9 Mind-Bending Paradoxes
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- Опубліковано 31 лип 2024
- No list of paradoxes would be complete without the liars paradox and the Ship of Theseus. But what about Hilbert's paradox of the Grand Hotel, or the sorites paradox? Erin breaks down 9 mind-melting paradoxes in this episode of The List Show, from visual tricks to irresolvable thought experiments.
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I attempted to create a paradox one year when I made, as my only new years resolution, the commitment to break my new years resolution- and thus by keeping my resolution I was breaking it, and by breaking my resolution I was keeping it, all at the same time
That’s really awesome, I love it! And you didn’t just attempt to create a paradox, you succeeded!👍
I've done that it's the only time I've ever kept it hahaha
Sounds like a fancy form to the Liar's Paradox
If there was a box that contained absolutely everything in the universe, would it contain itself? Now there's a noodle-scratcher.
I can't take credit for it though. I forget the source. But the way it's usually stated is "does a set of all sets contain itself?" But I find using the box analogy is much more relatable, and fun to consider. It also makes me want to try making a program in some language, or maybe several to see how each handles it where I take an array (list of variables) made of other arrays, would I be able to include itself?
But you can make all sorts of paradoxes in programming. Usually the people who made the compilers already thought of it and prevent you doing anything like that. Cuz usually it'll just crash the program or freeze things up. I don't want to assume you know about programming in case I go over your head here. So forgive me if this is painfully simplistic.
But one example is an infinite loop where I would tell the program to say "add 1 + 1" and then tell it to do it again, but do nothing to stop it from going back and doing it again and again and again for all eternity (ideally). But usually the program would just freeze as it's stuck doing these infinite calculations as quickly as it can without ever stopping. Which is where the pause/break key was invented. You used to press that button to stop a program that was going haywire like that.
So yeah, sorry this turned into such a long reply. But hopefully it was interesting and I didn't make anything too painfully simplistic. Like I said, I didn't want to assume you knew something about programming and then say a bunch of stuff that goes over your head and then you end up feeling dumb or something. You never know. And I just want to share interesting things that I enjoy with others. So that's all my goal is here. I hope I at least accomplished that to some degree. If not with you, then perhaps someone else.
@@VoidHalo you’re breaking my brain but I love ya for it👍
The UA-cam paradox. I wasted the day watching UA-cam. But I learned something, so I didn't waste the day. But since I didn't get anything done, I did waste the day. Thus, I both wasted and didn't waste the day.
I can see the pain behind your eyes as you recant these paradoxes. You did a great service, Erin.
If you always expect the unexpected than there will be nothing unexpected to expect
The Triggers broom reference surprised me, I didn't think may outside of the UK and of a certain age would get that. :)
Same here! Made my day
yeah when she first brought up that topic I was thinking "oh like triggers broom", was genuinely shocked when she said it
Love that Only Fools is referenced in philosophy!
@@julietlundie 🤣❤
I know! I was so happy! I've always preferred refering to it as Trigger's Broom, because the explanation is more pithy than that of Theseus's Ship.
"This sentence is false."
The way out of this is to acknowledge a third state: that a statement may be simply incoherent or meaningless. The statement, "this sentence is flfjdisogh," cannot be said to be properly true or false because, "flfjdisogh," is just a collection of random letters and does not refer to any real object or concept, so nothing can either properly be or not be it.
Similarly, a sentence that proclaims itself to be false doesn't refer to any real concept. The individual words all have meaning in this case, but their arrangement doesn't illuminate anything that actually exists in matter or thought.
A statement is a sentence that is either true or false, so you have to say "this sentence is false", since "this statement is false" isn't actually a statement :D
I like the "heap of sand" paradox because it calls into question what we would consider "firm" definitions and the implications of them. For example, say we have twins born an hour apart. One at 11:30 pm and one at 12:30 am the next day. Fast forward almost 21 years (in the US) the elder twin could have a beer at 12:00 am of his birthday even though they won't be 21 for 11 1/2 more hours. Meanwhile the younger twin can't have any even after an hour when the elder twin had their first beer. That twin would have to wait a day and only be "under age" by half an hour at midnight. That doesn't seem fair, does it. But the law has to be applied equally to everyone to be fair, yet in this case it's being unfair.
If the first twin is born on a train at 12:30 AM and the train changes time zones to where it's 11:30 PM the day before, the second born twin could start drinking first.
The heap of sand paradox is not a paradox either. Just a semantics augment over the definition of terms. If you take a heap to mean the number of objects that it takes in a pile for the units in that pile to seek the angle of self-repose then when the number of units goes below this threshold it is no longer a heap. Come up with another definition and you will have a different trigger point for inclusion/exclusion from that definition. if a heap is defined as a heap, then "one heap" is a heap and "0 heaps" belongs in the group of "not a heap".
Didn't captain Kirk burn out a couple of androids with the "Everything I say is a lie" paradox?
The problem is that "every thing I say is true" is not the only other possibility. It's possible that they only lie sometimes, and that was one of those times.
Spock's was better.
Erin is a great presenter. She's like the genius little sister who has studied everything, can explain it so we can understand it, and enunciates well enough so that even grandpa can hear her. How can you not love Erin?
I find her strangely attractive.
Idk if it's really worth staying in the Grand Hotel if every time someone new comes to stay I have to move rooms again.
Most philosophical paradoxes are just curiosities of human language and concepts that rest of a person's subjective perspective. They aren't an intrinsic part of reality.
This was a fun one, thanks Erin!
If time travel were possible at all our world would be totally screwed up.
Never mind.
Assuming there is only one world.
in that case, time travel definitely exists and is confirmed.
The hotel rooms paradox sounds like the inspiration for pyramid schemes.
My brain just melted. Thanks! LOL
I am sad to see that the tree paradox is not on this list.
You have probably heard of it.
"If a tree falls in an alone forest, does it still make a sound?"
I remember when I was little, my friend said this was how we could know whether time travel would become possible in our lifetime: if so, we could come back and tell ourselves. And we didn’t. I was like truuue
Big Bang Theory did the same joke. The Roommate Agreement said that if either of the two main characters discovers time travel then they will appear at that very moment. Both leads look around. Darn.
I remember someone jokingly using The Grand Hotel paradox to free Sisyphus of his eternal torment. Essentially, Sisyphus asks that, if all the rooms in the hotel are technically an Alph 0 set, then everything in Alph 1 must be vacant. He checks himself into the first room in the Alph 1 floor and immediately ceases to exist as they are, by definition, empty.
Thanks Erin! My melted too brain 😂
Makes me wonder why "Doxe's" always come in pairs ;-) Keep up the good work, always fun & informative.
My favorite is the Barber Paradox or otherwise as Russell's Paradox. As it goes, "The barber shaves everyone who does not shave themselves. Who shaves the barber?"
Barbar from the next town over.
If Pinocchio says “My nose is about to grow”😐
I don’t think the Pinocchio paradox is actually a paradox. The nose doesn’t grow based on what happens, it grows based on if Pinocchio was lying. If he believed his nose would grow when he said it, it’s not a lie, even if it doesn’t. Being wrong and lying are different things.
Agreed, an inaccurate prediction is not a lie.
I think with the time travel thing, I believe if you exist and go back in time, that is a new timeline. You still exist as a being made of matter in the universe.
That depends on the assumption that branching timelines is a possibility. What if only matter can branch into multiple realities based on quantum possibilities, but not time?
I always remember Delaware for being the least memorable state. Also, I’m slightly disappointed but not very surprised to learn that I was not the first stoner to think of “This is a false statement.”
A paradox that isn't mentioned in here is the omnipotence paradox. "Can a being with true omnipotence create an object that they cannot lift?"
I can do that. Just give me a barrel filled with pebbles and a tub of superglue (and some heavy metal montage music). Does that make me more powerful than an omnipotent being?
@@Alverant Uh, kinda sorta in a way.
The way it works is if the being is all powerful, and can create a rock he cannot lift, he's therefore not all powerful. And the inverse is also true. If he can't create a rock he cannot lift, he's not all powerful.
i feel like this video did the opposite of floss my brain like it literally put more things in my brain that need flossed
"If I told you that the last thing I said was a lie but the next thing I say will be the truth, would you believe me?"
And now I have a heap of sand in my head.
The Grand Hotel paradox is just an example of bad hotel management. Why are they moving guests?
10:11 Me too. Imagine due to such shuffling you don't have time to unpack. No, I mean you end up in say room 100k, imagine how long you had to walk to get to the lobby!
Thanks for the brain tickle! 🧠❤️👍🏼
As someone in England, it was nice to hear the Trigger's broom reference 👍🏻
That 2nd one was played out in Legend of Zelda Ocarina of Time. The song of storms. You learn in the future replay it in the past guy learns it till he teaches you it in the future. So yeah. Pretty cool.
Of course, I tend to see "bootstrap paradoxes" like that has having it's actual origin retconed out of existence due to the time shenanigans.
With Ocarina of Time as an example, I imagine there's a lost version of that game's timeline where either, that guy in the windmill, Link, or someone else just happens to compose the Song of Storms...but then Link engages in said time shenanigans and... That happened.
an immovable object and an irresistible force
Now I have to look up "countably infinite"
The Fermi Paradox is always a fun one.
It's more like a puzzle than a paradox. We could be the first civ out there.
Taking the boot strap paradox further, there's the question around whether an item involved in a bootstrap paradox "timeloop" ages/degrades.
So you're a kid, your older self comes back in time and gives you a watch. Then you grow up, go back in time and give that watch to your younger self.
Where did the watch really come from, and does it age/degrade like normal items?
(Neo) Woah... I had never considered that for when an item gets shown looping
Simply solution to that: Buy a identical watch when you are older and give that one to your younger self while keeping the old one. The question now is, after how many loops will you have a heap of watches? 😉
Mind-bending episode 😂😂😂How about another one about optic illusions?
The Epicurean Paradox is my favorite. For many reasons.
Ack! I shouldn't have started this before trying to sleep!
People in the comments trying to explain things or just getting upset.
Anyway, the novela By His Bootstraps by Robert Heinlein is a good read.
Then there's the idea of finite infinities. An infinite number of points on a finite line section.
Oof!
but this would have more points than the Hilbert Hotel has rooms (and it has been proven)
With the opening Shakespeare one. I have two answers for that one but the short answer is it's his own idea being given back to him. So it's still Shakespeare's story.
"Triggers Broom" 🤣
10:20 I think you mean "I hope your melt hasn't brained into a big pile of goop"
first i've thought time travel isn't real cause of all the damage someone could cause if they go back and make changes. but then i wondered, maybe that is happening and thats where we get all these "changes to the matrix" effects you see videos about. something gets slightly changed but some of us still remember it being the old way
My brain only melted into a pile of goop only if a pile of goop is equivalent to a heap of sand. Otherwise it has always been goop without having to melt or compile itself into a pile.
But if my brain melts, is it still my mind?
Since every cell in my body is replaced every 8 years, is it still my body?
An infinite number of buses, each carrying an infinite number of people, arrives at the Hilbert motel (which is filled). Can the hotel accommodate these new people? YES.
because THAT'S how "infinity" works, it honestly surprises me how few people get that, and ACTUALLY think its a paradox.... iall types of "infinity" are LITERALLY infinite, even if it would take longer than the age of the universe to add 1 to a number that number still "exists" as part of the set of "infinity" so no matter how many people came in at once, you would NEVER have to move people around to give them new rooms, they would just LITERALLY have to walk the length of an entire universe to get to their room.
@@stapuft So, the Hilbert Hotel "paradox" is trickier than just having guests walk the length of the hotel to get to their rooms. Countably infinite guests would need to matched with a specific number to be "counted." Constructing a way to match an infinite number of new guests to specific room numbers is part of the fun of this problem. I think the "paradox" is really about the counterintuitive nature of this problem.
@@SuperMtheory if the hotel has infinite rooms, and infinite keys, then it can only be assumed that the ledger can hold an infinite amount of names, (i mean how else could the hotelier reasonably keep track of it all?) matched to the infinite number of rooms, all youd have to do is keep track of the rooms via writing a number down, followed by a name, and then handing them the matched key. add one to the last number written to get the next one. as there are literally infinite number of countable numbers this would work until the end of time. (plus you'd never have to worry about keeping rooms clean/tidy as you would NEVER re-issue a key using this method, you wouldn't need to, as there are infinite rooms, so returned keys could just be discarded, you would ALWAYS have both an infinite number of empty rooms, and an infinite amount of filled rooms, provided a constant flow of infinite guests.)
even without the ledger, all you'd have to do is hand them a key, and at the point they have they key, they have been "matched" to that room, that's kind of how keys work. especially older hotels, which used actual keys, they had the room numbers engraved on the keys, or attached to them via a keychain.
@@SuperMtheory i mean it seems counterintuitive, and even counterproductive to have an infinite amout of empty rooms, but infinity in of itself is a counterintuitive thing, we as humans cant really comprehend it even...i mean we can try, but the concept itself is so mindbogglingly huge its almost impossible. its like the concept of "never ending" or even the concept of "nothing", like "nothing" itself, isnt "nothing", it due to how the laws of reality work, would actually posses more energy than currently exists in the entire universe, and so, "nothing" due to the energy it has, if it existed, ever, would instantly destroy itself, giving "birth" to "everything".... the concept of "infinity" is kind of similar, and throws most laws of "logic" out of the window when dealing with it, this kind of, makes, the almost "childlike logic" of just handing people new keys, while throwing away the old ones, actually work. due to "infinity" being, well, "infinite".
@@stapuft I think you will enjoy this video: ua-cam.com/video/OxGsU8oIWjY/v-deo.html
To be fair aren’t all the cells in our body replaced every so many years. Yet I am still me. I feel like the changing of a person over time thing is not a paradox as everyone and everything changes with age and experience. So every person is a different person to who they were.
When is a door not a door?!
When it's a -Jar :)
When the band breaks up.
Thanks for braining my melt 🤯
I once made a wish that my wish *wouldn't* come true, so I got my wish - or did I?🤯......
The ship of Theseus reminds me of the Wonderful one horse shay.
a lot of these are less parodoxes for me and more "ideas that some or most humans can't jive with."
My favorite is Escher’s never ending staircase.
When I was in kindergarten I made my teacher and classmates really mad. She talked about the chicken and the egg and how there's no right answer. I thought for a bit and proposed that the egg had to come first. In my mind there had to have been two creatures that genetically were Almost chickens. But not quite. Then they mated and produced an egg. The new egg now contained the DNA we would now be able to call "a chicken". Therefore the egg came first. My teacher for some reason was really angered by this reason and thus all my classmates joined in. I still stick by my theory to this day lol
It's scientifically correct, but comes across one problem. The question wasn't meant as a science question. It's a meditative one. Same with "If a tree falls in the forest, and nothing is around to hear it, does it make a sound?"
Scientifically, we understand it as yes, but without a way to measure it, we can't prove that it does. (You're looking at the core of nihilism.)
Most of these paradoxes comes from denying subjectivity.like grandfather's axe will be grandfather's axe after changing all part of grandfather's axe because u decide what is called grandfather's axe and what defines grandfather's axe.this is just exercise of what defination we give to concepts and things.
What about Hilberts hotel
@@nosuchthing8 i think problem lies in concept of infinite itself,there is many paradoxes related to infiniteness because as we don't fully try to grasp or understand it and try to regular maths that we invented to do with reguler objects like,infinite is bigger than infinite + 1 is surely bigger.but you can't just do that because you said something is infinite and now you are doing math with it like it's regular number like 1 or 2.thats my thoughts i maybe wrong please reply if you have any interesting thing to say.
@@prafulchauhan6114 yeah, I agree. Very astute comment about infinity. It's not really a number so if you treat it like one, watch out.
@@nosuchthing8 thanks.
If a person goes back in time and dies at some point before they are born, are they immortal?
The sand grains need to be heaped to be called a heap. 4 grains.
I too enjoy VSauce2
The Ship of Theseus is not a paradox. The ship was repaired with new pieces, not all at once making it the same ship. If you reassembled all the parts of the ship that were replaced, then it is a replica built with the original parts. It can't be his ship because his ship was already repaired with new pieces. That's like saying you get your arm chopped off and have a transplanted one. But then someone uses your arm to transplant another person. That person doesn't become you, and you are still you.
Separate timelines solve the time paradoxes
2:53. Every cell in your body dies and is replaced over time. Do you remain you when that has happened?
The answer to that, obviously, is yes. Therefore the Ship of Theseus that has had all its parts replaced is still the same ship.
Why would then someone try to make a new ship from all the rotten & replaced parts? That would be like trying to make a new human from dead cells. BTW, Frankenstein is the doctor, not the monster.
The crux comes down to *how do you define what something is.* If "you" is a particular collection of cells, then you now is not you before. But "you" is not defined as a collection of cells. In fact, for the most part, "you" has more to do with your brain than anything. And your brain is ultimately a structure rather than a collection of material.
If the Ship of Theseus parts were reassembled into another ship, would it still be the Ship of Theseus? No, of course not. But it's the same parts, right? Except it's a different structure.
So if you define the "Ship of Theseus" as a structure, then it is the same ship after all parts have been replaced. But, that isn't necessarily how people generally would define that specific ship. It may still be the Ship of Theseus -- but the point is, is it *the ship that Theseus sailed?* Not really.
It gets all very Alice in Wonderland White Knight's Haddock's Eyes, really.
Ever since I considered the question I've considered the "new ship" to be a completely different ship. It's like if you consider who you are now vs who you were say, 10 years ago. That person 10 years ago may have had your name, family, maybe a few other similarities, but they also would have looked different (younger), acted different, thought different, felt different, had different likes and dislikes which I'm sure you've grown out of. So on and so forth. So in my opinion at least, that person is a completely different person. As for WHEN you become that different person, as the ship of Theseus tries to define. There is no such singular moment. It's a continuum which occurs gradually over that 10 years or however long you wanna look back. Very few things in like (especially the important ones) are black and white where you can give something a specific definition. Reality just doesn't work like that. At least not this reality.
Unless...you consider the monster to effectively be the doctor's (artificially created) son. In which case, (due to being a family name) Frankenstein could refer to either of them.
@@amegenshiken Only if he registers the monster as his legal child. And I think there might be a bit of red tape with that adoption process. And it would essentially be adoption from a legal standpoint since the doctor clearly didn't physically give birth to the monster. I'll be honest though, even though I meant for this to be a silly reply, it does bring up some interesting questions.
For example, say there was a similar situation where some time in the future, a software engineer creates a sentient AI and wants to adopt it as their child. Or perhaps to protect its interests as it would no doubt be poked and prodded and treated like a lab animal more than a sentient being.
Heck, I bet it's been long enough since ET The Extra Terrestrial was a popular movie that everyone's forgotten about it. So you could probably make a movie about something like that and it'd be a best seller. lol
Dr. Frankenstein thought of his creation (the monster) as his so and therefore would have thought of him as a Frankenstein as well.
I just traveled back in time by 8 months
Mirror paradox: looking yourself everyday in the mirror. When did you get old?
There are and equally infinite number of numbers between the numerals 0 and 1, or any two consecutive numbers for that matter, as there are numbers between 0 and infinity.
If I am digging a hole how do I know when I have a whole hole and not a fraction of a hole?
Does a set of all sets contain itself? 🤔
No reference to the Song of Storms paradox in Zelda Ocarina of time?
Three men going to business trip. They need a room for the night they want to save money so they will all share one room. The hotel manager says that will be $30 for the room, so they each pitch in $10. the three men go up to the room. Well the Bell hop is collecting their bags to bring up to the room the manager remembers there was a business discount of $5 he had forgotten. So he gave the $5 to the bellhop and told him to give it to the three men. On the way up the Bell hop realizes he can't split $5 between three men so he keeps $2 gives the $3 to the men who in turn split it between themselves each getting a dollar bringing the amount each businessmen has paid to $9.
$9 x 3men = $27 + $2 from the Bellhop = 29.
There is one more Dollar on accounted for.
what happened to the missing dollar?
The 3 men pay in ones. The change is provided in ones. Easier to imagine. The 3x9 is the mistaken assumption. They didn't pay $9. They ended up with a bogus refund.
3x10= 30. 5-2=3.
I've thought a lot about the grandfather paradox and in my mind it isn't a paradox. On paper it is but realistically it is self correcting. Reply with questions and I will answer (specifics).
Time travelers went back, and got stuck, in the neanderthal time period, and having few "humans" to breed with they bred with the neanderthals and so evolution of us began.A "heap" is a quantity of something that is not countable without having to touch and or move the pieces to count further.
If time travel will be possible at any time in the future, it would be possible now. Either that, or nothing so far in history will be considered worth bothering with at whatever point in the future time travel becomes feasible. Or the future time travelers have returned to stop atrocities, that we now don't have and don't know about, and the things that we do still know about won't be considered awful enough to bother to stop.
Or they're causing the attrocities? 🤔
Wow😀👍👍
The liar's paradox is what GLaDOS used to try to kill Wheatley. (It didn't work. He was too stupid.)
OK OK made it to 9:12 Had to Stop Brain is hurting. (Calm down,Take a Min. ) OK go ahead, ( Mark my work, you will find me in a pile at my desk) Hitting Play Now!
Does a hypothetical box which contains everything in the universe contain itself?
A variation on one of the set paradoxes by russel
@@nosuchthing8 Russel! Thank you! I couldn't recall where it originated and felt bad I couldn't credit the original author of it.
The thing I find most interesting about paradoxes is that they don't exist.
The numeric ones do. They affected math, set theory, computer programming, etc.
@@nosuchthing8 Well... Not really. By "don't exist" I meant to say they are never expressed in the physical universe. Paradoxes are always contrived. Or in some cases the result of our limited understanding of the physical world. Mathematics and set theory are systems we have contrived in an attempt to understand the universe. But the universe doesn't follow our rules. Rather our rules follow the universe to varying degrees of accuracy and precision. And computers are just machines we created to help us do math. If there is a paradox in computer science, it just means we need to make a better math machine.
The rotted ship can't sail, therefore isn't a ship
It seems to me the idea of something being interesting is a matter of individual opinion. What if you find no numbers interesting? What makes something not interesting? Also what I’m a talking about?
0:54 Bawdler
In a way, reverse time travel is made possible by photography and video (including film). That may be the only way type of time travel is possible, to the past, only as an observer. I time travel to the future at a rate of 60 seconds per minute, 60 minutes per hour... Although as I get older I feel the rate of time travel is increasing.😉
Cells in our body are object to permanent replacement. But it‘s the information that makes our body and not the age or origin of the individual cells. Same for the Theseus ship. But we can argue if we should call a certain surgery a head- or body-transplantation. 😉
And when you assume, that you can only lose things you have, you also only have things that you already had but didn‘t lose. Therefore you didn‘t lose horns because you didn‘t had them. Paradox solved. 😉
Mobius strip?
Huh?
I see all of the truth type paradoxes as false dichotomies. By asking if "This statement is false" is true or false, you're using the premise that there are only two possible answers, when in fact there's a third possibility. It is neither false or true.
the bootstrap paradox is only a paradox if _you_ claim ownership and publish the book before shakespear, if you give it to him he's the auther both times, only the second time he copied from himself
All cells in the human body refresh over time, so are you yourself in any age?
But time travel is impossible, so it doesn't matter what you do in the story. You can make it up as you go along.
Is it?
Early Prediction: At least 1 will not be a Paradox, just a head scratching coincidence. Lets watch and See!
There are zero infinities…. FIGHT!
There where only 2 and half paradoxs
0.5: assuming time travel is in a singler deterministic timeline , instead of multi verse ( separate timelines , basically never really traveling time it self , but to a timeline that started later)
1: you had 4 variation of the self falsifying statement . Which is solved by treating it as a commend .
2. The hotel one is a classic
the hotel one is also illogical, as "infinity" is LITERALLY "infinite" so it would NEVER fill up, you could continuously give out new keys till the end of time, and would NEVER run out of rooms, or keys, because that's how infinity works. even if an infinite amount of customers came in at the same time, you would still NEVER run out of rooms. no moving of anyone from any room to any other needed. just give them one of your infinite keys to one of your infinite rooms, and repeat for the next person.
Ah, Dragon Ball Z time travel then.
the heap of sand is not a paradox. there is just no defined definition of "heap."
hilbert parardox sophmoric
Time travel paradoxes are tedious, everybody likes to fantasize that time travel is possible, when in reality it probably is not
I've never found The Ship of Theseus to be _that_ much of a paradox. It would obviously not be the same ship if all the planks were replaced at once, but they're not, they're replaced slowly. That's the key to the paradox, there's always an original plank somewhere on the ship, and because the new planks are directly replacing the old ones, they're being positioned exactly how the original ones were. A copy of the ship wouldn't have all the planks in the exact same positions or even the same number as the original ship. Even if you eventually replace all the planks, this is still the same ship since:
A) There's still no other Ship of Theseus out there to contend this title
B) The replacement planks are exact replacements for the original planks. Again, a copy of the ship would be built with slight differences.
C) You can trace the "lineage" of the replacement planks back to the original planks, sort of like a family tree.
Even if you you were to gather up the old planks and rebuild the ship (assuming this is even possible, since the planks are rotten) this is a copy, as it was built recently, entirely from scratch. You could even argue that since it uses rotted planks, and the original ship didn't, that it's even more of a copy.
It seems to depend on the speed of the replacement. Which is arbitrary.
The same could crop up when a person is transported star trek style. If the persons atoms are reassembled at the other end, is that the same person?
What if you copy the atoms and keep the original. Who is the real person?
The Ship of Theseus
If the old reconstructed ship is the Real Ship of Theseus, then would it not also mean that the boards of the ship are actually the trees? So there is no ship, since the original source is the true one. Just some floating trees. And if a bunch of floating trees is called a ship, then they are both the Ship of Theseus. Since it's the construct that we are naming, not the identity of the original.
One is the original, the other is what the original evolved to be, both true. If there were to be only One, then you need to thoroughly go all the way back and we are all truly just wave peaks ( particles ) of the quantum field.