example  and then you count the number of vertices, edges and faces and form the sum VE+F you find the number is always that same 2. So if you take all the facets of a diamond and count the edges and vertices then just like a pyramid it also will be two. And it doesn't matter how the diamond is cut!
But if you take a torus or a donnut shape you can have it rotate with zero "centers"! The rotation is up and out the middle then around the top and down the outside then back up the center for example. And there are no points like the poles on the earth or the center of the record. All points have nonzero velocity and zero curl!....and sure enough if you triangulate the torus and count the vertices, edges, and faces you get a zero!
This is called the Euler characteristic and it can be formed for any solid. You just imagine the wind blowing and and count the centers and you will know the number of vertices  the number of edges + the number of faces. Its very interesting.
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