the five kinds of paradox
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- Опубліковано 17 тра 2024
- a list of paradoxes, organized into five categories
00:00 - introduction
00:43 - type one: logical contradiction
07:49 - type two: normal impossible question
14:19 - type three: counterintuitive fact
26:32 - type four: math prank
33:55 - type five: one guy getting very confused, writing it down, and getting it published
38:46 - conclusion
/ hbmmaster
conlangcritic.bandcamp.com
seximal.net
/ hbmmaster
/ janmisali
all errors in this video are my own
Impossible!
And yet you uploaded it. Curious
may I have one?
Thanks for telling me.
I trust you.
If you ask Rick Astley for a DVD of the movie “Up”, he will not give it to you because he is Never Gonna Give You Up. However by not giving you Up, even though you asked for it, he is letting you down. The Astley Paradox.
This assumes that you would be legitimately distressed if you asked for a copy of the movie up from Rick Astley, and he did not give it to you, so by knowing about this paradox you have made it nearly impossible for you to act as it's inciting factor. (because any query would naturally be in jest, thus eliminating the emotional significance of the outcome) Thus we should maximize the number of people who know about the Astley paradox to prevent the universe from collapsing in on itself.
@@accountid9681 So the only way for this to be resolved is for him to desert everyone('s legitimate request for this movie). We are doomed.
@@explosu Oh no. By deserting you, he is quite literally Saying Goodbye, and Turning Around And Deserting You. In addition, ha can't lie.
@@spcxplrr but he’s still letting you down
@@accountid9681 but he can't turn around, say goodbye, and/or desert you
If I ever get a book published, I'm going to put "none of the errors in this book are mine, the editors are conspiring against me" as the preface
Solid chuckle out of me
Or better yet, "all of the errors in this book are yours"
@@jamesblackburn8110 You bought the book. That's entirely on you for believing it.
@@saxassoon l
You can put that in if you like, but that's not how it will be printed.
the "irresistable force" rephrasing of the "unstoppable force vs immovable object" paradox was made specifically for me because I thought I was so clever saying the unstoppable force would pass straight through the immovable object without moving it
I've heard that answer a bit ago. Mind blown.
How would it do that? By just phasing through it? Because if the unstoppable force had to make a hole or something, then it still had to move the immovable matter that was filling in that hole before it went through.
@@poudink5791 yes, by phasing thru it C:
@@poudink5791 Yep. "Pass through without interaction".
the actual problem is that 'unstoppable force' and 'immovable object' are fanciful statements. They're essentially infinite quantities. but also as long as entropy exists, by my understanding, nothing is unstoppable. And neither can anything be immovable! These are not rational terms. We can imagine them to exist, even write them down, but they don't, and can't. So woooo, they're paradoxical. so what.
So to simplify this, if we take a question with two mutually exclusive answers.
Type 1: Both answers must be wrong
Type 2: Either answer could be true
Type 3: The right answer looks wrong
Type 4: The wrong answer has a subtly wrong proof
Type 5: The scenario is perfectly clear but has been phrased to make it not clear
Type 6: both answers are right
@@edwardmacnab354 isnt that just
not a paradox
@@edwardmacnab354the answers being mutually exclusive means they can't both be true.
@@hazelv.a.7976 but if the premise has a subtle flaw and if you choose one it is true but if you choose the other then the other is true then they are both true depending on which you choose
Type 7: both answers are self-contained paradoxes
“You’d expect the bread to land cat side down.” Is a great line out of context.
"The universe (assuming it exists) is very large"
Another available punchline from some video (likely an ad for a product I'll never remember without looking up) is that attaching buttered toast to a cat creates a "free energy" anti-gravity dynamo that continuously attempts to turn to the "correct" side.
It's also exactly the kind of staple line I've come to expect from this channel
@@cardboardhed1967 which at least is a callback to the previously mentioned Boltzmann brain, though definitely a mice line
@@GasparLewis a
I love that I know about the preface paradox now. Like without the context of, you know, how books get written and published, I could totally see how one could assume that "all errors in this book are my own" would mean "I checked all the errors in this book and confirmed that they were mine" (rather than what it actually means, which is "I fixed all the errors that I saw, so if any still remain, that's on me"), and then think "why would the author check all those errors but not fix them?" Wild. I love it.
It's really intended to be a version of the lottery paradox but stated in slightly simpler terms. To put it a different way, if a particular page of a book has a 1% chance of containing an error, then it's rational to believe of each page that it is free from errors, but not rational to believe that every page is free of errors.
The author would also need to check that everything in the book that is not from them is not an error
So if they had an editor that could potentially have made errors then it either is a different paradox, or just a white lie.
Unless the editor highlighted every section they edited in which case the onus falls back on the author to verify that everything is correct.
@@crumble2000 oh yeah, it's all coming together
Putting a preface at the beginning of all my books that just says "The errors in this book are mine", implying I know they exist and I left them there on purpose, just to be chaotic
I love math pranks, because they're either breaking the most subtle, obsure hidden math property to allow something to be true, or are incoherent insane rants about how all horses are the same.
I enjoy the really simple ones. "There's an exception to every rule" is my favorite. There should be an exception to that statement itself, which means there's a rule out there with no exceptions. But, we know that would break the statement. Fun all around.
I love and hate this one. YEAH In order for it to be true there needs to be a rule with no exceptions, it being the exception to the rule. It only further proves the point that every rule has exceptions, including this one.
My favorite way of saying it is that the rule itself is the exception to the rule.
@@veniankween130wait, does that make it a type 3 paradox?
@@lotarion I think so. It definitely takes a moment to understand and it’s not a logical contradiction (and definitely not any other category) so I would assume so
@@veniankween130 Actually, I was thinking it over recently, Wouldn't that statement turn into a version of "this statement is false" when you plug it into its own exception?
For simpler writing, let's assume that "Every statement has an exception" = A; and that we can refer to the properties of statements like we would in OOP
If A, then A.exception == A
If A.exception == A, then A is no longer an exception
If A is no longer an exception, then A.exception doesn't exist
If A.exception doesn't exist, then A.exception == A
Ad infinitum
@@lotarion it seems it would. But also, this is only if the rule was the only exception to the rule. there could be other rules that just don’t have exceptions, those being the exception to the rule of “all rules have exceptions”. Rules like all numbers are equal to itself that are just facts of reality. This doesn’t break the rule, because exceptions don’t break rules. In this case, a rule not having an exception further proves its own point.
I love the quote “Assuming it exists, the universe is very big” 😂
we don't know that for sure. maybe the universe is just a tiny jar of neurons perceiving large universe
@@staceynainlab888 everything is relitive.
The universe is only what I can see and hear, everything else is hearsay
@@thnecromaniac indeed, even spelling is relative apparently
@@Guidus125 the word color/colour would agree, seeing as both of those spellings are both incorrect, and correct spellings in the english language, as the awnser of wich one is correct changes on who you ask.
also random fun fact, the spelling of 'color' is older then the spelling of 'colour'.
same with armor, and armour; and Aluminium, and Aluminum, though in the case of aluminum, Aluminium is older, though only by a couple years, as the one who named the element first called it Aluminium, but then he felt that was stupid, and his last desicion fell on Aluminum.
My favourite model for Schroedinger's cat is that, using a more general definition of "observe" as "have any interaction with", the cat is indeed an observer, and collapses the wavefunction, but now the state of cat + contraption is in a superposition.
When we open the box, we ourselves enter a superposition relative to anyone who has not yet observed us, with our state being either "saw a dead cat" or "saw a cat that hadn't died yet"
The only way to break an unobserved superposition is to interact with it and thus become entangled with it.
Either the box is opaque or you're part of the box's universal wavefunction.
well, thanks for the new existential terror
@@grepgrok8735Don't worry about it nothing we experience here is real any ways.
Welp, time to open the universe!
I'm too sick to understand this but I'm none the less scared
Yeah...
The "heap" of sand to me honestly depends on where it is. If it is in my swimsuit, then 1 or 1000 grains of sand and every amount in between or bigger is a heap.
"the number ninety is not rising, it is remaining constant - at ninety"
this channel always has something to teach me
"people with a lot of friends are friends with a lot of people"
[citation needed]
Not all horses are the same color because it's possible for two horses to be different colors.
I laughed way harder than I should when I heard him say that shit
@@egon3705 I have a lot of friends, but I am only a friend to like two people
Oh god the last category is such a goldmine
If you made a sequel to this just listing more "guy got confused" paradoxes I would absolutely love that
I second this
You could do an in-depth video for each type and go through another list of paradox types you mentioned.
Yes guy got confused is so much fun 2 reaseach bc then there is 2nd guy who has more info but then confuses something in their explanation which makes 1st guy more confused!
God is Love
Love is blind
Therefore God is blind
Steve Wonder is blind
Therefore Steve Wonder is God
The elevator one is my favorite for just how fucking dumb it is lol. Like, if you are on a lower floor than the elevator currently is, it can just... come down to pick you up, and then go back up lmao
Interesting thing about the ship of Thesius is that it does technically have an answer. The "keel," that long piece on the underside of the ship which serves as the sort of backbone of the vessel, is the only part of a ship that is considered irreplaceable, as to do so would require you deconstruct the entire ship, and then reconstruct it onto the new keel and even then some things might have to be built differently. Thus, the ship of Thesius is the same boat, irregardless of how many parts or crew are replaced, until the moment the keel is replaced. Only then is it considered a different ship.
but you've created a definition for a particular ship of Theseus, one where the rest of the boat must depend on the keel, in order to still be the ship of theseus
what if someone comes along and cuts off the keel, but still leaves a single plank attached to the keel? Is the keel+plank the ship of Theseus?
tell me then- would _just_ the keel count as being the ship?
if it doesn't, at what point do you stop adding new parts over the keel for it to 'become' a ship and hence be "the" ship? Until it can float? Until it can carry passengers? Until it "looks" like how the ship used to look?
A core part of something's identity still can't define it.
The actual question is 'what is a 'ship' as a discrete object? Understanding atomic theory, in the end everything is just a collection of atoms anyway, so the relative continuity of objects is an illusion to begin with. This is also true of people. Our sense of ourselves as consistently the same is a comfortable fiction. It's merely that the change is usually tiny, and we only consider an abrupt change to be meaningful. Like an entire plank of a ship being replaced, or like losing your sense of smell. But the entire notion of the ship or of you, yourself, is not what you think it is. It's not as discrete as you think, and what the Ship of Theseus actually exposes is something terrifying that people generally don't want to think about because it claws at the underlying (incorrect but useful) assumptions about reality we all share. It's best to maintain this fiction of discrete objects because it works well enough for ordinary life.
The Ship of Theseus honestly isn't that different from a sports team. The players change, the coaches change, the uniforms change, but people call it the same team. Why? It's an agreed upon fiction.
Ask yourself - what is your personal 'change threshold' where the change makes the current object too different from the original to be considered the same? And why do you use that threshold as opposed to being more or less strict about it?
ah yes, the unibody/lower receiver answer. we just decide one part that contains the inherent thingness of the thing
as the keel was invented by the vikings, it seems unlikely that any ship belonging to ancient greek theseus would have one
I love the crocodile voice so much
My favorite "one guy getting confused" paradox is the cheese paradox, similar to the temperature paradox:
Cheese has holes
The more cheese you have, the more holes you have
The more holes you have, the less cheese you have
Therefore the more cheese you have, the less cheese you have.
It's pretty obvious what the problem is, like you don't even have to rephrase it, but I still like it for the split second before you realize it doesn't make sense
It also reminds me of envelope paradox for some reason.
My favorite is the same thing but worded differently. The more net you have, the less net you have.
This isn't a paradox one finds with Provolone. IJS. #notallcheese
Its like the taxes paradox where ppl genuinly think if theu make more they make less money that gets ppl who actually work in payroll very mad
It's more like, the more cheese you have, the more not cheese you have
God I hope this categorization scheme really takes off in wider academia so we can finally have a jan Misali Wikipedia page talking about your various unhinged video topics and toki pona translations
As well as disambiguation (2017 album) and disambiguation (2017) (2022 album).
@@timothymclean
_This article is about the 2017 album by _*_jan Misali._*_ For the 2022 album, see _*_disambiguation (2017)._*_ For other uses, see _*_Disambiguation (disambiguation)._*
jan Misali is speedrunning pre-article appendices. "The title of this article is "jan Misali". Due to technical limitations..."
@@timothymclean and disambiguation (disambiguation)
At least he got a mention on the Caramelldansen page (it might have been removed though…)
Shrodinger's Cat made way more sense to me when I realized that observe in the scientific sense used for quantum particles doesn’t mean the particles know if a human is looking at them and more refers to the fact that to observe things we often have to bounce light or something else off of it, and quantum particles are small enough that photons are significant.
It's like trying to describe someone but you can only see them by throwing dodgeballs at them. Of course that's going to trigger some sort of reaction, such as collapsing the state they are in.
I hate to break it to you, but no. That's wrong.
@@samlewis6487 Can you explain how?
@@samlewis6487What? That's completely correct
Quantum physics isn't magic. There is literally no reason that because a human is observing something it changes its behavior, even if that's not how it's portrayed in media.
The description I heard is imagine trying to find a balloon in a room but you can't see and the only way you can observe it is throwing a golf ball at it. Sure if the golf ball hits a balloon it'll make the noise but by doing so it'll move it from its position.
So you're saying that "taking an observation" means exposing it to light. I don't think that explains it
Zeno's paradox is just what executive dysfunction feels like, there are infinitely many steps to the task I have to do, therefore I can't do it
Never having heard the solution to the "buttered cat paradox" spoken out loud before because, well, nobody wants to be "that guy" that ruins the joke, it honestly felt like a healing experience to hear you explain the actual answer to it after the years of hearing it retold as if it was something clever or funny.
Wdym by "joke"? It's an actual paradox
@@unfortunateness Since when are jokes and paradoxes mutually exclusive? A paradox can be a joke if it's said in a humorous tone and is meant to make people laugh.
@@arvin390 so... you struggle to identify sarcasm?
Unfortunately did he explain how? I mean I heard him give a couple ideas but they did seem kinda silly plus I'm pretty sure the cat would land On their feet. However if you were to butter 4 small pieces of bread then butter side up stick the bread to that bottom of the cats feet; Then even if you were to drop the cat, from counter height feet down, I don't think the cat would want to land on his feet. I think the cat would try and throw itself sideways it would not want to land on that bread butter. I think that is the only way they might not land on their feet.
@@unfortunateness🙄
Even if you originally meant it as sarcasm, it didn’t succeed at being funny, or even amusing. This one’s on you, bud, not the person who “missed” your bad joke.
These always remind me of the " i can turn invisible but only as long as if everyone closes their eyes and keeps them shut" thing
Crime is legal, as long as you're not caught
@@Vaaaaadim gottem
Technically, invisible just means not visible, which means nobody can see you, and if everyone has their eyes closed, they can't see you.
Wait, no. You can see yourself. At the very least you see the back of your eyelids. But that's a body part, so you can see yourself, therefore you can be seen and are not invisible.
@@tardigradesystem what if the person claiming to invisible is completely blind? But also, if the person claiming to be invisible is blind how can they be sure that everyone has closed their eyes and that their are no secret observers. They exist is a state of maybe being invisible but never certain
A really nice example of “some guy getting confused” that you didn’t mention is the barbershop paradox-not the barber paradox, but instead a situation where three barbers work at a barbershop, and one of them only ever leaves when another specific barber leaves. If the ship is open, then the “paradox” is that one specific barber can never leave. Of course, the problem is that the law of implication doesn’t work that way. Yet somehow Victorian logicians were convinced there was a contradiction here and couldn’t figure it out.
I feel like the Fermi paradox would fall under the "unknowable because it's a secret" category. Like, if there are aliens that know about earth, then they certainly know why we don't know about them.
Well, you guys do kinda know about us at this point. The American government even let that cat out of the bag to distract your people from more important issues.
Supposing, of course, that aliens do exist
but that's not necessarily true
What if there are aliens that DON'T know about Earth 🤔
4:58 A version of this story is the etymology behind the Chinese word for paradox, 矛盾, literally meaning "spear-shield". There was once this vendor who was selling spears, which he claimed could pierce any shield, and also shields, which he claimed could block any spear. Some smartass asked him what would happen if he set his own spear against his own shield.
Interestingly, the Chinese word has expanded in meaning outside of just "paradox", and could mean any "difficult problem to solve", regardless of whether it contradicts itself or not.
Same thing happened with the english word for paradox
I think this is why he put the word "objection" at 4:19, because the Ace Attorney series mentioned that exact story at one point.
well tbf, that situation is not a paradox or a difficult problem. The solution is that the vendor is lying.
@@aguyontheinternet8436 but what is the vendor suppose to say?
@@aguyontheinternet8436 Yes, that's exactly what the smartass was pointing out. In that way, he's kinda like the kid pointing out the emperor has no clothes.
I love how they sound increasingly confused at the end from reading the article
"This statement is false" cannot be proven true or false, but "jan Misali's videos are bangers" can definitely be proven true
Here we go: jan Misali's videos are bangers. Bangers are British sausages. Therefore jan Misali's videos are British sausages.
and you can provide evidence for it by finding something that isn't a banger and showing that it isn't a jan misali video
@@decare696 true but how many videos can you remove from their channel before they are no longer jan Misali?
I would say you would need to at least remove the videos before season 3 of company critic were announced because at that point he called himself conlang critic so doing that functionally means he is conlang critic.
my introduction to the idea of paradoxes as a child was my mother telling me the buttered cat situation - assuming both idioms as true and setting up a perpetual motion machine of buttered cats. She defined paradox loosely as "a thing that makes no sense if all cases are true" - and handily used the scenario to include perpetual motion machines in that definition. Good memories, great video.
I also love the ship of thesius because a lot of people in my extended family own boats and they are VERY emotionally attached to them, and they all agree that the thesius that's had all it's parts exchanged is more worthy to be 'The' ship of Thesius than the reconstructed one, because the one with the bits replaced is what they'd have been sailing on all that time, like it's kept the spirit in it. :)
In my discrete math class the professor used the "all horses are the same color" induction proof to show us an example of a faulty proof and for us to try to figure out where it went wrong, but my one classmate just kept trying to argue that all horses actually AREN'T the same color and I could see my professor losing his mind in front of me lol
Lol I imagine the guy thought he must have been losing his mind seeing how everyone suddenly started believing this weird fact. Like a dream I had once where negative numbers didn't exist, and I was trying to explain people about 7 - 9, and everyone was saying I was making stuff up.
@@pepijnstreng4643 Go back a few hundred years, there was a time when negative numbers didn't exist in math and people just re-arranged problems so the end result would be positive. Apparently it made geometry very difficult.
I mean- TECHNICALLY that classmate is right, but we cannot perceive all the infinite in-labeled colors, therefore if all horses are brown, through at least 1 set of eyes that would be confirmed true
Also, that is HILARIOUS
Every discrete math and formal logic class has a few of these people, I'd bet. Some people have a really tough time separating the real world pretense of the provided information from the representation of logic. It can make finding good premises/predidcates/statements fun and really frustrating at the same time. I was actually one of these people. Thankfully I didn't really argue too much but it took a bit for my brain to flip that switch.
@@smack007 back in grade school I got really annoyed with algebra because "how can one x have 2 values?"
The worst part of the raven paradox (19:06) is not just that a green apple is, in fact, evidence that all ravens are black -- it's that, by the same reasoning, the green apple is also _equally_ good evidence that all ravens are white!
As OJ. Simpson's new lawyer, you just made me a lot of money.
"Your Honor, as you can see, I have here a basket of green apples. Now each of these apples, indeed even the basket itself, is evidence that my client is not a murderer. By the simple fact that these apples are not my client, nor are they murderers. While this proves that things that are not my client are not murderers, it is, by the same reasoning proof of the opposite. Anything the prosecution says is heterological. I rest my case.
Is this accusation of OJ Simpson not an attempt to claim that all murderers are black? After all, my client being both black and a murderer would certainly be evidence that things that are black are murderers, however this use of the raven paradox by the prosecution neglects the simple fact that a murder does not involve ravens, but crows. Theretohence, all arguments to the contrary are heterologically perchance. I rest my case
@@aceman0000099 surely you would need objects that were murderers, because in this case the negation of “things that aren’t murderers aren’t my client”, is that the client is a murderer. So you should have a basket of evil murderous apples instead
@@chlli objection your honour, leading the witness
@@aceman0000099 your honor, please prove that OG Simpson isn’t an apple ! Because we have a case of apples assassins : Michigan 1995”
One interesting note about the Boltzmann Brain is that people often underestimate the simplicity of the universe and the complexity of the brain: it is fully possible that the full universe with all it's complexities IS simpler than a thinking thing that can exist without such a universe
also I find it hard to believe that a brain capable of hallucinating the universe could just pop into existence by itself without other brains or evolution etc
With Schrodinger's cat: the Geiger counter would count as an observer in reality. The cat in a box was more a metaphor to help explain how bizarre subatomic particles behave.
nah it was made to show how silly the idea is schrodinger hated his own discoveries
Schrödinger’s cat just raises the normal impossible question of “at what point does something stop being an observer?” more than anything.
This was my thought all along; I'm glad someone agrees. How could a human really observe a photon without interacting with it? It would have to fly into your eyeball.
@@leeroyjenkins0 Schrödinger was specifically against the idea of particles changing their stage upon observation. He made the thought experiment specifically to mock the idea, not to say that the definition of observer is imprecise. It was to just to say that the very concept of particles changing state upon observation was ridiculous when applied in a macro scale.
Though it's relatively easy to answer- there is a fault in our language, and a bit of misunderstanding. Observation at a quantum level is very, very intimate. It's an action the observer takes. At the quantum lev3l, you have to get out a metaphorical sharp stick and metaphorically poke the particle in question and listen for its exclamation of "ouch!".
The act of shining a light on something actively interacts with it, to extract information. The act of shining that light also fundamentally changes the something's properties, collapsing its superposition (if any). The machine doing the measurements is an observer, in this case.
@@ferociousfeind8538 Exactly!
@@ferociousfeind8538 very interesting, thanks
I love when Douglas Adams encountered a proper Ship of Theseus (or rather, Building of Shinto) where he was in Japan and came across a Shinto Shrine that had been around for centuries but looked brand new, and when he asked a custodian about this the custodian revealed that the building had burned down multiple times over the years but had always been rebuilt to the same designs.
When Douglas asked if it was still the same building then if it's been rebuilt over the years the custodian said that "It's always been the same building".
Douglas concluded that one of them was missing the point but was willing to concede it was him.
"The shrine has stood in this spot and been built a certain way for hundreds of years. If it stands in this spot and is built the proper way, it is the shrine."
@@android19willpwn also the shrine is just wherever the kami's renting at the moment. it's a building defined not by its construction but its function
similar to your example is the immutable fact that the ship of theseus ceased to be when the mast was replaced, as in that moment by law it required an inspection with relevant taxes paid to be a legally seaworthy vessel. the ship of theseus obviously cannot be a vessel which is not seaworthy: removing the mast irrevocably introduces a hole into the timelime before which the original may or may not exist, during and after which it does exist as it is not the ship of theseus (theseus' must always be seaworthy or it isn't his).
Well, this is also the og ship of Theseus
According to Plutarch, ship of Theseus was preserved in Athens and was on display up to some point. And Athenians of course were replacing parts that were rotting away.
Like, according to the sources it is not just thought experiment, but a thing that happened (of course the question is that is Plutarch record about it is true given he lived about 300 years after the ship got lost/destroyed/not there, according to him, and if it is true what is original origin of the ship given that Theseus was pretty much just a legendary figure)
@@boldCactuslad What if you install the replacement mast before the old mast is removed (so there's a moment where you have two masts)
5:00 I have an answer to this paradox: If the sword hits the shield, they both shatter. The sword got through the shield, but the shield blocked the sword.
"Any errors in this book are my own" in any case also accounts for the possibility that there aren't any errors. It doesn't say that there ARE any errors, it just says that if there are, they can be attributed to the author. Funnily enough, a similar phrase "All of the errors in this book are my own" causes a type one paradox if there aren't any errors in the book that aren't in the phrase itself.
"This is my Grandfathers axe, my father replaced the handle and i replaced the head"
This is my favourite Theesius ship type conundrum, it's short and to the point, it makes the statement that it was his Grandfathers axe but you can't help but question if that is true anymore.
"This is my Grandfathers axe, my father replaced the handle and i replaced the head"
this is from a pretty good book series
It's not
@@TheReZisTLust not what
@@happyman9117 Is it? I have no idea where it originally came from, can't even remember where i heard it.
@@archygrey9093 it's from "the fifth elephant" by Terry Pratchett
Tokyo Afterschool Summoner's story has lots of "swords that break any shield" and "shields that block any sword" and it solves their interactions by breaking the universe and summoning giant monsters that try and kill everyone involved. I think its a fun way to deal with that type of paradox.
The "universe gets mad and says fuck this" approach?
we love housamo
I approve of this approach
then the sword goes ahead and slices and dices them up while the shield blocks the attacks the monsters throw at them
Then the sword and the shield realized along the way that they are soulmates
Decided to crochet while watching this video and somehow managed to crochet two rows on a project where that usually takes over an hour. I might need to watch your videos while crocheting again.
Objection, when Bilbo asked what he had in his pocket he did *not* know the answer, he was speaking to himself because he felt something unexpected there. Of course, he then used his fingers to identify it as that ring he'd found, Gollum accepted the question, and the riddle game in the dark ended with an angry shrivled hobbit leaving his caves and getting tortured by Sauron.
Additionally, there is not, in fact, always one person not drinking unless everyone is drinking. The bar could be empty.
At an empty bar, everyone is drinking.
"Everyone is drinking" is equivalent to "There is no person not drinking" and at an empty bar there indeed isn't.
Most people oversimplify Occam's Razor. It doesn't say that the best explanation isn the simplest one, but that an explanation with fewer assumptions is preferred to one that has more assumptions if both have the same explanatory power. Getting to a simpler explanation by making an outlandish assumption doesn't necessarily make the simpler explanation better; many conspiracy theories work on this logic.
True. Also, many unconventional explanations that happen to be true get dismissed by the presumed implication from Occam's Razor (simpler is better, more likely to be true, etc.). Unfortunately, many of these dismissed ideas (that also happen to be true despite being unconventional) aren't vindicated until some time has passed and the person, people, population, group, etc., that initially dismissed the idea as a conspiracy theory -- well, they don't realize that their heuristic led to an incorrect conclusion. So, they continue to apply the heuristic, thinking that they must be correct and, typically, never realizing that they're putting too much confidence in a heuristic -- as if it was a rule rather than a rule of thumb. This perpetuates the practice of dismissing things simply because they're unconventional. Not a bad rule of thumb, but a terrible rule.
Occam's razor is basically to avoid unnecessary leaps in logic... basically keep it simple stupid....
@@hunnybadger442 Consider:
_"Occam's razor is not an embargo against the positing of any kind of entity, or a recommendation of the simplest theory come what may."_
If you consider this insight in light of how Occam himself used to invoke the notion (which, by the way, didn't actually originate with him; it's just that he used it so much that it has become his namesake), it becomes clear that the way many people today invoke the razor to dismiss things isn't at all the way William himself applied it.
In short: many people who invoke the razor don't actually understand it correctly; their understanding is 'contaminated' by personal interests rather than by historical accuracy.
_"Occam's razor is used to adjudicate between theories that have already passed "theoretical scrutiny" tests and are equally well-supported by evidence."_
When considered along with the previous insight, we see that *until* the theories under consideration have been scrutinized, none of them are to be preferred or rejected. It's only *after* such scrutiny occurs that Occam's razor finds relevance. To use it before qualification of each idea is to misuse it as a 'blanket dismissal'. That's not how William himself used it, and when it's used that way today, it's being invoked erroneously.
Well put Koala. I do get annoyed when people get this wrong. I do not mind too much when people just use the shorthand of this. But when they get it wrong, we get a lot of bad assumptions about the world. Turns out it is not simpler at all. Though again this has a lot to do with what people mean by simple. And so a more formal way of putting it like you did work better.
One can view it from a pragmatic perspective too and use that as an argument for using Occam's razor. If you have two models that has the same explanatory power, then using the one that use the least amount of assumptions is preferable as it is easy to use a model with less assumption. And we are all lazy here. We are pragmatists, after all. ;)
The video do put forth a good explanation for why one should actually see the world as real, even if you can not be 100% certain it is. (I mean, this sort of thinking that the world might just be an illusion is one that existed before Boltzmann's brain. Look up Descartes demon, but Plato allegory of the caves touches a little on this, as well as the concept of Maya in Hinduism. They explore it all from a different perspective. But they all question the notion of reality.)
Again, a Pragmatist view on reality is that it does not really matter. Your actions seem to have a response when you act. And those responses seem to be consistent. So even if it is just a dream (illusion, whatever) there seem to be rules in that dream world. And so act accordantly.
That first sentence, without reading the rest of the paragraph, is, an absolute mind-screw, and possibly also an example itself, or something similar.
The "some guy getting confused" examples made me laugh so hard. I normally get irrationally angry/frustrated when these kinds of things are called paradoxes, but you made it so funny. I think they won't bother me anymore. Thanks Jan Misali
**Fnaf 3 good ending music plays**
Why tf you get angry when you hear about a paradox? Is this some kind of strange kind of phobia ?
jan Misali*
@@PwerGuido -- I think they were just mad that people were calling just any confusing thing a paradox.
It's frustrating when people equate a cornerstone of logic with Dave forgetting how money works again, but calling that out as "a guy getting confused" as a separate subset of paradox from the important logical kind is nice.
I love the fact that you included things that are not paradoxes as a type of paradox, in turn creating a paradox.
Occam's Razor does NOT say that the simplest answer is usually correct, rather that it's the position that makes the fewer assumptions that is more likely to be correct. An easy oversight, but an important one.
This fact is also why the brain paradox listed is irrational, as it requires a lot more assumptions than just assuming that empirical analysis of data is reliable and therefore you exist as a physical being and your experience of reality is your brain interpreting input it receives through your sensory organs(not me trying to criticize Mitch for including it btw I just thought this was a relevant place to bring it up)
the error is not his own, the creator of the theory is conspiring against him
For anyone wondering about Zeno's Paradox: the solution from a mathematical standpoint is that the arrow completes infinitely many tasks in a finite amount of time, and that's perfectly fine, because as you subdivide the tasks, the time it takes to complete approaches 0.
Also it entirely depends on how you model the arrow. For example in a video game the arrow will go through a finite number of positions in a finite number of ticks
On the other hand, our universe could have real-valued time (and then limits, infinite sums, etc. all apply) or it could be based on some other type of numbers. It's pretty obviously not integers nor rationals - a lot of physics would be _really_ broken - but we still have surreals &co. on the other side
But the math to prove that didn't exist in Zeno's time, because calculus is hard. I'm sure Plato could have intuited the answer, but he couldn't have _proven_ it, and Plato kinda had a thing about saying things you can't prove.
Also, the paradoxes were apparently intended as proof for Parmenides of Elea's Eleatic philosophy, which among other things claimed that change and motion...I'm not sure if he was arguing that they were illusory or just that they weren't literally everything, as lots of his contemporaries did, because I'm skimming a Wikipedia article.
@@timothymclean Yeah, providing things about infinity when your conceptual framework is specialized for geometry, constructions, and next to nothing else.
No, it's not enough for the subdivisions to approach 0 time, think of the harmonic series divergence.
We need the sequence of partial sums to converge, and there are lots of conditions for this.
In this case the easiest way to show it is to already know that the 1/n^2 series converges, and 2^-n terms approach 0 way faster than 1/n^2 terms due to exponentials dominating polynomials, so the series converges way faster than the 1/n^2 series.
@@MagicGonads if I were going to be that rigorous, I'd set up an ε-δ proof or pull something from measure theory. My goal wasn't to prove it, it was to introduce the idea of super tasks to people who haven't ever used calculus.
Regarding Zeno's paradox, he came up with dozens of these things because other philosophers were making up paradoxes to troll his buddy Paramides. So Zeno was like "ok well what about this, huh? How is motion possible at all when we must first travel an infinite amount of half-steps in order to take a single step??? Bet you feel dumb now!"
Diogenes, upon hearing this, simply stood up and walked across the room.
And everyone was left speechless looking in shock saying "how did he do that?"
@@MouseGoat he then called them unwise men, hardly smarter than chickens, and kept walking out 😂
That is a very Diogenes thing to do
Diogenes straps on the heelys
Schrodinger's cat... My stance is, the detector is the observer. What is the difference between a detector that someone is looking at, and one that is unattended? The detector is itself an observer because it alters the wave function of the radium just a little.
“imagine a bar”
aw i wanted a real one
“it can be real if you want”
so considerate!
One of my favorite math pranks is the fact that .9 repeating doesn't exist, because it's just the number one.
".9 repeating doesn't exist" - This statement goes to the 5th category of paradoxes!
@@martinkunev9911 Not exactly
Part of it is basically that if you have 999999 repeating, and you add 1, it’ll become 0000 repeating
If it’s truly infinite, then the carried 1 will never resolve. So 9999 repeating plus 1 equals zero.
Same applies to .99999 repeating
I think this is what they meant
@@willowbarrelmaker8269 Wouldn't 999999 repeating + 1 = 1 followed by an infinite amount of zeros?
@@redcoder09 Yes and no. Like... I'm not an expert in this at all, but as I understand it, because that 1 goes after a literally infinite amount of zeroes, it would never actually resolve and become a number greater than zero.
Though again, this is all half-remembered stuff I learned years ago, so idk
@@willowbarrelmaker8269 First, adding one to a number consisting of infinite nines results in a one followed by infinite zeroes (the one is at the start of the number, not the end)
Second, every integer has an infinite number of zeroes before it, with no effect on its value
7:10 i just imagine the prisoner explaining all of this to the executioner as he's being led to the gallows as a reason not to be hung just to finish his explanation by triumphantly crossing his arms just to realize he's been tied in the noose and look to the camera and go "i did *NOT* expect that!"
The unexpected hanging paradox's paradox: if the prisoner has anxiety, and thus, despite of all logic, expects to be hanged every single day, they can never be actually hanged
@@fulana_de_talremember kids, it pays to be paranoid sometimes!
@@cheshirecreeper3743mr grips always said i should stay noided...
It's kinda ironic that you have a Dave strider profile picture in a video on paradoxes
@@samuel-rw3xt the five kinds of irony
You missed the "paradox" part of the twin paradox. It's not just that relativity does counterintuitive things with time (like slowing down for faster moving objects).
The paradox is that both twins see the other moving away from them and returning so why should either of them be younger? After all relativity is based on the idea that there is no absolute velocity of an object, just *relative* velocities between two objects. From Rocket Twin's (R) perspective why shouldn't Earth Twin (E) be younger because they flew away on Earth and returned to the space ship (similar to how R flew away on a rocket and returned to Earth).
The solution is (essentially) that R actually accelerates while turning around but E doesn't. In the math of relativity, all inertial observers agree that R accelerated and E did not.
I think this would instead be a math prank paradox because it incorrectly implies that there is a symmetry between the twins.
Additionally, when the travelling twin returns the deceleration needed to not instantly crash into the planet has the opposite relativistic time effects and the twins will be the same age. Though, that's only exactly true if they return to the same starting point.
@@memyselfishness Does that require that they launch from something like a Lagrange point, or that they return with the planet they launched from at the same place in its orbit? What does "same location" mean--oh shoot it's inertial reference frames isn't it
@@memyselfishness No. R would still end up younger than E.
The acceleration isn't what causes the time dilation, it's just the thing that breaks the symmetry between the twins.
@@noellelavenza494 did u name urself because of deltarune if so that's so based :)
(I'm a trans gamer also so uh just, respect to ya :D)
@@noellelavenza494 if you get really nitpicky, every reference frame is accelerating under special relativity because they’re all under the influence of gravity from far-off objects. But then GR steps in and says that’s not actually acceleration, so idk. It’s usually insignificant either way.
Buttered bread tends to land face-down due to the fact that it starts butter-UP and doesn't have TIME to land face-up and has nothing to do with a difference in weight.
I.e. if you have a slice of bread on the table and you knock it off, it starts spinning due to one edge hanging over as it slide off sideways. It generally can only complete 1/2 spin from the average table height before it lands. Try elevating the table 50' in the air and then knock slices off and they'll wind up more 50-50 for butter up and butter down.
Wow this is the best video I’ve ever seen on paradoxes. Moreover the best overall explanation of them that I’ve come across after years of casual interest and countless hours watching other videos on individual paradoxes. Looking at paradoxes as a whole, and being able to categorise them, adds context for me that I didn’t have until now. I love how you accurately and concisely broke down many of the most common ones and explained them so simply. You are a brilliant communicator it’s a blessing to have seen how well you express yourself.
I have always hated that bellhop question because as a kid it was told to me, but I knew math didn't work like that. You can't just loose numbers, so I sat there and actually figured out where the error was but literally no one in my family would believe me because I was just a stupid kid and it was a computer technician that showed them that trick.
I also got frustrated by this with a used furniture salesman who pretended not to understand as I explained to him why he was wrong. I went back over and over, even used props to demonstrate, and he just refused to accept the answer. I was so frustrated over convincing him and eventually I accepted that I knew the truth and the conflict wasn't worth it.
Six months later I went back to the store and he admitted that I was right, he knew I was right, and he just wanted to see how mad I would get. :(
@@rwbyab7423 LMAO THAT'S SO EVIL
@@rwbyab7423 did you punch him because i would have
@@rwbyab7423 broooooo
@@rwbyab7423 honestly chad
4:56 the traditional Chinese example is a man sells an unblockable spear and an impenetrable shield, and then a kid asks what happens if you try to pierce the shield with the spear
In fact the Chinese word for 'contradiction' can be literally translated to 'spear-shield'
This is directly referenced in the bonus case (at least in the English version) for the rereleased Ace Attorney Investigations.
OBJECTION! indeed
@@twiexcursori OBJECTION! It’s actually from Rise From The Ashes, which was from the DS remake of the trilogy. Rise From The Ashes went after the first game’s final case.
@@curlamus4452 yep, it's the logo for the Prosecution Department, I think, been a while since I played through Rise From The Ashes
矛盾
I knew the one at 15:20 from Vsauce!! He has a wonderful video about this paradox which is called a supertask. One is about Achilles, and a race. If he has a blue and a red flag and changes a flag half of the distance he ran previously, will he be holding a red or a blue flag? (This is just from memory) there is always an infinite number to divide the distance by so we dont know. On Vsauce there was also the switching doors paradox too!!
I just looked at your channel and realised that you did some of my favourite meme mash ups and video essays. Great job another banger as always (apparently)?
There's a Mythbusters episode where they test the buttered toast thing, turns out if you drop the toast from up high with no bias toward either side, it'll fall butter-up due to the slight dome that buttering the toast gives the toast. If you knocked the toast off of a surface about the height of a table, however, the toast will do a flip and consistently land butter-down.
Yep, the weight of butter on toast is pretty negligible
The thing is, the butter moves the center of mass toward the butter side, but it doesn't change the aerodynamics of the toast. The most stable orientation for an object in freefall is the one which maximises drag (this fact falls into the "unintuitive facts about the universe" category of paradox). Butter makes one side smoother and less porous, so it would actually reduce drag on that side. Think about the pores of the non-buttered side like little parachutes and it makes sense.
Thanks! Since I know this I no longer butter the toasts evenly, but with a dome to minimize risk. My quality of life has improved.
@@joeg451 yeah but that’s only if you don’t dent the bread by buttering it.
AFAIK the reason that the butter side usually goes down is because of the combination of their usual rotating angular speed and height they start to fall, in other words, the height of the usual dining table
My favorite version of the temperature paradox is "all men are mortal, Socrates was mortal, therefore all men are Socrates" because of how obvious the flaw in this logic becomes when you extend it outside of just numbers
I’m pretty sure I’ve heard that exact same logic on the moon, it goes “everyone looks at the moon, everyone who has looked at the moon has died, therefore the moon kills people.”
@PuppoI find the implications of this comment's vocabulary paradoxical.
So, women are not mortal?
@@matanglawinX That's not a paradox, that's just a fact of life.
@@holl0918 #Rhetorical
36:30 got so close to making a counterintuitive fact. “This book contain errors” is always correct because either the book contains errors and the sentence is true, or the book contains no errors and the sentence itself is an error.
I like this one solution to the immovable object vs unstoppabke force:
They just go through each other, where the unstoppable force just keeps going, and the immovable object well.. Stayed still.
One thing i love about paradoxes is their ability to anger people who think they're smarter than they really are
thinking really hard to see if there’s a paradox in this statement and getting upset because i’m not that smart
Do they? ... I suppose I'd like to test that, but I'm not sure of a situation where I could smoothly make use of such a thing.
@@SotiCoto
try "hey! listen to this paradox i heard"
Alright this seems like the best reply section to share my Alright here's my paradox it's name is who did the crime paradox so it goes like this " your in a 5 sorry aprament and your running away from a man that ones to call you he slits up and you push him out of the window he falls but at the last second he gets hit by a car before he falls to the ground. Who's charged for the murder?
@cyancat8633 both. But if you were to share this anywhere else I would fix the Grammer and spelling g
To be fair, all the authorities agree that "What is in my pocket?" isn't really a riddle, but they also agree that the other party's response (asking for three chances to guess the answer, instead of exercising his option to protest the riddle itself) was an implicit allowance of this non-riddle into the contest.
I like how this paints Tolkien scholars as if they're legal scholars.
@@vigilantcosmicpenguin8721 they should be
“[Bilbo] knew, of course, that the riddle-game was sacred and of immense antiquity, and even wicked creatures were afraid to cheat when they played at it. But he felt he could not trust this slimy thing to keep any promise at a pinch. Any excuse would do for him to slide out of it. And after all that last question had not been a genuine riddle according to the ancient laws.”
Nothing has ever made me want to tape a piece of buttered bread to a cat and then drop it off something more than seeing ‘do not attempt’ written in big letters throughout an explanation of the buttered cat paradox.
My favourite "paradox" is the friend paradox: one average, your friends will have more friends than you.
25:34
That's not a suprise, I'm antisocial.
I really enjoyed the statement "if you break the rules of math, you get the consequences of breaking the rules of math." There's a simple beauty to that statement - the universe as it should be.
Along that line, I've heard it said that Ayn Rand wrote something along the line of, _"We may ignore reality, but we may not avoid the _*_consequences_*_ of ignoring reality."_ Really cool insight, in my view.
yes
@@RichardHarlos
I'm a fan of this thread so far. Too bad I don't have anything creative too add...
@@RichardHarlos truly, it is too bad that she did just that, and ruined the lives of many with her book.
@@anabsentprofessor6120 I don't know enough about her to have an opinion about her.
To be fair, we all live in reality bubbles, it's just a matter of how much, or how little reality makes it inside. Part of what governs access to our bubble are the several cognitive filters, and biases, that we accumulate over our particular life experience.
I suppose of any of us were even to approach reality *as-it-is* with a high degree of understanding and confidence... all the world's problems would relatively quickly disappear, and we might all find ourselves with access to an interim evolution toward utopia, without the many privilege-gaps that we see today.
I've always been a fan of the statement 'there is an exception to every rule', which may seem wrong at first, but then consider that that statement itself must also have an exception if it is to comply with itself. Therefore, either everything else has an exception, in which case the exception to the statement is itself, or something (or multiple) else(s) simply have an exception.
+
Big brain time
(Have a great day, God bless ❤️)
If everything else has an exception, then the rule is its own exception because it does not have an exception. But if it has an exception (itself), then it does not have an exception, because every rule including itself has an exception. If, on the other hand, there is at least one other rule that has an exception, then that rule always has an exception and there is no problem. There is at least one rule that has an exception, therefore there is no problem.
@@samueldimmock694 Yes, I am aware (and included a similar explanation in my original comment). My point was more that it's a statement that *can seem* wrong at first glance, but is actually true.
@@gawain855 I guess that just wasn't clear to me. Maybe it's because I've never really done formal logic before.
32:40
jan Misali's Drawing of a Horse my beloved
Man the crocodile riddle unlocked a childhood memory. We have a song in croatian about a crocodile kidnapping a kid
The "some guy getting confused" category reminds me of something fun I think you'd really enjoy if you haven't seen it already: garden path sentences. Unless my memory is failing me which often happens, I don't recall seeing that on this channel before. They're fun to look at and try to decipher all the possible meanings and the underlying grammatical structures
You mean like "The horce raced past the barn fell"?
Honestly, there's lots of other linguistic example sentences that are fun too.
"Buffalo buffalo buffalo buffalo buffalo buffalo buffalo buffalo" is a famous one, but my favorite is "James while John had had had had had had had had had had had a better effect on the teacher".
@@brianb.6356 i like "bison from new york - that bison from new york beat - beat bison from new york" better because "james - while john had had 'had' - had had 'had had'. 'had had' had had a better effect on the teacher." is literally not grammatically correct unless punctuation isn't part of english, to the point of having two sentences without a period between them lol.
@@shelvacu Time flies like an arrow. Fruit flies like a banana.
More people have been to Russia than I have.
"There are a lot of angles people have taken to try to explain this one and I will be explaining none of them, because I'd rather move on" is now my official conversational segue
The Fermi paradox doesn't even really apply to us yet. We don't really have good technology for reading signals from outside of our solar system -- the big problem is hearing it over the noise from the sun. It's like shouting east from New York, not hearing anything back and then asking why you haven't heard from Europe yet
sorry could you repeat that
Liar paradox- example: this sentence is false... This is false because they say the sentence is false, but that makes it true, meaning it's false. It repeats foreeeverrrrrr
Irresistible force paradox- example: a sword that can cut through anything, and a shield can cut through anything... They can't exist at the same time!
Other self-referemtial paradox- example: the following sentence is true- the previous sentence is false... This is a paradox because, y'know... The clear issue of it being a loop of true and false!
Unexpected hanging paradox- 6:52 a man is gonna be hung, the judge says it'll be next week on a work day at random... He can say that it won't be Friday because he'd expect it if he makes it to Thursday, meaning he can say it won't be Thursday... And so on.
I can explain any of them further if you'd like me to!
I have to say your explanation for the monty hall problem made it so much more intuitive for me. Also I have to say my favorite example of the "unstoppable force meets immovable object paradox" has to be the myth of the Teumessian Fox and Laelaps from Greek mythology. In it the Teumessian fox is a fox that was destined to never be caught and Laelaps was a magical dog that never failed to catch what it was hunting. So as can be assumed Laelaps started hunting the Teumessian Fox thus causing a paradox. The end result was that when Zeus realized what was happening he just turned them both into stone.
he's a problem solver you gotta give him that much
@@Iggy_Dogg “nope, not about to deal with those ramifications”
27:43 "Even though it looks like this infinite process keeps getting closer to the line we're trying to measure, the end result isn't really a line at all; it's a weird, infinitely zigzagy thing"
(Funny, we actually just talked about this paradox/prank in my real analysis class!)
This is actually a common misconception of the staircase paradox - the prank is even more devious than it appears! The limit of the zigzagy curves _really and truly is_ the straight diagonal line, in the exact same way that 0.9999.... = 1. The gap between the zigzag and the straight line gets smaller and smaller as the zigzags get closer and closer, and in the limit, they are equal. So - what's the flaw in the "proof" that sqrt(2)=2?
(Especially considering Archimedes' famous approximation of π! He approximated the circumference of a circle by the perimeter of polygons with more-and-more sides. It's basically the same thing! We're approximating one curve with a series of other curves, such that the limit of the approximations is the true curve. So why does one set of approximations let us figure out the length, and the other doesn't? What on Earth is the difference? And in fact, that style of idea is sorta the key to calculus - we analyze something complicated with a sequence of better-and-better approximations. So fundamentally, this sort of thing often works. Why does the staircase break things?)
Since I can't draw pictures in a youtube comment: let Dₙ refer to the curve with n zigzags. And let D be the perfectly straight diagonal line. We know these three facts are true: (a) You showed that the length of each Dₙ is 2; (b) I claim that the limit of the sequence of Dₙ's is D; and (c) we know that the length of D is sqrt(2). Summing it all up, here's the core of the prank:
lim(Length(Dₙ)) = lim([2,2,2,2,...]) = 2
Length(lim(Dₙ)) = Length(D) = sqrt(2)
(First line is: Take the length of each Dₙ. You get 2 each time. Now take the limit of that sequence of 2's; you get 2. Second line is: Take the limit of the sequence of Dₙ's. You get the straight diagonal. Now take the length. You get sqrt(2).)
So, the prank is that the limit of the lengths doesn't necessarily equal the length of the limit: lim(Length(Dₙ)) ≠ Length(lim(Dₙ))! That's why the proof that sqrt(2)=2 is flawed: it implicitly assumed that the limit of the lengths equals the length of the limits. It might feel intuitive that that's always true (which is how you can slip it into a "proof" without people noticing the first time they see it) - but _a priori,_ there's no particular reason why it has to be the case. Sometimes it's true (eg Archimedean approximation), but sometimes it's false (eg the staircase)!
So how can you tell in advance whether that hidden assumption - that lim(Length(Dₙ)) = Length(lim(Dₙ)) - is valid? How could you tell in advance that the Archimedean π approximation will work and the staircase one won't? When is it valid to swap "lim()" and "Length()"?
Briefly, the answer is - it's not enough for the limit of the staircases to be the line; you need the the limit of the *derivatives* of the staircases to be the *derivative* of the line.
Why? Well unfortunately explaining that in full detail requires some real analysis and is best done in person, and youtube comment boxes don't come with chalkboards. The closest I can get over the internet is a couple of interactive Desmos graphs I whipped up: www.desmos.com/calculator/5sufafga3w. The explanation continues there if you're curious! I don't rigorously prove anything but I try to communicate the visual picture explaining why the staircase doesn't work but the polygons do. (It'd make more sense if I could explain it with realtime two-way communication, but I tried to get across the key result anyway.)
You put a whole math lesson into a youtube comment and I gotta commend you for that. Playing around with those graphs was fun!
I think I got it. The limit of a length D subscript N is not always the length of the limit D subscript N.
I am about to start calculus. This will be fun.
This is how I (a lay person who never went further into math than AP calculus) distinguish between the two approximations:
When approximating a circle with polygons of an increasing number of sides, each step does get physically closer to the circle, so you're making progress toward reaching it.
When approximating a diagonal line with right-angled zigzags, each step looks exactly the same if you zoom in, so you aren't making progress toward the diagonal line.
This was a lovely and very interesting experience, thank you for putting it all together friend
@@emilyrln That doesn't help things, because you're proving the very fact that the diagonal line has the same length as the stepped line, so of course you aren't making progress! The real key to understanding here is that you can't always two different mathematical operations that are swappable in certain circumstances. The length of the limit is not always the limit of the length, even if it is most of the time. Part of real analysis is learning when you CAN swap two operations like this.
That was the most straightforward answer to the Monty hall problem I've heard so far. Thank you.
Bonus: The reassembled Ship of Theseus is used as a pub 🍻 by the retired crew members of said ship, like a VFW.
Part of this addresses that there will likely be some extra parts due to pieces that need to be replaced more often than others in the original, such as extra ropes, sails, barrels, deck planks, railings, etc., which could be used as tables, chairs, the bar, and decor, like a nautical themed Shenanigans.
I would argue this majes it easier, because you can argue the ship preserves the original intent of the ship of theseus compared to the pub.
@@user-burner an ancient ship called the ship of theseus crashed, and is buried in almost perfect condition. legends say the crew members are using the ship as a pub. scientists made a recreation of the ship of theseus, though it is not perfect. it is being used for sailing. which is the real ship of theseus?
@@official-obama I suppose in this case, being in near perfect condition takes precedent over the intent. To some extent though, you could say they are both equally the ship of theseus
The Monty hall problem holds up until you realize that a goat is a much better prize than a car
Is it? I mean, I have no clue where to keep a goat or how to get it vaccinations, or what to feed it...I'm not sure i'm zoned to own one in the first place...
@@billyweed835 but they're cute so it's worth it
If you get another goat, you can get more goats. If you get another car... You have two cars.
@@gabrielhermesson9926 A car you could sell for EVEN MORE GOATS
The monty hall problem is how to pay the tax on all that capital gain.
One of my favourite Ship Of Thesei is that British Girl Group The Sugababes started with three bandmates. One by one they got replaced until the final lineup consisted of people who were not original members. When the last original Sugababe left she joined the other original Sugababes to form a new girl group. These two groups overlapped for around a year or two, so there were I'm fact actual questions about who was the "real" Sugababes
According to en.wikipedia.org/wiki/Sugababes, 'In September 2009, after 11 years in Sugababes, Buchanan, the final original member, was replaced by Jade Ewen. Range, Berrabah and Ewen released the group's seventh studio album, Sweet 7 (2010), after which they signed to RCA Records, before taking an indefinite hiatus in 2011. That year, the original lineup reformed as Mutya Keisha Siobhan and released the single "Flatline". The trio regained the name Sugababes in 2019, and recorded a rendition of the song "Flowers" with DJ Spoony.'
@@SolomonUcko "The ship made from the original parts then got called The Ship of Theseus" is such a boring workaround
My favorite one is the histories of the NFL franchises Cleveland Browns, Cincinnati Bengals, and Baltimore Ravens
This is very similar to what has happened with Yes, although a lot of their former members are dead now. There was a time that there were two full bands consisting of former Yes members that toured separately.
@@stevenglowacki8576 "So which one is Yes?"
"Yes."
Oh this just reminded me! The math pranks section reminds me of this one time I got so frustrated with people claiming that 1 is prime (it's not) that I came up with this buck-wild proof of why 1 is actually composite that was built on complex numbers. Can't remember the details but I should probably write that up at some point 'cause I thought it was really funny.
I almost got into a fight at a bar over insisting that a groups intelligence decreased with the more people added.
"Assuming it exists, the universe is very big" amazing quote I love it
So I was actually in a class of 26 people at one point, and three people shared the same birthday. Two were twins, but another person just happened to have the same birthday as them.
June 22, in case you were wondering.
I've been in a room with 2 people and both shared the same birthday
I’ve been on a school bus where I shared a birthday with three other people in my grade and neighborhood (one set of twins). I wonder what the probability of that is?
Makes me wonder what percentage of twins share the same birthday. 🤔
my class (of 28 or maybe 29 i can't remember) had three pairs of shared birthdays, and two of them were a 15th (of march and of july) which i never thought about that much but that has to be very unlikely right
@@chad_bro_chill interestingly it wouldn't actually be 100%. I don't feel like doing the math rn but there would be a small percentage of twins where one was born before midnight and one after midnight
The friend paradox is like the card paradox: a hat has two cards, one is red on both sides and the other is red on one side and black on the other side. You pull out a card and see a red side: what is the chance that the other side is red? Most people say 50-50 but it is 2/3.
For the Monty Hall "paradox", the trick is that the host KNOWS which doors are goat doors, so in fact, opening them DOES NOT change the initial probability of your door being the right one, which is 1 in X doors, and it does not change the probability that the right door is in the remaining set, i.e., X-1 / X. If the host did not know, then they could open the right door, and you either win, or the game is replayed. In that scenario, you would not have any advantage in switching.
and I agree with the fact that a "heap" is not well-defined, and that it is the origin of the paradox. However, I'd apply the same explanation to the ship of Theseus: "ship" only refers to the intended use of a combination of objects, but it is not clear when it stops being a ship. Is a sunken ship still a ship? How many pieces can you remove from the ship before it stops being a ship? So I guess most of our everyday words, e.g., only defined by aggregation or by usage, have a fuzzy meaning.
Three logicians walk into a bar. The barkeeper says "what a great pleasure to see you again" and asks: "Do you all want a beer?". The first logician says: "I don't know". The second logician says: "I don't know". The third logician enthusiastically says "Yes!".
After a moment the barkeeper comes back, puts one glass of beer on the table and leaves.
The second part caught me off guard, hadn't heard it before lmao
Obviously the logicians should have gone to a logicians' bar.
@@juanausensi499 They did! They just weren't "perfect logicians"
Well yea cus only one of them outright asked for a beer
@@G00dTaste No, it's because the question didn't specify if they wanted one beer each, so a logical conclusion would be that the logicians wanted only one beer to share between them
My philosophy professor argued that the word "heap" meant at least 4 arranged in a layer of 3 with a layer of 1 on top in a non-flat configuration. He was fine with all the vagueness stuff, we even had the book Vagueness by Peter van Inwagen as a textbook. He just didn't think a heap was a good example.
a heap is a structure wherein the root node has multiple children. these children may or may not have children or a child. the root and children are a or are many instantiations of a class. the heap is arranged accordingly. obviously it follows that the heap begins when it is instantiated (say, between zero and infinitely many grains of sand, inclusive) and ceases to be at cleanup (specifically zero non-grains of un/deallocated nothing), regardless of its size interim. qed the paradox is solved thank me later philisophers need not reply
Mathematicians have long since discovered that it's simpler to allow 0 grains and 1 grain to be heaps. In particular, 0 grains is the "empty heap"
the four arrangement is also my answer. whenever I say it, it either starts the conversation into fun nonsenseland discussions, or with them responding like Lisa when she asks Bart if a tree falls in a forest does it make a sound.
based
@@WodkaEclair The tree doesn't make a sound. Sound means stuff you can hear. You already said "you can't hear it" therefore, by definition, no sound.
Thank you for finally explaining the game show doors question in a way that actually makes sense.
35:49
They're basically talking about two different kinds of desires. "Wants" and "beliefs".
A "want" is something that would make you happy if it happened, but that you wouldn't necessarily force to happen. The guy in this paradox WANTS their policy to be enacted; they might be happy if some corruption in the political system occurred and their policy was put into place, but they wouldn't choose to make that happen.
A "belief" is something you think should happen. You would force it to happen, even if you don't "want" it to. This guy believes that whatever policy is democratically chosen, regardless of how much they like it, should be enacted. It's what they'd choose if presented with that choice. A belief is formed from a logic equivalent (such as justice or personal morals) whereas a want is purely the realm of emotions.
So, basically, it's a paradox because someone's wants and beliefs are in conflict. The paradox is essentially stating "emotions aren't logical", which, like, yeah.
4:55 is actually a famous one in East Asia, so much that the word contradiction itself can be translated to spear and shield
I know this fact thanks to Ace Attorney
@@CT-1118 now i do too, playing rise from the ashes right now and when they started talking about the award i was like :0 this is what they were talking about in jan Misali's comments!!!
I mean, I'm pretty sure that story is what Jan Misali is referencing here. Heck, given the pretty deliberate "Objection!" at the end, he might actually be referencing Ace Attorney's usage of that story.
In what language? I'm pretty sure nobody speaks "East Asian"
@@samanteater the Chinese characters the word for contradiction is 矛盾
矛= spear
盾= shield
This was loaned into Japanese, Korean, and Vietnamese.
A bearded man goes up to Bertrand Russell, clearly distraught.
"Bertrand," he says, "I can't stand my beard, and yet I cannot shave it!"
"Fear not," says Bertrand Russell. "The great barber Pagliacci is in town. He is known for only shaving men who do not shave themselves. He will help you."
The bearded man then bursts into tears.
"But Bertrand," he says...
(one of my favorite paradox jokes, somewhat paraphrased)
A little late to the party, but can you explain the joke/paradox for me? I don't quite get it.
@@MorePowerToYah it's a reference to a joke orignally from _Watchmen_ It goes:
“Heard joke once: Man goes to doctor. Says he's depressed. Says life seems harsh and cruel. Says he feels all alone in a threatening world where what lies ahead is vague and uncertain. Doctor says, "Treatment is simple. Great clown Pagliacci is in town tonight. Go and see him. That should pick you up." Man bursts into tears. Says, "But doctor...I am Pagliacci.”
This paradox joke combines the Pagliacci joke with the barber paradox (described in this video). I think it's quite funny, but the setup relies on the listener being familiar with both.
If you're interested in more jokes of this kind that combines two unrelated concepts with similarities in structure, the webcomic _xkcd_ is full of them.
You’ve been the only person to explain the Monty hall problem in a way I can actually understand
It feels like everyone else says that choosing to switch ups your odds to 50% because you are choosing from two options is nst ad of three
50% *is* the naïve guess, so it's a reasonable one.
Thank you for finally explaining the Monte Hall paradox in a way I could understand.
My answer to the heap paradox:
A "heap" is not about the number of constituents, but their arrangement (piled on top of eachother in a disorderly manner). So, to make the heap of sand not a heap, you don't need to remove any sand at all. Spreading it out one grain thick over a large area would eliminate the heap too. But if you want to do it by removing grains, then it stops being a heap the moment there are not enough grains for them to pile up without deliberate arrangement.
Gonna need you to clarify “enough” (grains), “pile up” and “deliberate arrangement”.
I think "the moment that gravity can overcome the friction that keeps any grain of sand elevated above another" might be better, but yeah.
but where is that point
Ok now try to solve the bunch paradox
@@passtheyaoi probably calculable with sufficient data on the materials and conditions, but only because it's a less-than-ideal example for the given conundrum
I like the kind of "self-sustaining" paradox like when you go back time to become your own grandfather and therefore your existence is predicated upon you existing to go back in time to create your own existence. The way the timeline currently plays out is perfectly logical, but how it got into that state in the first place seems impossible.
so the plot of the raven cycle
This is called the bootstrap paradox, and given the taxonomy in this video would fall under, I think, the "normal impossible question" category, as it's essentially impossible to answer how the loop 'started' while also having always existed in its stable state.
Stable time loops!
The lifelong question: Who wrote Beethoven's fifth?
see, my issue with that is you'd just become infinitely inbred
Peaceful note by your friendly neighborhood physicist, never say “dead and alive” when referring to Schrodinger’s cat, it’s “dead or alive”… this is an incredibly important distinction in the world of quantum mechanics
“White horses are not horses” sounds like a great premise for a surreal horror story. Imagine a world where horses are known to be many colors, but never white. If you see a white horse, run. That’s not a horse.
the guy at 38:36, "a hypothetical guy who exists so we can argue against them" is one of my favorite types of guy and unfortunately I carry several thousand of them around in my brain at any given time. also rly good video! i rly enjoyed it
It's a bad sign when you start losing those arguments. XD
@@christophermarsh1580 Au contraire, losing arguments against your own devil's advocates is a good way of changing your mind about things you were previously wrong about.
I think my favorite one may be the phrase "You're unique, just like everyone else"
If everyone is unique no one is- Syndrome.
Isn't that one a counterintuitive fact? Because every person is indeed unique by the fact that it's impossible for two people to be exactly the same, so it's a situation in which every single component can be unique while all of them are still unique, because each of them is unique for different reasons
not a real paradox. it's a natural language slip. "Unique' is used in two ways, implicitly. People are unique in that no two people are exactly alike, BUT they share the commonality of uniqueness as a shared quality everyone has.
The propositions
Everyone is unique
There are traits everyone shares
are not contradictory. Right? Because 'unique' doesn't have to imply that every aspect of someone is different from every other aspect of someone else. That couldn't possibly be true to begin with, because 'everyone' implicitly refers to humans, and all humans need to breathe, are born, die, are made up of cells containing DNA and mitochondria, consume things and drink water or water based liquids to replenish lost water from sweat and urination, etc. Those are commonalities generally agreed to be true. You could say 'everyone' also includes 'people' that don't share any of these traits, but first of all, those people don't exist as far as we know and are purely in the realm of conjecture, and second, people that read the initial statement are likely going to assume it refers to humans, and it's dishonest to claim afterwards that no, it can refer to other entities as well.
@@fulana_de_tal yes, but in this context it is okay because even if it isn’t a true paradox it is mentioned in the video, also it never specified what “one” is
the quality of being unique is not in of itself unique
I cant believe i had half of your vids on my watch later list since 2 years ago or so, not knowing all were from you while somehow not watching them either, got a sub but F.
18:22 isn't actually the twin paradox. The paradox arises from the fact that motion is relative (that's why it's called relativity) - from the astronaut's point of view, they're motionless, and the twin on Earth (along with, you know, the entire Earth), is the one moving at nearly the speed of light, and should experience time dilation. So when the twins finally meet, does each one sees the other as younger than themself?
This is in fact more of a mathematical prank type of paradox. Special relativity tells us that inertial motion is relative, and indeed, when the astronaut is moving at constant speed, they would experience their twin ad younger (but in order to experience each other, the twins must send signals to each other at the speed of light, which would add delay, so in order to know that the other one is actually younger, and not just appear this way because of the delay, they would have to do a bunch of math). However, for the twins to meet in person again, the astronaut must turn and fly back to Earth, which means they must accelerate, at which point they are no longer inertial, and are not equivalent to the twin that stayed on Earth.