The beauty of paradoxes

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The beauty of paradoxes

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Armed with the laws of logic and a few simple, plausible, and apparently harmless assumptions, philosophers can construct proofs of the most absurd conclusions. These proofs can give us pause; should we believe the unbelievable? This is the power of a paradox.

This site is a celebration of such proofs. The most interesting philosophical arguments are those that proceed from undeniable premises, via inescapable
logic, to incredible conclusions.
http://www.logicalparadoxes.info/

Also see: http://en.wikipedia.org/wiki/Xeno's_paradox
Status of the paradoxes today

Mathematicians thought they had done away with Zeno's paradoxes with the invention of the calculus and methods of handling infinite sequences by Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century, and then again when certain problems with their methods were resolved by the reformulation of the calculus and infinite series methods in the 19th century. Many philosophers, and certainly engineers, generally agree with the mathematical results.

Nevertheless, Zeno's paradoxes are still hotly debated by philosophers in academic circles. Infinite processes have remained theoretically troublesome.
[...]
Some claim that a rigorous formulation of the calculus ... has not resolved all problems involving infinities, including Zeno's.

As a practical matter, however, no engineer has been concerned about them since knowledge of the calculus became common at engineering schools. In ordinary life, very few people have ever been much concerned.

The quantum Zeno effect

In recent time, physicists studying quantum mechanics have noticed that the dynamical evolution (motion) of a quantum system can be hindered (or even inhibited) through observation of the system. This effect is usually called the quantum Zeno effect as it is strongly reminiscent of Zeno's arrow paradox.
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"To forbid us anything is to make us have a mind for it."
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re: The beauty of paradoxes

Post by ken_behrendt »

I visited the paradox site an have seen all of the described paradoxes elsewhere. Most are sophistry left over from the early Greek culture's fascination with logic and are easily resolved today with the concept of the mathematical limit and by simply carefully defining terms.

However, I do agree with the phrase:
Infinite processes have remained theoretically troublesome.


In an article I did for my own website titled "Playing with Infinity", I tried to come to terms with the concept of infinity and came up with some rather interesting conclusions.

For example, I reached the conclusion that the cosmos was infinite both in extent and duration and, thus, contained an infinite amount of matter and energy. This implied that, because of the laws of probability theory, there had to be an infinite number of Earth's that were perfectly synchronized with our present Earth. By "synchronized", I meant that there had exactly the same number of identical atoms, each of which was exactly in the same energy state as ours.

Thus, as I now type this post, there are an infinite number of Ken Behrendt's also typing the exact same post. Even if, at any instant, I suddenly decide to change a particular word I am using, the infinity of me's will do the exact same thing! This kind of reasoning led me to conclude that we humans really do not have the so-called "free will" that many religions (like Catholicism) claim exists. However, I did find a few loop holes in this annoying deterministic structure of reality that may interest some members...


ken
On 7/6/06, I found, in any overbalanced gravity wheel with rotation rate, ω, axle to CG distance d, and CG dip angle φ, the average vertical velocity of its drive weights is downward and given by:

Vaver = -2(√2)πdωcosφ
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re: The beauty of paradoxes

Post by trevie »

Ken
For example, I reached the conclusion that the cosmos was infinite both in extent and duration and, thus, contained an infinite amount of matter and energy.
How did you conclude that the universe is infinite? Surely it must end at the beginning of the big bang theory.
This implied that, because of the laws of probability theory, there had to be an infinite number of Earth's that were perfectly synchronized with our present Earth. By "synchronized", I meant that there had exactly the same number of identical atoms, each of which was exactly in the same energy state as ours.
You are saying now that there are two or more parallel universes, If so how did you find this out and where are they?
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re: The beauty of paradoxes

Post by trevie »

who ever wrote this, must be mad, stupid or brain washed. Never read so much C*** in my life.

http://www.logicalparadoxes.info/arrow.html
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re: The beauty of paradoxes

Post by scott »

Wow Trev, you are easily flustered. Do all pardoxes upset you or just the Arrow Paradox (aka. the Paradox of Motion)? It was Zeno who first formulated it between 500-400 BC.

In modern times, it applies to the Quantum Zeno Effect and the Heisenberg Uncertainty Principle. Thus I'd say Zeno was a pretty advanced thinker.

You may not agree, but many people believe the Paradoxes, including the Arrow Paradox, are well worth studying and thinking about.
E.g.
http://faculty.washington.edu/smcohen/3 ... Arrow.html
http://plato.stanford.edu/entries/paradox-zeno/
http://plus.maths.org/issue17/xfile/index.html
Zeno's paradoxes still challenge our understanding of space and time, and these ancient arguments have surprising resonance with some of the most modern concepts in science.
Thanks for visiting BesslerWheel.com

"Liberty is the Mother, not the Daughter of Order."
- Pierre Proudhon, 1881

"To forbid us anything is to make us have a mind for it."
- Michel de Montaigne, 1559

"So easy it seemed, once found, which yet unfound most would have thought impossible!"
- John Milton, 1667
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re: The beauty of paradoxes

Post by rlortie »

Hey! Trev,

You want to hear my favorite paradox!

The universe is said to be everything, but yet it is expanding. If it is already everything, then what is it expanding into?

Actually my favorite just took place on this forum. I thought it was timely of Scott to start this thread at such an appropriate time.

You have a wheel that has ran for X length of time, but not long enough to meet the forum standards as a runner. You make such a statement but you cannot reveal or substantiate because of confidential agreements with others. Where as you cannot substantiate without loosing integrity, what do you do.

After 50 pages of accusations and name calling you dismantle the wheel with your partners blessing, so you can tell all, that no! you do not have a running wheel. In the meantime that same partner that you are in confidence with has the same results with the same basic design.

Most viable recourse is to shut down the thread. After 50 pages the forum has learned nothing.

Zeno's arrow is stationary after all.

Ralph
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re: The beauty of paradoxes

Post by trevie »

Scott, Some of those paradoxes did rub me up the wrong way ie the Achilles and the Tortoise, but the arrow paradox beats them all. Its the sort of thing politicians may say, and most of their policys are most probably full of paradoxes anyway.
Last edited by trevie on Tue Oct 10, 2006 8:00 pm, edited 1 time in total.
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Re: re: The beauty of paradoxes

Post by trevie »

rlortie wrote:Hey! Trev,

Zeno's arrow is stationary after all.

Ralph
A little like Besslers wheel hidden secret.
rlortie wrote: The universe is said to be everything, but yet it is expanding. If it is already everything, then what is it expanding into?
Probably antimatter, although it will be too far off to even see the end of the universe.

Maybe the atoms that make up the universe thin out at the end, bit like our Earths atmosphere the higher you go. So whats in between the atoms? Maybe the answer lies here to beginning/end of the universe.
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re: The beauty of paradoxes

Post by John Collins »

My favourite paradoxes concern time travel. The simplest one is "if time travel is possible what happens if I go back in time and kill my own mother before I was born?" - Do I cease to exist? The universe now has a very basic problem: If I do exist then I don't exist, if I don't exist then I do exist.

There is a web site which gives an excellent appraisal of the ramifications of such a paradox at http://www.exaflop.org/docs/th_sci/paradox.html

JC
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re: The beauty of paradoxes

Post by ken_behrendt »

trevie asked:
How did you conclude that the universe is infinite? Surely it must end at the beginning of the big bang theory.
and:
You are saying now that there are two or more parallel universes, If so how did you find this out and where are they?
In my various website articles, I postulate that the cosmos must be infinite in both extent and duration. Believing this is tantamount to believing that God is eternal and omnipresent with the exception that one does not have to invoke spirit beings to rationalize the "cause" for physical reality. If the cosmos was not infinite in both extent and duration, then we would have a situation where everything we can observe around us would have come into existence from nothingness and, due to the laws of thermodynamics, would only eventually dissipate into nothingness again. That is, a cosmos that was not infinite in extent and duration would be a very transitory and improbable one, indeed. In any event, you might find my two website articles, A Destiny for Cosmic Life and Playing with Infinity, to be of interest.

No, there is only ONE cosmos. I do not believe in "parallel universes". However, there should, logically, be an array of identical regions of the cosmos (separated by unimaginably great distances from each other) within our one cosmos. Again, this is justified by probability theory.


Scott wrote:
Thus I'd say Zeno was a pretty advanced thinker.
The ancient Greek philosophers and mathematicians were a somewhat advanced as a class and their ideas influenced later concepts that were developed in physics, chemistry, and mathematics. However, they also, occasionally, dug themselves into a pit when improperly applying their new plaything...logic.

All of Zeno's paradoxes can be satisfactorily resolved with the concepts of modern mathematics. For example, the paradox involving the hypothetical race between the tortoise and Achilles is flawed because it relies upon an argument that considers ever decreasing time intervals. It can be shown with simple algebra that, regardless of the head start the tortoise is given and the ratio of the velocities of the two, there is a certain distance at which Achilles will pass the tortoise and be in the lead. However, it is the case that the tortoise will always win IF the distance of the course is less than the calculated distance for Achilles to reach the tortoise.


Ralph wrote:
After 50 pages of accusations and name calling you dismantle the wheel with your partners blessing, so you can tell all, that no! you do not have a running wheel.
It sounds like the issues dismissed in the General Discussion thread that just got "locked up" are, once again, beginning to surface!

So, are you, Ralph, now suggesting that for the earlier part of that go-nowhere 50 page thread, James Kelly DID have a working wheel, but then purposely disabled it so that he could, finally, truthfully admit that "no" he does not currently have one?


trevie, again, wrote:
Maybe the atoms that make up the universe thin out at the end, bit like our Earths atmosphere the higher you go. So whats in between the atoms? Maybe the answer lies here to beginning/end of the universe.
What I am convinced is happening is that we actually inhabit a "multiverse" and not just a universe. That is, what I call the "cosmos" is, in reality, a multiverse made up of an infinite array of separate expanding Big Band universes. While our best telescopes can see out to about 10 to 12 billion light years, they can not see the light of our immediately surrounding expanding Big Bang universes that is now radiating toward our local universe.

Over the course of the next, perhaps, hundred billion years, the outwardly expanding galaxies of our Big Bang universe will begin to encounter those of the immediately surrounding expanding Big Bang universes. As that happens, these burned out, dead galaxies will, via mutual gravitation, collapse into each other an, over the course of tens of billions of additional years, form Super Black Holes which are the several times the size of our solar system. Eventually, ALL of the matter and energy of the infinite multiverse will be "locked up" within an infinite array of these Super Black Holes.

After several more tens of billions of years of complete darkness, suddenly this array will begin to destabilize. Some process will come into action that will allow all of that highly energized neutronium to explode out of the Super Black Holes. When this happens, an infinite array of expanding Big Bang universes will be created that will go on to form galaxies, stars, planets, life, sentient beings, and, yes...mobilists like us! This process will be on that has always occurred, is occurring now, and always will occur...


John...

The simplest way to cope with the time travel paradoxes is to keep in mind that 20th century relativity theory established that backward time travel is not physically possible. When that is accepted as true, ALL such time travel paradoxes disappear...thankfully!



ken
On 7/6/06, I found, in any overbalanced gravity wheel with rotation rate, ω, axle to CG distance d, and CG dip angle φ, the average vertical velocity of its drive weights is downward and given by:

Vaver = -2(√2)πdωcosφ
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Re: re: The beauty of paradoxes

Post by trevie »

ken_behrendt wrote:What I am convinced is happening is that we actually inhabit a "multiverse" and not just a universe. That is, what I call the "cosmos" is, in reality, a multiverse made up of an infinite array of separate expanding Big Band universes. While our best telescopes can see out to about 10 to 12 billion light years, they can not see the light of our immediately surrounding expanding Big Bang universes that is now radiating toward our local universe.

Over the course of the next, perhaps, hundred billion years, the outwardly expanding galaxies of our Big Bang universe will begin to encounter those of the immediately surrounding expanding Big Bang universes. As that happens, these burned out, dead galaxies will, via mutual gravitation, collapse into each other an, over the course of tens of billions of additional years, form Super Black Holes which are the several times the size of our solar system. Eventually, ALL of the matter and energy of the infinite multiverse will be "locked up" within an infinite array of these Super Black Holes.

After several more tens of billions of years of complete darkness, suddenly this array will begin to destabilize. Some process will come into action that will allow all of that highly energized neutronium to explode out of the Super Black Holes. When this happens, an infinite array of expanding Big Bang universes will be created that will go on to form galaxies, stars, planets, life, sentient beings, and, yes...mobilists like us! This process will be on that has always occurred, is occurring now, and always will occur...
Ken, That is quite some theory you have there!
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re: The beauty of paradoxes

Post by ken_behrendt »

Thanks, trevie...

Actually, I've been kicking this "theory" about for almost a decade now. And, recently, there seems to be a slow shift in the scientific community taking place toward this view after two cosmologists over in Britain announced that they reached the conclusion that our present Big Bang universe is only one in an infinite sequence of such universes. They favor the Big Bang / Big Crunch model for our universe. All I did was expand the model so that it extends throughout space in all directions for infinity.

I still wrestle with the "ultimate" philosophical problem, however: why should any universe (or in my version, multiverse) exist at all? Why, for example, is not everything just a complete void of infinite extent and duration?

Well, I think I have a partial solution to that question that is somewhat satisfactory. IF one truly had an infinite void, then it could contain no matter and energy. That seems quite obvious. However, without matter and energy, it becomes impossible for space and time to exist!

So, IF one had a truly infinite void, then it would immediately disappear because it could have no volume or duration. As it winked out of existence, something would have to take its place. Well, apparently, something did...our cosmos!

However, the present nature of our cosmos is really determined by about 20 or so physical constants. I won't list them all, but they are well known to physicists and have been determined to a great degree of accuracy. The problem is that no one has the faintest idea why they have the values that they do! They were determined through either observation or theoretical calculations. When we truly understand the cosmos on its most fundamental level, then we will know exactly why those constants have the values that they do and how they are subly related to each other. Maybe, like in another millenium or so, we will discover that there is only one or two or three physical constants that are some sort of property of space containing matter and energy and that all of the other physical constants can be derived from them.

Wow...would that not be something incredible? We might be able to reduce all of the cosmos to a handful of equations from which all the other know physical constants and laws of physics could, by appropriate mathematical manipulation, be derived.

As many know, I am a student of the UFO phenomenon and a firm believer in the reality of extraterrestrial life. I often wonder if there could be some advanced spacefaring race out there that might already have this knowledge. What must their civilization be like?


ken
On 7/6/06, I found, in any overbalanced gravity wheel with rotation rate, ω, axle to CG distance d, and CG dip angle φ, the average vertical velocity of its drive weights is downward and given by:

Vaver = -2(√2)πdωcosφ
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