If you ask Rick Astley for a copy of the movie Up, then by giving it to you he would be giving you up, but by not giving it to you he would be letting you down. This conundrum is known as the Astley paradox.
I actually came up with a quite elegant solution for this a while back. Rick would tell you exactly where to find a copy of the film, thus not giving it to you whilst still not letting you down. He would drive you there and stay with you the whole time so as to not run around or desert you.
@@liamosborne6859 I think it's unreasonable to expect Rick Astley to give you a copy of Up especially as he has already stated that he's never gonna do it and therefore any sense of being let down by him is unjustified. He probably would have to drive you and stay the whole time though.
And then if you asked him to run laps of a circular running course and high-five you so hard at the end that it hurt but he refused to do this then he'd be doing exactly what he said he'd never do, which would be a good thing... I guess... but then he'd be disobeying and letting you down, which is kinda not a good thing... I guess...
@@lukesoares7117 Two persons having a similar characteristic does not prevent them from being unique. Unique is "a different set of characteristics" not "completely different."
@@lukesoares7117 They do not contradict each other. It is possible for everyone to be unique in a different way to everyone else. Therefore meaning you would be unique _"like everyone else"_ with everyone else being unique.
If I had 5 stones, all having a different colour, one would be unique, just like the other 4, wouldn't it? The "(...) like everybody else" doesn't mean that you are unique in the same attributes as everybody else
Regarding #3: Some infinities are larger than others. My younger brother, who is a mathematician, explained to me once how we work with this concept all the time.
The whole number are more because if we say the infinity of whole numbers is x then the infinity of even number is x-n(n being odd numbers) . X-n is less than x
@@tusharyadav4982 If x = ∞ then arithmetic with x does not make much sense without mathematical extensions. If you want to reason about sizes of sets then you would use the notion of cardinality. The cardinality of a set is the concept of the size of a set extended to infinite sets. The set of natural numbers (some say whole numbers) is countably infinite and any set with the same cardinality is countably infinite as well. Two sets have the same cardinality if there is a bijection between the elements of one set to elements of the other. And there is a bijection from the set of natural numbers to the set of even numbers, namely x→2*x. That is, there is a unique natural number for every even number and vice versa. Therefore, the set of natural numbers has the same cardinality as the set of even numbers.
This one honestly took me a long time, but the easiest way to think about it for me was alluded to in the video. We know that the set of whole numbers are infinite and we know that when counting from 1 to 100 there are half as many even numbers as there are whole numbers. But we can count from 1 to 100 by doubling each number as well, effectively making them all even, and since there is a double to every number that is countable that means there are as many doubled numbers as there are whole numbers making the infinities of whole numbers and the infinities of doubled numbers(or even numbers) the same size. Hope that helps.
It wouldn't be a surprise, because if all the days passed Monday through Thursday and he still wasn't killed, then he would know it's on Friday. So no surprise
I have the answers for all the paradoxes, wanna hear them? 1. The judge, immediately after sentencing the prisoner, jumps at the prisoner and stabs him to death. Surprise! 2. There's no rule that there can't be 2 of the same ship. Ship and Ship prime. 3. Same amount because you can always go n+1. 4. Oh fuck, it's just the Pinocchio paradox again! FUCK 5. Can God microwave a burrito so hot even he can't eat it. Yes because to create something that God can't do is still his will and his will be done! 6. Time machines don't exist. I know that's a cop out but I've studied this stuff enough to know it doesn't exist -- and I need to also state that he didn't describe Multiverse theory, he described the "many worlds interpretation." 7. The twin traveling near the speed of light is less old than the others because he had to change his rate of acceleration. Ta da?
1. But not a suprise in week 2 as promised -> judge is a liar. 2. C++-Template of a ship? 3. What about signed integers, will it double infinity? 4. Unbeatabe 5. But we are his counterpart, also too hot for us? 6. Time machines existed 300 years ago, but only if I will use one in 300 years when they will exist to create them then. 7. I am too stupid and lazy to follow this one.
@@TheDeterminer if it were opposite day the person asking the question has to know that the person responding would answer the question "is it not opposite day" because of that, you can respond normally without any paradoxes
While I don't believe on opposite day its opposite day would be the opposite of its not opposite day, but even so if it's not a paradox because it would just be lying
@biggs949597 s I'm pretty sure that was satirical, and that's only because I know a decent bit about European history and what you were saying was obviously joking, but it came off as really sincere, I just wanted to tell you that so you know structure of your jokes differently in the future.
@biggs949597 s well his reasoning is to be fair, just because a lot of Christians believe God should be called a man that doesn't mean all of them do, I meanshe never specifically talked about a Christian God, he was just talking about an omnipotent being, he wasn't trying to bring religion into, at least at that point. Also the fact that it really doesn't make sense for God to have a gender, so he brought up the idea of a she to get us thinking, he doesn't believe that God is a he or a she because he doesn't believe there's a God, he's just trying to give us a logical paradox. Also I do want to say I wasn't trying to spark a debate I was just trying to tell a joke... But I'm glad it created a productive conversation
@biggs949597 s Have you seen the episode of Family Guy where they did time travel to an alternative universe where everyone had stopped being christians/religious? (For 200 years I think, don't remember exactly) They were SO FAR ahead of us. Sure, Family Guy is just a silly show but it doesn't sound weird at all to me if what they showed could be reality if we did really stop being religious. Religion have given us a lot of history, etc. but science is what gives us facts.
I asked a Christian friend the omnipotent power paradox, in regards to God. He said that if God created something that he himself cannot lift then he could create something to lift it for him. I then said that we do that all the time, for example cranes. He got angry and accused me of saying that I am as powerful as God. That is stupidity in itself, right?
At first, I didn't understand why he get mad at you and I even thought his answer was creatively good. The problem is that his creative answer suggest that God is not omnipotent: if he was, he shouldn't have to create something to lift it for him because he could do it himself. So maybe he was mad at you because he was mad at himself for giving you the opportunity to say that he himself acknowledge that god was not omnipotent and thus, not a god at all. I say that because his attack doesn't make sense. You didn't imply that you were as powerful as god. I'm probably wrong PS: I hope you answered by "God created us in his image, didn't he?"
Most apologists have explained gods omnipotence as the ability to do things that are logically possible. It creates a loophole around the omnipotence paradox.
My answer to the omnipotent power paradox is this: when God creates something that he himself cannot lift, he gives up his omnipotence. He will no longer be omnipotent after that creation.
TaiFerret - that's a meaningless answer. You can't come to that conclusion through logic, even if it makes some kind of sense to you. Sure, it's a possibility, in that anything is a possibility, but there's no reason to believe that is what would happen.
To answer your last paradox about the twins moving at the speed of light, the answer falls within that although movement is relative, acceleration is NOT relative. The twin who accelerated away from the other twin would be the younger one, because both twins are going relatively the same speed to one another, but only one is accelerating and decelerating. Yeah, I know, physics are weird XD
How do u know who is accelerating? acceleration is the amount of distance/time from one point to another. But here there are only 2 points like he stated in the vastness of a univers ;)
+Gent Boy What was missed in the equation here is that both twins are at rest or otherwise constant velocity of zero miles per hour. Side note - we are never at mass rest. Continuing - Special relativity only works in these matters. However one twin is accelerating because there is an actual force acting on the twin and there goes special relativity down the drain. This is simply physics. Both twin cannot be accelerating. So the twin that is accelerating will be the younger one because only that twin experiences the time dilation while the other one does not. Not sure why this is a Paradox but okay I will bite. I still hate physics even at this old age :-(
Actually, relativity does affect my everyday life. I work with GPS based survey equipment. Because of special relativity, the orbital speed of GPS satellites is sufficient to create a time dilation effect that causes the satellites to lose about 7 microseconds per day. However, because of general relativity and the fact that the satellites are further from the Earth's mass, they gain about 45 microseconds per day. If GPS software did not adjust for these effects, it would be worthless for surveying in a matter of minutes, and within a day even simple navigation systems would be off by kilometers.
So the gps software does it, I get what ur saying though. By your standards my cable guy also deals with this, though I doubt he knows it. I was a 25s in the army, what company do you work for? Anything based in Georgia? Legitimately curious
This is a 30-minute video condensed down to less than 7 minutes by the speed CosmicSkeptic is speaking, which gives us extra time to read Al-Khalili's book on paradoxes. Cheers, Alex :)
This video is such a special one. It shows us younger Alex in his formative year as a content creator. His presentation is rushed, the choice of background music is a little distracting, and the departure from the subject matter for which he is usually well known gives an appearance that he is yet to settle concretely on what to talk about in his channel. Seeing him now and coming back to this video makes apparent just how far this bright lad has come. I cannot overstate the joy of sharing the contemporary generation with Alex in the large course of cosmic events. Keep on keeping on, friend.
I've always felt that statements like these can be the only "true" existence jn a domain. So there could be a universe in which all categorical statements are flawed as a aspect of existence in that universe. From a metaphysical viewpoint we would have a universe with the only true categorical statement being "categorical statements are inherently flawed"
Can't believe no one has addressed this yet, the solution to the twins paradox is that relativity states that the only "real" and not-relativistic "force" is indeed acceleration (which is indistinguishable from gravity), therefore, if only one of the twins experiences it, that's the twin that time slows down for.
@@natalieelskamp03 but only one twin would "feel" the acceleration (from the rocket or whatnot). Only that twin would be experiencing the true movement and hence the time dilation.
So, two dudes are on a rock travelling near the speed of light, but no acceleration, so no worries. One dude steps off (into a v large atmosphere) he decelerates significantly cos of the air friction. And he is the one who doesn’t age right? Deceleration being acceleration backwards? But he is not actually accelerating, he is slowing down - coming closer to no speed at all. But then it’s relative yeah? So you can remain young also by slowing down from the speed of light. ??
So two guys are past by a girl on a rock travelling the speed of light. But nobody is accelerating, so no ageing. One guy accelerates toward the rock. when he arrives he is now younger than everybody else cos acceleration. The he gets off and slows down back to his friend. Now relative to the girl he is twice as young, but what is he relative to his friend - he accelerated, then slowed back down. His mate is same age as the girl. Does slowing down also keep u young????
@Adam Romanov my nigga, u are going straight into my cringe compilation. You would think a student from Stanford would be civil.... Oh well, every rule has it's exceptions
@Adam Romanov Someone thats actually smart doesnt equate their academic achievements with how intelligent they are. So even if you did go to Stanford, all youre intelligent at is memorization.
@Adam Romanov No, you being triggered and listing off academic achievements is you trying to prove that youre smart. Dont just assume someone is trying to sound smart just because they talk fast, he mightve been in a hurry or something.
@Adam Romanov What exactly makes him being in a hurry impossible? Im not saying he is, im just saying there are several reasons why he would talk fast.
It’s not a paradox it’s just incorrect, in every case you should say, “It’s not Opposite Day.” On Opposite Day you say, it’s not Opposite Day and when it’s not Opposite Day you say the truth which is, “Its not Opposite Day.”
One of my favorites is the Bootstrap Paradox, where an object continually travels through a loop in time, with no origin point. One of the most well-known examples (though the paradox itself might not be) is probably the Song of Storms in LoZ: Ocarina of time. In that game, you learn the song as adult Link from a man who reveals that he learned the song from a kid in green seven years prior. Of course, he is referring to child Link, so that's your cue to travel back seven years into the past and play the song for him in the past. So...he learned it from child Link, and taught it to adult Link, who traveled back in time to play it as child Link so that the guy can learn the song so he can teach it to adult Link so that adult Link can travel back in time to play it as a child so that and so on and so forth. At no point is the song originally written/discovered, it's just kinda stuck in this little infinite loop.
5 year old comment I know, but this paradox gets especially strange when a physical object is passed through one of these loops. The object must necessarily degrade over time, but this would lead to the object eventually decaying to nothing.
The way i percieve Theseus's boat is that the original planks that make up the boat and the planks that have replaced the boat are simply moments in time. Living people are essentially living examples of Theseus's boat. Asking which boat is the original is like asking which YOU is real? 5 year-old you, or 23 year-old you? Our entire build of atoms which makes up our body and brain are 100% replaced by new atoms every 5 years. If Theseus's boat is a paradox, that means that life is a paradox too. The only thing that isn't a paradox is our consciousness because that is made up of our collective past and present.
"What do you mean?" In pre-scientific days one could say that there was a durable soul that remained the same even if the parts of the body changed, like if "the atoms which makes up our body and brain are 100% replaced by new atoms every 5 years." But if we regard the mind as having no metaphysical components as most do today, and consciousness is just the result of the arrangement and states of those atoms, how do we know our memories and recollections are durable and consistent? Rearrange them and we remember something else, something counter-factual. But I like very much your question, "which YOU is real? 5 year-old you, or 23 year-old you?" because in many ways we believe we're the same person at 23 that we were at 5, but in other ways we believe we're very different people after the passage of years. It's a good philosophical question.
Hey Alex, I really like the content of your videos, but your speed of talking in this one is quite annoying for non-native speakers. Please reduce the pace a tad and expand your audience.
I love paradoxes! Unfortunately, there's very few that actually pose a problem. I'll explain, because I like to do that. 1. This one is simple. No matter what day the prisoner is executed, it will be a surprise. Clearly, this is true simply by virtue of the prisoner ruling out every day. The prisoner establishing that he won't be executed because it wouldn't be a surprise is what makes it a surprise to him. 2. Ah, the ship of Theseus. This is one of my favorites. The ship of Theseus is one with all of the components replaced. The parts taken off of the ship are no longer part of the ship of Theseus. Each time a component is replaced with a new one, the ship new parts are incorporated into the ship. The new ship built with the old scrap parts is a replica of the ship of Theseus built from discarded scraps. 3. The set of all whole numbers is infinitely large. The set of all even numbers is also infinitely large. The set of all odd numbers is again, infinitely large. All infinitely large sets are not equal though. It is incorrect to say that the number of all whole numbers is infinity. Infinity isn't a number that can be compared to other numbers. It's a concept. For this reason, the question is flawed. 4. It's neither true or false. It's a contradiction. 5. Omnipotence is a poorly defined term. Its ambiguity is what leads to problems like this. If it simply means that she can do anything, then she can violate the logical absolutes meaning that she can both make the rock too big to lift and lift it. If omnipotence only establishes that she can do all that is logically possible, then you've already answered the question. The question is, at its core, simply about whether or not she can instantiate a logical contradiction. Since that is not logically possible, she can't do it but is still omnipotent. 6. Simple. There isn't multiple time lines. You were there and failed your attempt to kill your grandfather, which is why you were born in the first place. There is only a problem with this paradox if you establish that there are multiple attempts at a timeline. 7. Like you said, there are multiple ways to establish what happens.
Atheist In Louisiana, the quantity of natural numbers is not a natural number, but it is a transfinite number. Specifically, it is Aleph-null. So also is the number of even numbers. en.wikipedia.org/wiki/Transfinite_number
The "solution" to the "omnipotence paradox" is that there is no paradox. The answer to the question is just...yes, it can make a rock it can't lift and then it would no longer be omnipotent. People for some reason incorporate some sort of time component...like an omnipotent being MUST remain omnipotent....which is entirely antithetical to omnipotence.....An omnipotent being would be able to remove all or some of its power, or else, by definition it wouldn't be omnipotent.
I remember reading a study where a group of physicists and a pilot did an experiment. The physicist had two synchronized clocks on the ground, they gave the pilot one and he flew in a jet for an hour as high as he could go. When the pilot landed, the physicists' clock was ahead.
Sorry I didn't bother scrolling through all the comments to see if anybody responded to the prisoner paradox. That being said, there is a solution: The prisoner can actually be executed on any day but friday. And this is why: If he doesn't think the logic through, it's trivial. He will be surprised on any day except friday. If he, however, followed your reasoning, he'll come to the conclusion that he cannot be executed at all. And thus, when the executioner comes to get him on, say, wednesday, he'll be utterly surprised, totally meeting the requirements for the execution.
@fynes leigh I'm just laughing at how some people like you act like children. The guy didn't even insulted you and you wrote a whole paragraph my dude. Like it would be ok if you made an actual point but after you said the reason why are you using double spaces you were just being toxic for no reason. Also, my dad had a stroke and barely survived and I take care of him every day so if anyone replays ti me why am I arguing with a person with stroke I can say that having had a stroke doesn't give you a permission to be toxic to anyone for no reason.
I actually made videos on 2 of the paradoxes you mention. The twin paradox is one of them. I explain how it works in special relativity, so leaving acceleration aside for now. Anyone who cares is very welcome to check it out! (I don’t have a huge number of videos so you should be able to find it!)
Slow down when speaking, it will give your points emphasis. I enjoy your content, just giving some helpful criticism:) let your points settle with your audience
The problem with the twin paradox lies with our understanding of relativity. See, the paradox here arises from a flawed notion that both the twins experience equal but opposite situations. But relativity is based on the idea that physics must be the same in all inertial frames, and not all frames are inertial. In order for a frame to be inertial, it must maintain a constant velocity. This means no acceleration of any kind, be it a change in speed OR a change in direction. Looking at the problem now, it’s easy to see the situation is a bit more complex than we gave it credit for. While Alice, who doesn’t move, maintains her inertial frame, Bob, who must accelerate in order to change direction and head back to Alice, doesn’t. When we look at the situation from Bob’s point of few, we find that we can no longer just pretend he stayed still while Alice moved, because she didn’t experience any forces or accelerations. Bob is the one who activated his thrusters, and felt the force of being pushed into his chair, while alice did not. Now that we can prove their situations are completely different, we can say without a doubt that Bob with return the younger twin.
That's how I interpreted it. It's the difference in reality vs perception. In reality, only one party is moving. They may perceive movement, but that is because perception is based on visual cues. If I start scrolling through text at a rapid speed and then I stop, it still appears as though the text is moving, but this is only because my brain is interpreting the movement still.
I took a class on General Relativity a while back, and though I could do the math just fine, I can't say as I really understood the concepts. From what I did understand though, inertial frames of reference have to do with the fact that space is something. There is a such thing as velocity within it. Moreover, space and time are not separate. When you alter the movement through space you alter the movement through time. Gravity, too, alters time because it alters space. So, with regard to the twins, It's not the acceleration at all. If it were, all the time slowing would only happen during the accelerations, and once the one twin reached constant velocity on the trip he would resume aging at the same rate as the other twin. It would also mean that if the suit exerted a constant acceleration, the full change in time would would take place upon launch. Neither are true. The time differences become greater as the actual velocity becomes greater and stays even when the velocity is constant, i.e. zero acceleration. I guess it would also follow that if the twins were born on a spaceship which had accelerated through space generations before they were born, it could be true that if the one twin "accelerated" in a direction that actually slowed his velocity through space, he would actually speed up his aging relative to the other twin. Like I said, I don't really understand this stuff and it just doesn't seem right to me, though a accept that it is even if my little brain can't really comprehend it. I asked the professor, Leonard Susskind, if he could explain what was happening physically. He just smiled and said it's true because the math works. He said that's enough for him and all his colleagues.
***** You are fundamentally misunderstanding the concept of space. It is something. This is easily understood if you take those two same objects and spin one. Is the one object spinning or is the other object orbiting around the other really quickly. Or you don't even need two objects. Imagine you are in space all by your lonesome. If you put your arms by your side and relax, and they stay there, you are not spinning in relation to space. If they "fly" outward, you are generation centrifugal force, and are thus spinning, in relation to space. Just as there is rotational velocity in space, there is linear velocity. That velocity will alter the objects relation to time relative to other objects in space. Well, at least that's how I understood it.
You might like a book called, "The Paradoxicon," that looks at a lot of paradoxes, quasi-paradoxes, etc. One of my favorites was about a Greek lawyer who trained someone in law. They agreed that the student would pay the teacher after the student won his first case. However, after his training was over, the student decided not to go into law. Wanting his payment, the teacher took his student to court. The teacher put forth this argument in court: If I win the case then the student must pay me the money, however if I lose, that will mean he has won his first case, which meets our original agreement, and he must pay me the money. However, the student reasoned: If I win the case, then I owe the teacher nothing, but if I lose, then I also owe him nothing because I will not have had my first winning case.
The first few are contextual paradoxes; once you include the context in which the statements are made, you solve the paradox. That’s the beauty of the English language, we’re so tactile with our dialect that we interpret language with plenty of nuanced inferences of context. Once we begin to take the sentences literally, the paradoxes disappear.
The twin that traveled the speed of light was in an accelerated frame of reference, whereas the stationary twin was not. While all motion is relative' the experience of g-forces is the important point.
For the prisoner scenario, I’d say only Friday can be ruled out. Because only when you are living Thursday you know for sure it’s Friday. But when you are on Wednesday you initially on that spot won’t know if it’s Friday or Thursday despite your ability to rule out. Let’s imagine when the sentence is set, and the judge writes the day of the execution on a piece of paper (not Friday) the excecution will happen regardless and the prisoner would not be able to Guess if it was not Friday. Everyday would be the day the prisoner will “know” his last day was today until he wakes up to survive it. He was sentenced to death on Tuesday. It was what was written on the paper and the prisoner did not know what day he would die.
From taking a minute to think about it: 1. Two possibilities (at least). For the first, suppose it happens on Friday. Up until Friday, it WILL be unknown to the prisoner, thus a surprise. For those that say the paradox is supposed to say it won't be known by the prisoner until it happens (not just the day before, but continuously), it could take place in the prisoner's sleep. The second possibility is because the prisoner thinks it can't happen on any day, the prisoner will either always be surprised no matter what, or that (execution during the week) implies (the judge lied). That, or it happens in the prisoner's sleep again. If you're not conscious, you can't expect anything. 2. Neither because the passage of time. 3. This is only a paradox because of definitions like (infinity) = (infinity) + (infinity) AND other definitions which are contradictory like (original something) + (something else) != (original something). The former is only used in mathematics because infinity is not treated the same as anything else. 4. Yields falsehood when preceded by its quotation yields falsehood when preceded by its quotation. This is an example of something that would require context to either be true or false. Imagine a scenario where the first statement is in a function of a computer program and yields falsehood. The statement itself would be true, but could easily yield falsehood for some other purpose. However, if you look at the ambiguity of the first part of the statement, it is not specifically referring to anything. This means you can either change it to what you want it to mean (e.g. the name of a function), or it has no meaning. 5. All-powerful beings by definition can do anything, including defying logic and doing things we can't comprehend, but the easiest way to refute this would be to say the all-powerful being makes themselves powerless. Any way to do it while retaining the powers? They make themselves powerless for a certain duration. While retaining powers the entire time? Creates a copy of themselves and does both simultaneously. Hopefully the get the picture. An all-powerful being would be able to do anything you could ask of it, contradictory or not to logic, as logic could be changed. 6. Multiverse. 7. I don't know enough about physics for this, but I'm sure there must be an answer.
"This would mean that the grandfather could never give birth to the father that would give birth to the time traveller" Is the time traveller a seahorse, or did your school's biology classes omit certain details?
I've always had a problem with the paradox of omnipotence as it seems simple to me that an omnipotent being could remove there omnipotence so it's not that if they created something so heavy they can't lift they're not omnipotent it's that at that point they're no longer omnipotent. Am I missing something or is this a good answer?
About #3: I don't think that what follows is a paradox per say, but I remember finding it very counterintuitive when I first realized it was true. Let N = {1, 2, 3, ....} be the set of natural numbers (aka positive integers). Let P = { p1, p2, p3, ....} be the set of all prime numbers. For example, p1 is the first prime number (that is, p1 = 2), and p2 is the second prime number (that is, p2 = 3), and so on. For each natural number k, let Pk be the set of all powers of the kth prime number. For example, P1 contains 2 (this is p1 raised to the first power) , and P1 contains 4 (this is p1 raised to the second power), and so on. P2 contains 3 (p2 raised to the first power), and P2 contains 9 (p2 raised to the second power), and so on. Observe that each set Pk contains infinitely many natural numbers. (To make sure this is clear, P2 is the set {3, 9, 27, 81, ...} containing all positive integer powers of 3. Of course there are infinitely many such powers of three.) In fact, observe that each set Pk contains exactly as many numbers as N! Now, we can show that the sets P1, P2, P3, etc., are all disjoint. That is, if m and n are two different natural numbers, then Pm and Pn have no numbers in common. So, we have infinitely many distinct sets Pk---a different set for each positive integer k. And each of these sets is drawn from N. Last step: Recall that each set Pk contains as many numbers as N, and there are infinitely many such sets Pk. Now, take the set N, and remove from N all the numbers in P1. Then remove all the numbers in P2. Then remove all the numbers from P3. Keep going, until you've removed from from N all the numbers in Pk for each k. Call the set that is left N*. You got N* by starting with N, then removing infinitely many sets, each having as many elements as N. Is anything left in the set N*? Yes! In fact, there are are many numbers left in N* as there were originally were in N! (For example, N* contains all numbers of the form 2x, where x is a positive integer greater than 2.) (If you accept that the countable union of countable sets is countable, then there is nothing puzzling here. But like I said up top, the first time I realized that infinite sets can behave this way, it struck me as very strange!)
The omnipotence paradox has a simple resolution: if omnipotence is the ability to do anything, then an omnipotent being must be able to do what is logically impossible as well. So, an omnipotent being would be able to create a stone that it cannot move, and then move it, even though it would be logically impossible.
Exactly. People are jerking themselves off of superficial paradoxes. An omnipotent being is not a physical being. Infinity comes in sets, and is endless. Infinity has no end, the being`s powers` has no end. The Universe is a perfect example of that, it is all scaling. A grain of sand is the Earth to the galaxy as the galaxy is to the Universe as the Universe is to the Multiverse as the Multiverse is to... and so on, because how long has time been flowing? The creator could make such an infinite weight stone. If we compare that stone to a grain of sand, then the Creator can create a stone that is like the Universe compared to a single grain of sand, which was the previous infinite weight stone. Lol. Because scaling is sort of an illusion, and a being that is non-physical, outside MATTER (SIZE OF THINGS AND WEIGHT LMFAO), can literally endlessly blow our minds. Knowledge is infinite.
#6 - The Grandfather Paradox makes the supposition that Free Will exists but that aspect is not demonstrable unless a person is able to rewind their own life and literally re-take any decision they've ever made but choose an alternative which, as far as I am aware, is not within anybody's power so it is not possible to verify that we were ever capable of having made any other choice.
For the third "paradox", you can have bigger and smaller infinities in math. As a simple example, if take the limit of 2x/x as x approaches infinity you have infinity/infinity. But the top infinity is twice as big so the answer is 2. So the set of all whole numbers is obviously a a bigger infinite set than the smaller infinite set of all even numbers.
Following the prisoner's logic, they would realize that the only possible time to not be surprised is that exact instant, so the prisoner would know with 100% certainty they would be executed then. But because they claimed the would surprise the prisoner, they can't execute him at this moment, the next moment comes, and the prisoner realized they were wrong, but this time they are right, this next moment will be their last, but it won't be. And this would continue until the time is up, and the court would have to just execute him without surprising him. But if for a single instant the prisoner does not believe that is the instant they will be executed, they can be surprised in that instant. There is a clear outcome for the prisoner, dependent entirely on his thoughts.
Speaking about time travel I remember being told that we can't see the present because it takes 50 milliseconds for our brain to receive information from our eyes. So everything we see is in the past. You can say the same for smell, touch, taste, etc. So there really isn't a present, just a future and past.
The third one is not a paradox, it’s a simple consequence of the mathematical definition of equipotency between sets. We say that two sets are equipotent if we can find a bijection between them. Since it’s quite easy to find a bijection between the set of positive integers and the set of even numbers, we conclude that those two sets are equipotent. Two sets that are equipotent have the same cardinality (“number of elements”). Your reasoning is based on an incorrect implication that if two sets are infinite, we can find a bijection between them. Both the set of whole numbers and the set of real numbers are infinite, but they do not have the same cardinality (the cardinality of the set of whole numbers is aleph zero, while the cardinality of the set of real numbers is continuum (2 to the power of aleph zero, which is a cardinal number greater than aleph zero).
There's a 2nd part to the prisoner paradox (the first one). "After deducing that he could not be executed, he was executed on Wednesday and was surprised.".
1:28 Just because there are an infinite amount of both doesn't mean they have the same amount. And its not really a paradox There is the same number because you can make a 1 to 1 mapping of one set to the other. Like this isn't true for the reals. There are more real numbers than odd, even, or whole despite there being an infinite amount of each. Again, the reason there are more reals is because you can't map one to one between them. So the infinite set of the reals is larger than the infinite set of the odds. Likewise, the set of non algebraic numbers is infinitely larger than even the reals.
It kinda does. Infinite=infinite. One infinite cannot be larger than the other, by definition, infinity never ends. It's a hard idea to wrap your head around, but because the numbers never end, both are equal.
@@akoskormendi9711 Cantor proved, within the respect of set theory, that there exist larger and smaller infinities, by proving the fact that there exists no surjection from some set A to a set of all A's subsets, meaning the latter has bigger cardinality than the former, which applies to infinite cardinalities. Your statement is really an oversimplification of infinity.
john atlas actually the last sentence is incorrect. There are indeed more Non-algebraic (or transcendental) than algebraic ones, however not more than the reals. Idk if you define the two in respect with complex or real numbers, but either way, all the complex numbers consist of all the algebraic and transcendental numbers, but since there exists a bijection between R and C (I even proved this myself), then there can't be more transcendental numbers than the real numbers. But there is an equal amount.
Many of this "logical paradoxes" are rooted in the human mind or language, not in the physical world. You could say, it's only paradox cause we can't catch it or the premise doesn't make sense in the first place. They are just funny little games with nonsense.
Monte Hall and cardinality of Naturals vs the even Naturals are straight up math results that are just unintuituve If you want a math result slightle more deserving of the name paradox, Banach-Tarski os where it's at
TheLuckySpades The Monte Hall thing to me was just so stupid. Like how much debate it caused amongst really smart people. Now I don’t find it ridiculous because of the logic, but the fact that anyone could set up an easy at home experiment and do like 200 rounds or so and then there’s no denying who’s correct.
@@natalieelskamp03 that or excel simulations Or just drawing the decision trees for each option, seriously it ain't hard However it is very unintuitive if you aren't used to it, similar to the birthday problem, or any of a large variety of probability problems, they can get very confusing at times
TheLuckySpades yeah those would work too. However, even a four-year-old could test it despite not knowing how to illustrate it in those other ways, which was my point.
I've studied paradoxes quite a bit, so this should be interesting. 1. Prisoner ~ Not a paradox, this has a solution 2. Theseus ~ Not a paradox, this has a solution 3. Numbers ~ Not a paradox, this has a solution 4. Quotation ~ Not a paradox, this has a solution 5. Omnipotence ~ Not a paradox, this has a solution 6. Grandfather ~ Not a paradox, this has a solution 7. Twins ~ Not a paradox, this has a solution
No.2 The ship is not the same ship as soon as you replace a plank. It's the 'improved' ship.(presumably you replaced the plank with a better, newer plank) When you get to the last original plank it's the vastly improved ship and of course it's not the same ship as the original ship at all since, if you had kept all the planks you might reassemble them into the original ship!
Ian Taylor your molocules of ur body change everyday and u r completely new than u were an year ago so u mean to say u r not the same person u were an year ago?
On the omnipotence paradox, i think an omnipotent being making a rock that they can't lift is equivalent to the omnipotent being removing their own omnipotence, which they obviously can do. There's no reason omnipotence has to be indestructible. If there were a being with indestructible omnipotence though- then the paradox would certainly apply
If you rephrase the question to say, "If an omnipotent being wasn't necessarily trying to create a rock they could not lift but instead making heavier and heavier rocks. Would the being ever create a rock they could not lift?" If not then there is a physical limit to how heavy they can make the rocks with respect to their strength. If they do eventually create a rock they cannot lift then they are not omnipotent.
@@slowsatsuma3214 OP is correct. If you've already defined an omnipotent being as one that can lift every possible rock, then the only way for the omnipotent being to not lift a rock, would be to reduce it's power. The question is basically a specific example of "can you do something that would cause you to not be able to do something". And the answer is yes, it can remove some/all its power/ability.
Tater N Well that’s with the assumption that the being WANTS to create something it cannot lift. If the being is simply just trying to create heavier and heavier rocks then that logic doesn’t work.
@@slowsatsuma3214 I'm not following. The question is basically "Can you do X, which would cause you do no longer do Y". It doesn't matter what X is, it would have to entail losing omnipotence somehow...because that's the meaning of omnipotence. Omnipotence isn't the problem, it's the question that's the problem. By definition, he can already lift any rock...so if you want him to "not be able to lift a rock (or not do anything)"...the necessary condition is that he lose "power". It doesn't matter if he's transferring his power into the rock while creating it or what...he has to lose the ability/power, in order to not have the ability/power.
Tater N Let me explain what I mean because I 100% agree with your logic but it comes with the assumption that the omnipotent being is TRYING to create a rock that it cannot lift. I proposed a subtly different question: By virtue of creating heavier and heavier rocks can an omnipotent being create a rock that it cannot lift. Now that being could create a pebble and then take away its omnipotence so that it could not lift it, sure, but the being’s inability to lift said pebble does not make the pebble any heavier which is the prime goal of this rock obsessed deity. So if the beings goal is to make the heaviest possible rock will it ever make one that it cannot lift? That is the paradoxical question. The being isn’t TRYING to create something it cannot lift . And historically that’s where the paradox stems from, “Could an almighty all powerful God create a rock so heavy that they could not lift it?” with connotations of the God NOT wanting to lose any omnipotence to create a rock that it cannot lift but also trying to create the heaviest rock possible. The solution given is perfectly fine for this question because it is an ambiguous retelling of the actual God paradox.
For the last one you have to be aware that light travels at a constant speed ( no mass) , but space and time are malleable by gravity. Speeding objects gain mass with velocity , and therefore distort time more and more.The first paradox is invalid, if the prisoner knows hes going to be executed then whatever day it happens its not going to be a surprise.
for the prisoner paradox, surely the prisoner can only deduce that its not on friday by the time its reached Thursday, he cant make that same claim on a Wednesday though no?
The "paradox" only works on created beings within a limited existence. When you operate outside of time and space the kinds of things that people ponder don't apply.
If I use the simple analogy of a videogame, physical people who create videogames operate under drastically different rules than the worlds they create.
I graduated In 2004, and I think at that time, you would have been smarter than me at around age 4? Lol, you're wise beyond your years Alex still, funny to see you so young here!
Surely the prisoner paradox is solved by the fact that the surprise that comes on a Thursday can take two forms ("you're to be executed today" or "you're not to be executed today" which obviously means it will happen on the Friday) versus the kind of surprise that can occur on a Monday through Wednesday ("you're not to be executed today" but there are are multiple days remaining). If you wind up getting excecuted on a Friday, it still came as a suprise... but on the previous day. The wording of the judge's statement doesn't specify when the surprise will occur in relation to the actually execution.
As far as I understand it, there are two things that affect how time passes for the one experiencing one or both of those two factors. One is the traveling speed and the second is gravity. The more heavier the planet, the slower time passes. Than you would have to add the mass of the star wich the planet is surrounding and also the speed of travel. So yeah, it would affect how time passes but only to someone who isn't on the planet and observes all this happening while standing still or at least moving slower than the planet. You wouldn't notice anything changing while being on the planet. Sorry for my poor english skills but I did my best, I hope u're still able to unterstand it.
A couple responses here: In the first one, however, it is a surprise on a day-to-day basis whether you're going to be executed or not. I love mathematical paradoxes like this one. My favorite is Hilbert's Hotel. For the omnipotence one, C.S. Lewis wrote that God can't do anything self-contradictory like the Omnipotence Paradox. He also said that saying this doesn't diminish God's omnipotence because if you say that God can't make round corners, you haven't actually succeeded in saying anything about God. Don't take my word for it; there's a chapter in Problem of Pain about this. The final paradox with relativity is a fun one for sure! One that I've thought about in the past is this: if you're traveling at 95% of the speed of light, when you factor in that time slows down, aren't you actually traveling faster than 95% of the speed of light? Because velocity is distance over time, so when you decrease the time over the same distance (like when time slows down), velocity increases. Or does the change in distance/displacement change accordingly so it's still the same velocity?
The ship of Theseus paradox reminds me of the "beaming" procedure on the "Enterprise" ("Beam me up, Scotty!"). If you destruct a being, transmit it's WHOLE information and reconstruct it there, it is not the original anymore. Even if you could copy each single chemical reaction so precisely that life/thoughts just go on on the other side. It would not be the same organism. So how much emphasis do we put on our original body in the 23rd century?
So with your "Even or whole numbers" paradox, TECHNICALLY, there are more even numbers, because things like 0.2, 0.4, and 0.8 are all even numbers. Since there is an infinite amount of decimal numbers in whole numbers, no matter how far you count, you'll have more even numbers, just not by conventional means of counting (1,2,3, etc.)
Concerning the prisoner's "paradox", you can absolutely be hanged on Friday because you can't figure out you weren't going to be hanged on Thursday until Thursday is over. Even if you make it to Friday, you still haven't learned anything since you have no idea what time it will happen, all you know is it won't be on Saturday, but you already knew that.
Also the ultimate paradox of the Prisoner’s Paradox is that since all days are bad choices, ALL days are good choices as the prisoner, if a perfectly rational agent, would conclude no Day is possible, hence expect none of the days.
to the question of omnipotence: Just think of life as an computergame and god the creator/admin of the game. The question "Can the admin create a rock that he can't lift" becomes inrelevant, because the admin can't even touch it. But he is still omnipotent.
Eitan Blumin i think a alot about questions like this. I also think we can't answer the question if god exist or not. We simply know way to less about the universe itself. Watch some videos of exurb1a. Then you'll know what i mean.
Yeah it solves the paradox, but there's one catch: It redefines and limits the definition of "omnipotence" in this context. i.e. God is no longer omnipotent in the literal sense. He does remain omnipotent in the sense of his control of the universe that he created. But he's NOT omnipotent within the confines of the universe that he himself exists in.
Eitan Blumin omnipotence is the quality of having unlimited power. But is gods onmipotence limited to this world? Does a world outside of this one exist? Was this world created? Or are we just living in a simulation?...All in all we have way too less answers for way too many questions. In my opinion god isn't a omnipotent being. I think he personifies the search of humanity for answers. Everything we can't explain happens through god until we are advanced enough to understand how it happened. I need to stop before i get offtopic any further.
Yes. And you kind of answered your own question. It's not a number. I THINK you can find a great video about the different types of infinities on ViHeart youtube channel, if not, well you'll find some cool video if this topic interests you.
NDT explained this: For example, the infinity of numbers with one decimal place is larger than the infinity of integers. As the OG comment said, it is unintuitive, but it checks out.
Infinity is a mind-fuck concept, because its where all paradoxes lie. It's counter-intuitive because it goes against everything we sense in our lives, since every different object or thing is limited by it's own dimensions, as well as all living things have a start date and an end. But it's also intuitive, because whatever number you think of, you can add another one, and whenever some timeframe ends, you can see as the start of another one; so every thing is limited because another thing starts, which makes infinity an intuitive concept because whenever you think of an end, you can think of something else existing afterwards, but at the same time counter-intuitive because "all things come to an end". That's why paradoxes are circular logic, because any time you get to the end of a circle you're actually at the start (spatially speaking). So, spatially, the end of a loop in a circle is also the start, what makes the start and end being the same, making it a paradox. Infinity will always be undefined because once you define it it is not infinite anymore, so infinity is itself a paradox, home to all other paradoxes, where two parallel lines meet, fall in love, get married, and have a large offspring of other baby infinities.
about the twin paradox, i have one theory: those who sit all day and doesn't move at all will get older faster, and one who always travels on a plane will age slower, since they are closer to speed of light than those who doesn't move at all. So when we retire, make sure we at least drive or run everyday because that will slow down the time around us.
The grandfather giving birth to the father giving birth to the time traveller seems unlikely anyway. Usually it would be the time traveller's female ancestors who would give birth.
1. The prisoner's fault was that he was looking at things backwards. He could only know that it couldn't be Friday because he was out of days, but any days Monday-Thursday would work. The paradox ends with "He was surprised to be executed on Wednesday." He didn't see it coming because he assumed he couldn't be executed by surprise. 5. An omnipotent power could create a stone he couldn't lift but then the omnipotent power could alter itself to be able to lift it.
The Grandfather paradox is not a paradox, you can't simply change the history and all the action you take there ends up as it is now, so you may ask your grandmother "Who was my real grandfather" and "Who did your lover died", or you just fail in every attempt even you sometime think you did killed your grandfather. The better paradox/riddle is; a old man manage after a long time to invent a time machine, this has made him a poor and broken man just for all saw him as crazy, he then use this machine to travel back 30 years to give himself the blueprint for the time machine and to tell himself everything he did wrong and what to do to get a better life; so why was he poor and broken when manage to build the time machine and why took it 30 years for him to build it?
Rex Kenny did you miss the entire point of the grandfather paradox? ofc if you kill your grandfather it will change the future, that's the whole point. if you kill your grandfather then you wouldn't exist and wouldn't be able to go back in time to kill him, so he wouldn't die. so you would still exist and you'd kill him.
Let me first say that this is a silly debate for we debating something that can never happen, even as mental thought is it stupid for we can never say who is right, when you go back in time he is not your grandfather and you are not born, and if you travel back to the future you will pass the time when you are born and at that point there is two of you. You can twist fantasies in what way you want, but I just took the examples of this paradox that may not be a paradox, a bit to point out that it is a fantasy. Even the god paradox can be broken down with a bit of down to earth arguments: - If god exist and he creates a rocket that... - God does not exist. - But if god exist. - Okay? - can he then create a rock that is... - The christian God? - Yes. - But, he created earth and all rocks on the third day. - Yes, but this is an Example. - It is a silly example, can you not take another example. - Okay, do you know about the grandfather paradox? P.S Do not take this to serious, paradoxes are more for fun, and it more creative to find a story that take you around them.
I think I understand that a bit better than you, a paradox is a self contradictory statement, and I just pointed out that the Grandfather paradox can have solutions that give you an answer that is not self contradictory to the statement and therefore is not a paradox. Btw, to say that a paradox is not a paradox, is that not a paradoxical statement too?
For the twin paradox the reference point isn't the boy who traveled at nearly light speed or the girl who stayed put, but the teller and listener of the paradox. In space where there only reference point is each other its almost impossible to tell which one started moving (I guess this is a universe where stars don't exist) but we are the constant. We know the boy moved because we are the third perspective needed to tell wtf is going on. So the boy is younger
In regards to the omnipotence paradox, theists believe that God is infinite and absolute in his essence, and therefore he can never be less than infinite, or else it contradicts his very essence and invalidates him from being God Almighty; this is why he never eats, sleeps, dies, ceases to exist, etc. Therefore God cannot limit his power in any way, since it is part of his essential attributes as God. It is not about ability, but essence. Thus this question itself is inherently contradictory and meaningless.
Wendi Ipad Theoretically, I could build a crane that can lift a rock that I cannot lift on my own. Conclusion: I am God. This is the second video today where I've used creationist claims to prove that I am God.
The paradox is created in the very proposition, because if God is omnipotent that already implies he can do whatever he wants, therefore presenting any concept where he CAN'T do anything, is a contradiction to the very definition of God (as the omnipotent). You can create paradoxes about anything by simply stating the opposite of what you just presented as the premise, only using synonyms or word play to pretend you're saying something different.
I don't get the numbers paradox. Even accounting for infinite numbers, there should be more whole numbers than even numbers. If you stop at 10, there's 5 even and 10 whole. If you stop at 100, there are 50 even and 100 whole. And so on...
_"And so on..."_ That's true, but is not an argument for infinity. As another example consider decimal numbers x=0.333...3 with finitely many digits, all 3s. If you stop after 10 digits, then x
smokert5555 The point is that something doesn't need to be true for infinite many if it is true for all finitely many (as opposed to what your "and so on" seems to say). Example: 0.33... is smaller than 1/3 for finitely many 3s (digits after the period), but 0.33... with infinitely many 3s is not smaller than 1/3. In the paradox comparing whole numbers to even numbers, you need a precise definition of "more" to understand the paradox. In a nutshell, "contains as a smaller subset" and "has more elements" are the same for finite sets, but are different for infinite sets. Indeed, the whole numbers contain the even numbers as a smaller subset, but do not have "more" elements. In order to have more whole numbers than even numbers, the precise definition of "more" would require that you cannot identify the whole numbers with a subset of the even numbers. This is possible, though: identify 1 with 2, 2 with 4, 3 with 6, and so on, see 1:48 in the video. This identifies the whole numbers with the even number itself (and the even number are a subset of the even numbers), so you can identify the whole numbers with a subset of the even numbers, therefore, according to the definition given above, there are not more whole numbers than even numbers.
Theo0x89 That's what's bugging me about your example. If .33 is smaller than 3, then .3333333... is still smaller than 3. I don't see how it can be larger. I also don't understand the example given in the video. If you start with a set of whole numbers, in sequence, wouldn't you always have more whole than even? The only way i see around it is if the set you started with were not sequential. Infinite numbers wouldn't seem to be a factor. I'm sure i'm just not getting it, but the association in the video and reiterated by you (1 with 2, 2 with 4,...) i just don't get. It appears to be ignoring all the uneven numbers you would count as whole. Thanks for your continued patience in helping me understand this.
smokert5555 _"If .33 is smaller than 3, then .3333333... is still smaller than 3."_ Yeah, I'm sorry for that. I kept writing 3 instead of 1/3 throughout my replies (some sort of mental copy and paste error). I made edits to correct that. Since 0.33...=1/3 (for infinite many digits), 0.33... is not smaller than 1/3. _"The only way i see around it is if the set you started with were not sequential."_ Indeed, when you compare the "number of elements" of infinite sets (called "cardinality" in mathematics), the order of the elements is irrelevant. So the symbols "1", "2", "3", ... are nothing but labels. When you relabel "1" to "2", "2" to "4", "3" to "6", ... you see that the whole numbers and the even numbers can be identified with each other as sets, and therefore have the same "number of elements", i.e. the same cardinality.
My favorite is certainty, I've had people say to me that we can not be certain of anything, but yet they are certain that there is no certainty. To say that we cannot be certain of anything is a statement of certainty.
DrGerbils I'm not re-watching it. But if memory serves it's worse than that. Remember that semantics are not a paradox. If I recall, one of them was the childish ""can god make a rock so big that god cannot lift it?"" This simply shows that the definition of ""omnipotent"" is flawed, it does not demonstrate a paradox. p.s. just in case....if you intend on challenging that example. I was informing, not engaging. There is no debate. There is only an understanding of linguistics, and ignorance of linguistics. And now that I'm thinking about it, time travel may have been in there as well. Time travel does not exist. Therefore there are no paradoxes associated with it.
Frank Sanders As I noted, albeit by number only, the omnipotence and time travel examples are paradoxes only if you allow his premises. With those gone, you are correct. He could have gone with any two of Xeno's paradoxes. They're resolvable, but at least facially paradoxical.
The dilemma posed by the last paradox can be explained by the fact that the traveling sibling must markedly accelerate relative to the other sibling. During this acceleration phase, the time dilation is not symmetric.
For the Grandfather Paradox, I always thought about the idea that whenever you go back in time you create a new timeline. Let's say you were to go back and kill your grandfather. That timeline is separate from yours. So in that timeline, your gramdfather is dead and you were never born, but you present timeling doesn't change. If any of you have watched dragon ball z this sort of thing happens
I have a masters in Physics, and I specifically studied relativity (marvellous by the way, would recommend), and the short answer to the twins paradox is that it demonstrates why special relativity is not enough, and we must invent general relativity to account for it.
If you ask Rick Astley for a copy of the movie Up, then by giving it to you he would be giving you up, but by not giving it to you he would be letting you down. This conundrum is known as the Astley paradox.
Who are you so wise in the ways of science.🙌🙌🍺
Only if there was a movie called DOWN.
I actually came up with a quite elegant solution for this a while back.
Rick would tell you exactly where to find a copy of the film, thus not giving it to you whilst still not letting you down.
He would drive you there and stay with you the whole time so as to not run around or desert you.
@@liamosborne6859 I think it's unreasonable to expect Rick Astley to give you a copy of Up especially as he has already stated that he's never gonna do it and therefore any sense of being let down by him is unjustified. He probably would have to drive you and stay the whole time though.
And then if you asked him to run laps of a circular running course and high-five you so hard at the end that it hurt but he refused to do this then he'd be doing exactly what he said he'd never do, which would be a good thing... I guess... but then he'd be disobeying and letting you down, which is kinda not a good thing... I guess...
"can god microwave a burrito so hot even he cannot eat it?"
LoL. You're using quotes, so who are you quoting?
It's a quote by Homer Simpson
But that isn't the meaning :/
can god make a particle so small that he cannot see it himself
No.
Thats called intelligent design.
My favorite paradox: You are unique, like everybody else.
It's not really a paradox but it is a nice saying about humility I guess.
Me AndMeToo how is it not a paradox? The two statements absolutely contradict each other
@@lukesoares7117 Two persons having a similar characteristic does not prevent them from being unique.
Unique is "a different set of characteristics" not "completely different."
@@lukesoares7117 They do not contradict each other. It is possible for everyone to be unique in a different way to everyone else. Therefore meaning you would be unique _"like everyone else"_ with everyone else being unique.
If I had 5 stones, all having a different colour, one would be unique, just like the other 4, wouldn't it? The "(...) like everybody else" doesn't mean that you are unique in the same attributes as everybody else
Regarding #3: Some infinities are larger than others. My younger brother, who is a mathematician, explained to me once how we work with this concept all the time.
Yes but in the case of that paradox, they are the same level of infinity, the countable infinity.
The whole number are more because if we say the infinity of whole numbers is x then the infinity of even number is x-n(n being odd numbers) . X-n is less than x
@@tusharyadav4982 If x = ∞ then arithmetic with x does not make much sense without mathematical extensions. If you want to reason about sizes of sets then you would use the notion of cardinality. The cardinality of a set is the concept of the size of a set extended to infinite sets. The set of natural numbers (some say whole numbers) is countably infinite and any set with the same cardinality is countably infinite as well. Two sets have the same cardinality if there is a bijection between the elements of one set to elements of the other. And there is a bijection from the set of natural numbers to the set of even numbers, namely x→2*x. That is, there is a unique natural number for every even number and vice versa. Therefore, the set of natural numbers has the same cardinality as the set of even numbers.
This one honestly took me a long time, but the easiest way to think about it for me was alluded to in the video. We know that the set of whole numbers are infinite and we know that when counting from 1 to 100 there are half as many even numbers as there are whole numbers. But we can count from 1 to 100 by doubling each number as well, effectively making them all even, and since there is a double to every number that is countable that means there are as many doubled numbers as there are whole numbers making the infinities of whole numbers and the infinities of doubled numbers(or even numbers) the same size. Hope that helps.
@@tusharyadav4982 No. If you reduce any number from infinity, the result is still infinity.
If the prisoner really thought this much about it, the real surprise would be if the execution did happen on Friday.
The answer is the judge immediately jumps towards the prisoner after the sentencing and stabs him to death. Surprise!
It wouldn't be a surprise, because if all the days passed Monday through Thursday and he still wasn't killed, then he would know it's on Friday. So no surprise
The surprise would be that there was no surprise.
+Johnathon Shakovitz he dies on Saturday. Surprize!
Or he would realize it would be a Friday going back on the paradox and seeing that it truly would never be a surprise and he doesn't get hung ever
Great Alex, you know this one: What will happen if Pinocchio says "My nose will now grow!"
It won't gr-- It will cuz--...................... **head explodes**
aqouby Could be...
I have the answers for all the paradoxes, wanna hear them?
1. The judge, immediately after sentencing the prisoner, jumps at the prisoner and stabs him to death. Surprise!
2. There's no rule that there can't be 2 of the same ship. Ship and Ship prime.
3. Same amount because you can always go n+1.
4. Oh fuck, it's just the Pinocchio paradox again! FUCK
5. Can God microwave a burrito so hot even he can't eat it. Yes because to create something that God can't do is still his will and his will be done!
6. Time machines don't exist. I know that's a cop out but I've studied this stuff enough to know it doesn't exist -- and I need to also state that he didn't describe Multiverse theory, he described the "many worlds interpretation."
7. The twin traveling near the speed of light is less old than the others because he had to change his rate of acceleration.
Ta da?
1. But not a suprise in week 2 as promised -> judge is a liar.
2. C++-Template of a ship?
3. What about signed integers, will it double infinity?
4. Unbeatabe
5. But we are his counterpart, also too hot for us?
6. Time machines existed 300 years ago, but only if I will use one in 300 years when they will exist to create them then.
7. I am too stupid and lazy to follow this one.
You're giving me a migraine. :D Happy New Year!!!
How about saying it's Opposite Day on opposite day
If you said that, you don't understand the game. Simple.
@@TheDeterminer if it were opposite day the person asking the question has to know that the person responding would answer the question "is it not opposite day" because of that, you can respond normally without any paradoxes
@@noahduller6646 "is it not opposite day" isn't the opposite of "is it opposite day", it doesn't work in questions.
They cancel themselves out!
While I don't believe on opposite day its opposite day would be the opposite of its not opposite day, but even so if it's not a paradox because it would just be lying
Alex: *Calls an omnipotent being a "she"*
Christians: *Surprised Pikachu face*
He should have used it as he reffered to an omnipotent power not being.
@biggs949597 s I'm pretty sure that was satirical, and that's only because I know a decent bit about European history and what you were saying was obviously joking, but it came off as really sincere, I just wanted to tell you that so you know structure of your jokes differently in the future.
@biggs949597 s also there are plenty of religions wear an omnipotent being is a "she"
@biggs949597 s well his reasoning is to be fair, just because a lot of Christians believe God should be called a man that doesn't mean all of them do, I meanshe never specifically talked about a Christian God, he was just talking about an omnipotent being, he wasn't trying to bring religion into, at least at that point.
Also the fact that it really doesn't make sense for God to have a gender, so he brought up the idea of a she to get us thinking, he doesn't believe that God is a he or a she because he doesn't believe there's a God, he's just trying to give us a logical paradox.
Also I do want to say I wasn't trying to spark a debate I was just trying to tell a joke... But I'm glad it created a productive conversation
@biggs949597 s Have you seen the episode of Family Guy where they did time travel to an alternative universe where everyone had stopped being christians/religious? (For 200 years I think, don't remember exactly) They were SO FAR ahead of us. Sure, Family Guy is just a silly show but it doesn't sound weird at all to me if what they showed could be reality if we did really stop being religious. Religion have given us a lot of history, etc. but science is what gives us facts.
I asked a Christian friend the omnipotent power paradox, in regards to God.
He said that if God created something that he himself cannot lift then he could create something to lift it for him.
I then said that we do that all the time, for example cranes.
He got angry and accused me of saying that I am as powerful as God.
That is stupidity in itself, right?
At first, I didn't understand why he get mad at you and I even thought his answer was creatively good. The problem is that his creative answer suggest that God is not omnipotent: if he was, he shouldn't have to create something to lift it for him because he could do it himself. So maybe he was mad at you because he was mad at himself for giving you the opportunity to say that he himself acknowledge that god was not omnipotent and thus, not a god at all.
I say that because his attack doesn't make sense. You didn't imply that you were as powerful as god. I'm probably wrong
PS: I hope you answered by "God created us in his image, didn't he?"
Fali Akuna I did not, we decided to not argue over it.
Most apologists have explained gods omnipotence as the ability to do things that are logically possible. It creates a loophole around the omnipotence paradox.
My answer to the omnipotent power paradox is this: when God creates something that he himself cannot lift, he gives up his omnipotence. He will no longer be omnipotent after that creation.
TaiFerret - that's a meaningless answer. You can't come to that conclusion through logic, even if it makes some kind of sense to you. Sure, it's a possibility, in that anything is a possibility, but there's no reason to believe that is what would happen.
To answer your last paradox about the twins moving at the speed of light, the answer falls within that although movement is relative, acceleration is NOT relative. The twin who accelerated away from the other twin would be the younger one, because both twins are going relatively the same speed to one another, but only one is accelerating and decelerating. Yeah, I know, physics are weird XD
^^yes
Carroll Addington: Bingo. You stole my thunder. LOL
How do u know who is accelerating? acceleration is the amount of distance/time from one point to another. But here there are only 2 points like he stated in the vastness of a univers ;)
+Gent Boy
What was missed in the equation here is that both twins are at rest or otherwise constant velocity of zero miles per hour. Side note - we are never at mass rest. Continuing - Special relativity only works in these matters.
However one twin is accelerating because there is an actual force acting on the twin and there goes special relativity down the drain. This is simply physics. Both twin cannot be accelerating. So the twin that is accelerating will be the younger one because only that twin experiences the time dilation while the other one does not. Not sure why this is a Paradox but okay I will bite. I still hate physics even at this old age :-(
+gent boy
Eh, no. Acceleration is the magnitude of change in velocity.
"...The grandfather could never have given birth to the father..."
Logic, by Alex.
Five years on from this comment, it’s 2023, and men can now give birth. Look how far we’ve come!
Love this channel. But bro SLOW DOWN, LET OUR MIND BREATHE.
What does that even mean!?
@@jaymeanderson5121 He is talking crazy fast here.
Pause the vid :P
Actually, relativity does affect my everyday life. I work with GPS based survey equipment. Because of special relativity, the orbital speed of GPS satellites is sufficient to create a time dilation effect that causes the satellites to lose about 7 microseconds per day. However, because of general relativity and the fact that the satellites are further from the Earth's mass, they gain about 45 microseconds per day. If GPS software did not adjust for these effects, it would be worthless for surveying in a matter of minutes, and within a day even simple navigation systems would be off by kilometers.
that is fascinating! :D
So the gps software does it, I get what ur saying though. By your standards my cable guy also deals with this, though I doubt he knows it. I was a 25s in the army, what company do you work for? Anything based in Georgia? Legitimately curious
There's always inertial navigation. That's precise enough for most uses.
This is a 30-minute video condensed down to less than 7 minutes by the speed CosmicSkeptic is speaking, which gives us extra time to read Al-Khalili's book on paradoxes. Cheers, Alex :)
This video is such a special one. It shows us younger Alex in his formative year as a content creator. His presentation is rushed, the choice of background music is a little distracting, and the departure from the subject matter for which he is usually well known gives an appearance that he is yet to settle concretely on what to talk about in his channel. Seeing him now and coming back to this video makes apparent just how far this bright lad has come. I cannot overstate the joy of sharing the contemporary generation with Alex in the large course of cosmic events. Keep on keeping on, friend.
Here’s one for you: “All categorical statements are flawed.”
The statement is a categorical statement, so therefore, it is inherently flawed.
this is basically "this sentence is false" with extra steps
@@george64826 That's a good observation.
I think that as you wrote it it isn't a paradox. It's just false
I've always felt that statements like these can be the only "true" existence jn a domain. So there could be a universe in which all categorical statements are flawed as a aspect of existence in that universe. From a metaphysical viewpoint we would have a universe with the only true categorical statement being "categorical statements are inherently flawed"
@@cadenphilley9728 all categorical statements arent flawed though. all water is H2O, for example.
Can't believe no one has addressed this yet, the solution to the twins paradox is that relativity states that the only "real" and not-relativistic "force" is indeed acceleration (which is indistinguishable from gravity), therefore, if only one of the twins experiences it, that's the twin that time slows down for.
How so? Wouldn’t each twin accelerate relative to the other?
@@natalieelskamp03 but only one twin would "feel" the acceleration (from the rocket or whatnot). Only that twin would be experiencing the true movement and hence the time dilation.
dotdotdotdesign oh yeah. Fair point.
So, two dudes are on a rock travelling near the speed of light, but no acceleration, so no worries. One dude steps off (into a v large atmosphere) he decelerates significantly cos of the air friction. And he is the one who doesn’t age right? Deceleration being acceleration backwards? But he is not actually accelerating, he is slowing down - coming closer to no speed at all. But then it’s relative yeah? So you can remain young also by slowing down from the speed of light. ??
So two guys are past by a girl on a rock travelling the speed of light. But nobody is accelerating, so no ageing. One guy accelerates toward the rock. when he arrives he is now younger than everybody else cos acceleration. The he gets off and slows down back to his friend. Now relative to the girl he is twice as young, but what is he relative to his friend - he accelerated, then slowed back down. His mate is same age as the girl. Does slowing down also keep u young????
Did you have somewhere to go after this video? Seemed a tad rushed.
@Adam Romanov my nigga, u are going straight into my cringe compilation. You would think a student from Stanford would be civil.... Oh well, every rule has it's exceptions
@Adam Romanov Someone thats actually smart doesnt equate their academic achievements with how intelligent they are. So even if you did go to Stanford, all youre intelligent at is memorization.
@Adam Romanov No, you being triggered and listing off academic achievements is you trying to prove that youre smart. Dont just assume someone is trying to sound smart just because they talk fast, he mightve been in a hurry or something.
@Adam Romanov What exactly makes him being in a hurry impossible? Im not saying he is, im just saying there are several reasons why he would talk fast.
@Adam Romanov dude you just straight assumed that he was trying to show off how smart he is just from the talking speed
When I was a kid I discovered the paradox of saying "It's opposite day today"
It’s not a paradox it’s just incorrect, in every case you should say, “It’s not Opposite Day.” On Opposite Day you say, it’s not Opposite Day and when it’s not Opposite Day you say the truth which is, “Its not Opposite Day.”
It's always false
One of my favorites is the Bootstrap Paradox, where an object continually travels through a loop in time, with no origin point. One of the most well-known examples (though the paradox itself might not be) is probably the Song of Storms in LoZ: Ocarina of time. In that game, you learn the song as adult Link from a man who reveals that he learned the song from a kid in green seven years prior. Of course, he is referring to child Link, so that's your cue to travel back seven years into the past and play the song for him in the past. So...he learned it from child Link, and taught it to adult Link, who traveled back in time to play it as child Link so that the guy can learn the song so he can teach it to adult Link so that adult Link can travel back in time to play it as a child so that and so on and so forth. At no point is the song originally written/discovered, it's just kinda stuck in this little infinite loop.
5 year old comment I know, but this paradox gets especially strange when a physical object is passed through one of these loops. The object must necessarily degrade over time, but this would lead to the object eventually decaying to nothing.
The way i percieve Theseus's boat is that the original planks that make up the boat and the planks that have replaced the boat are simply moments in time. Living people are essentially living examples of Theseus's boat. Asking which boat is the original is like asking which YOU is real? 5 year-old you, or 23 year-old you? Our entire build of atoms which makes up our body and brain are 100% replaced by new atoms every 5 years. If Theseus's boat is a paradox, that means that life is a paradox too. The only thing that isn't a paradox is our consciousness because that is made up of our collective past and present.
Well done!... Except... how does one know one's consciousness of the past is reliable?
ThePeaceableKingdom What do you mean?
"What do you mean?"
In pre-scientific days one could say that there was a durable soul that remained the same even if the parts of the body changed, like if "the atoms which makes up our body and brain are 100% replaced by new atoms every 5 years." But if we regard the mind as having no metaphysical components as most do today, and consciousness is just the result of the arrangement and states of those atoms, how do we know our memories and recollections are durable and consistent? Rearrange them and we remember something else, something counter-factual.
But I like very much your question, "which YOU is real? 5 year-old you, or 23 year-old you?" because in many ways we believe we're the same person at 23 that we were at 5, but in other ways we believe we're very different people after the passage of years. It's a good philosophical question.
Actually some human cells do not replace in our lifetime, such as the central nervous system or some of our heart cells
The atomic energy that makes up those cells are replaced.
Hey Alex, I really like the content of your videos, but your speed of talking in this one is quite annoying for non-native speakers. Please reduce the pace a tad and expand your audience.
KlausM54 there’s a feature on TH-cam where you can slow down or speed up videos.
No he needs to talk closer to the speed of light so that time slows down and then you could understand him. :) LOL
I love paradoxes! Unfortunately, there's very few that actually pose a problem. I'll explain, because I like to do that.
1. This one is simple. No matter what day the prisoner is executed, it will be a surprise. Clearly, this is true simply by virtue of the prisoner ruling out every day. The prisoner establishing that he won't be executed because it wouldn't be a surprise is what makes it a surprise to him.
2. Ah, the ship of Theseus. This is one of my favorites. The ship of Theseus is one with all of the components replaced. The parts taken off of the ship are no longer part of the ship of Theseus. Each time a component is replaced with a new one, the ship new parts are incorporated into the ship. The new ship built with the old scrap parts is a replica of the ship of Theseus built from discarded scraps.
3. The set of all whole numbers is infinitely large. The set of all even numbers is also infinitely large. The set of all odd numbers is again, infinitely large. All infinitely large sets are not equal though. It is incorrect to say that the number of all whole numbers is infinity. Infinity isn't a number that can be compared to other numbers. It's a concept. For this reason, the question is flawed.
4. It's neither true or false. It's a contradiction.
5. Omnipotence is a poorly defined term. Its ambiguity is what leads to problems like this. If it simply means that she can do anything, then she can violate the logical absolutes meaning that she can both make the rock too big to lift and lift it. If omnipotence only establishes that she can do all that is logically possible, then you've already answered the question. The question is, at its core, simply about whether or not she can instantiate a logical contradiction. Since that is not logically possible, she can't do it but is still omnipotent.
6. Simple. There isn't multiple time lines. You were there and failed your attempt to kill your grandfather, which is why you were born in the first place. There is only a problem with this paradox if you establish that there are multiple attempts at a timeline.
7. Like you said, there are multiple ways to establish what happens.
Atheist In Louisiana, the quantity of natural numbers is not a natural number, but it is a transfinite number. Specifically, it is Aleph-null. So also is the number of even numbers.
en.wikipedia.org/wiki/Transfinite_number
Therefore it would be impossible to kill your grandfather?
@@yeast4529
Basically, at least before you were concieved it would be impossible
Atheist In Louisiana did you just assume god’s gender?!?
The "solution" to the "omnipotence paradox" is that there is no paradox. The answer to the question is just...yes, it can make a rock it can't lift and then it would no longer be omnipotent. People for some reason incorporate some sort of time component...like an omnipotent being MUST remain omnipotent....which is entirely antithetical to omnipotence.....An omnipotent being would be able to remove all or some of its power, or else, by definition it wouldn't be omnipotent.
I remember reading a study where a group of physicists and a pilot did an experiment. The physicist had two synchronized clocks on the ground, they gave the pilot one and he flew in a jet for an hour as high as he could go. When the pilot landed, the physicists' clock was ahead.
Not just synchronized clocks - atomic clocks.
2spooky4me _Not a paradox - science.
By how much? I’d like to know.
Time doesn't likes to fly :)
Relativity
You talked so fast, It's hard for us who's not native english speaker
Irun Mon slow down the video in the settings maybe that'll help :)
True story i did, but too slow :p
Irun Mon I thought the same !!
If you increase the speed to 1.5 for a while and then turn it to normal it feels really slow. haha
If you lower it down to 0.5 speed, you get how I talk on friday night, without 'making the sense' bit
Sorry I didn't bother scrolling through all the comments to see if anybody responded to the prisoner paradox.
That being said, there is a solution: The prisoner can actually be executed on any day but friday. And this is why:
If he doesn't think the logic through, it's trivial. He will be surprised on any day except friday.
If he, however, followed your reasoning, he'll come to the conclusion that he cannot be executed at all. And thus, when the executioner comes to get him on, say, wednesday, he'll be utterly surprised, totally meeting the requirements for the execution.
The Ship of Theseus is my absolute favourite paradox cause of the implications it has in biology
Flup
Augustus flup
@fynes leigh Why do you double space like this its really hard lol
@fynes leigh Couldn't you have simply said that your eyesight is getting bad?
@fynes leigh no you fuck off. Even tho you are an old man you act like a child.
@fynes leigh I'm just laughing at how some people like you act like children. The guy didn't even insulted you and you wrote a whole paragraph my dude. Like it would be ok if you made an actual point but after you said the reason why are you using double spaces you were just being toxic for no reason. Also, my dad had a stroke and barely survived and I take care of him every day so if anyone replays ti me why am I arguing with a person with stroke I can say that having had a stroke doesn't give you a permission to be toxic to anyone for no reason.
hanging out with this guy has to be so fun, imagine the amazing conversations you'd have
I actually made videos on 2 of the paradoxes you mention. The twin paradox is one of them. I explain how it works in special relativity, so leaving acceleration aside for now. Anyone who cares is very welcome to check it out! (I don’t have a huge number of videos so you should be able to find it!)
Slow down when speaking, it will give your points emphasis. I enjoy your content, just giving some helpful criticism:) let your points settle with your audience
I really shouldn’t be watching this at 3 am
I watched it at 2:51 am 😂
You mean I’m not the only one?
The problem with the twin paradox lies with our understanding of relativity. See, the paradox here arises from a flawed notion that both the twins experience equal but opposite situations. But relativity is based on the idea that physics must be the same in all inertial frames, and not all frames are inertial. In order for a frame to be inertial, it must maintain a constant velocity. This means no acceleration of any kind, be it a change in speed OR a change in direction. Looking at the problem now, it’s easy to see the situation is a bit more complex than we gave it credit for. While Alice, who doesn’t move, maintains her inertial frame, Bob, who must accelerate in order to change direction and head back to Alice, doesn’t. When we look at the situation from Bob’s point of few, we find that we can no longer just pretend he stayed still while Alice moved, because she didn’t experience any forces or accelerations. Bob is the one who activated his thrusters, and felt the force of being pushed into his chair, while alice did not. Now that we can prove their situations are completely different, we can say without a doubt that Bob with return the younger twin.
That's how I interpreted it. It's the difference in reality vs perception. In reality, only one party is moving. They may perceive movement, but that is because perception is based on visual cues. If I start scrolling through text at a rapid speed and then I stop, it still appears as though the text is moving, but this is only because my brain is interpreting the movement still.
I took a class on General Relativity a while back, and though I could do the math just fine, I can't say as I really understood the concepts. From what I did understand though, inertial frames of reference have to do with the fact that space is something. There is a such thing as velocity within it. Moreover, space and time are not separate. When you alter the movement through space you alter the movement through time. Gravity, too, alters time because it alters space. So, with regard to the twins, It's not the acceleration at all. If it were, all the time slowing would only happen during the accelerations, and once the one twin reached constant velocity on the trip he would resume aging at the same rate as the other twin. It would also mean that if the suit exerted a constant acceleration, the full change in time would would take place upon launch. Neither are true. The time differences become greater as the actual velocity becomes greater and stays even when the velocity is constant, i.e. zero acceleration. I guess it would also follow that if the twins were born on a spaceship which had accelerated through space generations before they were born, it could be true that if the one twin "accelerated" in a direction that actually slowed his velocity through space, he would actually speed up his aging relative to the other twin. Like I said, I don't really understand this stuff and it just doesn't seem right to me, though a accept that it is even if my little brain can't really comprehend it. I asked the professor, Leonard Susskind, if he could explain what was happening physically. He just smiled and said it's true because the math works. He said that's enough for him and all his colleagues.
but if both object were in a vacum, hhow could you know which is moving and which one is not?
***** You are fundamentally misunderstanding the concept of space. It is something. This is easily understood if you take those two same objects and spin one. Is the one object spinning or is the other object orbiting around the other really quickly. Or you don't even need two objects. Imagine you are in space all by your lonesome. If you put your arms by your side and relax, and they stay there, you are not spinning in relation to space. If they "fly" outward, you are generation centrifugal force, and are thus spinning, in relation to space. Just as there is rotational velocity in space, there is linear velocity. That velocity will alter the objects relation to time relative to other objects in space.
Well, at least that's how I understood it.
But yeah, you cant tell which one is spinning, if the theory of relativity is about observation, that is just not possible.
You might like a book called, "The Paradoxicon," that looks at a lot of paradoxes, quasi-paradoxes, etc. One of my favorites was about a Greek lawyer who trained someone in law. They agreed that the student would pay the teacher after the student won his first case. However, after his training was over, the student decided not to go into law. Wanting his payment, the teacher took his student to court. The teacher put forth this argument in court: If I win the case then the student must pay me the money, however if I lose, that will mean he has won his first case, which meets our original agreement, and he must pay me the money. However, the student reasoned: If I win the case, then I owe the teacher nothing, but if I lose, then I also owe him nothing because I will not have had my first winning case.
The first few are contextual paradoxes; once you include the context in which the statements are made, you solve the paradox. That’s the beauty of the English language, we’re so tactile with our dialect that we interpret language with plenty of nuanced inferences of context. Once we begin to take the sentences literally, the paradoxes disappear.
Marty_Ventura Well said! It’s not often you have someone solve anything Alex says!
The twin that traveled the speed of light was in an accelerated frame of reference, whereas the stationary twin was not. While all motion is relative' the experience of g-forces is the important point.
+CosmicSkeptic
Why is video so fucking fast?
I can barley understand what's being said.
The Wheat Is Growing Thin Me too, I could understand it perfectly:)
+The Wheat Is Growing Thin
Dammit. I'll delete my comment before I am further embarrassed by my age.
The Wheat Is Growing Thin Yeah you are right, actually it's quite encouraging:)
Then learn english
Isn't it ironic that the first comment says barley and the second comment is someone named wheat?...
I had to watch this at 0.75x speed to keep up
For the prisoner scenario, I’d say only Friday can be ruled out. Because only when you are living Thursday you know for sure it’s Friday. But when you are on Wednesday you initially on that spot won’t know if it’s Friday or Thursday despite your ability to rule out. Let’s imagine when the sentence is set, and the judge writes the day of the execution on a piece of paper (not Friday) the excecution will happen regardless and the prisoner would not be able to Guess if it was not Friday. Everyday would be the day the prisoner will “know” his last day was today until he wakes up to survive it. He was sentenced to death on Tuesday. It was what was written on the paper and the prisoner did not know what day he would die.
From taking a minute to think about it:
1. Two possibilities (at least). For the first, suppose it happens on Friday. Up until Friday, it WILL be unknown to the prisoner, thus a surprise. For those that say the paradox is supposed to say it won't be known by the prisoner until it happens (not just the day before, but continuously), it could take place in the prisoner's sleep.
The second possibility is because the prisoner thinks it can't happen on any day, the prisoner will either always be surprised no matter what, or that (execution during the week) implies (the judge lied). That, or it happens in the prisoner's sleep again. If you're not conscious, you can't expect anything.
2. Neither because the passage of time.
3. This is only a paradox because of definitions like (infinity) = (infinity) + (infinity) AND other definitions which are contradictory like (original something) + (something else) != (original something). The former is only used in mathematics because infinity is not treated the same as anything else.
4. Yields falsehood when preceded by its quotation yields falsehood when preceded by its quotation. This is an example of something that would require context to either be true or false. Imagine a scenario where the first statement is in a function of a computer program and yields falsehood. The statement itself would be true, but could easily yield falsehood for some other purpose.
However, if you look at the ambiguity of the first part of the statement, it is not specifically referring to anything. This means you can either change it to what you want it to mean (e.g. the name of a function), or it has no meaning.
5. All-powerful beings by definition can do anything, including defying logic and doing things we can't comprehend, but the easiest way to refute this would be to say the all-powerful being makes themselves powerless. Any way to do it while retaining the powers? They make themselves powerless for a certain duration. While retaining powers the entire time? Creates a copy of themselves and does both simultaneously. Hopefully the get the picture. An all-powerful being would be able to do anything you could ask of it, contradictory or not to logic, as logic could be changed.
6. Multiverse.
7. I don't know enough about physics for this, but I'm sure there must be an answer.
"This would mean that the grandfather could never give birth to the father that would give birth to the time traveller"
Is the time traveller a seahorse, or did your school's biology classes omit certain details?
I've always had a problem with the paradox of omnipotence as it seems simple to me that an omnipotent being could remove there omnipotence so it's not that if they created something so heavy they can't lift they're not omnipotent it's that at that point they're no longer omnipotent. Am I missing something or is this a good answer?
Good answer
About #3: I don't think that what follows is a paradox per say, but I remember finding it very counterintuitive when I first realized it was true.
Let N = {1, 2, 3, ....} be the set of natural numbers (aka positive integers).
Let P = { p1, p2, p3, ....} be the set of all prime numbers. For example, p1 is the first prime number (that is, p1 = 2), and p2 is the second prime number (that is, p2 = 3), and so on.
For each natural number k, let Pk be the set of all powers of the kth prime number. For example, P1 contains 2 (this is p1 raised to the first power) , and P1 contains 4 (this is p1 raised to the second power), and so on. P2 contains 3 (p2 raised to the first power), and P2 contains 9 (p2 raised to the second power), and so on. Observe that each set Pk contains infinitely many natural numbers. (To make sure this is clear, P2 is the set {3, 9, 27, 81, ...} containing all positive integer powers of 3. Of course there are infinitely many such powers of three.) In fact, observe that each set Pk contains exactly as many numbers as N!
Now, we can show that the sets P1, P2, P3, etc., are all disjoint. That is, if m and n are two different natural numbers, then Pm and Pn have no numbers in common. So, we have infinitely many distinct sets Pk---a different set for each positive integer k. And each of these sets is drawn from N.
Last step: Recall that each set Pk contains as many numbers as N, and there are infinitely many such sets Pk. Now, take the set N, and remove from N all the numbers in P1. Then remove all the numbers in P2. Then remove all the numbers from P3. Keep going, until you've removed from from N all the numbers in Pk for each k. Call the set that is left N*. You got N* by starting with N, then removing infinitely many sets, each having as many elements as N. Is anything left in the set N*? Yes! In fact, there are are many numbers left in N* as there were originally were in N! (For example, N* contains all numbers of the form 2x, where x is a positive integer greater than 2.)
(If you accept that the countable union of countable sets is countable, then there is nothing puzzling here. But like I said up top, the first time I realized that infinite sets can behave this way, it struck me as very strange!)
The omnipotence paradox has a simple resolution: if omnipotence is the ability to do anything, then an omnipotent being must be able to do what is logically impossible as well. So, an omnipotent being would be able to create a stone that it cannot move, and then move it, even though it would be logically impossible.
Exactly. People are jerking themselves off of superficial paradoxes. An omnipotent being is not a physical being. Infinity comes in sets, and is endless. Infinity has no end, the being`s powers` has no end. The Universe is a perfect example of that, it is all scaling. A grain of sand is the Earth to the galaxy as the galaxy is to the Universe as the Universe is to the Multiverse as the Multiverse is to... and so on, because how long has time been flowing?
The creator could make such an infinite weight stone. If we compare that stone to a grain of sand, then the Creator can create a stone that is like the Universe compared to a single grain of sand, which was the previous infinite weight stone. Lol. Because scaling is sort of an illusion, and a being that is non-physical, outside MATTER (SIZE OF THINGS AND WEIGHT LMFAO), can literally endlessly blow our minds. Knowledge is infinite.
"Is it true that whan you say yes it means no?"
"Yes!"
No!
Haha funny that in arabic language there is a way to overcome this question
@@alaayaseen4160
Please explain, that actually sounds super interesting to me. :)
@@squishyoctopi7042 i want to know, too
Love how you used the word she for a god.... my r e teacher used to say the same
In economics studies everybody is a "she", for some reason. It took me years to get used to it!
@@JamyOats but why
You got me curious too, why?
I don't know why! I always assumed it was just a mild attempt to counter the male-centric convention.
#6 - The Grandfather Paradox makes the supposition that Free Will exists but that aspect is not demonstrable unless a person is able to rewind their own life and literally re-take any decision they've ever made but choose an alternative which, as far as I am aware, is not within anybody's power so it is not possible to verify that we were ever capable of having made any other choice.
It's a great video, but most of us have already heard these paradoxes
If you put instant coffee in a microwave, will it go back in time?
i think your videos are really cool. i think you are gonna go places and be very successful- that's my gut feeling. keep going duuude
For the third "paradox", you can have bigger and smaller infinities in math. As a simple example, if take the limit of 2x/x as x approaches infinity you have infinity/infinity. But the top infinity is twice as big so the answer is 2. So the set of all whole numbers is obviously a a bigger infinite set than the smaller infinite set of all even numbers.
Another variation of the 'This statement is false' paradox - 'This page has been intentionally left blank'.
Following the prisoner's logic, they would realize that the only possible time to not be surprised is that exact instant, so the prisoner would know with 100% certainty they would be executed then. But because they claimed the would surprise the prisoner, they can't execute him at this moment, the next moment comes, and the prisoner realized they were wrong, but this time they are right, this next moment will be their last, but it won't be. And this would continue until the time is up, and the court would have to just execute him without surprising him. But if for a single instant the prisoner does not believe that is the instant they will be executed, they can be surprised in that instant. There is a clear outcome for the prisoner, dependent entirely on his thoughts.
I love when ontological paradoxes are used in Science Fiction :D
Speaking about time travel I remember being told that we can't see the present because it takes 50 milliseconds for our brain to receive information from our eyes. So everything we see is in the past. You can say the same for smell, touch, taste, etc. So there really isn't a present, just a future and past.
The third one is not a paradox, it’s a simple consequence of the mathematical definition of equipotency between sets. We say that two sets are equipotent if we can find a bijection between them. Since it’s quite easy to find a bijection between the set of positive integers and the set of even numbers, we conclude that those two sets are equipotent. Two sets that are equipotent have the same cardinality (“number of elements”). Your reasoning is based on an incorrect implication that if two sets are infinite, we can find a bijection between them. Both the set of whole numbers and the set of real numbers are infinite, but they do not have the same cardinality (the cardinality of the set of whole numbers is aleph zero, while the cardinality of the set of real numbers is continuum (2 to the power of aleph zero, which is a cardinal number greater than aleph zero).
There's a 2nd part to the prisoner paradox (the first one). "After deducing that he could not be executed, he was executed on Wednesday and was surprised.".
1:28 Just because there are an infinite amount of both doesn't mean they have the same amount. And its not really a paradox
There is the same number because you can make a 1 to 1 mapping of one set to the other.
Like this isn't true for the reals. There are more real numbers than odd, even, or whole despite there being an infinite amount of each. Again, the reason there are more reals is because you can't map one to one between them. So the infinite set of the reals is larger than the infinite set of the odds.
Likewise, the set of non algebraic numbers is infinitely larger than even the reals.
It kinda does. Infinite=infinite. One infinite cannot be larger than the other, by definition, infinity never ends. It's a hard idea to wrap your head around, but because the numbers never end, both are equal.
Yes there are different degrees of infinite and some are bigger than others john atlas is right. Check reals vs ratio al numbers
@@akoskormendi9711 Sorry bro....it may be a hard idea to wrap your head around...but different infinities can be larger/smaller than each other.
@@akoskormendi9711 Cantor proved, within the respect of set theory, that there exist larger and smaller infinities, by proving the fact that there exists no surjection from some set A to a set of all A's subsets, meaning the latter has bigger cardinality than the former, which applies to infinite cardinalities. Your statement is really an oversimplification of infinity.
john atlas actually the last sentence is incorrect. There are indeed more Non-algebraic (or transcendental) than algebraic ones, however not more than the reals. Idk if you define the two in respect with complex or real numbers, but either way, all the complex numbers consist of all the algebraic and transcendental numbers, but since there exists a bijection between R and C (I even proved this myself), then there can't be more transcendental numbers than the real numbers. But there is an equal amount.
Many of this "logical paradoxes" are rooted in the human mind or language, not in the physical world. You could say, it's only paradox cause we can't catch it or the premise doesn't make sense in the first place. They are just funny little games with nonsense.
Monte Hall and cardinality of Naturals vs the even Naturals are straight up math results that are just unintuituve
If you want a math result slightle more deserving of the name paradox, Banach-Tarski os where it's at
TheLuckySpades The Monte Hall thing to me was just so stupid. Like how much debate it caused amongst really smart people. Now I don’t find it ridiculous because of the logic, but the fact that anyone could set up an easy at home experiment and do like 200 rounds or so and then there’s no denying who’s correct.
@@natalieelskamp03 that or excel simulations
Or just drawing the decision trees for each option, seriously it ain't hard
However it is very unintuitive if you aren't used to it, similar to the birthday problem, or any of a large variety of probability problems, they can get very confusing at times
TheLuckySpades yeah those would work too. However, even a four-year-old could test it despite not knowing how to illustrate it in those other ways, which was my point.
I've studied paradoxes quite a bit, so this should be interesting.
1. Prisoner ~ Not a paradox, this has a solution
2. Theseus ~ Not a paradox, this has a solution
3. Numbers ~ Not a paradox, this has a solution
4. Quotation ~ Not a paradox, this has a solution
5. Omnipotence ~ Not a paradox, this has a solution
6. Grandfather ~ Not a paradox, this has a solution
7. Twins ~ Not a paradox, this has a solution
No.2
The ship is not the same ship as soon as you replace a plank. It's the 'improved' ship.(presumably you replaced the plank with a better, newer plank)
When you get to the last original plank it's the vastly improved ship and of course it's not the same ship as the original ship at all since, if you had kept all the planks you might reassemble them into the original ship!
Ian Taylor your molocules of ur body change everyday and u r completely new than u were an year ago so u mean to say u r not the same person u were an year ago?
On the omnipotence paradox, i think an omnipotent being making a rock that they can't lift is equivalent to the omnipotent being removing their own omnipotence, which they obviously can do. There's no reason omnipotence has to be indestructible.
If there were a being with indestructible omnipotence though- then the paradox would certainly apply
If you rephrase the question to say, "If an omnipotent being wasn't necessarily trying to create a rock they could not lift but instead making heavier and heavier rocks. Would the being ever create a rock they could not lift?" If not then there is a physical limit to how heavy they can make the rocks with respect to their strength. If they do eventually create a rock they cannot lift then they are not omnipotent.
@@slowsatsuma3214 OP is correct. If you've already defined an omnipotent being as one that can lift every possible rock, then the only way for the omnipotent being to not lift a rock, would be to reduce it's power. The question is basically a specific example of "can you do something that would cause you to not be able to do something". And the answer is yes, it can remove some/all its power/ability.
Tater N Well that’s with the assumption that the being WANTS to create something it cannot lift. If the being is simply just trying to create heavier and heavier rocks then that logic doesn’t work.
@@slowsatsuma3214 I'm not following. The question is basically "Can you do X, which would cause you do no longer do Y". It doesn't matter what X is, it would have to entail losing omnipotence somehow...because that's the meaning of omnipotence. Omnipotence isn't the problem, it's the question that's the problem. By definition, he can already lift any rock...so if you want him to "not be able to lift a rock (or not do anything)"...the necessary condition is that he lose "power". It doesn't matter if he's transferring his power into the rock while creating it or what...he has to lose the ability/power, in order to not have the ability/power.
Tater N Let me explain what I mean because I 100% agree with your logic but it comes with the assumption that the omnipotent being is TRYING to create a rock that it cannot lift. I proposed a subtly different question: By virtue of creating heavier and heavier rocks can an omnipotent being create a rock that it cannot lift. Now that being could create a pebble and then take away its omnipotence so that it could not lift it, sure, but the being’s inability to lift said pebble does not make the pebble any heavier which is the prime goal of this rock obsessed deity. So if the beings goal is to make the heaviest possible rock will it ever make one that it cannot lift? That is the paradoxical question. The being isn’t TRYING to create something it cannot lift . And historically that’s where the paradox stems from, “Could an almighty all powerful God create a rock so heavy that they could not lift it?” with connotations of the God NOT wanting to lose any omnipotence to create a rock that it cannot lift but also trying to create the heaviest rock possible. The solution given is perfectly fine for this question because it is an ambiguous retelling of the actual God paradox.
For the last one you have to be aware that light travels at a constant speed ( no mass) , but space and time are malleable by gravity. Speeding objects gain mass with velocity , and therefore distort time more and more.The first paradox is invalid, if the prisoner knows hes going to be executed then whatever day it happens its not going to be a surprise.
for the prisoner paradox, surely the prisoner can only deduce that its not on friday by the time its reached Thursday, he cant make that same claim on a Wednesday though no?
Anyone else had to watch on 0.75x speed?
Nah I watched it on 1.25 instead
Omnipotence is a sort of "my dad is stronger than your dad" bragging. It is religious twaddle. It does not mean anything.
The "paradox" only works on created beings within a limited existence. When you operate outside of time and space the kinds of things that people ponder don't apply.
Bud 10001100101000 thats a special pleading logical fallacy
If I use the simple analogy of a videogame, physical people who create videogames operate under drastically different rules than the worlds they create.
even if we use video games, I have a paradox, can you create a 3 d model so large that you can't delete it? XD
I graduated In 2004, and I think at that time, you would have been smarter than me at around age 4? Lol, you're wise beyond your years Alex still, funny to see you so young here!
Surely the prisoner paradox is solved by the fact that the surprise that comes on a Thursday can take two forms ("you're to be executed today" or "you're not to be executed today" which obviously means it will happen on the Friday) versus the kind of surprise that can occur on a Monday through Wednesday ("you're not to be executed today" but there are are multiple days remaining). If you wind up getting excecuted on a Friday, it still came as a suprise... but on the previous day. The wording of the judge's statement doesn't specify when the surprise will occur in relation to the actually execution.
i liked that video i also have that book and enjoyed reading it, my favourite was maxwells demon.
Thanks man, I was nearly going to include Maxwell's Demon actually, but I didn't want to use more than 2 examples that featured in the book.
So following on from Einstein’s paradox, the speed at which a planet travels through space can absolutely affect the way time passes on that planet?
As far as I understand it, there are two things that affect how time passes for the one experiencing one or both of those two factors. One is the traveling speed and the second is gravity. The more heavier the planet, the slower time passes. Than you would have to add the mass of the star wich the planet is surrounding and also the speed of travel. So yeah, it would affect how time passes but only to someone who isn't on the planet and observes all this happening while standing still or at least moving slower than the planet. You wouldn't notice anything changing while being on the planet.
Sorry for my poor english skills but I did my best, I hope u're still able to unterstand it.
Yes. GPS satellites have to account for relativity because they're moving swiftly relative to the planet.
Yes, but at the speeds planets travel the difference is tiny.
A couple responses here:
In the first one, however, it is a surprise on a day-to-day basis whether you're going to be executed or not.
I love mathematical paradoxes like this one. My favorite is Hilbert's Hotel.
For the omnipotence one, C.S. Lewis wrote that God can't do anything self-contradictory like the Omnipotence Paradox. He also said that saying this doesn't diminish God's omnipotence because if you say that God can't make round corners, you haven't actually succeeded in saying anything about God. Don't take my word for it; there's a chapter in Problem of Pain about this.
The final paradox with relativity is a fun one for sure! One that I've thought about in the past is this: if you're traveling at 95% of the speed of light, when you factor in that time slows down, aren't you actually traveling faster than 95% of the speed of light? Because velocity is distance over time, so when you decrease the time over the same distance (like when time slows down), velocity increases. Or does the change in distance/displacement change accordingly so it's still the same velocity?
The ship of Theseus paradox reminds me of the "beaming" procedure on the "Enterprise" ("Beam me up, Scotty!"). If you destruct a being, transmit it's WHOLE information and reconstruct it there, it is not the original anymore. Even if you could copy each single chemical reaction so precisely that life/thoughts just go on on the other side. It would not be the same organism. So how much emphasis do we put on our original body in the 23rd century?
i liked one i came up with... i'm sure i'm not the first one to come up with this but:
"When you answer this question, will you're answer be no?"
Jordan21Michael Probably Not
Well when you come up with a more solidified and certain answer, let me know. :P
That wasnt a question ;)
Ha ha! So far, every answer has been something besides "no"...
so their answers were "No."
(Mine's "42!" of course...)
What question?
So with your "Even or whole numbers" paradox, TECHNICALLY, there are more even numbers, because things like 0.2, 0.4, and 0.8 are all even numbers. Since there is an infinite amount of decimal numbers in whole numbers, no matter how far you count, you'll have more even numbers, just not by conventional means of counting (1,2,3, etc.)
nope
What about 0.1, 0.3, 0.5, 0. 7, 0.9, Between 0 and 1 only using the tens place. There are more odd numbers than even. 5 odd verses 4 even.
Concerning the prisoner's "paradox", you can absolutely be hanged on Friday because you can't figure out you weren't going to be hanged on Thursday until Thursday is over. Even if you make it to Friday, you still haven't learned anything since you have no idea what time it will happen, all you know is it won't be on Saturday, but you already knew that.
Also the ultimate paradox of the Prisoner’s Paradox is that since all days are bad choices, ALL days are good choices as the prisoner, if a perfectly rational agent, would conclude no Day is possible, hence expect none of the days.
to the question of omnipotence: Just think of life as an computergame and god the creator/admin of the game. The question "Can the admin create a rock that he can't lift" becomes inrelevant, because the admin can't even touch it. But he is still omnipotent.
That's a good answer actually. I never heard that one before.
Eitan Blumin i think a alot about questions like this. I also think we can't answer the question if god exist or not. We simply know way to less about the universe itself. Watch some videos of exurb1a. Then you'll know what i mean.
mmm i think so? he can do everything with every object but can not directly interact with it. He can just modify the source code behind everything.
Yeah it solves the paradox, but there's one catch:
It redefines and limits the definition of "omnipotence" in this context.
i.e. God is no longer omnipotent in the literal sense.
He does remain omnipotent in the sense of his control of the universe that he created.
But he's NOT omnipotent within the confines of the universe that he himself exists in.
Eitan Blumin omnipotence is the quality of having unlimited power. But is gods onmipotence limited to this world? Does a world outside of this one exist? Was this world created? Or are we just living in a simulation?...All in all we have way too less answers for way too many questions. In my opinion god isn't a omnipotent being. I think he personifies the search of humanity for answers. Everything we can't explain happens through god until we are advanced enough to understand how it happened. I need to stop before i get offtopic any further.
ouch... I've just had surgery and I'm on lots of medication. After this video I think I may need to double my dose.
Fast delivery worked. Very enjoyable video. Packed with nice bits of brainfood. Good production Alex.
Now that I have learnt Greek much better, I am recognizing English words of Greek origin. Paradox is one of the many such words
Number 3 isn't a paradox either.
There are smaller infinities and there are larger infinities.
The math is EXTREMELY unintuitive, but it works out.
MrRolnicek infinity isn't a number, how can there be larger infinities? Do you even realize what you're saying?
Yes. And you kind of answered your own question. It's not a number. I THINK you can find a great video about the different types of infinities on ViHeart youtube channel, if not, well you'll find some cool video if this topic interests you.
NDT explained this: For example, the infinity of numbers with one decimal place is larger than the infinity of integers. As the OG comment said, it is unintuitive, but it checks out.
Infinity is a mind-fuck concept, because its where all paradoxes lie. It's counter-intuitive because it goes against everything we sense in our lives, since every different object or thing is limited by it's own dimensions, as well as all living things have a start date and an end. But it's also intuitive, because whatever number you think of, you can add another one, and whenever some timeframe ends, you can see as the start of another one; so every thing is limited because another thing starts, which makes infinity an intuitive concept because whenever you think of an end, you can think of something else existing afterwards, but at the same time counter-intuitive because "all things come to an end". That's why paradoxes are circular logic, because any time you get to the end of a circle you're actually at the start (spatially speaking). So, spatially, the end of a loop in a circle is also the start, what makes the start and end being the same, making it a paradox. Infinity will always be undefined because once you define it it is not infinite anymore, so infinity is itself a paradox, home to all other paradoxes, where two parallel lines meet, fall in love, get married, and have a large offspring of other baby infinities.
while there are larger and smaller infinities those are both countable infinities and are thus equal
My fav paradox: When everyone is super. No one is.
about the twin paradox, i have one theory:
those who sit all day and doesn't move at all will get older faster, and one who always travels on a plane will age slower, since they are closer to speed of light than those who doesn't move at all.
So when we retire, make sure we at least drive or run everyday because that will slow down the time around us.
Maybe just as you're about to get in the time machine, your grandson appears from the future and kicks you in the flux capacitor.
I should not be watching this at 2 in the morning... too much to think about
Yikes! Too fast. I can't keep up. Slowed It down and you sound like you're on downers. Love your blog.
The grandfather giving birth to the father giving birth to the time traveller seems unlikely anyway. Usually it would be the time traveller's female ancestors who would give birth.
1. The prisoner's fault was that he was looking at things backwards. He could only know that it couldn't be Friday because he was out of days, but any days Monday-Thursday would work. The paradox ends with "He was surprised to be executed on Wednesday." He didn't see it coming because he assumed he couldn't be executed by surprise.
5. An omnipotent power could create a stone he couldn't lift but then the omnipotent power could alter itself to be able to lift it.
The Grandfather paradox is not a paradox, you can't simply change the history and all the action you take there ends up as it is now, so you may ask your grandmother "Who was my real grandfather" and "Who did your lover died", or you just fail in every attempt even you sometime think you did killed your grandfather.
The better paradox/riddle is; a old man manage after a long time to invent a time machine, this has made him a poor and broken man just for all saw him as crazy, he then use this machine to travel back 30 years to give himself the blueprint for the time machine and to tell himself everything he did wrong and what to do to get a better life; so why was he poor and broken when manage to build the time machine and why took it 30 years for him to build it?
Rex Kenny did you miss the entire point of the grandfather paradox? ofc if you kill your grandfather it will change the future, that's the whole point. if you kill your grandfather then you wouldn't exist and wouldn't be able to go back in time to kill him, so he wouldn't die. so you would still exist and you'd kill him.
Let me first say that this is a silly debate for we debating something that can never happen, even as mental thought is it stupid for we can never say who is right, when you go back in time he is not your grandfather and you are not born, and if you travel back to the future you will pass the time when you are born and at that point there is two of you.
You can twist fantasies in what way you want, but I just took the examples of this paradox that may not be a paradox, a bit to point out that it is a fantasy.
Even the god paradox can be broken down with a bit of down to earth arguments:
- If god exist and he creates a rocket that...
- God does not exist.
- But if god exist.
- Okay?
- can he then create a rock that is...
- The christian God?
- Yes.
- But, he created earth and all rocks on the third day.
- Yes, but this is an Example.
- It is a silly example, can you not take another example.
- Okay, do you know about the grandfather paradox?
P.S Do not take this to serious, paradoxes are more for fun, and it more creative to find a story that take you around them.
no offense rex, but i dont think you understand what a parodox is.
I think I understand that a bit better than you, a paradox is a self contradictory statement, and I just pointed out that the Grandfather paradox can have solutions that give you an answer that is not self contradictory to the statement and therefore is not a paradox.
Btw, to say that a paradox is not a paradox, is that not a paradoxical statement too?
Rex Kenny yeah, you dont understand paradoxes.
3:20 grandfathers and fathers don't give birth mate
But they make women give borth
They impregnate checkmate
For the twin paradox the reference point isn't the boy who traveled at nearly light speed or the girl who stayed put, but the teller and listener of the paradox. In space where there only reference point is each other its almost impossible to tell which one started moving (I guess this is a universe where stars don't exist) but we are the constant. We know the boy moved because we are the third perspective needed to tell wtf is going on. So the boy is younger
The last one is only a paradox when you don't understand relativity.
In regards to the omnipotence paradox, theists believe that God is infinite and absolute in his essence, and therefore he can never be less than infinite, or else it contradicts his very essence and invalidates him from being God Almighty; this is why he never eats, sleeps, dies, ceases to exist, etc. Therefore God cannot limit his power in any way, since it is part of his essential attributes as God. It is not about ability, but essence. Thus this question itself is inherently contradictory and meaningless.
Abdul S. nope.God will make a huge crane to lift it up for him. He can't lift it himselt, but he can find a way to lift it.checkmate from a christian
Wendi Ipad Then god is still unable to lift it. The crane can lift it, but god cannot.
Maybe you hadn't noticed, but God is still MIA. Obviously, God is still preoccupied struggling to lift that rock after thousands of years.
Wendi Ipad Theoretically, I could build a crane that can lift a rock that I cannot lift on my own. Conclusion: I am God.
This is the second video today where I've used creationist claims to prove that I am God.
The paradox is created in the very proposition, because if God is omnipotent that already implies he can do whatever he wants, therefore presenting any concept where he CAN'T do anything, is a contradiction to the very definition of God (as the omnipotent). You can create paradoxes about anything by simply stating the opposite of what you just presented as the premise, only using synonyms or word play to pretend you're saying something different.
I don't get the numbers paradox. Even accounting for infinite numbers, there should be more whole numbers than even numbers. If you stop at 10, there's 5 even and 10 whole. If you stop at 100, there are 50 even and 100 whole. And so on...
_"And so on..."_ That's true, but is not an argument for infinity. As another example consider decimal numbers x=0.333...3 with finitely many digits, all 3s. If you stop after 10 digits, then x
Theo0x89
I'm sorry, but i didn't quite follow your example. Can you restate it for me?
smokert5555 The point is that something doesn't need to be true for infinite many if it is true for all finitely many (as opposed to what your "and so on" seems to say). Example: 0.33... is smaller than 1/3 for finitely many 3s (digits after the period), but 0.33... with infinitely many 3s is not smaller than 1/3.
In the paradox comparing whole numbers to even numbers, you need a precise definition of "more" to understand the paradox. In a nutshell, "contains as a smaller subset" and "has more elements" are the same for finite sets, but are different for infinite sets. Indeed, the whole numbers contain the even numbers as a smaller subset, but do not have "more" elements.
In order to have more whole numbers than even numbers, the precise definition of "more" would require that you cannot identify the whole numbers with a subset of the even numbers. This is possible, though: identify 1 with 2, 2 with 4, 3 with 6, and so on, see 1:48 in the video. This identifies the whole numbers with the even number itself (and the even number are a subset of the even numbers), so you can identify the whole numbers with a subset of the even numbers, therefore, according to the definition given above, there are not more whole numbers than even numbers.
Theo0x89
That's what's bugging me about your example. If .33 is smaller than 3, then .3333333... is still smaller than 3. I don't see how it can be larger.
I also don't understand the example given in the video. If you start with a set of whole numbers, in sequence, wouldn't you always have more whole than even? The only way i see around it is if the set you started with were not sequential. Infinite numbers wouldn't seem to be a factor.
I'm sure i'm just not getting it, but the association in the video and reiterated by you (1 with 2, 2 with 4,...) i just don't get. It appears to be ignoring all the uneven numbers you would count as whole.
Thanks for your continued patience in helping me understand this.
smokert5555 _"If .33 is smaller than 3, then .3333333... is still smaller than 3."_
Yeah, I'm sorry for that. I kept writing 3 instead of 1/3 throughout my replies (some sort of mental copy and paste error). I made edits to correct that. Since 0.33...=1/3 (for infinite many digits), 0.33... is not smaller than 1/3.
_"The only way i see around it is if the set you started with were not sequential."_
Indeed, when you compare the "number of elements" of infinite sets (called "cardinality" in mathematics), the order of the elements is irrelevant. So the symbols "1", "2", "3", ... are nothing but labels. When you relabel "1" to "2", "2" to "4", "3" to "6", ... you see that the whole numbers and the even numbers can be identified with each other as sets, and therefore have the same "number of elements", i.e. the same cardinality.
Every time someone travels in time, a branch falls off of Yggdrasil and kills a squirrel.
My favorite is certainty, I've had people say to me that we can not be certain of anything, but yet they are certain that there is no certainty. To say that we cannot be certain of anything is a statement of certainty.
Pretty lame. Most of these are not paradoxes at all.
If you allow the almost certainly counterfactual premises of numbers 5 and 6, five of the seven are paradoxes.
DrGerbils I'm not re-watching it. But if memory serves it's worse than that. Remember that semantics are not a paradox.
If I recall, one of them was the childish ""can god make a rock so big that god cannot lift it?"" This simply shows that the definition of ""omnipotent"" is flawed, it does not demonstrate a paradox.
p.s. just in case....if you intend on challenging that example. I was informing, not engaging. There is no debate. There is only an understanding of linguistics, and ignorance of linguistics.
And now that I'm thinking about it, time travel may have been in there as well. Time travel does not exist. Therefore there are no paradoxes associated with it.
Frank Sanders As I noted, albeit by number only, the omnipotence and time travel examples are paradoxes only if you allow his premises. With those gone, you are correct. He could have gone with any two of Xeno's paradoxes. They're resolvable, but at least facially paradoxical.
DrGerbils ""facially""??
Frank Sanders On their face. At first glance. I just discovered that "facially" with that connotation is legalese and not standard English.
The dilemma posed by the last paradox can be explained by the fact that the traveling sibling must markedly accelerate relative to the other sibling. During this acceleration phase, the time dilation is not symmetric.
For the Grandfather Paradox, I always thought about the idea that whenever you go back in time you create a new timeline. Let's say you were to go back and kill your grandfather. That timeline is separate from yours. So in that timeline, your gramdfather is dead and you were never born, but you present timeling doesn't change.
If any of you have watched dragon ball z this sort of thing happens
I have a masters in Physics, and I specifically studied relativity (marvellous by the way, would recommend), and the short answer to the twins paradox is that it demonstrates why special relativity is not enough, and we must invent general relativity to account for it.