Paradoxes that No One Can Solve

welcome to a realm where logic spirals into enigmatic puzzles where the answers are as elusive as the questions themselves no it's on episode of The Twilight Zone today we're venturing into the world of paradoxes at the forefronts is the notorious liar Paradox a puzzle that will twist your perceptions of Truth and deception but that is just the beginning stay with us today because later in the video we're going to look at the bootstrap Paradox which is utterly mindbending let's get into [Music] it the liar Paradox dates back thousands of years to the ancient Greeks if not earlier there are many variations of this Paradox but the most simple version is a single sentence this statement is false if the statement itself is false then then it would mean that it is actually true and if the statement is true it would mean that it is actually false this means that whether you believe the statement to be true or false it would be both true and false at the same time which should be a logical impossibility early attempts to reconcile this Paradox suggested that the statement simply was neither true nor false which resulted in the strengthened Liar's Paradox for example the Paradox could be Rewritten as either this statement is not true or this statement is only false the first variation was designed to preclude the possibility that the statement was neither true nor false and the second was designed such that it couldn't be both true and false the Paradox gets its name from the earliest accounts of the Paradox such as from Greek philosopher ubiles of militti who posed the Paradox in the 4th Century BC as quote a man says that he is lying is what he says true or false while it may seem like a somewhat nonsensical Paradox focused on semantics language was built on classical binary truth value every statement must be either true or false there have been numerous attempts to resolve the Paradox but unless someone is willing to just dismiss it as pointless nonsense no such resolution can yet be found this particular Paradox is also proven to not just be completely pointless having played a large role in mathematics self-referential paradoxes are easy to create in semantic language but it was believed that such things didn't exist in maths I have a question for all of you men out there does anyone like anything things like acon blackheads dead skin on your face no of course you don't Everyone likes having Clean Skin everyone wants to be their best self and if you don't well today's sponsor T Handley isn't for you but for everyone else in the world which is like 99.999% of you T Handley is for you their goal is to help keep your skin fresh and clean creating a routine for you to follow in order to deal with any unwanted skin blemishes and on top of that it's unbelievably easy to start and keep up with only a few clear steps to keep your SK skin clear and healthy honestly it is the best skin care system for guys like you and me plus it is super affordable 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what matters is that it was a mathematical rephrasing of the liar Paradox as the set of sets that did not include themselves would have to simultaneously include and not include itself which is impossible this was extended by Kurt godal in 1930 to create his incompleteness theorems by showing that a self-referential liar Paradox could be written as a formal arithmetic statement godal proved that no system of mathematics could ever be complete while it's unusual for a paradox to have practical applications godel's incompleteness theorems and his proof that no consistent formal system of maths can prove its own consistency is regarded as one of the greatest intellectual achievements of modern [Music] times the bootstrap Paradox gets his name from the phrase pulling oneself up by the bootstraps while the meaning of that phrase has changed over time the saying was originally intended to refer to something that was ludicrously impossible after all when confronted with a massive wall or fence a person could not simply grab their bootstraps and pull on them to lift themselves over the barrier there are many forms of this Paradox so we'll look at one of the more popular versions let's imagine a person who was both a huge fan of Albert Einstein and who also has access to a time machine this person takes a copy of Einstein's theory of relativity then travels backward in time to meet Einstein before he had begun work on his theory the time traveler uses his book to teach Einstein about relativity before returning to his own time Einstein then goes on to publish the work as his own never making any reference to the time traveler his work gets published repeatedly over the coming decades or even centuries until a copy of it finally winds up in the hands of our time traveler so where did the theory of relativity actually come from Einstein learned it from the time traveler but the time traveler learned it from Einstein the theory appears to have no point of origin it pulled itself up by its bootstraps and created itself out of nothing Well therein lies the Paradox there are countless examples of these self-referential closed Loops in metor such as in 12 Monkeys The Terminator series Back To The Future Doctor Who Game of Thrones even Fraggle Rock while the notion of an object or idea being trapped in a recursive time Loop like this seems paradoxical to us many scientists argue that it isn't actually a problem at all in future armor for example fry went back in time and slept with his grandmother thus becoming his own grandfather however he was always his own grandfather nothing in the causal chain of events was broken or changed and the only Paradox comes from how the original fry could have come into existence in the first place but because each iteration of the time Loop is identical it can be argued that such a Time Loop is self-sufficient and consistent with the laws of physics now this becomes a little less clear when an object is part of the time Loop rather than an idea or action in the 1980 film Somewhere in Time For example an old woman gives Christopher Reeve a pocket watch he later travels back in time and gives the pocket watch to Jane Seymour playing the same character as the old woman before inadvertently returning to the present the difference in this scenario is that the watch should be continually aging as it travels through each iteration of the loop Loop there are proposals for how this might still be possible though they tend to involve a lot of complicated thermodynamics for the purposes of Storytelling most writers choose to have the object be something like a letter that gets worn over time and is Rewritten on Fresh paper before being taken back in time thus eliminating these concerns while these time Loops are paradoxical because they have an idea or object that seems to have created itself many scientists and philosophers alike agree that the bootstrap Paradox doesn't create a logical impossibility despite being really really weird but sometime travel paradoxes present much bigger [Music] problems the bootstrap Paradox preserves the train of causality but in the grandfather Paradox we throw that entirely out the window this Paradox gets its name from the most common example of breaking causality which is going back in time and killing your own grandfather before your parent is born if you kill your grandfather then you will never be born but if you were never born then your grandfather won't be killed and thus you will be born not only is this logically inconsistent but it is also an example of reverse causation which should not be possible normally a cause results in an effect but in the Paradox the cause results in the effect negating the cause and if you happen to like your grandfather there's the famous variant in which you go back in time to kill Baby Hitler Instead This creates a similar problem because if Hitler was dead at the time then he wouldn't have done all that stuff that made you want to go back in time and kill him in the first place nor would you have any knowledge of it as such you wouldn't go back in time to kill him and he would rise to power and so on should something like the grandfather Paradox come to pass we have no idea what would happen the bootstrap Paradox is weird but it is still consistent the grandfather Paradox creates an inconsistency and there is absolutely no consensus on how such an event could be handled but there are a lot of theories one popular theory is the idea of infinite parallel universe if you go back in time some would argue that you're not going back to your own timeline rather you're going back to that point in a different universe as such the actions you take there would not break the chain of causality that had previously existed in your Universe another theory is that the Universe simply will not allow actions to take place in the past that would change the future if you Tred to change the past the universe will employ comic book logic to prevent you from actually doing so for example if you go to the past to try and shoot your grandfather the gun will Jam or if it didn't jam and you shot him then you never saw the body or if you did see the body then it wasn't really him it was a robot or a clone or something like that comic book logic or if somehow you actually succeeded in killing your grandfather then it would turn out that he was never really your grandfather in the first place your parent was born because your grandmother had an affair or you were actually adopted and your entire family kept into de secra your whole life no matter how ridiculous the end scenario the theory speculates that the Universe would ensure that no actions you took in the past could result in Reverse causation so well why is this Paradox important why are honest to God scientists spending so much real time and effort debating what on the surface seems like a ridiculous Paradox and the answer to that is that general relativity is pretty great while it may be incomplete general relativity has shown to be incredibly consistent at making accurate predictions about the universe around us and according to general relativity reverse time travel should theoretically be possible not only that but in 1949 goo produced a solution to the Einstein field equations his solution for the equations resulted in a model of SpaceTime that would inevitably create closed Tim like curves his wasn't the only solution to the field equations but the notion that physics allows for reverse time travel is pretty consistent as a result any time travel Paradox is of particular concern to physicists no matter how ludicrous it may sound as it could have very real implications on the universe around us the Greek philosopher Zeno of AA is famous for his nine paradoxes the most famous of these are the dichotomy argument the arrow in flight and achilles and the Tortoise but since they're all very similar and all relate to motion we'll stick with just the dichotomy argument the argument states that which is in Locomotion must arrive at the halfway stage before it arrives at its goal that certainly makes sense and seems to be obviously true but let's take this argument a little further F like Xeno did let's say you want to run a mile before you finish the mile you must run half a mile but before you can finish the second half mile you must run a quarter of a mile then an eighth and a 16th and so on the remaining distance can be divided in half an infinite number of times so the runner must complete an infinite number of tasks before arriving at the destination according to Zeno this means that it would be impossible to arrive at a destination because doing so requires a person to complete an infinite number of tasks in a finite amount of time which can't be done similarly this argument could apply to the start of the journey as well instead of dividing the Second Mile we can divide the first before reaching the half mile point the runner must reach the quarter mile the eighth of a mile and so on extending the infinite divisions this way it would be impossible for the runner to ever start or stop running Zeno argued then that all motion must be an illusion in his writings the Greek philosopher simplicius wrote that upon hearing Zeno's argument the abely named diogenes as the cynic stood up and walked around disproving the idea that motion was impossible now of course this story is almost certainly apocryphal you know it was only 11 years old when diogenes died and simplicius was writing about it several centuries later but even if this story isn't true it still makes a really valid point motion is real however to properly solve these paradoxes it isn't good enough to show that the conclusion is incorrect we need to show what exactly in the arguments is incorrect that caused the false conclusion this is where Zeno's paradoxes become much more interesting the conclusions seem fairly ridiculous but the arguments seem perfectly sound or at the very least they appear to be mathematically sound thousands of years of debate over Zeno's Paradox have had some pretty profound impacts on maths and philosophy it has caused people to question how we think about the relationship between pure mathematics and the real physical world it also helps lead to the development of calculus which deals heavily with infinite sequences and introduced the idea of limits xeno's paradoxes are so foundational to Modern maths and science that there are mult possible phenomena in physics named after them such as Xeno Behavior and the quantum Zeno [Music] effect a man has been sentenced to death for one reason or another first time the judge told The Condemned you will be executed at noon on one weekday during the following week but which day will be a surprise to you you will not know the day of of your hanging until the Executioner knocks on your door at noon that day now that's a depressing verdict to be told but after being taken back to his cell and given time to reflect the prisoner was delighted to realize that he would Escape his execution because a surprise hanging was impossible first The Prisoner concluded that it was impossible to be hanged on a Friday if he was still alive after noon on Thursday then the date of the execution could be deduced with absolute certainty following this Logic the prisoner realized that the execution couldn't take place on Thursday either Friday already wasn't an option so if the Executioner hadn't knocked on his door by noon on Wednesday then the execution would have to take place on Thursday since this could be deduced it would again not be a surprise extending this logic out further The Prisoner was able to eliminate Wednesday Tuesday and Monday as options for the same reason he realized that there was no way to carry out the sentence and so he would have to be let free at the end of the week and noon on Wednesday much to the surprise of the prisoner the Executioner knocked on the door for the hanging this is the newest of the paradoxes that we've looked at today first coming to public attention thanks to a 1963 issue of Scientific American though the Paradox have been discussed since at least the 1940s the Paradox stems from the fact that while the prisoner was able to logically eliminate all possible days as being the date of his execution the result was that an execution on any day became a surprise there have been dozens of Papers written about this Paradox but there's no agreed upon resolution one of the issues is the somewhat vague language and assumptions being made first the term surprised is somewhat subjective there is also the possibility that the judge is lying that future psychological stress could reduce the prisoner's certainty of his initial conclusion and other more opaque factors while the arguments over semantics and definitions are relevant the more common argument is that the prisoner's logic doesn't extend beyond the last day rather than focusing on the definition of the word surprise the judge's decision can be rewarded as the prisoner will be hanged next week and the date will not be deducible the night before from the assumption that the hang in will occur during the week this change in wording means that being hung on a Thursday would still be a surprise as it could not be deduced on Wednesday solely from the knowledge that it would occur at some point during the week as of Wednesday night there were still two options available for the date and there was no way to definitively conclude which date the execution would take place on it is only on Thursday night that the original statement becomes contradictory and then it would be possible to deduce the date of the hanging now if that still sounds a little confusing think of extending the sentence out to a 100 days instead of just five while the final day would not be a surprise and it would certainly become less of a surprise as it reached the last week or so it becomes much more intuitive that the prisoner's original conclusion shouldn't hold the execution can still never be on the last day but trying to reason that none of the other 99 days would be a surprise is a bit more difficult instead of extending the sentence to 100 possible days other potential resolutions attempt to limit the sentence to a single Monday which the judge still claims the prison ER will not be able to predict unlike the other paradoxes that we talked about this one has yet to show any practical applications that may be because it's so much newer or it could be because it relies on a lot of vaguely defined terms within the original story either way the prisoner probably should have stopped being so confident in his logic and uh files an appeal or something just before we end today's video for those of you who missed it earlier please don't forget to check out today's fantastic sponsor that's te Hanley you'll get 30% off your first box and a free gift from them by clicking the link below and thank you for [Music] watching

Channel: Sideprojects

Views: 325,728

Keywords: megaprojects, construction, engineering, projects, sideprojects

Id: v52k23hHkd4

Length: 17min 40sec (1060 seconds)

Published: Tue Feb 27 2024