A reality bending puzzle. (now with a video!)

"

Wazz72 wrote:

Sorry but you're simply confusing the rotation of square x around itself - which happens twice - with the "rotation" (revolution would suit better) of square x around square y - which happens once. Relative points of observation don't change this.

There is some confusion in this conversation, but i feel it is yours. You seem to have your imagination locked into the state of an outside observer, unable and unwilling to see the truth of another perspective. I find this trap all to common. Just because one thing is true doesnt necessarily mean that another answer is wrong. And therein lies the depth of this puzzle.

Imagine the sides of the rotating square each correspond to 'head' left' 'feet' and 'right'. Now examine closely how it rotates about the other center square. It only is in contact with one of each of its sides before it returns to its initial position. Thus it only made one revolution relative to the center square.

And from the center squares perspective, the same is true.

Think of it as a giant titan doing a cartwheel around the world.

"

Sneakypaw wrote:

You also frogot to mention on which celestrial body this happens.
They move through the universe. So depending on how long this procedure took, the square could have had several rotation in relation to his starting point in the universe.

I was going to mention something similar to this as well:) But i thought i best not confuse ppl any more.

"

SkyCore wrote:

"

Wazz72 wrote:

Sorry but you're simply confusing the rotation of square x around itself - which happens twice - with the "rotation" (revolution would suit better) of square x around square y - which happens once. Relative points of observation don't change this.

There is some confusion in this conversation, but i feel it is yours. You seem to have your imagination locked into the state of an outside observer, unable and unwilling to see the truth of another perspective. I find this trap all to common. Just because one thing is true doesnt necessarily mean that another answer is wrong. And therein lies the depth of this puzzle.

Imagine the sides of the rotating square each correspond to 'head' left' 'feet' and 'right'. Now examine closely how it rotates about the other center square. It only is in contact with one of each of its sides before it returns to its initial position. Thus it only made one revolution relative to the center square.

And from the center squares perspective, the same is true.

Think of it as a giant titan doing a cartwheel around the world.

It still makes 2 rotations, from both perspectives. If the observer on the central square looks towards the satellite square that is rotating, that observer would indeed only see each side of the satellite square once. That does not preclude the perception of two rotations by the central square observer.

It's like looking at someone's back, then having them do a backflip in the air to land behind you. If you turn around and see their front, you still perceive that they have made a 360 spin, else they would be upside down.

Chirality is not subject to relativity or perspective, rather it is one of the underlying reference frames that determines perspective. Without it, there is no spin, no circumnavigation, or movement at all.

CPT (Charge conjugation, Parity and Time) theorem allows for an object to flip twice and yet appear to only have flipped once (same eigenvalue), but then it must have travel backwards in time or have its charge reversed. (imagine the writing of AMBULANCE not being backwards when you turned around and looked at the ambulance instead of seeing the writing in the mirror)







You can find some detailed explanations of it here

http://scipp.ucsc.edu/~haber/susybook/feyn115.pdf ( a little heavy on the math)

and here

http://arxiv.org/pdf/1010.0943.pdf

Hawking radiation, and the "conservation of mass/energy" are just two examples of things that result from CPT invariance.

"

DalaiLama wrote:

It still makes 2 rotations, from both perspectives.

"

DalaiLama wrote:

If the observer on the central square looks towards the satellite square that is rotating, that observer would indeed only see each side of the satellite square once

These 2 statements are in contradiction. If you perceive only one side of an object once as its turns around, then by definition it has rotated only once. From the center squares perception the other square has indeed only rotated once.

"

DalaiLama wrote:

It's like looking at someone's back, then having them do a backflip in the air to land behind you. If you turn around and see their front, you still perceive that they have made a 360 spin, else they would be upside down.

A backflip is a subtly a fundamentally different problem then the one presented. A backflip suggests a 3 dimensional world.

This puzzle is a 2 dimensional plane involving 2 squares and no other reference points.

In addition, i should point out that in the backflip scenario at no point did the center perception see the bottom of the backflipper so it never was a full rotation, it was actually half a rotation from the point of view of either of these ppl. It is only the implicit suggestion that there was a 3 party 'ground' as a reference point in which the backflipper made the full 360 degree flip.

"

DalaiLama wrote:

Chirality is not subject to relativity or perspective, rather it is one of the underlying reference frames that determines perspective. Without it, there is no spin, no circumnavigation, or movement at all.

CPT (Charge conjugation, Parity and Time) theorem allows for an object to flip twice and yet appear to only have flipped once (same eigenvalue), but then it must have travel backwards in time or have its charge reversed. (imagine the writing of AMBULANCE not being backwards when you turned around and looked at the ambulance instead of seeing the writing in the mirror)

You are off base talking about chirality here. It does not factor into puzzle whatsoever.

"

Dan_GGG wrote:

The answer can't be both once and twice unless you're observing two different kinds of revolution though.

Thats where the reality bending begins. Our logic says properties (such as rotation) are absolute. But they are not. They are indeed relative.

That is not to say absolutes dont exist. Just that rotation is one of the properties which is relative.

"

Dan_GGG wrote:

It's one rotation if X (blue) slides along Y's (red's) outer edges, such that the same edge of X always faces the center of Y.

Correct. At least for Blues perspective, red did rotate once. For an outside observer blue rotated once. From reds perspective blue never rotated, it merely circumnavigated.

"

Dan_GGG wrote:

It's two rotations if the revolution works as in Mark's diagrams.

It's two from an OUTSIDE observe yes. But imagine if you ARE one of those squares. It will appear as if the other has rotated once.

"

Dan_GGG wrote:

Your position in this system, whether inside these shapes or outside doesn't change how much motion occurs, or how much you observe occurring.

Incorrect. If you are either the red or the blue square. It will appear as if the other has rotated only once before it returns to its initial position.

Instead of looking at a top down perspective imagine you are a square. What you see in each quarter circumnavigation is a rotation of the other square by exactly 90 degrees. NOT 180 degrees.

I realize it is difficult to change your perspective. Once youve seen something one way, its hard to see it any other way. Think of it this way. Focus on just the adjacent edge of the 2 squares. You will see it then.

Just because something is not perceived, doesn't mean it didn't happen.

"

RobbieL_GGG wrote:

But what if the square isn't a square.

What if it was a circle all along...

What if time is a flat circle?

"

RobbieL_GGG wrote:

"

TheWretch wrote:

"

RobbieL_GGG wrote:

But what if the square isn't a square.

What if it was a circle all along...

What if time is a flat circle?

But is your strength of character enough?

My ascension removes me from the disk and the loop. I am near final stage. Some mornings, I can see the infernal plane