## Does the center of a disk exist?

What is the basis for reason? And mathematics?

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Philosophy Explorer
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### Does the center of a disk exist?

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

A_Seagull
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### Re: Does the center of a disk exist?

A problem is only a problem if you think it is a problem.. I have no problem with this.

Perhaps you might find it interesting to investigate Coriollis 'forces', they are relevant to your scenario.

Philosophy Explorer
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### Re: Does the center of a disk exist?

A_Seagull wrote:A problem is only a problem if you think it is a problem.. I have no problem with this.

Perhaps you might find it interesting to investigate Coriollis 'forces', they are relevant to your scenario.
I think for some people, just because the rest of the disk is moving doesn't mean that the exact center moves too. Then there are some people who just don't believe in points, mathematical or otherwise, because they are
dimensionless.

As I said I believe in them partly because without them, this universe wouldn't exist. It'll be interesting to hear from others on this.

PhilX

Dalek Prime
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### Re: Does the center of a disk exist?

If you stand at the center of a spinning disk, you will notice a 360° panoramic view. Then tell me the center is not moving.

Philosophy Explorer
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### Re: Does the center of a disk exist?

Dalek Prime wrote:If you stand at the center of a spinning disk, you will notice a 360° panoramic view. Then tell me the center is not moving.
Exact center (you've been eating too much ice cream).

PhilX

Dalek Prime
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### Re: Does the center of a disk exist?

Philosophy Explorer wrote:
Dalek Prime wrote:If you stand at the center of a spinning disk, you will notice a 360° panoramic view. Then tell me the center is not moving.
Exact center (you've been eating too much ice cream).

PhilX
Exact enough. And I'm lactose intolerant.

wtf
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### Re: Does the center of a disk exist?

a) Case of a physical disk. You can't precisely find or define the center to arbitrary precision because of measurement error. And any physical rotational mechanism is imperfect and has some amount of wobble. So there is no stationary point in a physical spinning disk.

b) Case of a mathematical disk. Consider the unit disk D consisting of all points of the plane whose distance from the origin is at most 1. Apply a nonzero rotation to the plane. Every point moves except the origin. This is obvious. The center of a spinning mathematical disk is stationary with respect to any rotation of the disk's plane centered at the center of the disk.

Dalek Prime
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### Re: Does the center of a disk exist?

Someone needs more fiber in their diet. So, what about quantum spin? Forgot that one, if we're going to be retentive about it.

Hobbes' Choice
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### Re: Does the center of a disk exist?

Dalek Prime wrote:If you stand at the center of a spinning disk, you will notice a 360° panoramic view. Then tell me the center is not moving.
You are not really appreciating the problem here.
The problem does not stop here, because the outside of your head is turning faster than the inside of your head and the closer you get to the centre of rotation the slower is the rotation, which tends to zero.
So as you stand in the middle of the rotation the centre of your brain, if you have one, tends to zero.

Dalek Prime
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### Re: Does the center of a disk exist?

Hobbes' Choice wrote:
Dalek Prime wrote:If you stand at the center of a spinning disk, you will notice a 360° panoramic view. Then tell me the center is not moving.
You are not really appreciating the problem here.
The problem does not stop here, because the outside of your head is turning faster than the inside of your head and the closer you get to the centre of rotation the slower is the rotation, which tends to zero.
So as you stand in the middle of the rotation the centre of your brain, if you have one, tends to zero.
I'm assuming a hypothetical one-dimensional visual cortex. If there's spin at the quantum level, there must be spin, somewhere. Again, I am not an expert, and am not suggesting I'm correct. More, I'm thinking out loud.

Throng
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### Re: Does the center of a disk exist?

I guess it's just because we imagine the centre as inert, but the same 'motionless point' applies to any point within any shape we imagine to be inert. Because the point itself is 'sizeless', or at least, 'has no parts', there is no motion there when it's imagined to be inert.

wtf
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### Re: Does the center of a disk exist?

Throng wrote:I guess it's just because we imagine the centre as inert, but the same 'motionless point' applies to any point within any shape we imagine to be inert. Because the point itself is 'sizeless', or at least, 'has no parts', there is no motion there when it's imagined to be inert.
The center of a mathematical disk is sizeless and does not turn during a rotation. When you rotate the unit disk through an angle, the origin does not move.

Any physical disk is imperfect and does not have an exact center. If there is some tiny particle or subparticle of it that is truly fixed in space while the rest of the disk turns, we could not measure it and would have no way of knowing anyway. The best you could do would be to get a machinist or a physicist to tell you, "The wobbliness of the center is within such and so of zero, with such and such probability."

Surely all this is clear.

Greta
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### Re: Does the center of a disk exist?

I would think that, if you're going to rotate, you have rotate about some point - the eye of the storm, the calm at the centre of the vortex. The "singularity" (or at least inner horizon) at the centre of Sag A*, around which we all rotate.

What is everything spinning around? Some central, pivotal area, and if that point disappears when inspected at the smallest of scales, then it must be quantum

ken
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### Re: Does the center of a disk exist?

Philosophy Explorer wrote:
This seems to defy common sense.
Obviously, by what you write here, what makes sense to you is NOT really at all that common. Common sense, to Me, is what is common to ALL human beings, and that what makes sense to every one. The former is what is commonly experienced by ALL human beings, the latter is the knowledge or knowing that is gained by those experiences through any or all of the five senses.

For example what is common to ALL people is being born gasping for air. The common experience shared by ALL human beings is the desire breath air, that is the breathe of life. So, what is common knowledge or commonly known, from our senses, by ALL human beings is we need air to live. We can not live without it. This can also be very easily experimentally proven, that is if any person disagrees here. Therefore, common sense, in this particular example, would be to not pollute the air we need to breath for our continued survival. To pollute the actual air that we actually need to live on, to Me, would defy common sense. Whether a spinning disk has a moving center or not, to Me, does not defy common sense. That is just a question to ponder over for amusement. It has no real bearing on what is actually important in Life.

After we answer and fix up our real problems in Life first, then i think it is time to look at stuff like this.
Philosophy Explorer wrote: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.

So you ask a clarifying question about how could this happen, yet instead of waiting for any response you jump straight to just deny the center, as it makes sense to you, and accept it as part of your own reality, even though you do not know the truth yet.

I am just curious as to why you would do this? I see this kind of behavior a lot in human beings and truly wonder how I could get them to stop doing this?

What is going on in your own life that you need to deny, or to not deny, the center of a spinning disk to form part of your own reality? How is that of any real importance?

Also, why accept some thing, without its truth being known first, and form your own reality?

Why not just look at what really is, instead of making up a new reality?

Philosophy Explorer wrote: How about you?

PhilX
I just look at what really is, from a truly open perspective. I do not see any sense in accepting any thing just for the sake of it. I do not need to accept any thing as part of my own reality. There is only One true reality, which I look at, see, and understand. What is truly meaningful in Life is what I look at, have answers to, and am learning how to express succinctly. As for all the, lack of a better word, "meaningless" scientific answers in Life, well I just do not have the capabilities in answering those questions, like the one posed here. They are for the ones who are really smart.

Throng
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### Re: Does the center of a disk exist?

wtf wrote:
Throng wrote:I guess it's just because we imagine the centre as inert, but the same 'motionless point' applies to any point within any shape we imagine to be inert. Because the point itself is 'sizeless', or at least, 'has no parts', there is no motion there when it's imagined to be inert.
The center of a mathematical disk is sizeless and does not turn during a rotation. When you rotate the unit disk through an angle, the origin does not move.

Any physical disk is imperfect and does not have an exact center. If there is some tiny particle or subparticle of it that is truly fixed in space while the rest of the disk turns, we could not measure it and would have no way of knowing anyway. The best you could do would be to get a machinist or a physicist to tell you, "The wobbliness of the center is within such and so of zero, with such and such probability."

Surely all this is clear.
yep an origin 'has no parts', so any point relative to which other points are said to move doesn't move. It exists in the sense that we imagine it to exist, but it doesn't occupy any space, which is a pretty sparse existence.

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