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    Thread: Unsolved paradoxes

    1. #51
      Xei
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      Heard about this yesterday:

      The paradox begins with the observation that certain expressions in English unambiguously define real numbers, while other expressions in English do not. For example, "The real number whose integer part is 17 and whose nth decimal place is 0 if n is even and 1 if n is odd" defines the real number 17.1010101..., while the phrase "London is in England" does not define a real number.

      Thus there is an infinite list of English phrases (where each phrase is of finite length, but lengths vary in the list) that unambiguously define real numbers; arrange this list by length and then dictionary order, so that the ordering is canonical. This yields an infinite list of the corresponding real numbers: r1, r2, ... . Now define a new real number r as follows. The integer part of r is 0, the nth decimal place of r is 1 if the nth decimal place of rn is not 1, and the nth decimal place of r is 2 if the nth decimal place of rn is 1 (i.e. Cantor's method).

      The preceding two paragraphs are an expression in English which unambiguously defines a real number r. Thus r must be one of the numbers rn. However, r was constructed so that it cannot equal any of the rn. This is the paradoxical contradiction.

    2. #52
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      Two hands clap and there is a sound. What is the sound of one hand?

    3. #53
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      That's not a paradox it's a koan. Technically one hand can't clap, unless you call slapping it against your stomach or something clapping, and to me that doesn't qualify. Clapping means two hands, so no paradox. One hand can't clap.

    4. #54
      Xei
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      There isn't one. You need two hands to be able to clap them, so the question is not defined.

      I hope you learned a lot today.
      Dianeva likes this.

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      Ok why does it seem that in subatomic physics the outcome of experiments appears to be determined by the observer of the experiment? It seems like some of these particles can be in various possible states at the same time, but when observed they choose a state according to the observer's mindset.

      Schrodinger's cat is an example in a way, but very difficult to decipher. What this sort of shows to me is that there may be many things that are much different than we presently have figured out.

      So somebody said they hoped someone learned a lot today. What I think I am learning is that the world is something different than what we presently think it is, and that paradoxes probably can be teachers to help us see more deeply into the real nature of all things.

    6. #56
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      I believe this thread is about paradoxes in the strict sense, according to the actual definition:

      A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition. Typically, however, quoted paradoxical statements do not imply a real contradiction and the puzzling results can be rectified by demonstrating that one or more of the premises themselves are not really true, a play on words, faulty and/or cannot all be true together. But many paradoxes, such as Curry's paradox, do not yet have universally accepted resolutions. The word paradox is often used interchangeably with contradiction. Literary and other artistic uses of paradoxes imply no contradiction and may be used to describe situations that are ironic.[1] Sometimes the term paradox is used for situations that are merely surprising.
      From Wikipedia: Paradox - Wikipedia, the free encyclopedia

      The ones you're posting are just ironic or strange statements - nothing in one part contradicts any other part. If you look back at the ones listed in this thread, there are two statements made, each seemingly logical, and yet the second contradicts the first.

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      Most sources I have come across consider Schrodinger's cat a paradox, and most consider Zen Koans as also paradoxes. Schrodinger was indeed very ironic and strange, but also had great powers of logic - is that a paradox as well? Probably not.

      There are differing sorts of paradoxes. Any paradox is just a sort of mind play, like a Zen Koan is meant to break through self-imposed mental beliefs and constrictions.

      In science, paradoxes are for the purpose of the same sort of mental barrier breakthroughs as they are in Zen, but usually more in the physical understandings where Zen is usually more for psychological understandings...

      So allow me to bring this together. What is the sound of one hand clapping? It is science without psychology or psychology without science. It is not being whole.
      It is also not Quantum Entanglement without which I think no thing could be.

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      I can't believe I'm still trying - and this isn't even a subject I'm really interested in, but from reading things people (mostly Xei, who is a very logical fellow) have said, I understand it like this:

      A paradox is a pair of statements that taken individually seem perfectly logical, but that contradict each other. In neither of your examples did you provide a pair of statements.

      In fact what you just posted above isn't a logical solution to a paradox at all, it's just a Zen Koan and then your own rather loose interpretation of one thing it could be taken to mean. No logic, no rigor.
      Last edited by Darkmatters; 11-17-2011 at 05:17 PM.

    9. #59
      Xei
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      Quote Originally Posted by crackers View Post
      Ok why does it seem that in subatomic physics the outcome of experiments appears to be determined by the observer of the experiment? It seems like some of these particles can be in various possible states at the same time, but when observed they choose a state according to the observer's mindset.
      It sounds like you have been listening to New Age propaganda ('What The Bleep', maybe?). The above is simply not true and you will find no experiment in quantum physics that shows it to be true.

      It is true that the presence of an observer plays a central and weird part in quantum physics, but this is a binary, on/off thing; either you're observing something or you're not. In no way do your mental states interact with quantum events.

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      In the early work of Max Planck, Albert Einstein and Niels Bohr, the existence of energy in discrete quantities had been postulated, in order to avoid certain paradoxes that arise when classical physics is pushed to extremes. Also, while elementary particles showed predictable properties in many experiments, they became highly unpredictable in certain contexts, for example, if one attempted to measure their individual trajectories through a simple physical apparatus.

      The Copenhagen interpretation is an attempt to explain the mathematical formulations of quantum mechanics and the corresponding experimental results. Early twentieth-century experiments on the physics of very small-scale phenomena led to the discovery of phenomena which could not be predicted on the basis of classical physics, and to the development of new models (theories) that described and predicted very accurately these micro-scale phenomena. These models could not easily be reconciled with the way objects are observed to behave on the macro scale of everyday life.

      The predictions they offered often appeared counter-intuitive and caused much consternation among the physicists—often including their discoverers.

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      The German physicist Werner Heisenberg (1901-1976) received the Nobel Prize in physics in 1932 for his work in nuclear physics and quantum theory. The paper on the uncertainty relation is his most important contribution to physics.

      Heisenberg impressed his teachers with his ambition and brilliance. He never produced other grades than straight A's, except on one occasion: During his doctorate, professor Wien of the university of Munich gave him an F in experimental physics, because he handled the laboratory equipment clumsily. Reportedly this left Heisenberg so disconcerted that he did not speak to anyone for days.
      Fate had it that a few years later, Heisenberg demonstrated the very limitations of experimental physics, which unquestionably constituted a setback for its advocates, including Professor Wien.
      The observer becomes part of the observed system. This directly correlates with Zen and the principle of Interdependence, and again correlates why one hand cannot clap by itself.

    12. #62
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      This one popped into my mind the other day, not sure if it's a paradox or not, and if it is it may be solved =\

      Bob: "Phill, can you answer a question of mine?"
      Phill: "No."

      He just answered the quesiton by stating that he can't answer a question. thoughts?
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    13. #63
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      Well in common language Bob would be referring to a question he's about to ask, not the one he's asking now. If he was asking Phil if he's capable of answering any questions, then his reply, 'no', would be false. I don't see it as a paradox.

    14. #64
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      A paradox I have had stuck in my head for a long time.

      A star roughly 29.39 trillion miles away is dated to explode 5 years from now. 5 light years is roughly 29.39 trillion miles, so it takes 5 years to reach the star while traveling at the speed of light. Time slows down at the speed of light and 5 years at light speed would be 35 years for everything else. If I were to travel to this star at the speed of light to see it just before it explodes, would I get there before or after the star has exploded?

      I'm sure you guys will find an answer.
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    15. #65
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      Quote Originally Posted by Oreoboy1996 View Post
      Time slows down at the speed of light and 5 years at light speed would be 35 years for everything else.
      How did you come up with this number? (pretty sure that time stops for an observer traveling at the speed of light)

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      Quote Originally Posted by Spartiate View Post
      How did you come up with this number? (pretty sure that time stops for an observer traveling at the speed of light)
      I don't think time is supposed to stop at the speed of light, but I guess I could be wrong. The 35 years thing is just a number beyond 5 that I picked. It's supposed to be like in that movie Flight of the Navigator where David was gone for 4 hours but the world had changed by 8 years.
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    17. #67
      khh
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      Quote Originally Posted by Oreoboy1996 View Post
      I don't think time is supposed to stop at the speed of light, but I guess I could be wrong. The 35 years thing is just a number beyond 5 that I picked. It's supposed to be like in that movie Flight of the Navigator where David was gone for 4 hours but the world had changed by 8 years.
      When you approach the speed of light, time approaches a standstill. However if you actually do reach the speed of light (which according to special relativity is impossible for objects with mass, as it would take an infinite amount of energy), our formulas break down and we can't say for certain what happens.
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    18. #68
      Xei
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      If you approach the speed of light, the universe moves faster. If you're arbitrarily close to the speed of light, you will go to the end of the universe arbitrarily quickly.

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      Quote Originally Posted by Xei View Post
      If you approach the speed of light, the universe moves faster.
      What makes you say this? I thought it would be slowing down.

      Quote Originally Posted by Xei View Post
      If you're arbitrarily close to the speed of light, you will go to the end of the universe arbitrarily quickly.
      Yeah, this really is an awesome effect of Lorentz contraction.

    20. #70
      Xei
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      I was actually talking about the historical 'end'.

      And yes it would go faster... just consider the twin paradox, where the one left behind ages faster.

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      Isn't that dependent on the turn back toward earth? Say the one closer to the speed of light doesn't change direction, could we say which one is really going faster? This is really the twin paradox I think, the popular solution is only a special case where you compare the two after the one closer to the speed of light has made a round trip. Interesting though, I wonder if the paradox is still unsolved when considering the constant relative direction case.

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