Oops!
Well, I really don't have that much sympathy right now, I am in a manufacturing facility that is about 95 degrees F.
Number Pi = religion ,sacred geometry = truth ?
- Thread starter tom5806
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Well, I really don't have that much sympathy right now, I am in a manufacturing facility that is about 95 degrees F.
Oops!
Well, I really don't have that much sympathy right now, I am in a manufacturing facility that is about 95 degrees F.
That's fine, I'll grab a beer for you after this
danshawen
Valued Senior Member
I'm really glad this quote has the original wording. Elsewhere folks change "thinking" to "level of consciousness", which is not what he said nor meant.
The same type of thinking about a luminiferous aether or a aether wind will never produce something like the theory of relativity.
That is exactly what Einstein said meant, and it's very true.
A book published with a mangled version of the quote went viral on the Internet in 2002. Once the misquote does that, it's difficult to impossible to make people understand or believe that the meaning never changed.
danshawen
Valued Senior Member
Pi is not a constant in relativistic (real, actual., non Euclidean or Pytagorean) space, in which circles may rotate.
Ancient Greek varieties of geometric space are ones in which nothing can ever move, and is used by mathematicians whose grey matter is grey because of an infusion of Portland cement, hardened over aeons to do geometry as if everything and everything were static. Time is not related to space by means of the theorem of Pythagorus. There is only time and energy, and time is much grainier than the propagation of energy. As such, you need a theory beyond the bounds of the propagation of matter or energy (or relativity) to describe it.
Ancient Greek varieties of geometric space are ones in which nothing can ever move, and is used by mathematicians whose grey matter is grey because of an infusion of Portland cement, hardened over aeons to do geometry as if everything and everything were static. Time is not related to space by means of the theorem of Pythagorus. There is only time and energy, and time is much grainier than the propagation of energy. As such, you need a theory beyond the bounds of the propagation of matter or energy (or relativity) to describe it.
Nonsense. Pi is just a number. It doesn't change, regardless of what space you're talking about.
I'll wait for him to clarify. If he is saying that in a curved geometry it is not necessarily true that the circumference of a circle is $$2\pi r$$ that's true. But it is important to be clear that nothing changes the number $$pi$$, even if the measured ratio of circumference to diameter changes.
danshawen
Valued Senior Member
That's a comment I would expect of someone like Spellbound, Daecon. What reality is it that makes anyone believe that mathematics is more solid than the real world? Mathematics comes out of your head, reasoning with what you already think you know. Reality, more often than not defies whatever is between your ears and sometimes raises the ante, because your very survival may sometimes depend on understanding things that outside your finite mind or beyond your grasp. Did anyone outside of the Manhattan Project really understand nuclear physics before the first atomic bomb was dropped?
It's the Ehrenfest paradox, yes.
https://en.wikipedia.org/wiki/Ehrenfest_paradox
Don't just brush this off like some folks dispense with the very idea of the Lorentz contraction as something not real or "solid" like matter itself, which is mostly empty space anyway. Mach's rotating bucket was made of the bound energy we call matter, wasn't it? Can it rotate at relativistic speed with respect to the fixed stars and remain a bucket of the same diameter or can it not? If the bucket were replaced with a laser gyroscope (an actual device, made of round coils of fiber optic cable), would the energy Doppler shift change as a result of any circular motion of the gyroscope itself or would it not (it does!)? These are important questions, more real than anything that comes out of the mind of a mathematician based on his or her experience with the geometry of Euclidean solids. Straight lines and circles are as basic to geometry as they are to the real world, but one does not get a sense of how things work in reality unless you consider, they might move a smidgeon.
This is actually a great example of how Newton's basic calculus fails because dt is also changing as a function of the rate of rotation, which is to say, dt is something quite different motionless observer at the axis of rotation vs. what is observed by someone who is riding the rim of the merry-go-round. The latter could not help but conclude, either pi is not a constant, or that he/she has evidently gone insane, possibly from nonsensical endeavors like trying to calculate pi to the last decimal place.
What Ehrenfest calculated is as real as anything Mach ever wrote, and there is no paradox. For something riding the rim of a very large circle, that contraction is as real as it is for something traveling in a straight line for anything that is matter or energy. The number of wavelengths a photon orbiting a rotating black hole would be another example. It's basic physics to be able to explain what happens to the number of wavelengths, is it not? So, count them.
What about circles that don't rotate, but jitter, vibrate, or jump up and down?
Danshawen, just to clarify, "pi" isn't shorthand for "circumference divided by diameter", it's shorthand for the number 3.14159265 etc. It just so happens that it's the same number that you find when you divide the circumference by the diameter of a static, non-rotating circle.
If a circle is rotating at relativistic speeds, the length of the measured circumference would be shorter, and so the value of that specific circle's circumference divded by its diameter will be different, but there would be a correlation between the speed and that value.
However, it would be incorrect to refer to that value as "pi", for the reasons mentioned in the first paragraph.
If a circle is rotating at relativistic speeds, the length of the measured circumference would be shorter, and so the value of that specific circle's circumference divded by its diameter will be different, but there would be a correlation between the speed and that value.
However, it would be incorrect to refer to that value as "pi", for the reasons mentioned in the first paragraph.
danshawen
Valued Senior Member
OK then, let's try this exercise:
An observer at rest near the rotating rim of a large rotating merry-go-round (or alternatively something like Larry Niven's Ringworld) and is doing geometry. He has already calculated pi in the static case to as many decimal places as needed to specify the circumference of the rotating ring. He knows what circumference to expect and sets out to actually measure it as it flies past. He checks and finds that circumference from his calculation is considerably different from what he measures. Which one of those is "pi" again? Of what possible use is a constant ratio of lengths that does not conform to the same ratio observed in the case of a moving frame as opposed to a stationary one? Nothing is stationary in this universe with the possible exception of static geometry in the minds of mathematicians.
These are not issues that are trivial, mathematically or physically. There are physical laws which govern how photons are able to produce pairs of bound particles and antiparticles. Without a careful consideration of the propagating energy states AND PHASES of such systems, you will likely find it impossible to predict important and fundamental things like:
1) Exact energies of photons needed in order to produce a particular type of particle pairs and why
2) The physical properties of the particles produced
3) The nature of the forces that bind the energy into those particles
4) The likelihood that particles produced will decay in a given length of time
Would it not be nice and/or useful to have a functional mathematical model for something like this? You aren't very likely to get there by insisting that pi is a constant in a universe with translational and rotational motion going on at every scale. Similar paradoxes in relativity have found resolutions that have changed the way we think of the universe. Why is this one always left as a paradox, as though it was never a problem that needed to be solved? We could have ignored the twin paradox or time dilation and tried without success to synchronize GPS clocks without taking relativity into account. This paradox is no different, so deal with it.
Pi is which ever value is a number equal to 3.14159265...
It's a number, not a ratio.
The ratio of a non-rotating circle's circumference to its diameter is 3.14159265... it's cumbersome to keep writing out 3.14159265... all the time so we use "pi" to mean 3.14159265...
The ratio of a spinning circle's circumference to its diameter is a different number. (A number that isn't equal to 3.14159265...) But the value of that ratio changes depending on how fast that circle is rotating. I'm sure that it's possible to work out the relevant equations, but I'm not good enough at maths to do so.
In essence, what you're trying to say is that 3.14159265... isn't a constant, which doesn't make sense. 3.14159265... is and always will be 3.14159265...
It's a number, not a ratio.
The ratio of a non-rotating circle's circumference to its diameter is 3.14159265... it's cumbersome to keep writing out 3.14159265... all the time so we use "pi" to mean 3.14159265...
The ratio of a spinning circle's circumference to its diameter is a different number. (A number that isn't equal to 3.14159265...) But the value of that ratio changes depending on how fast that circle is rotating. I'm sure that it's possible to work out the relevant equations, but I'm not good enough at maths to do so.
In essence, what you're trying to say is that 3.14159265... isn't a constant, which doesn't make sense. 3.14159265... is and always will be 3.14159265...
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A calculation of pi doesn't make any reference to externalities. Pi is mathematically defined. It has no dependence on measurement.
So, the one that comes out as 3.1415926536... is the one that is pi.
danshawen
Valued Senior Member
Right. It makes no difference whether someone wastes the length of a human lifespan getting an arbitrary number of additional digits of that constant using the most advanced computing machinery available to get there, or wastes a week of that same computing machinery's time equivalent to thousands of savant lifetimes in an attempt to approximate the mass of the proton "from scratch".
Either way, it's a human failing that doesn't seem to grasp, it's the wrong problem on many levels. It's ultra-orthodoxy applied to a methodology that has evidently achieved the status of a religion and whose precepts are deemed more important than probing what might otherwise be accessible to reason about that derives of the source of the power to reason.
I suppose it's just another failing of a finite mind such as ours that it doesn't necessarily recognize when a problem to be solved is important and when it is not.
Thanks for the finest demonstration of the power of ignorance I have yet seen. Who really cares if the sides of a spinning polygon contract until they can no longer reach the next vertex? Don't resolve the paradox. Simply ignore it. It's no sin. Or cosin (misspelling intentional).
Is the energy bound in the aforementioned proton propagating internally in straight lines, or is the path curved relative to the center of the particle? What do you mean, it doesn't matter? Can't you even count? Don't you understand, pi CHANGES when something is rotating? Why wasn't that idea even taken into account?
Either way, it's a human failing that doesn't seem to grasp, it's the wrong problem on many levels. It's ultra-orthodoxy applied to a methodology that has evidently achieved the status of a religion and whose precepts are deemed more important than probing what might otherwise be accessible to reason about that derives of the source of the power to reason.
I suppose it's just another failing of a finite mind such as ours that it doesn't necessarily recognize when a problem to be solved is important and when it is not.
Thanks for the finest demonstration of the power of ignorance I have yet seen. Who really cares if the sides of a spinning polygon contract until they can no longer reach the next vertex? Don't resolve the paradox. Simply ignore it. It's no sin. Or cosin (misspelling intentional).
Is the energy bound in the aforementioned proton propagating internally in straight lines, or is the path curved relative to the center of the particle? What do you mean, it doesn't matter? Can't you even count? Don't you understand, pi CHANGES when something is rotating? Why wasn't that idea even taken into account?
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danshawen
Valued Senior Member
The sinusoidal nature of the propagation of energy and the complex (imaginary) rotational motion necessary to describe both EM field theory and even more important things (potential, kinetic energy of a harmonic oscillator) combined with attitudes shown in small part here demonstrate better than I ever could, mathematics is still using static modeling for dynamic processes. A single errant assumed constant is more than sufficient cause to doubt any theory that is heavily based on it. Using Einstein's field equations to describe the behavior of rotating black holes is another example of such misapplication of static geometrical constants.
Moreover, string theory (all of it) is a purely mathematical theory about the scale below that of quarks. I can't even imagine a scale more dynamic than that one. Check how many times pi comes up in those equations. Each and every time you see it, someone has miscalculated the veracity of the static geometric teachings of Ancient Greece.
Moreover, string theory (all of it) is a purely mathematical theory about the scale below that of quarks. I can't even imagine a scale more dynamic than that one. Check how many times pi comes up in those equations. Each and every time you see it, someone has miscalculated the veracity of the static geometric teachings of Ancient Greece.
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No, the number 3.14159265... doesn't change when something is rotating. It's still 3.14159265...
However the ratio of circumference to diameter does change when something is rotating at relativistic speeds - and when it does change, the value of that number is no longer 3.14159265...
Pi is just the word used to refer to the number 3.14159265...
In this situation, you need a different word to refer to the ratio. And probably a different word depending on the speed of rotation, which would just become cumbersome for every possible speed of rotation.
How about we use the word "pu" to refer to the ratio of circumference to diameter when a circle is rotating? For every possible speed, there would be a different pu. Lots and lots of pu's. Pu everywhere.
So Danshawen as the diameter shrinks does the circumference also shrink or does it stay the same while the diameter shrinks?
The circle that shrinks does it still remain similar or does it change shape?
The circle that shrinks does it still remain similar or does it change shape?
danshawen
Valued Senior Member
The diameter (radial) shrinkage is one means to resolve the paradox, and it was also my first idea to resolve it, about 40 years ago.
Acceleration does not mean the same thing for energy as it does for matter.
Positronium decays back into energy in milliseconds whereas atomic structure persists without energy loss, apparently confined to another mode of propagation which is, for all intents and purposes, lossless in terms of energy.
Likewise, the mean lifetime of a photon is many times the current age of the known universe, so there is no particular reason why uniform rotation should not also be lossless in terms of energy.
The twin "paradox" still works just fine if one twin travels a circle at uniform angular velocity. Notice that at no time between departure and arrival does the accelerated twin remain in the same inertial reference frame because the direction of motion changes continuously.
When energy travels at c, no additional acceleration is possible. But Doppler shifts still work just fine. Time dilation for matter traveling at less than c is the equivalent of Doppler shift for energy propagating at c.
Can anyone answer the paradox now? What does the shrinkage of the tape measure or odometer around the circumference of a relativistic rotating wheel represent? If Pi is simply your unit length, is it constant in such a situation or is it not? Hint: NOT.
A wheel composed of matter can never spin at c, but the time interval needed to complete one revolution will be different in the moving frame than measured at rest. Pi is not constant, and neither is dt, as viewed by observers in different states of motion. Other than atomic structure, no clock based on the principle of rotational motion of matter will ever yield a consistent measure of time. Nor will a clock based on atomic structure, either. It's the Doppler shifts that spoil those. Yet the propagation of energy or matter are not the root of time or time's arrow.
Don't tell your math teacher, because he/she/neutral gender hasn't solved it yet. Armed with only Euclid's geometry and the theorem of Pythagoras (another overused bit of triangulation), it would take more than the combined lifetimes of every mathematician who ever lived on our planet to deduce this solution from first principles, and they would never succeed. About the same amount of time they would like to draw a paycheck for things like calculating pi to the last decimal place, because one thing they have managed to work out is that compound interest is the most powerful force in the universe. Nice work if you can get it.
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