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Hey all, I will make this quick and easy. I just wanted to know what unsolved paradoxes you guys know. They can range anything from math to philosophy to science to puzzles. I would of said one but I don't know any that is why I created this thread :)
Well I don't know if this has a formal name but as a consequence of special relativity, two people witnessing the same event but traveling at different speeds will have different accounts of the same event because the way we experience time depends on how fast we are traveling.
There is also the barber paradox. If a barber shaves everyone who do not shave themselves, then who shaves the barber?
To explicate the 'different accounts' thing; for one person, two events can occur simultaneously, but for another at a different velocity, the events occur at different times. The really paradoxical thing is that they're both correct. It's not actually that hard to deduce; google for simultaneity and the train thought experiment.
Simple. Someone else.Quote:
Originally Posted by stormcrow
Right. So the barber does.
That isn't a paradox, it's just a contradiction. There is no answer. Whether he shaves himself or not, the requirements aren't met.Quote:
Originally Posted by stormcrow
@Darkmatters If someone else shaves him, he does not shave himself. And therefore, according to the rule, he needs to shave himself.
@Xei It's implied that he shaves people only iff no one else does.
I still think the Hangman's Paradox is unsolved.
And there are others like the heap paradox, which seem less impressive to me. But, if you look at one of them, it is kind of interesting that the argument seems undeniably sound, yet the conclusion is false:
P) If a girl is young, the next day she will still be young.
C) If this is applied every day, after 60 years she will still be young.
Well whoever does it would then be a barber yes. I don't see any contradiction or paradox.Quote:
Originally Posted by Xei
The Barber is a person. If somebody else shaves him then he doesn't shave himself. As he shaves everybody who doesn't shave themselves, this means he shaves himself. Which means somebody else doesn't.
Ok, I get it. Hurt my brain a little but I get it now.
So basically, like most paradoxes (paradoces?)it's just a word game that doesn't apply to reality an any way. The initial statement contains an arbitrary made-up rule that's then contradicted in the second one.
I suspect if we were able to examine them closely enough eventually we'd realize this is true for every paradox. Just word games.
This statement is false.
Whoopdidoo, logical paradoxes are boring.
Yeah, those types are boring.
One paradox I've found interesting involves the stock market. Over the years I've noticed that stock market crashes tend to occur in the September/October time period. Now, if I noticed this, then actual stock traders have certainly noticed it. But if they know it's going to happen (or if it's more likely than pure randomness would allow) then the rational choice would be to short sell your portfolio just prior to this time period (say, August). But if all the big players in the market do this, then the market would crash in August. But they also know this, so the market will actually crash in August. So they should they should really short sell their portfolios in July. But everyone knows this, so the market should crash in July. They should really be short selling in June. But they all know this... on and on.
It seems as though the rational choice is to always short sell immediately. So there are two paradoxes: why does the market go up over time if the players are rational, and why do the crashes actually occur in September/October, even though everyone knows it's going to happen?
solv'dQuote:
Originally Posted by cmind
I can't see an obvious reason for irrationality though... It could only be an emergent property.Quote:
Originally Posted by Xei
My favourite is the grandfather paradox: Suppose a man traveled back in time and killed his biological grandfather before the latter met the traveler's grandmother. As a result, one of the traveler's parents (and by extension the traveler himself) would never have been conceived. This would imply that he could not have traveled back in time after all, which means the grandfather would still be alive, and the traveler would have been conceived allowing him to travel back in time and kill his grandfather. Thus each possibility seems to imply its own negation, a type of logical paradox.
Grandfather paradox - Wikipedia, the free encyclopedia
Also there is the Monty Hall problem which is quite interesting: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1 [but the door is not opened], and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Monty Hall problem - Wikipedia, the free encyclopedia
Does a set of all sets contain itself?
If it existed then obviously it would, because it contains all sets. That is not actually paradoxical in any way.
It doesn't exist however, for completely different reasons.
Any questions about infinite sequences of sets would be easily dealt with using simple analysis techniques.
Depends what exactly you mean; Indeed's question is related to set theory and cardinality, not matters of analysis, unless there's something I don't know about.
Some of my favorite "paradoxes" have to do with induction. Below I describe the Raven's Paradox and the Tacking Paradox.
The Raven's Paradox
Let's first make two very reasonable assumptions about the concepts of evidence and theory and how they relate to one another.
First we assume that if we have a generalization T (e.g., a theory that says "all lawyers are greedy"), and we observe an instance E of this generalization (i.e., we observe a greedy lawyer), then this instance E serves as some positive evidence for T.
Second we assume that if E serves as evidence for T, and T is logically equivalent to another theory S, then E serves as evidence for S.
As I said, both of these assumptions seem entirely reasonable.
Now consider the theory T that "all ravens are black." Note that this theory is logically equivalent to the theory S that "all non-black things are non-ravens." Now imagine that I have just seen a green apple. Since this apple is a non-black thing which is also a non-raven, then by the first assumption we made above, this serves as evidence for S. But since S is logically equivalent to T, then by our second assumption, this also serves as evidence for T. So my observation of a green apple is evidence that all ravens are black. But this seems absurd.
The Tacking Paradox
We start with two more assumptions.
First we assume that if E is a logically necessary consequence of T, then E serves as evidence for T. For example, say we have a T which says "my roommate was out drinking last night." We combine this with the proposition "if T, then my roommate will sleep through his alarm clock's ringing." Now I observe the event E that my roommate has slept through his alarm. So on this assumption, E serves as evidence that my roommate was out drinking last night.
Second we assume that if E serves as evidence for T, and S is some other logically necessary consequence of T, then E serves as evidence for S. Continuing with the roommate example, suppose we add a second proposition that "if T, then my roommate will sleep with his shoes still on." So on this assumption, observing that my roommate has slept through his alarm clock's ringing serves as evidence that he has also slept with his shoes still on, by virtue of the fact that the former serves as evidence that my roommate was out drinking last night.
Again, these are reasonable assumptions.
But now let's take any other proposition P, such as "the moon is made of green cheese." Since T from above entails E, then by hypothesis, T & P (that is, my roommate was out drinking last night AND the moon is made of green cheese) also entails E (that my roommate will sleep through his alarm clock's ringing). So by our third assumption, E serves as evidence for T & P. Now, it is obvious that T & P entails P (trivially). But then, by our fourth assumption, it follows that E serves as evidence for P -- that is, my observation that my roommate has slept through his alarm clock's ringing is evidence that the moon is made of green cheese. But again, this seems absurd.
Here is a kind of boring paradox:
If I succeeded at failing which have I done? I think that you have succeeded personally but some would take this as a paradox.
Also isn't a paradox by nature unsolvable?
DuB you are basically the best poster on DV. :bowdown:
I think it's clear that there are some big problems with classical logic and philosophy of science. I recently read an article about metamathematics and a concept I think they called 'pseudoconsistency' about similar things; basically regarding the rift between classical logic and intuitive reasoning. The principle of explosion, which I'm sure you know about, basically relies on exactly the same trick; using formal operators (like AND) to make conclusions about things they clearly should have no relevance to.
I also think this stuff will ultimately turn out to have great relevance to neuroscience. It's something I intend to read much deeper about when I'm not so busy on my degree.
How are theories T and S reasonably equivalent? T is making a statement about the color of ravens while S is making a statement about the entity of other things.Quote:
Originally Posted by DuB
How does proposition P logically fit into the relationships of E,S, and T at all?Quote:
Originally Posted by DuB
They are not only "reasonably" equivalent, they are exactly equivalent. We can even say that they are synonyms. I think this can be made clear by thinking about the two theories in terms of possible worlds.Quote:
Originally Posted by Wayfaerer
First imagine a world where T is true, that is, a world where all ravens are black. There may be all kinds of other things besides ravens in this world, but in this world, if the thing in question is a raven, then it is a black thing. Call this a T-world.
Next imagine a world where S is true, that is, a world where all non-black things are non-ravens. There may be things of all colors besides black in this world, but in this world, none of these non-black things are ravens. Call this an S-world.
Now let's try to think of a way within T-world in which S could be falsified. That is, we are trying to imagine a world where T is true but S is false. But it doesn't seem that this is possible. In order to falsify S, we would have to find some non-black thing which is a raven. But in T-world, by definition, all ravens are black. And since finding a non-black thing which is a raven would entail that not all ravens are black, then it can never be possible to falsify S in any T-world.
Conversely we can try to think of a way within S-world in which T could be falsified. That is, we are trying to imagine a world where S is true but T is false. But again, this doesn't seem possible. In order to falsify T, we would have to find a raven which is non-black. But in S-world, no non-black things are ravens. Just like above, by definition we could never falsify T in any S-world.
This is of course the case because T is logically equivalent to S. Any world in which T is true is also a world in which S is true, and vice versa. No other state of affairs is logically possible.
It doesn't have any prior relevance at all. That's the entire point of the Tacking Paradox: that we can take any arbitrary proposition P, no matter how ridiculous or how far removed from the relevant theory it may be, and yet--by "tacking" P onto T by use of a conjunction--we can rigorously prove that evidence for T must also be evidence for P. The fact that this flies completely in the face of our intuitions is why we call it a paradox. If you're asking me for a way to make it seem non-paradoxical, I'm afraid I cannot.Quote:
Originally Posted by Wayfaerer
That's all fine but I can still see how evidence for one of these two completely different claims does not support the other. Evidence to support them seeks two different types of properties for two different types of things.Quote:
Originally Posted by DuB
How can you rigorously prove this? It seems to me you just disproved this notion. Why not conclude this kind of thinking is wrong in the first place rather than seeing it as some confounding logical glitch?Quote:
Originally Posted by DuB
Well... it's clearly not all fine if you still think that you can imagine such evidence. It would be like saying that you can imagine a situation where a person is an unmarried man but is not a bachelor. Obviously there can be no such situation simply due to our definitions of "unmarried man" and "bachelor." For the present case, could you illustrate for us how some event could be evidence for T but not S, or vice versa?Quote:
Originally Posted by Wayfaerer
The proof (summarized from Carl Hempel) was laid out pretty straightforwardly in my first post--however, I don't want to defend that proof too much because I do actually think that this paradox can be resolved in a satisfying way by taking a Bayesian perspective on the problem, a perspective which I think is actually quite intuitive. It would take a fair amount of space to fully explicate the Bayesian argument (it is based on Bayes' Theorem, a result from probability theory), but I think the important points can be summed up adequately.Quote:
Originally Posted by Wayfaerer
Recall that the Tacking Paradox depends on two assumptions about how evidence can bear on theory: (1) if T entails E, then E is evidence for T; and (2) if E is evidence for T, and T entails P, then E is evidence for P. If we accept both of these seemingly innocent assumptions, then the paradox can always be derived.
Basically, the Bayesian accepts (1) but does not fully accept (2). Instead, the Bayesian accepts that (2) is sometimes true, but denies that it must always be the case: if E is evidence for T & P, then E is allowed to provide different degrees of support for T and for P separately, says the Bayesian. Crucially, E serves as evidence for T or P only to the extent that E would be correspondingly less likely to have obtained if T or P were NOT true. With respect to P, for example, the Bayesian says that if E is equally likely to have occurred whether it is the case that T & P or that T & not-P, then E cannot be considered as evidence for or against P, whether or not it may be evidence for T. In this way the Tacking Paradox is blocked.
To make this more concrete let's return to my running example of the roommate. We had arrived at the paradoxical conclusion that, because my observation that my roommate had slept through his alarm served as evidence for the joint hypothesis that "my roommate was out drinking last night AND the moon is made of green cheese" (by [1] from above), then it must also be the case that my roommate having slept through his alarm must also be evidence for the simple hypothesis that "the moon is made of green cheese" (by [2] from above). However, the Bayesian points out that the probability that I would observe my roommate to sleep through his alarm given that "my roommate was out drinking last night AND the moon is made of green cheese" is exactly the same as the probability that I would observe my roommate to sleep through his alarm given that "my roommate was out drinking last night AND the moon is NOT made of green cheese." This is of course not true for the first part of the joint hypothesis, the part saying that my roommate was out drinking last night. In that case, the evidence is undeniably more likely to have obtained if my roommate had been out drinking last night then if he had not. So we can say that while my observation of my roommate sleeping through his alarm DOES serve as evidence that he was out drinking last night, it does NOT serve as evidence that the moon is made of green cheese.
I think you will agree that this is a pretty satisfying answer to the paradox.
The Bayesian also has a response to the Raven's Paradox, but it is somewhat less satisfying and also more difficult to explain without appealing directly to Bayes' Theorem, which I want to avoid. Roughly put, the Bayesian bites the bullet and concedes that observing any non-black thing that is a non-raven does indeed serve as some degree of evidence that all ravens are black. However, the Bayesian maintains that, for any realistic figures, such an observation provides such an infinitesimally small degree of support for the hypothesis that we can say that it has no practical bearing on the hypothesis "in the real world." So the Raven's Paradox is not blocked in the same way that we managed to block the Tacking Paradox, but its impact is lessened considerably.
Hangman's Paradox is a real brain breaker :D
My thoughts on The Grandfather paradox are that it depends on the way how someone views time:
1. If we look at it as a single line. Then the moment you go to the past and kill your grandfather you will vanish and the past and the future after it will be changed. The fact the in the future you do not exist to kill him wont change anything.
2. If we look at it a tree. Infinite number of parallel universes. Each created when there is a choice.
In that case when you go back in time and kill your grandfather. You will create another path of time (or parallel universe). But then you will be stuck in it. So when you try to go back in the future, you will go to a time where you do not exist. And the universe where you exist will not be available to you.
And the Monty Hall problem - you can prove it mathematically that if you swap the door the chances actually rise.
I'm studying the probability for the last 6 months in University. But even thou you can prove it, the chances are the same.
The fact is that your probability to win a car raises if you choose again between 2 doors. Not only if you swap the choice. (but this is only mathematically, actual chances are the same)
DuB, that's just mindblowing. Especially the Raven paradox.
This isn't a paradox, nor even a contradiction. There is nothing to say the barber can't shave himself, just because he additionally shaves all those who doesn't. And there's even the possible solution of him not shaving/being shaved at all.Quote:
Originally Posted by stormcrow
Strictly the paradox should say that the barber only shaves those who don't shave themselves. It is a contradiction.
lolwatQuote:
Originally Posted by Ivan452
Why do you think there is a difference between mathematical probability and 'chances'? They're the same thing. If you swap, your chances of winning are 2/3. If you don't, they're 1/3.
I used the different terms for the same thing (mathematical probability and 'chances')
and yea, I was wrong about the problem. I misunderstood it. Its kinda late here o.- :sleepmeditate2:
I figured, but it didn't. I had to pounce at that. But it still doesn't rule out that the barber just doesn't shave.Quote:
Originally Posted by Xei
There are some pretty nice paradoxes going on here. But Dub's was so far the most amazing one I've ever heard thanks a lot Dub. I'd like to see someone compete with Dub's paradox :D
Maybe The Raven paradox isn't such a paradox after all. Since everything we can see has a color, and all colors in our visual spectrum exist (lets just consider black a color for now), maybe observing a non-black thing really is ever so slightly increasing the chances of any other entity with a color being black, since there is a finite amount of entities with definite color at any given moment and a finite amount of black things that exist.
DuB, could you dispel the so-called "doomsday argument"? Basic intution tells us that without any empirical evidence or external reasoning*, you can't make any claims about the likelihood of human extinction. However, some people (like Xei) have gotten lost in the math and actually believe it's true, despite common sense. Is there a Bayesian resolution to this madness?
Doomsday argument - Wikipedia, the free encyclopedia
*For clarity, by "external" reasoning I mean some line of reasoning other than the doomsday argument itself, like "I think we'll go extinct because we have nuclear weapons", etc.
http://s3.amazonaws.com/kym-assets/e...jpg?1301826641
> 2011
> Still dismissing probabilistic arguments on the basis that they don't accord with human intuition and common sense.
See also: Simpson's paradox, Monty Hall problem, Boy/Girl problem, et. al.
There are common sense solutions to all the examples you listed. For example, from a common sense perspective, the change in probabilities in the Monty Hall problem makes sense because the host is giving the contestant more information, thus altering the problem. The DA is on a whole other level of implausibility. Anyway, we've already heard your opinion, now I want to hear from someone who seemingly has a better grasp of statistics.Quote:
Originally Posted by Xei
It does seem a little arrogant to say that because something is contrary to your intuition, it is obviously wrong.
I looked over the header of the wiki article and didn't see anything obviously wrong with the argument. The exact figures they present are obviously a little dubious since they rely on a lot of assumptions extrapolated from current data, but that isn't really the important part of the argument is it. The main point of the argument is simply that, if we assume that there is definitely a discrete beginning and discrete end to human existence, and assuming that we have no good reason to suppose that we are at a particular position within that interval, then if we have an idea about how many humans there have been, we can make some pretty straightforward probabilistic statements about how many humans there will be.
I don't see why this is a controversial conclusion. Probabilistic conclusions are not particularly strong, binding conclusions after all. I assume you wouldn't object to the conclusion of this same argument if instead of talking about humans, we were talking about something more mundane like the total number of times that lightning will strike during a discrete thunder storm.
This is a little disappointing that even you've fallen for this. What about the fact that there is no "we", there is only each separate living individual experiencing life? If you constructed the probabilities taking into account each person's lifespan, not just the "year", then you might get different results. In other words, consider the probability of living at this time as person #161,706,435,603 versus living at this time as person #161,706,435,604. In other words, the argument only works if you consider the human species as one entity.Quote:
Originally Posted by DuB
About the context, on the contrary. I think people with pre-conceived bias about the lifetime of our species (because they think we'll die in nuclear fire or whatever) are more likely to fall for this ambiguous probabilistic argument because it supports their bias. If we were talking about lightning strikes, the absurdity would become more clear to everyone because no one has a psychological attachment to thunder storms.
Every human who ever lived says "chronologically I am within the middle 80% of humans". How many turn out to be correct?
How? I cannot see any way of connecting what you just said with the argument as I understand it. We are simply talking about the total number of humans there will be. How is lifespan even relevant.Quote:
Originally Posted by cmind
80 % of them?Quote:
Originally Posted by Xei
edit: Assuming every human that has lived and will live.
omigod i dont believe you cant do basic statistics youre so biased raaaaaaargh
The grandfather paradox
Imagine you build a time machine. It is possible for you to travel back in time, meet your grandfather before he produces any children (i.e. your father/mother) and kill him. Thus, you would not have been born and the time machine would not have been built, a paradox
All You Zombies paradox
A baby girl is mysteriously dropped off at an orphanage in Cleveland in 1945. "Jane" grows up lonely and dejected, not knowing who her parents are, until one day in 1963 she is strangely attracted to a drifter. She falls in love with him. But just when things are finally looking up for Jane, a series of disasters strike. First, she becomes pregnant by the drifter, who then disappears. Second, during the complicated delivery, doctors find that Jane has both sets of sex organs, and to save her life, they are forced to surgically convert "her" to a "him." Finally, a mysterious stranger kidnaps her baby from the delivery room.
Reeling from these disasters, rejected by society, scorned by fate, "he" becomes a drunkard and drifter. Not only has Jane lost her parents and her lover, but he has lost his only child as well. Years later, in 1970, he stumbles into a lonely bar, called Pop's Place, and spills out his pathetic story to an elderly bartender. The sympathetic bartender offers the drifter the chance to avenge the stranger who left her pregnant and abandoned, on the condition that he join the "time travelers corps." Both of them enter a time machine, and the bartender drops off the drifter in 1963. The drifter is strangely attracted to a young orphan woman, who subsequently becomes pregnant.
The bartender then goes forward 9 months, kidnaps the baby girl from the hospital, and drops off the baby in an orphanage back in 1945. Then the bartender drops off the thoroughly confused drifter in 1985, to enlist in the time travelers corps. The drifter eventually gets his life together, becomes a respected and elderly member of the time travelers corps, and then disguises himself as a bartender and has his most difficult mission: a date with destiny, meeting a certain drifter at Pop's Place in 1970.
Time travel paradoxes disappear when you have multiple worlds.
What about Zeno of Elea? His paradoxes are cool to look at. :)
Mathematical analysis has basically sorted those.
Agreed.Quote:
Originally Posted by khh
Ya, I didn't do a great job explaining it, it was supposed to say that the barber only shaves those who don't shave as Xei said.Quote:
Originally Posted by khh
More on the topic of induction here's one from Hegel: We learn from history that we do not learn from history.
Here's another pointless, stupid logical paradox: Everything in moderation.
Another one: All I know is that I know nothing. That was Socrates, by the way.
Logical paradoxes are boring.
Okay.Quote:
Originally Posted by cmind
This is one of my favorite paradoxes:
I think it's safe to assume that the majority of the people who will read this have also read the Harry Potter series. Of course, this is just a ripe example, anything with any form of cause-and-effect scenario could work with this.
So let's say that by Deathly Hallows, Harry comes across a Time Turner. Thinking that he could just go about 60 years into the past and stop (kill) Voldemort from ever beginning his career as the most powerful dark wizard to ever walk the planet, Harry sets off through time and space. Arriving in the 1940's, Harry goes into the orphanage where Tom Riddle lives, and kills him. This is a paradox though; the only reason Harry went back in time to kill Tom Riddle was because Tom Riddle caused Harry to go back in time to kill Tom Riddle. But, if Tom Riddle was never alive to cause Harry to go back and kill him, Harry wouldn't have gone back to kill him. But Harry is still there; Tom Riddle must have caused Harry to go back in time to kill him, but Tom Riddle was dead, meaning Harry wouldn't have gone back in time to kill him, but Harry DID go back in time to kill him, so Tom must have caused Harry to go back in time to kill him, but Tom couldn't have done so because Tom was dead, and so on and so forth.
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.
Two hands clap and there is a sound. What is the sound of one hand?
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.
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.
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.
I believe this thread is about paradoxes in the strict sense, according to the actual definition:
From Wikipedia: Paradox - Wikipedia, the free encyclopediaQuote:
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.
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.
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.
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.
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.Quote:
Originally Posted by crackers
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.
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.
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.
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?
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.
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.
How did you come up with this number? (pretty sure that time stops for an observer traveling at the speed of light)Quote:
Originally Posted by Oreoboy1996
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.Quote:
Originally Posted by Spartiate
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.Quote:
Originally Posted by Oreoboy1996
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.
What makes you say this? I thought it would be slowing down.Quote:
Originally Posted by Xei
Yeah, this really is an awesome effect of Lorentz contraction.Quote:
Originally Posted by Xei
I was actually talking about the historical 'end'. :P
And yes it would go faster... just consider the twin paradox, where the one left behind ages faster.
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.