5 Mind-Bending Paradoxes Explained
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- เผยแพร่เมื่อ 26 ก.ย. 2024
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Scary thought
thanks, now i understand loki.
hi knockoff vsauce!
Im hoping you talked about the Movie from the 80's "Time Rider". The loop that he created his own generation of family members, by accident.
@@latenighter1965 'predestination' is a good loop one too. 'Primer' seems to fit with the Novikov self consistency principle, if i remember correctly
The Astley paradox. You ask him for a copy of the movie Up. However, Rick cannot give you the movie because he’s never gonna give you Up. But by not giving you up he is letting you down.
I needed that laugh today. 🤣
Omg! Mind blown! He did say he's never gonna give you Up AND never gonna let you down!! Suck on that philosophers!!
an interesting thing is Up didnt exist in 1987 so either someone went back in time and gave him the movie or he came up with the idea and sat on it for 20 years
Never thought I’d be Rickrolled on Simon’s channel. Well done!
That's the definitional fallacy. But I applaud the effort.
The Ship of Theseus actually happened with the band Yes. All of the original members eventually left the band and then were replaced. The original members then re-formed a band. BOTH versions at one point toured as "Yes."
That's cool. Would be interesting how that would be solved legally. I would guess that the band with the new members would win. Maybe?
Grandfather's old axe. 3 new heads and 5 new handles.
@@Chris-hx3om Some people's PCs might also fit.
Molly Hatchet played down the road from my house a few years ago.
Or if you want to be more accurate, Molly Hatchet's 4th drummer and his band played right down the road from my house a few years ago.
HAPPENED WITH TRIIGERS BROOM TOO LOL
Paradox is infinite numbers of Simons with infinite numbers of youtube channels.
infinitely going off-script in infinite tangents
One day will make a video about everything
Feels more like reality at this point
Welcome to the Simonverse😂
That’s not a paradox - it’s just reality.
The Ship of Theseus paradox appeared in Only Fools and Horses when Trigger explains he's had the same broom for 20 years despite it having 6 new heads and 7 new handles.
I was going to make this reference ffs 😂
Me too. A gem. @@kieranbromiley4053
In Futurama Hermes upgrades his body with robotic parts peice by peice, while Zoidburg scavanges the old Hermes parts and builds a different Hermes. Eventually Hermes replaces his brain (the last original part) for a better robot brain and Zoidburg uses the old brain to complete his "Hermes" lol
As a crossover,I would have loved it if Rodger Lloyd Pack's character had once,just once,said to Harry Potter."Take care of your broom!"
Am I the only one who does not think it's a paradox? I mean, if you have a ship, buy a new item for the ship, do you say "I removed the old part and put in a new", indicating that you know you trow out a part from the ship and replaced with an item that is not the ship and incorporate it as part of the old ship. If you keep doing it, do you know that you have replaced every part in the old ship, so this is no longer the old ship.
That lottery paradox and throwing away the ticket is so stupid. You know there will be a winner, you've already paid for the ticket and every ticket has exactly the same odds of winning. It makes absolutely no logical sense to throw that ticket away.
Correct, it is not zero. However, in those mega 7 figure lotto's, I always say the odds of winning is only slightly larger if you buy a ticket. Which shows how limited the odds are for winning. There is a non-zero chance that you could find a ticket or win a ticket elsewhere, or are gifted a ticket: yeah the odds only a bit smaller but just about as small as buying and winning. So, it seems that as long as they exist, we are all playing the lotto.
The paradox comes in the decision to buy, not after.
@@Aleksandar6ix yeah so Simon (I think that's his name) explained it wrong IIRC (haven't rewatched the video). He said he threw the ticket away which implies he's already bought it. Once you've bought it it is absolute madness to throw it away
There is a radio contest here that might be interesting in this regard. You send in a text and then there is a drawing every two weeks. But the person who was drawn has to answer their phone within 10 seconds of being called and say a specific phrase. As a result it happens more often than not that the person who was drawn doesn't pick up and the winning sum is increased for the next drawing. They never announce how many people sent in texts so it's unknow what the odds of being drawn are. But it would seem that most people after going trough the effort of sending a text and paying for the entry simply aren't ready when the drawing is actually happening because maybe they think that they aren't going to win anyway.
exactly. thats why it isnt a paradox. this is a stupid example
Simon being on *ALL* the channels in the Whistlerverse, simultaneously putting out new content is most certainly a *paradox...*
Makes the mind swirl.
He probably has infinite amount of writers. :D
nah mate, It's been stated many times that Simon has several clones (two for each channel afaik, but after Simon cut ties with BG/GG/TT six of them were... terminated (with a bullet. To their heads.), plus a substantial number of -slaves- blazement dwellers to pump out scripts for every single Simon.
4th dimensional being in my opinion..
Sideprojects makes a special about megaprojects while viceversa. I dont care if universe explodes. Id watch it.
Not using Fry being his own grandfather is a missed opportunity.
Yess
There was a story written on this premise. They made it into a movie (1980) starring Peter Firth, 'The Flipside of Dominic Hide'. Well worth a watch.
Philip J. Fry made damn sure that he'd still be there
@@Chris-hx3om There's a movie from 2014 named "Predestination" that was loosely based on Robert Heinlein's1958 short story "All You Zombies." The short story is very entertaining and I recommend it. The movie was mediocre, but not a total waste of time. I recommend it if you've had a couple of Ouisghian Zodas on a Thursday evening and have nothing better to do or watch.
First thing I thought of also futurama season 9 episode 7 6 million dollar man is another futurama episode explaining another one
I love how the writers make him talk about Lord of The Rings when he couldn't care less.
They aren't really writers. They are time travelers who are huge fans of the exhaustive LOTR series he hosts from 2025 all the way until his on-stream death in 2072.
@@burbanpoison2494 Coincidentally, when I am asked what I would do if I could go back in time is that I'd take my entire J.K. Rowling library, go back to about five years before she started writing 'Harry Potter', type them out and send them to her very own publisher or one much like it. J.K. would be none the wiser, and I'd be the one with more money than the queen. I guess I might anonymously send Ms. Rowling a million one day.
Good ole bootstraps paradox...
Frankly, Simon's disdain for all things Tolkien makes this video amazing
@@samgamgee7384I'd take back my Stephen King collection, write and publish them as my own then make sure the movie adaptations stuck more closely to them so they'd end up being actually good!
Whenever Sideprojects doesn't have an idea for a video, they just talk about the same paradoxes again.
I loved the Ship of Theseus paradox, because in the classic car world, Standard-Triumph made 6 Le Mans Spitfire Race Cars, I was involved in tracking down survivors. After several years of work, involving travelling all over Europe to inspect cars & parts, we came to the conclusion that of the original 6 cars, at least 18 have survived to the present day! (Apart from total replicas, there are many cars which contain parts of the original cars, i.e. the roof, the wheels, the engine, the chassis etc, some being more, or less original than others)!
Can I have one?
That's fascinating and funny!
Now do the original Batmobile and the original Captain America chopper!!!
Car enthusiast here also, well said
Simon travels back in time and leaves his Ridge wallet with the creators of Ridge wallet who use his credit details to pay for producing the first Ridge wallet.
He left a virtual identical copy.
The Film 'Predestination' is a great example of the last one, it's based off the predestination paradox and, even though it isn't the highest quality film of all time, it's absolutely flawless for plot holes in the time travel paradox it is about. Definitely worth a watch.
Definately a movie worth watching.
I LOVE THIS MOVIE!! it's such a brain bender
Predestination is a good movie. I also like the movie called "Triangle" which has a time loop.
Thanks for the recommendation. Entering downloading mode...
The only real gripe I have with that movie is that half the run time is the dramatic backstory. They could've massively shaved that down and still touched on all the points and leaned heavier on the time travel part. But the time time travel part is amazing. Maybe one of the best time travel movies I've seen once those parts start.
The ship of Theseus seems like it would be a very important topic in the preservation of historical artifacts. To me, renovating an old building too much can indeed strip it of any historical significance. Also, a lot of times, collectors will reject certain types of items if they have been restored, but not other types of items.
It's subjective. One person may say once you pass 50% it is no longer the original. Another may say once you replace a single piece with a new one, it is no longer the original. You cannot pinpoint an opinion unless everyone agrees unanimously.
Once the last original piece is replaced, I feel like it’s no longer original.
@@augustyntchorzewski7615in my opinion objects are original if they retain the configuration they had when they were made. Classic cars are a good example. Basically no classic car is "original" because they all had services and maintenance during their lives. A model T that's had 90% of its parts replaced is still a model T.
Whether it is a model T does not matter. It can be a model T without being original. Again, it is subjective, not a paradox.@@bobbyrayofthefamilysmith24
I like the idea of virtually recreating structures. As computer graphics improve, the experience won't be distinguishable from the real thing. Something along the lines of VR but leveled up.
thesius' ship is like that futurama episode where hermes keeps replacing body parts with robot parts and zoidberg keeps and reassembles him
Except that in that episode the brain was pretty clearly the deciding factor.
Great episode! I’ve heard of one or two of these paradoxes before, but I didn’t fully understand them. Thank you for the simple explanations!
Triggers broom in only fools and horses is a bit like the ship of Theseus
I think a good analogy of the time travel grandfather paradox is like when you open a tab in Chrome and begin meandering all over the web. You are allowed to go back to your beginning but if for some reason, midway through your return to the start, you see something on one of those previous pages and decide to have a look.
You can still go back to the beginning but are unable to go to where you had originally got to and can only take the branch that you created when you got distracted by something interesting.
Something like that anyway. I didn't quite say it like I wanted because I got distracted.
I think there is something to that.
But going back in your browser history is actually still going forward because when you access any given page, that is the new present.
@@bsadewitz Exactly! You've started a 'new timeline'...
While the old timeline may still exist, you can't go there.
... at least not without a lot of gymnastics.
It's much more like you walked a way and then decided to walk back. You walk locations, not time. You can consider websites as virtual locations.
No, I gotcha. Well said, man.
As to the lottery paradox, there is one factor that you didn't mention, which, in my opinion, is the reason for people playing the lottery or even gambling. That reason is hope. They HOPE for what they perceive as a better future by winning a bunch of money. Emotions can play a major factor in most of these paradoxes, such as where to draw the line of certainty and other things that involve human perception.
hope, on the lottery side. then there is the flip side, politics, voter turnout why is it so low, the feeling of unimportance. did you vote? no. why? i wouldnt make a difference in the outcome. is the same result my 1 ticket against a million my chances are nothing of winning my vote aginst a million others my chnces of making a difference are nothing. two sides of the coin lottery hope, politics hopelessness. both being affect by the one against millions. In the case of politics it is often found there are more non voters than voters and could actually make a difference. i wonder of one feeds the other, by that i mean after playing the lottery and continually losing you taught yourself to believe your input (buying a ticket or voting) does not count. curious if voters are lottery players because they have hope. and if non-voters dont play the lottery due to lack nof hope. interesting thought.
Your example is more a kin to those who do'n't play the lottery in the first place due to the low chances of winning.
A more appropriate voting analogy would be going to the polling place, filling out the ballot then throwing away the ballot instead of presenting the ballot.
In both cases in which one totally opts out of the process, is rational, so is logically valid.
In the cases in wich one initiates engagement but fails a very simple follow through, is irrational, and therefore is logically invalid in my honest opinion. I find this not to be a parodox, but rather, irrational reasoning.
However, I do also think that the many worlds interpretation resolves cases also. As there is a world time line for each outcome, including the ones where noone chooses to buy a lottery ticket and everybody who bought a ticket but threw it away with out checking it against the winning numbers. It even covers the case of the fundraiser planning committee deciding on a silent auction in stead of a lottery as a fundraiser.
However, my personal admendment to the many worlds theory is that, all the worlds exist as virtual world time lines until wave function collapses at the instant the obervation or decision is made. This too would resovle any attempt of backward time travle as once the wave function collapses, it cannot uncollapse.
When I play the lottery, it’s because I can comfortably afford to lose a couple of quid for the minimal chance that maybe I’ll win a life changing amount of cash.
If I don’t buy a ticket, my chances are zero; if I buy one it’s nonzero. It’s worth a punt 🤷🏻♂️
@@slashnburn9234If you buy a ticket the chance of winning is so close to zero, that it might as well be zero. You buy a nice fantasy though, and that can be worth a few quid, if it makes you feel better.
This is how I look at the lottery: 1) While I know the odds are incredibly low that I will win I also know that 2) Someone will eventually win and 3) The odds of that person winning and me winning are identical.
When we are able to go back in time, I feel "a sound of thunder" is how this will work.
Speaking on the Gambler's Paradox, Lotto tends to skirt the line constantly. You can't make it PERFECT because people aren't perfect, but they do keep the odds close enough to keep people buying.
Scratcher tickets (run by lotto) keep that rate around 40% winrate, enough to turn a profit for Lotto but still make you feel like you got a chance when you win that $200 on a $5 ticket; in reality you lose 40% of every dollar you put in, win or lose. (If you keep buying... win big on your first ticket and never buy again, congrats... you just beat the system)
The loop paradox never added up for me the way it’s often portrayed. There still would have had to have been an original timeline that set off the events of the loop in motion. In the example of Tolkien, he still would have written the book in the original timeline and that time traveller would have inadvertently changed the origin by leaving the book with him. Had they left it with someone else, that person would have gained fame and there would be a branched timeline. That wouldn’t be a paradox…
That is true but only if traveling back in time will create new timelines. Then another question rises from me: how would these timelines be created? If me and my friend travel back in time to the same date, in separate machines, would we end up in different timelines? If you think about it, the act of traveling back in time should be enough to create a new timeline, because your mere presence is a deviant in that date. So your friend should end up somewhere else as well.
That's only works in multiverse. If there's only 1 timeline you have paradox
But what if Tolkien never wrote the book? Maybe he just copied it from the time traveler in the very first place. It is possible to imagine a scenario where Tolkien gets credit for something he never wrote, but simply was given by the time traveler.
The multiverse hypotheses is a reductio ad absurdum. The emittance of a photon through black body radiation is a random quantum effect, and each photon has a potential (i.e. non- zero propablity) to interact with every charged particle in it's light cone. To claim that the solution to the difference between potential and actuality is that all potential is actualiced in 'parallel universes' is the definition of absurd.
The book came from the real universe, but our simulated universe
Timetravel gives rise to so many fun models, but the grandfather paradox is only a paradox if we assume a single stable timeline. Other options are a timeline flipping between states, or even just a two timeline stable loop.
I’ve seen models where at each decision, at every turn a new branch of time begins. Kind of like they did in that Rick and Morty episode, where they got stuck between timelines. It does solve a lot of these paradoxes.
Or, if we agree that freewill is am illusion. We could go back in time, buy whatever we do back there is already what happened in the past, meaning we can't make any changes
Nope. Even in a single stable timeline it's easy. There's no paradox because it can't happen. You don't go back to kill your grandfather because you didn't. Even if you try to you won't be able to. Easy.
Well, that's what a paradox is, i.e. SEEMINGLY impossible/self-contradictory.
@@BethgaelYeah, this is my problem with some of these paradoxes. If something like time travel is impossible why waste mental effort in trying to resolve resulting paradoxes? I do get that they can be fun or part of a fictional setting where time travel is possible, but it’s not like those should be a big scientific mystery.
Yes, I am fun at parties.
Time loop paradoxes are destined to be destroyed, duh furturama, explained it perfectly. RIP Lars.
A friend of mine got in trouble bringing up Zeno’s paradox. Someone asked after it was explained ‘so…what’s the punchline?’
Fun fact: 90% of gamblers quit right before they win big
not true for me, i quit shortly after the big win.
How could this possibly be verified 😂
thats crap
The film Somewhere in time was a great reference to use. Love that film.
Bootstrap: Tolkien writes LoTR. You go back in time to a point where he hasn’t written it yet and he’s inspired by your praise and takes the book as his own work. Either way the end result is the book is written and published. Tolkien would have written it but having been handed it on a silver platter doesn’t need to. So the left behind book simply takes a different path to the same end. Like a fork in the timeline meeting back with itself and continuing
It's 2 separate timelines. There had to be one where he had to spend time writing that thing. But instead of hypothizing about such absurd stories rather think how they could be tested empirically.
But what if Tolkien never wrote the book at all? What if he just stole credit from the book the time traveler gave him?
@greywolf7577 Well, that is not logical. Such a loop has no beginning so where would it come from. At least once, in a now erased or abandoned timeline, everything must have occurred as we know it leading to the time travel that will erase or abandon the old timeline.
The “replacement parts” paradox occurs at the Tramway Museum at Crich. Are the renovated trams the preserved tram, or a replacement?
I can thank Vision for educating me on the subject of The Ship Of Theseus.
For the infinite room paradox....the solution I think is that the number of ppl transfering to a new room (and therefore outside the room) so that although the infinite room are infinitely filled, it is at the same time infinitely empty due to ppl moving out of their room to go to a new room.
I believe it makes a difference which order people move in and out of rooms, and which rooms people move into and out of. The order in which you add and subtract terms makes a difference in an infinite series.
In any formula with finite terms, changing the order of the + and - operations will not change the end result. The same is not true for an infinite series.
In summary, If you change the order of + and - in some infinite series formulas, you get a different end result.
The paradox conflates finite and infinite to create the paradox..
It the hotel is fully occupied with an infinity amount of rooms , it will always be full infinitely
That’s not an answer because it can’t infinitely be full and empty at the same time those to completely contradict themselves your just saying what the paradox is but in my other comment I explained why this isn’t even a paradox and how it’s not even possible to move anyone to another room in the first place
According to the premise of the video explaining the paradox, if you move person 1 from room A to room B, and person 2 from room ab to C and so on, that movement would essentially be infinite. And when I mentioned that it will be infinitely filled and emptied at the same time, I take it to mean that either everyone will be in the room before moving out (this emptying the rooms) to move to the next room...this the infinite empty room.
How could you move anyone to different rooms if every single room is occupied. its like saying there's a 100 rooms and they're all full but you can just move everyone up one room. It's not physically possible because every room is already full in the first place. @@112313
To be fair Tolkien came up with the stories as bedtime stories for his kids and later wrote them down. He would even send stories via letter to his son Christopher while he served with the South African airforce in WWII.
I thought he came up with it as a universe for his conlang.
@@ferretyluv well yea you're right. He created the languages but then made the stories based on the world they existed in from the bedtime stories he created for his children.
The bootstrap paradox only works with information (in a single timeline), an object such like a pocket watch would still suffer wear and tear and eventually stop working. Doctor who actually prevents this when shown why Amy arrived at a museum, she gives him a note in his handwriting, he throws the note away and immediately writes a new one, still a bootstrap paradox but prevents the note from deteriorating over many loops.
Very interesting. I want to follow your thinking, not question you, but how did you come to the idea of deterioration over multiple loops?
@@VictorRobotov00 my thinking is that you could tell yourself a password for example, that works forever, but if you were given a key which you then pass on, the key could potentially rust and break and couldn't be passed on to keep the paradox going.
Edit for clarification; the object would have to be the same one being passed timeline to timeline, if you made a copy and passed that on the paradox works fine.
Then along those same lines, won’t everybody continue to age then?
@@VictorRobotov00 the people in the paradox would be the same age every time it starts over, so if 30 year old me gave 20 year old me a key, when 20yo me reaches 30 and hands the key to the next 20yo me, the key has aged 10 years, do it again 20yo becomes 30, key given to 20yo is now 20 years older, if the loop continues 100 times, the key has aged 1000 years but the people involved only age 10 years (in this example).
It's not the most elegant explanation and I hope I'm making sense
@@richpdavies 🤔hmm…okay okay. I get ya. Thank you for your time. These kinda things are always some interesting stuff.
Throwing away a ticket is an invalid thought.
Do you keep tickets that didn’t win anything?
@@adameschete9165no, but THEY DIDNT EVEN BOTHER TO SEE IF THEY WON OR LOST. THEY JUST TOSSED IT. Stupid. Low odds, yes, but someone out there wins. Whose to say it won't be you next?
@@adameschete9165
You can throw it away after drawing, of course.
You just gave me the idea that the beginning of the universe is some kind of a paradox, which means it has no beginning or end
Somewhere back in time, Christopher Reeve’s Victoria principal total blast from the past. Thanks, Simon.
I prefer the idea that the universe would simply prevent paradoxes. It doesn't mean everything is predetermined, though. It could simply be that once something is in the past it becomes permanently solidified while the future is still like cement that hasn't dried and set yet.
Only the past is fixed. I can come back tomorrow and edit this reply but that just creates a new or modified reply. It won't change what you read yesterday and what you read yesterday doesn't prevent me from changing the reply tomorrow.
But if you can travel to the past, the future and the past are the same. Or, to put it more clearly, if someone came from the future, does that mean your future is now set, meaning you can't do anything other than what future guy knows you do?
@@QBCPerdition That would be another point where the universe would prevent such a paradox. Maybe by preventing you from even being able to do anything that would yield that result. Perhaps only big consequential things are set in stone and smaller individual things are governed by free will and can be changed so long as it doesn't create paradoxes/contradiction. Maybe a time traveler carries with them a pocket of their own time that also prevents them from even interacting with the past in any way that would cause issues. Maybe time travel is restrictive on an individual level and based on where and when you're trying to go.
As far as I'm aware, the arrow of time is defined by increasing entropy.
Time doesn't exist, like you I also don't understand itsproperties
I like the initial unintended paradox of buying one of the rings that you can exchange for resizing twice in a lifetime
??
Give us more videos of Simon being forced to talk more about Lord of the Rings 😂
When I was younger the paradoxical question that every single person knew was "If a tree falls in the forest and theres no one around to hear it, does it make a sound?" Its so weird that it was so universal as a question that cant be answered because even in youth many were able to confidently answer "No". Was that an American thing or was it everywhere
The first paradox is beautifully illustrated by Douglas Adams. A poet writes the most wonderful cycle of poems, called The Songs of the Long Land. Much later a correcting-fluid manufacturer sends a representative back in time to meet the poet and convince him to make a few mistakes - correcting them appropriately. The manufacturer then brings the poet forward in time so that they can put him on chat shows and tell everyone how brilliant the correcting-fluid is BUT he is so busy that he never gets round to writing the poems. No problem, they just send him back again with a copy of his poems (and some correcting fluid) and get him to copy his poems onto some leaves so that they can exist.
Once 50 percent is replaced, it's less original then replaced.
As soon as a single piece is replaced it is no longer exactly the same ship.
Legally it is the keel
@@rogerturner6377 that isn't the question, and then when you put furniture in a house it wouldn't be the same house.
Free will is a great topic I love to think about. I lean to the 'no free will' camp and that every action, thought is the result of a definable process (even if we are unable to do so ourselves). I personally dont think its a depressing thing as some do, and doesnt mean you can just sit back and let fate take the wheel (unless that was your fate). For this atheist, its probably the closest I can come to some sort of 'peace' with the world, knowing that even in failure, I did my best and that was the best I could have possibly done. Its hard to say how i think about it properly but yeah, I just find it comforting that none of us really are in 'control', in the purest sense
How did you do your best, if you had no free will?
Did you then also do your worst?
@@johnarcher9480 not believing in free will is not the same as giving up
@@BasicStealthcamping
If there is no free will, how would you give up? Or, how would you choose not to give up?
Or is it determined that you won’t give up, knowing that it isn’t up to you to give up or not?
@@johnarcher9480 dunno
we are a bunch of chemicals. they determine our mental and physical state. we are basically just a lab tube
#1 & 5: Paradoxons 1 & 5 only arise when we assume time travel is possible. I like Terry Pratchett's take on the grandfather paradox: When a group of wizards are projected back to the very distant past in "The last Continent", one of them cautions the others not to tread on any worms. These might be distant ancestors so they could stomp themselves out of existence. The counterargument goes: we exist, and HAVE BEEN here in the past, so whichever worms we tread on were not our ancestors.
#2: seems like an issue that mathematicians need to worry about, but which appears absurd when applied to a real-world situation. What I find more baffling about infinity is this: I cannot imagine an infinite universe. However, when I imagine a finite one, the question what is outside of it immediately arises. So apparently I am also unable to imagine a universe that is not infinite. Maybe there is just something wrong with my imagination.
# 3: I work in restoration, mainly historic buildings. We keep rather meticulous records about which parts have been worked over or replaced. I also have owned a motorcycle for 25 years that is following the path of Theseus' ship. In my opinion, they are what they are, old things parts of which have been replaced over time. The paradox only arises when we are pressed for a definition whether the thing as a whole is the original. When we understand the history of the replacement, the fact that two "originals" exist is no longer paradoxical.
As to #2, it's not just mathematicians, but laypeople in general. Perhaps thinking about it like this would make more sense, there are an infinite amount of numbers between the numbers 0 and 1 (or 1 and 2, 2 and 3, and so on). This is because you can add an infinite amount of 0's after the decimal and still have an actuial number.
Sounds like Terry Pratchett's solution is literally Novikov's self-consistency principle.
I love that you went from talking about Somewhere in Time to then talking about the Grand Hotel (which is where Somewhere in Time was filmed (on Mackinac Island, Michigan)
If you ever get turned away from a hotel, the problem is not that the hotel is full, but that it is full and FINITE
Also strange is, if you add an infinite amount of new guests to the infinite hotel, by moving the infinite amount of current guests to a room with an even number and putting the new guests in the rooms with the odd numbers, you still don't end up with more guests in your hotel than you had before. Double of infinite is infinite.
It isn't just adding though. There are an infinite number of integers. Between each consecutive pair of integers is an infinite number of rational numbers. So the total number of rational numbers is, infinity × infinity.
However, rational numbers can be paired 1 for 1 with the integers, so there are the same number of rational numbers as integers.
That is, there is 1 rational number for each integer, but also an infinite number of rational numbers for each integer.
Infinity paradoxes may be interesting from a mathematical perspective but to me they are really no different from time travel paradoxes or asking if Han Solo could beat up Indiana Jones. There can never be an infinite number of anything because the universe is not infinite.
Thanks for reminding me the time i enrolled to a seemingly uninteresting math course at uni and learnt about infinite and the many different type of infinites (i’d say there might be an infinite variations of infinites). Did you also know that in math when you run out of the cyrill alphabet, then you use up all capitals and lower cases in the greek alphabet, then you start using the hebrew?
When I was a teenager, I wrote a short story about a depressed time traveler at a bar. The way time travel worked in this story had no paradoxes.
I figured out at a pretty young age that, in general, the universe doesn't give a damn what i tis we're doing. This was reflected in this story.
The time traveler was depressed because his time machine was locked to go forward and back in time a set amount of time, so as time moved forward for him, so to did is returning time. The time traveler had gone back in time in order to save the world, and he had succeeded, only when he went back to his own time, nothing had changed, his time was still in ruins. He didn't have the means to build another time machine.
The reason, in the story, that he didn't see a change is because his change moved forward in time, rippling out against all objects he affected, at a rate of one second per second, so he wasn't going to be able to see the effects of his going back in time to save the future because he wasn't going to live for two hundred years.
So, if this story had a person who invented a time machine to go back and kill his grandfather, this would happen exactly once. The other "paradox" of an author being inspired by their own work would only hold true for subsequent "loops" of time and the "first timeline" to have ever happened would have the author creating a true original piece of art.
Interesting stuff.
I've always felt that 'the Ship Of Theseus' is more a philosophical question than anything else. Worth noting that, as I understand it, under maritime law, such a ship is in all respects, considered to be the SAME ship. Although I have no idea what status a ship made out of the discarded bits would have under maritime law..
Unseaworthy?
@@johnbishop5316 Possibly. Not necessarily though.
Probably would be considered a new ship built out of old parts.
The ship: the first replacement part interacted and served its purpose alongside all the remaining original parts. Each part replaced shared its purpose with some of the original parts until the very last original part was replaced. Even then, the very first parts ever replaced were present during the majority of the ships integrity and by bridging that generational gap by being a part of the overlap between the past and the present is enough to consider the very last replacement part as original as the first generation of parts via shared experience.
Interesting perspective Matthew. Well thought out....
@@logotrikes Thank you. I would also like to point out that the ship only exists as an idea any way, in reality it is just wood assembled in a manner as to allow it to float. It is the intention that exists as a real tangible thing when we call it a ship. But, one rogue wave and it becomes just some pieces of wood. At that point, the ship itself shares the same inevitable fate as its replaced parts, no matter how it got there. In that sense, it is the same ship because the ship is only a concept based on our definition which is based off a loose understanding of what matter really is. A ship loose in the wind and subject to the forces of nature is not engaged in the act of sailing. It doesn’t matter to anything not even the ship, what the ship actually is intended for. But when a sailor recognizes the concept of the ship, they use it to sail. The ship doesn’t sail. The sailor sails using a representation of a concept to carry out an idea. It is the intent which makes things what they are. And if the intent of the replacement parts is to be that ship, than that is what it is. Until it is not. And even then at the end of it all, all it ever was to the universe was a pile of wood.
Excellent video, I enjoy mathematical problems and Paradox is one that truly Bends the Mind.
Somewhere in time, such a great and terribly sad, poignant movie.
I saw it as a hard little 14 year old and was blinking tears away.
Haha.
Poor Chris Reeves.
One of my favorite paradoxes, and one that I actually think about quite often, is Zeno's Dichotomy Paradox; the more famous one goes like this: suppose someone wished to walk from one end of a street to another; before they can get there, they must traverse half the distance, but before they can traverse that half, they must traverse halfway to half, or a quarter; but before that, still halfway (e.g., an eighth) and into infinity, leading to the conclusion that it is impossible to go anywhere at anytime ever because to go somewhere, one must traverse an infinite number of tasks (going halfway), which is impossible, and yet it clearly is possible since to overcome the paradox, one need only take a single step.
simple solution like all paradoxes: the definition of the problem is semantic bs. it compares apples to oranges. half a task is not a real definition of an action, so comparing that to a real step is the mistake.
This is not a paradox because you are shrinking time while shrinking distance. If you instead want to tiptoe ever smaller toward infinitely small steps, go ahead, but leave us out of it because you will never accomplish it.
@@sshreddderr9409 I'm not sure where the false equivalency comes in per se, since Zeno does not argue that one must take half a step to take a step, so he is not comparing a theoretical half take to a "real" action. One demonstrates the impracticality of the paradox by moving, which has become a theoretical impossibility, but that does not, in itself, overcome the very real mathematical issue proposed by Zeno.
@@CaribbeanMischief And that is precisely the paradox: because one must accomplish an infinite number of steps to complete any action, any action is theoretically impossible.
@@jackturner214its because a step is a real action, while "half a step" is a theoretical , abstract and recursive mathematical definition of a certain length. as soon as you define the step as a step with a real, meaning non recursive length no matter how small, meaning there is no recursive reference being used, the paradox goes away cause now you are comparing real actions cause you are talking about real steps.
its a semantic error to treat an abstract concept like a real thing. recursion is in itself an abstract concept, so as soon as you say "half of anything" you are talking about a concept, not the actual thing with half the length. if you were to replace the word half with the length of that half, the paradox would never be created, because then its not a concept, its a real step you are talking about. no matter how much you divide, the moment you mention a concrete length, there is a concrete answer of how many steps it takes to cross the street, because in order to talk about a real step and not a concept, you have to give it a finite length, no a conceptual one.
My favorite time travel story mechanic is Harry Potter and the Prisoner of Azkaban. They traveled to the past and made changes, and then find out later that the older versions of themselves making the changes were already part of the timeline when their younger selves went through that period the first time.
It's a weird combination of being able to change things, but also not. They couldn't actually change the past, but it's because their changes were already part of the past they were trying to change, and their past happened the way it did because of their future time travel to make the changes they already lived through happen.
Prove to me you cant change the past. We have THEORIES about not changing the past. Until it is tried and failed your wrong.
@@kennethquinnies6023 it's literally a part of the story that you can't change the past. That's one of the things that made it one of my favorite time travel stories.
Do you realize I'm talking about a book, right?
Love the Somewhere In Time reference, I hardly ever find people who have heard of it.
i LOVE these types of video, although, they do make my head spin...
for the ship of Thesius, once you replace one plank its now "the repaired ship of Thesius". Once all planks are replaced its now "the replica ship of Thesius". And the "ship" built with the decayed parts is now "the dust heap that once was the ship of Thesius"
It's a question of definitions. In this case 'the ship of Theseus' can be defined as an artefact capable of performing the functions we associate with the word 'ship' and which is owned by a person called Theseus. If at every stage of its repair the artefact continues to satisfy these criteria it can reasonably be called 'the ship of Theseus'. That its original components have all been replaced is neither here nor there.
@richardfurness7556 okay... and? My explanation still stands true to your caveat
It all depends on subjective definitions on what constitutes "the ship" and "of Theseus". No single piece of matter ever exists in a stable state of being. If any subatomic particle in all the pieces of matter that were utilized for the construction of the object that was defined as the ship changes any of its properties - is that object now also changed? If yes, then Theseus never had one single ship - he had an infinitely large amount of ships, one morphing into the next in rapid succession. If no, then at what level of organization of matter does change become significant, if ever, and why?
As for "of Theseus" part - does it relate to the presence of Theseus on the ship, and with his departure from it no longer being so? His ownership of the ship, ceased upon transfer of deed or his passing? His former presence on or ownership of the ship, regardless of the current state thereof? Etc.
All of the above cannot be defined objectively, since it is all a conceptualization of an idea, which can mean different things to different people, depending on what they perceive to be true or significant.
I.e. the object might change, while the idea of the object, or perception of the object might stay the same.
Veritasium's video on infinities had a really in depth explanation of Hilbert's Hotel with really helpful visuals. A great watch for anyone whose interest was piqued by Simon's summary.
It's a flawed Paradox though. They specifically state every room is occupied. So they can't just shift someone up, or even try the "double the rooms" because they will all already be occupied by the rules they set forth in the paradox, meaning you cannot ever wind up with an empty room in the first place
@@justinlast2lastharder749
Just get everyone to move out of their room into the hallway at once, and simultaneously move forward towards the next room.
@@justinlast2lastharder749this video's thumbnail was made for you.
@@justinlast2lastharder749was looking for this thread. You are correct, but you be even more correct to say it's not even a paradox at all.
If you say you have infinite number of rooms, then it can never be full. Simple as that. By saying it's full, then it's not infinite.
Time travel to the past is impossible because time is just relative states of existence between things. To travel into the past, all things relative to the traveler would need their actions and physical forces to exactly reverse. That means all things relative - even down to the spin and wobble of sub-atomic particles.
Travel to the future, however, happens all the, uh, time. Whatever you move relatively to at a faster velocity, you move forward more slowly in time. We just don’t notice it because we all move relatively at about the same velocities to each other. If you hopped in a near-light-speed starship, you’d return to everyone on earth being much older.
Perfect example of the Bootstrap Paradox is the 1980 movie Somewhere in Time.
Shortly after I wrote that comment Somewhere in Time is mentioned in the video :)
Best way to describe Somewhere in Time is The Terminator without the killer robot :)
The Theseus' Ship paradox is one that is very often found in the more mundane field of modern music. There are bands such as Renaissance Fair and Tangerine Dream, for which currently not a single member is an original member. Many people feel that the band is essentially the same as long as the founding member is still involved, but in these two cases, even that is not so (because they are all dead). So when do they cease being the band that they were and become something that cannot be said to be the same band? • But in that section, I think that the comparison with cells in our body is not an adequate analogy. In the ship version, every piece of the boat was placed by something external to the vessel. When it comes to cells, they are not replaced by something external: the cells will typically divide, and the healthier part survives and the older part will die off and be either rejected or reabsorbed. So the new cell is not so much 'replacing' the old cell in the same way. It is a bit of an equivocation fallacy. • Lastly, I have always felt that time travel backwards is impossible, but for a reason that I have not heard anyone else use. The universe has a fixed amount of matter and energy at any one time. If we were to back in time, say a hundred years, what would that universe be made of? Matter and energy? But what matter and energy? All of the matter and energy in the universe is already taken up by, and dedicated to, the universe of the present. By our going back in time, this does not mean that the entire universe that we left has suddenly disappeared, as was every moment, and therefore every universe, in between. To go back in time physically would necessitate that every moment in time has its own universal quantity of mass and energy, so that no matter what time we went back to, there was sufficient there for such a universe materially to exist.
Fascinating insights!
In a discussion with my brother and dad, my dad and I gave the "conservation of matter and energy" as a reason for why time travel is not possible. My brother's response was great. He asked what about if there is equivalent exchange? It is a simple solution to that one problem but it hadn't crossed my mind at the time.
Dealing with the Lottery paradox: My favorite saying about the lottery is "Someone will win, but it won't be you." I did just realize that there is another paradox around the lottery, too. The more people playing, the lower your chance of winning, but also the higher chance that SOMEONE will pick the right numbers and win.
Why does the number of people affect your chances of winning? Your numbers are either drawn or not, irrespective of who else is playing
@@madams989 the more people picking numbers, the higher the chance of any set of random numbers having been picked by someone.
The hotel one supposedly has some complications around the difference between "countable" and "uncountable" infinities. The Ship of Theseus, when constrained to an actual ship instead of being metaphorical, depends on the model of ship: for some designs it is practically (if not actually) impossible to change the keel without effectively disassembling the entire ship; so some consider the keel the "soul" of the ship, and for them if you're changing the keel it's no longer the same ship, even if you decide to give it the same name after reassembling it.
"the ship" is an illusion. There are simply two ships in one place. One new copy ship being built while the other original is being disassembled
Mentally seperate them in space and there's no paradox. The paradox only appears because the two processes occupy one space and is referred to as "the ship".
"You built your time machine because of Emma's death. Had she lived, it never would have existed. So how could you use your Time Machine to save her? You are the inescapable result of your own tragedy, just as I am the inescapable result... of you." - Uber Morlock, "The Time Machine" (2002)
I’ve got a paradox I’ve thought about. 360* vision. Not like on Google maps, but TRUE 360* vision. Being able to see in all directions around you at the same time. I think that’s something no human can truly wrap their head around.
A question! Aren't most of these paradoxes primarily word games? Or to put that in a more precise way, play with the conceptual forms that words create, and the contradictions that can develop when one conceptual form comes into conflict with another. Example: every one of the infinite rooms is occupied is a concept, and double the room numbers, and all of the odd numbered rooms will therefore be open is another concept--but in reality, a concept that obviously CONFLICTS with the first principle, that all of the infinite rooms are occupied. If we return to the first principle, doubling the room numbers or shifting occupants WON'T solve the problem, as that principle states that all of the infinite rooms are occupied. So all that we're really doing in this "paradox" is creating two conflicting conceptual entities, which each seems plausible, but can't cooexist. Or to put that another way, part of our mind assumes that doubling infinity must make it MORE than just infinity (the concept that doubling must increase a number twofold), conflicting with the concept that infinity can never be more than infinity. That's the essence of the paradox. In other words, ithe paradox is purely conceptual, not in the world itself. The ship of Theseus is similar: a conflict between two coexisting concepts of identity, one that says that identity means that something is always the same thing, regardless of changes to it, while the other that says that something must be unchanged to retain its identity. This is the paradox of aging. Am I still the same "UTGFY" at 50 that I was at 20? My name says that I still telling UT to GFY, but I'm obviously not the same UTGFY that signed up for an account under that name. There are even different religious traditions based around these two concepts of identity: the Christian, which says that you are you regardless of age etc. and will be judged as a unity after death, and the Buddhist (especially Zen) which says that there is no you except that fleeting you of the moment, which will is always passing on. But these are paradoxes of coneptual forms, not of the world (where things don't have names and identities--it's us that supply them.)
The ship one reminds me of Only Fools and Horses with Triggers broom 😂😂😂
It’s not about cell replacement, since all our “new” cells are products of the division of our old cells; it’s about atomic/molecular replacement.
The Ship of Theseus isn’t actually a paradox because the identity of the ship is a mental construction, not the ship itself.
The reason lottery prizes get so high, is because there isn't always a winning number. And, sometimes multiple people split it, because multiple people choose the same numbers.
I always thought of catch-22 as pretty perfect paradox. A pilot in war finds a rule that says he can go home if deemed crazy. He tries to convince the doctor that hes crazy but the doctor cannot diagnose him as crazy because he wants out of the military which is not crazy
I believe time travel works like it did in end game. When you travel back in time, or forward in time, you're creating a new timeline but your past is still your past.
The ship becomes a "new ship" at whatever percentage you believe is reasonable, or upon which a consensus is formed by relevant parties. The "rebuilt" ship is the original ship if it contains either the entirety of the original parts, or the percentage of which that had been settled on.
Personally, my Ship of Theseus grants any new parts a title of being part of the Ship and so the Ship is always the Ship, no matter how many parts are eventually replaced, they are greeted into the Ship parts family 😊
My first philosophical thought was when i contemplated the concept of infinity. I was 4. The thought of an eternal existence frightened me.
The reason the hotel paradox doesn't work is because an infinite amount of rooms and guests means an infinite number of guests who refuse to move without a view/upgrade/compensation, infinite rooms with maintenance issues/bedbugs and an infinite number of guests who unfortunately did not wake up and the infinite number of paramedics will inevitably block the corridor.
I use the idea (not one that I came up with, but I don’t remember who did), that IF time travel were possible, we would have met people from the future. The main argument against that is “how do you know we haven’t?”.
I suggest that as technology improves, time travel would become more and more frequent. And as that is all in the future. People from the pinnacle of time travel, when it was cheap and easy, as it has been around for a long time and been perfected, SOMEONE would show others in a way that wouldn’t make them look crazy.
Assuming there's only one timeline, the first paradox is a good example of why time travel to the past is impossible. Your present self didn't exist in the past, therefore you can't be in the past because you can't be somewhere where you don't exist.
So the ship of Theseus is the eloquent version of Trigger’s broom
My first thought as well
You forgot my favorite paradox of all! Philip J Fry being his own grandfather.
Another solution to the Grandfather Paradox is, the you that unalived him is no more, but a different you is born. But we then bump into a Ship of Theseus.
Something I heard Neil DeGrasse Tyson mention once that stuck with me is that to travel back in time, we'd also have to travel back in time and space...and not just to the exact same time of year. We are orbiting the sun, which is orbiting the center of the galaxy, which is moving through the expanded universe. The Earth in never in the same place twice and certainly not even close to where is was hundreds or thousands of years ago. If we simply went back in time we would almost certainly be deposited into empty space nowhere near anything at all, let alone a habitable planet or Earth. While I never truly thought travelling back in time was even theoretically possible, that just truly confirmed it in my mind. (Travelling forward in time is theoretically possible due to time dilation, but you could never go back)
With regards to time travel. Everything that happened stays happened...also, the many worlds theory as explained here only applies to the quantum realm, where particles exist as waves of probability. They eventually collapse into all probabilities along the wave function, each happening in their own universe.
The bootstrap paradox comes up in the Terminator films. Nobody actually invents the tech they use. After the first Terminator is crushed at the end of the first film, the bits are given to Miles Dyson who basically reverse engineers the chips that came back in time to invent the chips that would eventually come back in time. Nobody ever builds one from scratch for the first time.
About that hotel paradox.
To confuse even more, it can fit an infinite number of busses and each one with an infinite number of guests.
But if there's only 1 bus with an infinite number of guests whose names are the combinations of 1 and 0 (so infinite combinations), suddenly it can't fit all the guests, because we can name 1 guest who won't get here.
If we write the guest on the list, even tho it's an infinite number of combinations, there's a combination that isn't on the list.
Just take the 1st digit from the 1st guest and change it (1 to 0 or 0 to 1), then take the 2nd digit from the 2nd guest and change it too.
And 3rd digit from 3rd guest, we can do this infinitely.
Doing that, we're writing a number which has at least 1 digit different from everyone from the list meaning that this number is different from every number from the list making.
And if it is different from any number from the list, then that does mean it's not on the list.
So the hotel can fit an infinite number and each number with an infinite number of guests, but cannot fit an infinite number of guests when their names are made of 1 and 0.
That's the best example for me of how much we don't understand the infinity, something that logically shouldn't be true is true
a paradox is what a guy with two boats need
In the Infinity Hotel Paradox, if every hotel room is taken, how would occupants be able to move “to the next room”? Wouldn’t that be a paradox in and of itself?
The lottery one isn’t really a paradox. It is both correct to assume that any individual ticket won’t win and know that a single ticket will win, which isn’t paradoxical in the slightest
My favorite version of "The ship of theseus" comes from John Dies in the End. The main character chops a dudes head off with an axe, breaking the handle in the process. He replaces the handle and, a few months later, breaks the head of the axe and then replaces it. In the meantime, the decapitated dude gets ressurected and seeks revenge. When he burst into the house, the main character is holding his axe. Decapitated dude says "Thats the axe that cut off my head." Was he right?
As a child, my father explained me, what Infinitiv is, this way :
Take all mointains of the world, stack them, and every morning comes a Sparrow and sharpens its beak. When the mointains are gone. . .thats infinity .. .
My example of the Bootstrap paradox is the first 3 Terminator films. Terminator 3 tried to remove the paradox created in the first Terminator film. In T2, the Terminators/Skynet were being created by Cyberdyne based on the remains of the Terminator in the first film. In Terminator 3, the natural creation of Skynet happened based on a military program. Thus restoring the original creation of Skynet. (At least that's how I see it.)
This first paradox was used in second season of Loki. Where Kang was inspired by book writen by guy inspired by work of Kang. Work that he made based on that book.
Bootstrap's simple if you allow for many worlds interpretation, object would originate in the normal way from your own timeline, whereas the paradox only occurs in a branch that you create.
The Ship of Theseus is only a problem because Two Ships occupy One Space.
What's happening is a copy of the original is slowly being built while the original is slowly being taken apart. BUT if we separate the two entities suddenly there's no problem.
Theseus's ship is kind of oddly satisfying rather than mind bogglingly weird 😂😂
Another good one is, how many band members can you replace before it’s a different band.
"This old broom has had 17 new heads and 14 new handles in its time"
The ship of Theseus: when a new part was added it became a part of the ship. The pieces are no longer NOT the ship of Theseus. Even when the last original piece is replaced it will be the same ship. Because we, as living organisms, ARE always who we are no matter how many new cells replace the old ones.
In an infinite space you already simultaneously inhabit all positions in that space and no positions.
I think all the time machine paradoxes forget that time machines don't and can't exist