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For everyone wondering, this new paradox is labeled with an epsilon (which looks like an E) because in math, that Greek letter is used to denote an arbitrarily small positive real number (basically, one over infinity). So it’s an appropriate character to describe entering an infinitesimally small space.
I know it's a bit late into the series to say this, but I would definitely recommend this as a first puzzle game. I've made it as far as Tyler does in this video and I haven't needed a single hint. In Baba I started needing a hint every level halfway through the game and in Understand every other level. If you want to recommend a game to a friend I would say this is a good one.
13:30 I love that you can both see and hear immersion here. Tyler actually feels squished for a split second, even though it's just a purple block that he controls. Games are amazing.
Your guess for the infantessimally small box is correct. Correct me if I'm wrong but Epsilon in math is used for a constant/value that is infantessimally small but not zero.
Right, some vague memories come from hearing about machine epsilon in one of my CS classes - which is the smallest floating point number a computer can store.
@@Nukestarmaster I see your pedantry and raise you a colloquialism. OP was not referring to the infinitesimals as part of the set of hyperreals, but in reference to the definition of the word infinitesimal: “taking on values arbitrarily close to but greater than zero.” (via Merriam-Webster)
When Carl is a better notification system than UA-cam. That said, these cycle levels are interesting as hell. Edit: At the level at 13:07, if you look carefully, the box's shape is distorted in the open space levels. That's the idea the game wanted, though you got it in the next level.
"I think I tried to enter something infinitesimally small" Yep! Hence the symbol, the math term is an epsilon number! The usual infinite represents becoming infinately big, as you become big when you exit a box, and you'd have exited infinite boxes in one move.
@@0NBalfa0 that’s weird, I’m not sure what you’re referring to. I mean by the definition you’ve just used, a is simply any ordinal bigger than ω_1 which doesn’t really fit the typical ε use cases as “generally arbitrarily small positive number”. Also no such finite ordinal exists because the ordinal a aren’t a dense order; the smallest ordinal is {} immediately followed by {{}}, then {{}, {{}}}, etc. similar to how the natural numbers don’t have an ε representation that makes sense
@FRIMI First off, no, it's not any number greater than ω_1 as, for instance ω_1 +1 doesn't have that property. The least possible ε number is ε_0 and it can be visually seen as an infinite tower of omegas ω^(ω^(ω^(...))). So, since this is a recursive game, I could see the getting inside or outside a box as an abstraction of applying this operation and the joke being here that writing ε could be saying this is where you are. Of course, there is also the mentioned before ε from the ε,δ limit definition which can be seen as the also mentioned infinitesimal; hence, you cannot escape (Though even without the infinitesimal thing, a similar argument can be made). But ya, the ordinals here I am viewing in terms of their representation, and they are still an analogy.
That looked like 2 paradoxes to me, 1. You entering an infinitly small space. 2. You entring a nonexistent space, the only place where the yellow block existed was within the clone of itself but without itself outside of the clone entering the clone is meaningless as it teleports you to a place that doesn't actually exist (inside of the clone). Edit: after some thinking I understand why the 2nd one wouldn't work as a paradox in the game but if you tried to push a block outside of its clone when there is no copy of it outside of the clone it would just end in the void
like two maizens edit:copy of maizen looks whiter and profile name:copymaizen. And ONLY copymaizen exists... ...,... ...wait,copymaizen doesn't exist coz maizeneven copy(copy(copymaizen)) doesn't exist.
With the epsilon case, there was another interesting thing you did. You put the real box inside itself, so even if it wasn't an infinitesimally small space, it would be impossible to ever leave the real box, as you'd only enter either the clone, or a void, depending on positioning.
This is such a small detail but I really love the rainbow cycle level, because they HAVE to be different colors. Otherwise they'd be clones of each other and the puzzle wouldn't work. An already understood mechanic, disguised as visual design. In a MINIMALIST game. Bravo, PP
In mathematics while the ∞ stands for "a number greater than any arbitrarily chosen number" The epsilon Ɛ stands far "a number closer to 0 (or sometimes a different number) than any arbitrarily chosen number" Both in maths aren't used as actual numbers but instead used to show that for every case a number exists that fulfills the requirement.
Wouldn't the epsilon be used to denote that arbitrarily chosen number with the close to 0 number being denoted as just 0? Like how x→0 doesn't necessarily mean x can reach the real 0?
it's funny how tyler found the epsilon boxes in the exact same level I did, I assume that a lot of people did given how the shapes of the boxes make it easy to do and think to do. Shows you how much thought went into this game
I'm so excited for when these different paradoxes somehow become necessary to solve a puzzle. I have no idea how that'll work, but BOY am I looking forward to it
1:20 literally a lock and key also, it is evident that a lot of people have either not taken or forgotten calculus here, as epsilon shows up regularly in the Delta/Epsilon proof as a positive real used to say 'not actually zero but as close as necessary'
u didn't even realize the first of the blue levels was meant to introduce u to the rectangular spaces. if u swapped the green and yellow empties the puzzle would actually b impossible, since the yellow 1 is 3x5 and the green 1 is 5x3
we got a few types of paradox/recursion 1-No recursion 2-Normal recursion: this is a level inside a level, and if you push the level outside you get to the void 3-Many levels recursion: A is inside B, and B is inside A, pushing a block outside creates a normal recursion 4-False recursion: A clone inside the block it is cloning. If you enter the clone, you get to the target, but exiting the target doesn’t take you to the clone 5-Infinite small space: a target inside it’s clone
As a Mathematics students; Epsilon is, just like Aleph 0 (or the magnitude of the natural numbers, a type of infinity), a concept from Analysis. If you have a sequence of numbers like x_k=1/k for k>0, then you say this sequence converges to a real number c if for every distance epsilon from c you can find a natural number n such that x_n as well as those x_k after x_n lie in that distance epsilon from c. So in this way, epsilon is often used to describe a number closd to 0, in some areas like derivatives it's actually defined as epsilon^2=0, so it is not 0 but so small that its square is 0
Another reason it's a paradox is that the real level is inside its clone. And since we know you can't exit a clone, you're stuck in there forever. You created an infinitely small bubble universe separate from the rest of reality.
That is not E, that is Lower case Epsilon- it is known in math to be a type of infinity. Yes, there are types of infinities. Such as, how many numbers are between 0 and 1. infinite infinities. There are the same number of even numbers as there are both odd and even numbers. That sort of thing. The person who designed this level is very smart, and is an admirer of mathematics.
Fun fact, the inverted 3 in the second paradox is, according to Google, "the closest number to zero, yet it is not zero." So it's like 0.000...1. The '...' means an infinite amount of 0's.
As someone who is majoring in game design rn, I really wanna know what the paradox’s looked like during production, because I bet they weren’t able to account for everything at the beginning and that shit got really trippy really fast.
I finally understood the new paradox problem, when you push the real both into its clone, and then enter the clone, a paradox is created because in entering the clone, you must enter the real box, but in entering the real box, you have just entered the clone, creating the paradox.
For the record, the backwards 3 symbol is epsilon which, in the Hyperreal numbers represents the smallest number greater than zero, I.e. infinitesimal.
Oh wow, the puzzle at 1:04 was neat. That whole world is neat, I like that they are able to keep making new types of puzzles without adding anything new. Edit: Oh jeeze, I commented too early. What a wild video
“What happens if I push this block into its clone” “OHHH WHAT- E???” Teeeechnically that’s Epsilon, representing infinitesimal instead of infinity. An endlessly small thing, 0.0000… instead of 999999… Turns out the paradox goes both ways!
10:06 you just made another paradox: If you go inside that box which has another inside And another inside it and it keeps going on You will become smaller than the plank thanks and become singularity and it’s a paradox
Oh yeah, that's what I'm talking about.
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Damn straight!
cool
Lets go !!!
Oh, what?? E?!?
For everyone wondering, this new paradox is labeled with an epsilon (which looks like an E) because in math, that Greek letter is used to denote an arbitrarily small positive real number (basically, one over infinity). So it’s an appropriate character to describe entering an infinitesimally small space.
Damn it I didn’t see this comment before I commented
@@SirHurricane_ so its a 1/∞ the thing intregals use
E
Εε
I came here to say this.
The squish puzzles demand the return of Wide Tyler
Yes
When was the last time he was wide again? Was that that rail game?
@@aloysiuskurnia7643 poly road, yeah i think so
I know it's a bit late into the series to say this, but I would definitely recommend this as a first puzzle game. I've made it as far as Tyler does in this video and I haven't needed a single hint. In Baba I started needing a hint every level halfway through the game and in Understand every other level. If you want to recommend a game to a friend I would say this is a good one.
Thank u lol
This game works pretty well at giving a good challenge without being completely mind-melting.
Same, this is my new puzzle game recommendation default too
@@NStripleseven It’s still mind melting at times, but you can just slosh over to the solution anyway
Well you were also trying to start with the dark souls of puzzle games for a “first puzzle game”
You discovered Epsilon early! Didn't even think to try that until a later world, so kudos for thinking inside of the infinitely small box
You can discover it even earlier in Clone 8
@@szy3993 people like yoy and I are just extra smart for seeing it when the possibility was first introduced
Did you know that you can do it even earlier?
@@dreamerofthorns i was like erm box go brr
13:30 I love that you can both see and hear immersion here. Tyler actually feels squished for a split second, even though it's just a purple block that he controls. Games are amazing.
Your guess for the infantessimally small box is correct. Correct me if I'm wrong but Epsilon in math is used for a constant/value that is infantessimally small but not zero.
Right, some vague memories come from hearing about machine epsilon in one of my CS classes - which is the smallest floating point number a computer can store.
Epsilon is used to denote an _arbitrarily_ small real number, infinitesimals aren't reals.
correct!
@@Nukestarmaster
I see your pedantry and raise you a colloquialism. OP was not referring to the infinitesimals as part of the set of hyperreals, but in reference to the definition of the word infinitesimal: “taking on values arbitrarily close to but greater than zero.” (via Merriam-Webster)
Mathematically epsilon is defined as 1 divided by the limit of x as x approaches infinity.
When Carl is a better notification system than UA-cam. That said, these cycle levels are interesting as hell.
Edit: At the level at 13:07, if you look carefully, the box's shape is distorted in the open space levels. That's the idea the game wanted, though you got it in the next level.
Yeah, he got lucky and used the correct boxes the first time, so he didn't notice
Yeah if he had put the yellow above and the green to the left instead, he would have understood the gimmick, since it wouldn't have worked.
@@UltraLuigi2401 just as I did
13:10 This level's fuckery is much more apparent with gridlines turned on.
I didn't even notice the squishing going on until I saw your comment. It's much more subtle than the next two levels.
@@ShimmeringSpectrum i did but i just ignored it, thinking it was my eyes or a bug or something
"I think I tried to enter something infinitesimally small" Yep! Hence the symbol, the math term is an epsilon number! The usual infinite represents becoming infinately big, as you become big when you exit a box, and you'd have exited infinite boxes in one move.
10:12 that funny little E is used in math usually to denote an infinitely/arbitrarily small value, because you you just entered ∞ layers deep.
Oh no.
I will dread the day where the parabox, or the void, or whatever you wanna call it... is used in a puzzle.
It is coming my friend. Oh boy is it coming. But not soon. You will know when it is upon us.
@Comic Nimn There is the infinity block, which makes the level the void
@@alephchung4742 but them if u get both the level and this block out u get doubleinfinite
World 16
Good thing Tyler is still a ways away from that.
...right?
The E is actually an epsilon which is when something comes close to 0. So in the case of the puzzle you came close to a hole so small it is nearing 0
Could also be referring to ε numbers which are ordinals with the property ω^α = α due to the similarities in structural representation
Infinitesimal?
@@0NBalfa0 that’s weird, I’m not sure what you’re referring to. I mean by the definition you’ve just used, a is simply any ordinal bigger than ω_1 which doesn’t really fit the typical ε use cases as “generally arbitrarily small positive number”. Also no such finite ordinal exists because the ordinal a aren’t a dense order; the smallest ordinal is {} immediately followed by {{}}, then {{}, {{}}}, etc. similar to how the natural numbers don’t have an ε representation that makes sense
@FRIMI First off, no, it's not any number greater than ω_1 as, for instance ω_1 +1 doesn't have that property. The least possible ε number is ε_0 and it can be visually seen as an infinite tower of omegas ω^(ω^(ω^(...))). So, since this is a recursive game, I could see the getting inside or outside a box as an abstraction of applying this operation and the joke being here that writing ε could be saying this is where you are. Of course, there is also the mentioned before ε from the ε,δ limit definition which can be seen as the also mentioned infinitesimal; hence, you cannot escape (Though even without the infinitesimal thing, a similar argument can be made). But ya, the ordinals here I am viewing in terms of their representation, and they are still an analogy.
@@igorjosue8957 yea
That looked like 2 paradoxes to me,
1. You entering an infinitly small space.
2. You entring a nonexistent space, the only place where the yellow block existed was within the clone of itself but without itself outside of the clone entering the clone is meaningless as it teleports you to a place that doesn't actually exist (inside of the clone).
Edit: after some thinking I understand why the 2nd one wouldn't work as a paradox in the game but if you tried to push a block outside of its clone when there is no copy of it outside of the clone it would just end in the void
like two maizens edit:copy of maizen looks whiter and profile name:copymaizen.
And ONLY copymaizen exists...
...,...
...wait,copymaizen doesn't exist coz maizeneven copy(copy(copymaizen)) doesn't exist.
Copy(:::halting problem next reply
This one is probably the best gimmick puzzle so far, really made my sides flying XDDD
With the epsilon case, there was another interesting thing you did. You put the real box inside itself, so even if it wasn't an infinitesimally small space, it would be impossible to ever leave the real box, as you'd only enter either the clone, or a void, depending on positioning.
This is such a small detail but I really love the rainbow cycle level, because they HAVE to be different colors. Otherwise they'd be clones of each other and the puzzle wouldn't work. An already understood mechanic, disguised as visual design. In a MINIMALIST game. Bravo, PP
I love how this game is so wild, you don't even need to make clickbait thumbnails.
god this series is so good!! easily a new classic on the channel!
I hope everyone is ready for the next episode, its probably my favorite feature in the game.
When I first played one of those, all I can say is:
O O
Tyler having the time of his life seeing Squished boxes fills me with immense joy
I like to think for that paradox, a game tester saw a bug and the coder thought 'feature' lmao
Great job explaining why the space was infinitesimally small, took me from F to A real quick 💯👏
they just made remote controlled levels, how insane
I really liked how he figured out the e paradox easily!
In mathematics while the ∞ stands for "a number greater than any arbitrarily chosen number"
The epsilon Ɛ stands far "a number closer to 0 (or sometimes a different number) than any arbitrarily chosen number"
Both in maths aren't used as actual numbers but instead used to show that for every case a number exists that fulfills the requirement.
Wouldn't the epsilon be used to denote that arbitrarily chosen number with the close to 0 number being denoted as just 0? Like how x→0 doesn't necessarily mean x can reach the real 0?
it's funny how tyler found the epsilon boxes in the exact same level I did, I assume that a lot of people did given how the shapes of the boxes make it easy to do and think to do.
Shows you how much thought went into this game
Epsilon paradox explanation: The player is trying to enter a space, but cannot do so due to it being infinitely small, resulting in an endless loop.
13:46 I liked that laugh, full of joy 🤣
I'm so excited for when these different paradoxes somehow become necessary to solve a puzzle. I have no idea how that'll work, but BOY am I looking forward to it
10:34 It’s either that or the fact that it’s a clone in the spot you’re trying to enter
The incredible thing about puzzle/logic games are loading times. I love how quick they are
God, these are so freaking short. I love the series except I leave every episode mad that it's cut so damn short.
Eventually you’ll have to enter the paradoxes…
Tyler should bring back wide cam for WIDE PUZZLES
1:20 literally a lock and key
also, it is evident that a lot of people have either not taken or forgotten calculus here, as epsilon shows up regularly in the Delta/Epsilon proof as a positive real used to say 'not actually zero but as close as necessary'
I remember it, but even our university profs say that the Delta/Epsilon proof is only remembered in Math Masters and above
I think you mean everyone here remembers calculus because this is half the comment section.
@@thegoosh6469 times have changed since 9 hours ago
This episode would’ve been a perfect return of wide Tyler
I was having a terrible day but that squish mechanic brightened it
13:24 Tyler absolutely losing his shit over stretchy squishy Patrick has now made my day.
I’m surprised wide Tyler didn’t make an appearance in this episode
I nearly cried at the tallness. It just hit me like a truck and drug my body across the highway.
10:03 I was waiting for that to happen.
I take it that 13:47 makes the return of wide tyler
14:25 All cycles in this game are recursive...
Ya got epsilon, the representation of infinity small
Now to listen to Tyler until I fall asleep.
Same bro
Interesting I did
13:47
Petition to have wide tyler
i need it
13:51 for those who don’t understand, these are blocks that aren’t 1:1 ratio, meaning the internal space is wider or vicerversa
Piston feed tape + patrick's parabox = cycle levels
Imagine an update:
- Level editor has been added, you can create your own level and publish them to the cloud now
u didn't even realize the first of the blue levels was meant to introduce u to the rectangular spaces. if u swapped the green and yellow empties the puzzle would actually b impossible, since the yellow 1 is 3x5 and the green 1 is 5x3
“OOO! What? E!”
we got a few types of paradox/recursion
1-No recursion
2-Normal recursion: this is a level inside a level, and if you push the level outside you get to the void
3-Many levels recursion: A is inside B, and B is inside A, pushing a block outside creates a normal recursion
4-False recursion: A clone inside the block it is cloning. If you enter the clone, you get to the target, but exiting the target doesn’t take you to the clone
5-Infinite small space: a target inside it’s clone
It’s like a slot machine.
10:05 EPSILON PARABOX
13:29 b e a m p a t r i c k
13:46 f l a t p a t r i c k
14:19 IT’S A RECURSIVE *SQUISH*
As a Mathematics students; Epsilon is, just like Aleph 0 (or the magnitude of the natural numbers, a type of infinity), a concept from Analysis. If you have a sequence of numbers like x_k=1/k for k>0, then you say this sequence converges to a real number c if for every distance epsilon from c you can find a natural number n such that x_n as well as those x_k after x_n lie in that distance epsilon from c. So in this way, epsilon is often used to describe a number closd to 0, in some areas like derivatives it's actually defined as epsilon^2=0, so it is not 0 but so small that its square is 0
The game does cool things with that and the other paradox.
my favorite is "and I can go in and win!" rhymes!!
I was waiting to see him discover the epsilon. I was surprised he never tried that during the first set of clone levels.
YES! Cycle!
this is one of my favorite worlds :)
well, you got into E because you put a block into it's copy, so when you entered it, you immediately went to an infinitely small space!
Another reason it's a paradox is that the real level is inside its clone. And since we know you can't exit a clone, you're stuck in there forever. You created an infinitely small bubble universe separate from the rest of reality.
babe, wake up. new paradox just dropped
Ooh, we're almost there, to where stuff *really* starts to get crazy. In the next episode, anyways.
ε is usually the machine error limit. So u are right, you went smaller than the machine tolerate
That is not E, that is Lower case Epsilon- it is known in math to be a type of infinity. Yes, there are types of infinities. Such as, how many numbers are between 0 and 1. infinite infinities. There are the same number of even numbers as there are both odd and even numbers. That sort of thing.
The person who designed this level is very smart, and is an admirer of mathematics.
Fun fact, the inverted 3 in the second paradox is, according to Google, "the closest number to zero, yet it is not zero." So it's like 0.000...1. The '...' means an infinite amount of 0's.
Ive been waiting for more of this game!
As someone who is majoring in game design rn, I really wanna know what the paradox’s looked like during production, because I bet they weren’t able to account for everything at the beginning and that shit got really trippy really fast.
Aliensrock: Quantumania
13:25 His laugh got me
i dont know why but "ohhh what!! E?!" is so funny to me
I can't believe you haven't explored the marvel that is the escape menu.
My favorites:
The Recurse Option
also Press 7 while playing :)
I love you videos and have loved them for the past 3 + years
I was NOT expecting the squish
W I D E P A R A B O X, what will it do?
I finally understood the new paradox problem, when you push the real both into its clone, and then enter the clone, a paradox is created because in entering the clone, you must enter the real box, but in entering the real box, you have just entered the clone, creating the paradox.
Or not, I don’t know anymore, this game now plagues my thoughts.
Honestly I'm waiting for the point when one of the goals is in the void
Epsilon can actually be found in one of the earliest clone levels. That's how I found it, anyways.
10:35 yes "Epsilon" is the symbol for the smallest number possible closest to ZERO AKA infinity small.
10:06
Oooooooooh!!
E?
*Makes me think of RUSH E!!!!*
not me finding this series from the finale and binging through it in a random order
i jus lovve watching this guy solve puzzle games like i think i watched one of these twice LOL
For the record, the backwards 3 symbol is epsilon which, in the Hyperreal numbers represents the smallest number greater than zero, I.e. infinitesimal.
Tyler should try out Fights in Tight Spaces
(The Purist mode)
10:04 Rush E be like
The Infinitely small space was a later gimmick
Your laugh is amazing
can't wait to see your reaction to the next world's mechanic
Everyone talking about the "new paradox" when it's been around since the Clone world.
You basically discovered the Quantum Realm.
“E???!?!??!” Funniest thing ever
Oh wow, the puzzle at 1:04 was neat. That whole world is neat, I like that they are able to keep making new types of puzzles without adding anything new.
Edit: Oh jeeze, I commented too early. What a wild video
you’ve seen ∞, now get ready for ε
"What?! E?!" is the Aliensrock version of "GRAND DAD. FLEENTSTONES?!".
No, I will not elaborate on that.
4:00 ok i mean it makes sense whta he did but he did it so damn cleanly
You got in a box with a real and a clone in one moment
“What happens if I push this block into its clone”
“OHHH WHAT- E???”
Teeeechnically that’s Epsilon, representing infinitesimal instead of infinity. An endlessly small thing, 0.0000… instead of 999999… Turns out the paradox goes both ways!
Take a shot for every time Tyler says puzzle game lol
13:22 how did he not notice?
Nevermind
10:04 *_...E????!?!?!?!?_*
10:06 you just made another paradox: If you go inside that box which has another inside And another inside it and it keeps going on You will become smaller than the plank thanks and become singularity and it’s a paradox