Number Pi = religion ,sacred geometry = truth ?

As far as relativity is concerned, Pi as applied to a unit of length is no more a constant than the number one is. The ratio of one length to another actually isn't a constant in this case, and this is why solving the paradox with relativity is so repugnant to mathematicians. Since Ancient Greece, their internal geometry is perpetually static. That's the answer.
 
The other beauty of this paradox is that time dilation related to linear velocities varies with radii. At the center, there is no time dilation. In this way, it resembles gravitational time dilation in some respects. The asymmetry of time dilation along a radius corresponds to our heads aging faster than our feet when we are vertical.

Shrinkage of the radius to explain the paradox is prohibited. Even though a radius experiences acceleration, the magnitude of time dilation will be less than lengths oriented along the rotating rim. Pi (as a ratio of lengths) is what really changes.
 
Hmm. That seems misleading.

I guess the issue of relativistic rotation isn't really something people encounter every day, hence why there isn't much distinction.
 
danshawen said:
The other beauty of this paradox is that time dilation related to linear velocities varies with radii. At the center, there is no time dilation. In this way, it resembles gravitational time dilation in some respects. The asymmetry of time dilation along a radius corresponds to our heads aging faster than our feet when we are vertical.

Shrinkage of the radius to explain the paradox is prohibited. Even though a radius experiences acceleration, the magnitude of time dilation will be less than lengths oriented along the rotating rim. Pi (as a ratio of lengths) is what really changes.
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Danshaven,

I feel, that there is nothing sacred about getting the numeral value of pi, from the most known formula that is circum/diameter of a circle. The numeral value of pi is associated with the surface area, with the volume of such geometrical shapes, and also the same can be derived from various mathematical series and integration methods, so attributing relativistic paradox to only poor circle is not a done thing.

Now coming to the highlighted paradox, the simple resolution, is that probably shape changes/distorts at relativistic speeds and no longer pi = Circumference/Diameter is applicable. Alternatively I am inclined to change the formula as..

Pi = F(gamma) * Circumference / Diameter.

Where F(gamma) is a function of gamma. This way at least the sanctity of the numeral value of pi can be kept.
 
e^(i x pi) = -1

That's sanctity. Can you show a graph?

The speed of light is "sanctity" to relativity physics because of its invariance. Energy or matter may propagate slower than this, but never faster.

Evidently Pi works in similar fashion (like an invariant limit). The Pi we understand is implicit with a state of rest. As things spin faster, Pi increases without limit analogous to it being possible to traverse large distances without incurring any passage of time. This is is key to understanding entanglement, which works the same way.

There is beauty and sanctity here too, if you understand how to look for it. Finding the last digit isn't useful unless there is a better motivation other than an OCD predilection to order.
 
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danshawen said:
e^(i x pi) = -1

That's sanctity. Can you show a graph?

The speed of light is "sanctity" to relativity physics because of its invariance. Energy or matter may propagate slower than this, but never faster.

Evidently Pi works in similar fashion (like an invariant limit). The Pi we understand is implicit with a state of rest. As things spin faster, Pi increases without limit analogous to it being possible to traverse large distances without incurring any passage of time. This is is key to understanding entanglement, which works the same way.

There is beauty and sanctity here too, if you understand how to look for it. Finding the last digit isn't useful unless there is a better motivation other than an OCD predilection to order.
Click to expand...

'Pi' is commonly referred as number, which incidentally is Circumference of Circle divided by its Diameter, my argument is that when you spin a ring or disk at relativistic speed, the shape distorts, its no longer a circular profile, thus the ratio may not give the same number.

On the lighter side I tried to define rest Pi and relativistic Pi, to cool down the argument. You too are giving a rest to Pi..I read somwhere that the value of Pi is useful till around 40 digits beyond decimal, beyond that it is just for kicks.
 
This Ehrenfest paradox should definitely be investigated further. The only other questions am curious about at the moment is the variable constants of circumference/diameter is rational or irrational. This change to me perhaps is what's behind energy configuration, this warping of space manipulates energy.
 
The God said:
Pi = F(gamma) * Circumference / Diameter.
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Not a bad attempt at a resolution, TG. I wonder if there's anything else hiding in there?


eipi.jpg

This is also the best example I can think of for a graphing theory fail. Why should anything other than an infinity misbehave like that? Does anyone even have a theorem that explains it? Not "derive it"; anyone can do that. Graph it. Show us how other similar functions in the vicinity of that one behave? Which is more sanctimonious to a mathematician: pi or this? Draw us a picture (like the theorem of Pythagorus) to show us what it can do. Shouldn't doing that at least be one of the millennium prize math mysteries or something? Why or why not?

This relation has allowed resolution to thousands if not hundreds of thousands of math problems unapproachable by any other means. Shouldn't we all understand this on a deeper level?

Think about it. This is how I feel about mathematicians simply ignoring relativistic space and replacing it with a static Euclidean version. I'm not even sure the calculus I was taught is rigorously justified in a mathematical sense any more. More likely than not, it is simply "close enough", and since when has that ever been something everyone could accept? It's the reason we keep hoping to compute that last digit I suppose.
 
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danshawen said:
As far as relativity is concerned, Pi as applied to a unit of length is no more a constant than the number one is. The ratio of one length to another actually isn't a constant in this case, and this is why solving the paradox with relativity is so repugnant to mathematicians. Since Ancient Greece, their internal geometry is perpetually static. That's the answer.
Click to expand...
Simplicity is more profitable and economically manufactured.
 
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danshawen said:
e^(i x pi) = -1

That's sanctity. Can you show a graph?

The speed of light is "sanctity" to relativity physics because of its invariance. Energy or matter may propagate slower than this, but never faster.

Evidently Pi works in similar fashion (like an invariant limit). The Pi we understand is implicit with a state of rest. As things spin faster, Pi increases without limit analogous to it being possible to traverse large distances without incurring any passage of time. This is is key to understanding entanglement, which works the same way.

There is beauty and sanctity here too, if you understand how to look for it. Finding the last digit isn't useful unless there is a better motivation other than an OCD predilection to order.
Click to expand...

I like this line of thinking.
 
BrianHarwarespecialist said:
Yeah we all love pi but the bigger question is why do irrational numbers exist in the first place?

Now that could be the million dollar question.
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Because in the deep quantum foam, virtual particles are created (and quickly destroyed) out of nothing. Each one of those is an event. Draw a single one dimensional "timeline" and plot each of those events in a discrete time interval from t=0 to t=1 (it doesn't even matter what unit one chooses). Is it an infinite number? Sure. Is time infinitely sub-divisible? You bet. Express what the experiment is doing in anything other than an irrational number. Between any two such events, there are an infinite number of other such events. Each one is a separate tic mark.
 
danshawen said:
Because in the deep quantum foam, virtual particles are created (and quickly destroyed) out of nothing. Each one of those is an event. Draw a single one dimensional "timeline" and plot each of those events in a discrete time interval from t=0 to t=1 (it doesn't even matter what unit one chooses). Is it an infinite number? Sure. Is time infinitely sub-divisible? You bet. Express what the experiment is doing in anything other than an irrational number. Between any two such events, there are an infinite number of other such events. Each one is a separate tic mark.
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Although you think of this differently I see the similarities of a logical structure in the attempt.
 
Daecon said:
All numbers exist.
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Except for the order, there really is only unity. The rest of the numbers are just the operation of addition repetitvely applied to unity, in whatever magnitude, to generate all the rest. This argument is not original. So there really is only one number, and/ or the lack of it, which is zero. I fell in love with this idea when I learned, units are arbitrary, even in math. It befits a finite mind to think small. Truth may be infinite, but if both your mind and lifespan is limited, who really needs such cumbersome concepts?

Does unity exist? Only if you disallow Multiverses, which is a great idea since it isn't good science anyway. Why count anything that isn't there?

Works for me. Counting to one means you don't need to remember any orderings.
 
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