ok, let me start.
all ravens black...
so all non-black-things are non-ravens
If truth does not exist, the statement "truth does not exist" is a truth, thereby proving itself incorrect.
The following sentence is true.
The preceding sentence is false.
You travel back in time and kill your grandfather before he meets your grandmother which precludes your own conception and, therefore, you couldn't go back in time and kill your grandfather.
got some more? thoughts?
... I've got nothin'.
ok, so does this make any sense;
all ravens are black right?
so if you see a raven, it will always be black.
so if the bird infront of you isn't black, it isn't a raven.
so; all non black bird's are not ravens..
this ofcourse is correct.. but the paradox is;
The statement "all ravens are black" is logically equivalent to the statement "all non-black-things are non-ravens"
so all non red things are not strawberries..
Is this a koan thread?
How about this one:
How does one walk in a circle in two directions at the same time?
>> How does one walk in a circle in two directions at the same time?
put a big mirror infront of the person and view from above..
direction<---- normal | mirror ---->
Why is the night sky black if there is an infinity of stars?
If a hotel with infinitely many rooms is full, it can still take in more guests.
The birthday paradox states that if there are 23 people in a room then there is a slightly more than 50:50 chance that at least two of them will have the same birthday. For 60 or more people, the probability is greater than 99%.
it is a paradox in the sense that it is a mathematical truth that contradicts common intuition. Most people estimate that the chance is much lower than 50:50.
> If a hotel with infinitely many rooms is full,
impossible assumption, not a paradox
> impossible assumption
forgot to add that to the thread name..
Consider a uniform rigid heavy rod of length l = r2 - r1 and two vertical concentric circles of radius r2 and r1. The rod is constrained so that one end remains on the inner circle and the other remains on the other circle; motion is frictionless. The rod is held so that it is horizontal, then released.
Now consider the angular momentuim:
1. The reaction force on the rod (from either circular guide) is frictionless, so it must be directed along the rod; there can be no component of the reaction force perpendicular to the rod. Taking moments about the center of the rod, there can be no moment acting on the rod, so its angular momentum remains constant. Because the rod starts with zero angular momentum, it must continue to have zero angular momentum for all time.
2. After release, the rod rotates, moving like the hands on a clock. When it gets to the six o'clock position, it has lost potential energy and, because the motion is frictionless, will be moving. It therefore posesses angular momentum.
>You travel back in time and kill your grandfather before he meets your grandmother which precludes your own conception and, therefore, you couldn't go back in time and kill your grandfather
If you kill your grandfather in the past you modify the timeline and therefore it's another timeline, by definition.
> If you kill your grandfather in the past you modify the timeline and therefore it's another timeline, by definition.
that is correct if you go by the M-theory, Many world interpretation of quantum physics.. or the multiverse theory.
If you kill your grandfather and can speak about it, you didn't kill your grandfather, beacuse you exist in the universe where you didn't kill him, beacuse you exist..
Almost like quantum immortality.
experiment: Quantum suicide.
A physicist sits in front of a gun which is triggered or not triggered depending on the decay of some radioactive atom. With each run of the experiment there is a 50-50 chance that the gun will be triggered and the physicist will die. If the Copenhagen interpretation is correct, then the gun will eventually be triggered and the physicist will die. If the many-worlds interpretation is correct then at each run of the experiment the physicist will be split into a world in which he lives and one in which he dies. In the worlds where the physicist dies, he will cease to exist. However, from the point of view of the non-dead physicist, the experiment will continue running without his ceasing to exist, because at each branch, he will only be able to observe the result in the world in which he survives, and if many-worlds is correct, the physicist will notice that he never seems to die.
there's no paradox in that paragraph. it's called fallacy.
>>10
Provided that death is instantaneous upon pulling the trigger, if the physicist performs his experiment in total isolation and notifies no one of his whereabouts or intentions, then the fact of his death can't be observed even in the timelines in which he dies. Does that cause him to exist in a state of limbo until such a time that he is observed to be dead by an outside party?
>Does that cause him to exist in a state of limbo until such a time that he is observed to be dead by an outside party?
he is either dead or alive, regardless of whether he's been observed or not, but he would appear to exist in a state of limbo to anyone who has not observed his current state.
here's something else for you to think about... if i offer you a deck of cards and ask you to choose any card, do you really have free will to choose any card in the deck? what if after you choose a card, i use a time machine to go back in time and tell myself which card you're going to choose?
Wave function collapse is not relative to the observer. Either the wave function collapses, or it doesn't. The problem is that there is no clear definition of what a measurement is, or for that matter what a wave function collapse is. It is pretty clear that quantum effects like the linear combinations of states does not translate into the macroscopic world. The reason why, however, is unclear.
That is to say: The cat (or for that matter, physicist) dies, or doesn't die, irrespective of if you observe it or not. Schrödinger's Cat is a mind experiment used for reductio ad absurdum. It is not something that actually happens in the real world.
> 14
for those who dont know;
Schrödinger's Cat experiment involves a sealed box (allowing no interference from the outside), which contains a cat, and a closed canister of poisonous gas. Attached to the gas canister is a mechanism containing a radioactive nucleus. When the nucleus decays, it emits a particle that triggers a mechanism which opens the canister, thereby killing the cat.
Since the nucleus, as long as it remains unobserved, is in a superposition of the "decayed" and "not decayed" states, then it logically follows that the cat must also be in a superposition of "alive" and "dead" states -- until the moment when the box is opened and its contents are observed by the scientist performing the experiment. The idea that the cat's fate is decided only when the box is opened seems to defy common sense
> Wouldn't the cat die of hunger anyway?
yes offcourse.. but it still WAS in the superposition of "alive-dead"
>>13
If you travel back in time to tell yourself which card I'm going to choose, the possibility that you already know what I'm going to choose doesn't change the fact that I made the choice.
When travelling back in time, you can't be certain whether it is the specific card that I choose that is retained by the timeline, or the relationship between the card I choose and the card you expect me to choose. In the latter case, I may (for example) always choose the card just to the right of the one you expect me to choose, a decision finalised at the precise moment my selection is made.
>>17 Well then when you open the box, do an autopsy to find the moment of the death. Uncertainty solved.
> Well then when you open the box, do an autopsy to find the moment of the death. Uncertainty solved.
facek!
> UNTIL the moment when the box is opened and its contents are observed by the scientist performing the experiment.
According to quantum mechanics, a physical system (such as a nucleus of a radioactive atom) can be in a superposition (mixture) of states (such as "decayed" and "not decayed"). Only when a measurement is performed by an observer, the system "collapses" into one of the states -- which is the state seen by the observer.
But wouldn't make that the cat the observer then? Or perhaps even the mechanism on the poison vial?
> ut wouldn't make that the cat the observer then? Or perhaps even the mechanism on the poison vial?
yes, but the for the scientists... it a superposition "A/D"
What is existence..
If existence is to be, then there are many 'senses' i wich an object can fail to exist.. put an pencil infront of a TOTALY blind man.. he does not see it, therefor it doesn't exist to him. only until he touches it, feels it or smells it "lets his senses interact with it" or until he is told about it.
As im writing this I have an apple beside me.. this apple is green and ripe... this apple i speak of is now existant to you, beacuse i mentioned it.. and even if i tell you that i lied, and i actually dont have an apple.. it still exists. how can it not exist? can you trust me? can your trust your own judgement?
Suppose one listed out all the properties and relations of an apple sitting on a table. It is red, it has a stem, it is four inches wide, it is juicy, it is on the table, it is in a room, and so on. Then, once one has listed out all the properties and relations of the apple, one could try claiming that the apple exists (or "is,"). But that does not add any new property to the thing. Therefore, existence is not another property over and above all these. So what is existence.. what does it mean for an object to exist. George Orwell defined existence in his popular novel Nineteen Eighty-Four. O'Brien explains to Winston that if both of them believed that O'brien had floated away like a soap bubble then he had.
>facek!
Huh?
>According to quantum mechanics, a physical system (such as a nucleus of a radioactive atom) can be in a superposition (mixture) of states (such as "decayed" and "not decayed"). Only when a measurement is performed by an observer, the system "collapses" into one of the states -- which is the state seen by the observer.
How do they know it's a mixture of states when it isn't observed, if it isn't observed at all?
> How do they know it's a mixture of states when it isn't observed, if it isn't observed at all?
it is a mixture of states beacuse the nucleus of a radioactive atom HAS to be decayed and/or not decayed..
facek = fack = fuck
>it is a mixture of states beacuse the nucleus of a radioactive atom HAS to be decayed and/or not decayed..
even if it is not observed.. - _ -
Ok, but isn't there a formula that can predict in which state the nucleus is when not observed?
Such and such mass at such and such speed means that after such and such time the nucleus is gonna decay.
Maybe such formula doesn't exist yet, and therefore the decayed/!decayed "problem". Once they come up with the formula there will be no more ambiguity. It seems to me that there is actually no ambiguity, but that the science is incomplete.
No love for the alternate realities theories?
something like with every random event, all possible outcomes occur but in separate universes. so in some universe, I must have won the lottery.
No, read >>14 again - wavefunction collapse is NOT relative to the observer. Once it's collapsed, it's collapsed.
And yes, as >>21 points out, the cat is a very capable observer in this case. As are many other parts of the system. As with all paradoxes, there is no actual paradox - just a misunderstanding or misstatement of facts. There is no mysticism of existence or consciousness here, as so many think.
The purpose this paradox actually serves to illuminate a fundamental problem in quantum mechanics: What is a "measurement", and what actually happens in a wavefunction collapse? Both of these are open questions, to some extent.
>>27
True randomness doesn't exist.
With the cat in the box example, it should be possible to find out when the trigger is gonna switch on - with sufficiently advanced technology. So alternate universes waiting to be created from true random events would never come into existence.
As for the scientist and his gun example, no matter how important a scientist thinks he is, his death has no bearing upon the reality's existence - why should a reality decide to split because some small fly dies? It doesn't make sense.
OTOH if one built a machine to visit alternate realities, then here we have a "random" event, or rather an external tampering with the reality's structure. Only them would the reality find cause enough to act up and split, IMO.
Spoken like a true CS major. Wavefunction collapse appears to be truly random. It is also trivial to construct a mechanism to use this to generate randomness on a macroscopic scale: http://fourmilab.ch/hotbits/
Even discounting non-deterministic wavefunction collapse, a completely deterministic system need still not be predictable: A chaotic system is extremely sensible to initial conditions, and the real bahviour will always diverge from the prediction because one cannot detetmine the intial state with infinite precision, no matter how advanced the technology.
So yes, true randomness exists.
> True randomness doesn't exist.
Prove it!
>>31
Use the same seed for the function random(), and you'll always get the same result.
See also http://en.wikipedia.org/wiki/Hidden_variable_theory
"In other words, quantum mechanics as it stands might be an incomplete description of reality. Some physicists maintain that underlying this level of indeterminacy there is an objective foundation. Such a theory is called a hidden variable theory."
> Use the same seed for the function random(), and you'll always get the same result.
AHduuuuuuurrrrrrrrrr
How's about use always a different seed for the function random (), and you'll end up with true randomness as a "proof"?
> Such a theory is called a hidden variable theory.
A few decades ago, mystical substances like these that would be required to get a near-perfect rationalizable universe was called "ether".
Really, this is more of a philosophical than a scientific problem.
I recommend Paul Feyerabend's "Against Method" as a classic introduction to the philosophical shortcomings of all scientific theories and methodological approaches.
The ether thingie is now called "dark energy". :)
http://en.wikipedia.org/wiki/Dark_energy
Dark energy is the new black ether!
CS MAJOR! CS MAJOR! CS MAJOR!
You cleverly omit all the points of the article talking about how unlikely such a theory is, and how it is generally not considered to be true.
And read my post, would you?
There are reasons why LCRNG, the Mersenne Twister, and other such algorithms are called pseudo-random. Real sources of entropy don't use seeds.
>>experiment: Quantum suicide.
A physicist sits in front of a gun which is triggered or not triggered depending on the decay of some radioactive atom. With each run of the experiment there is a 50-50 chance that the gun will be triggered and the physicist will die. If the Copenhagen interpretation is correct, then the gun will eventually be triggered and the physicist will die. If the many-worlds interpretation is correct then at each run of the experiment the physicist will be split into a world in which he lives and one in which he dies. In the worlds where the physicist dies, he will cease to exist. However, from the point of view of the non-dead physicist, the experiment will continue running without his ceasing to exist, because at each branch, he will only be able to observe the result in the world in which he survives, and if many-worlds is correct, the physicist will notice that he never seems to die.
I'm gonna make a comic based on this one.