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- Hey! Heads up. This video contains disturbing amounts of betrayal, deception, and abandonment.
- So if you're the faint of heart be warned. Also, there's this. With that out of the way...
- Hey. Remember me? I'm Cary KeyHole, and I'm so smart I made it into elementary school. Jealous?
- It's okay. A lot of people are. One day in fourth grade, I was pretending to be sick,
- so I spent the whole day watching TV in bed.
- (Future Cary here. Don't worry. I was a super obedient kid.
- I stayed home because I really did have a cold. In this video,
- I just wanted to seem edgy to impress y'all. I guess
- I just pretended to pretend being sick.) There weren't many interesting shows on TV,
- especially because it was mid-day when everyone over the age of five was either in school or work,
- so I was forced to watch baby cartoons on the Disney Channel. Now don't get me wrong,
- I was a typical 10 year old boy, so I loved shows like Foster's Home for Imaginary Friends,
- Ben 10, and Avatar: The Last Airbender. But this baby stuff?
- There's just a little too much awkward staring at the camera for me to enjoy. No Dora,
- I don't see Swiper even though he's the only thing that's moved on my screen for the last 10 seconds!
- Anyway, the TV schedule was giving me a marathon
- of Mickey Mouse Clubhouse, which teaches counting numbers and shapes,
- but I think the only thing I learned is that Mickey Mouse's ears always point to the camera,
- even when his head doesn't, leading to potential infinite twisting which makes me nervous. To prevent this discomfort,
- I will hereafter draw Mickey Mouse with one ear since
- infinite twisting is not possible this way. In one episode of the marathon, Mickey Mouse and friends were climbing some
- beanstalk to meet a giant, like that Jack and the Beanstalk
- fairy tale. The beanstalk itself had branches that the crew could climb like a ladder,
- but they had to pay attention to whether the branches were little or big.
- This beanstalk happened to follow the pattern, 'Little Little Big, Little Little Big' as you went up.
- So Mickey and the gang would shout that pattern as they climbed.
- I guess if they got a branch wrong, they'd fall to their deaths. I don't know that part wasn't made clear.
- Well, after the clan got to the top and fluffed around with a giant for a bit, it was time to return!
- What!? I don't remember what Mickey wanted to do with the Giant!
- It's irrelevant. Edit: They were trying to get Donald's pet chicken,
- Booboo back from the giant. That IS relevant. On the way down from the beanstalk,
- Mickey said something like, "Now we have to say our pattern backward! Big little little, big little little!" Now this is crucial!
- Based on pictures of the beanstalk,
- there is no separator between repetitions of this sequence,
- which means there is no beginning and no end, only a cycle.
- The exceptions are the top and bottom, but I'll deal with them later. What I want you to notice
- is that the cyclical pattern upward of 'Little Little Big' is
- actually the same as the pattern downward of 'Big Little Little', just offset by one.
- The truth is; The Mickey Mouse mob could have actually used the same
- mantra to both ascend and descend the beanstalk.
- Are you concerned that the repetitions no longer align with the end points of the stalk anymore?
- You shouldn't be. Sequences can legitimately start in the middle without issue. Need proof? I was born on a Tuesday!
- All this is to prove that when Mickey Mouse said that the original sequence wouldn't work, and we'd be forced against our will to
- reverse it before we could descend to freedom, he was LYING.
- Lying to friends is already a shameful atrocity,
- but Mickey made the emotional wound cut extra deep by first building trust with his listeners as a teacher.
- He taught us skills that were indeed truthful like the fact that the path to the blue stars leads to the tallest tower,
- but it was all a ploy to make us feel comfortable
- so we'd lower our guards. And then when we least expected it,
- he plunged the knife of deception deep into our
- unsuspecting hearts, and for that I have no forgiveness.
- As an innocent child sitting in bed watching this crime unfold on TV, I
- was devastated.
- Outside, I felt utterly debilitated,
- as if with every passing second my muscles were turning colder and colder into lifeless stone.
- But inside, it felt like fiery ants were crawling and chewing up my insides! The torment was relentless.
- Oh! I also wondered to myself,
- how could the giant have grown this beanstalk such that Mickey WOULD require a different mantra when descending?
- Specifically, what is the minimum-length sequence the giant could grow such that it forwards is different from it backwards
- unlike the beanstalk shown in the show? Seems like an interesting question, huh? Let's call this an
- apalindromic beanstalk. Since palindrome means something that's the same backwards,
- and what we want is the opposite of that. Assuming our only types of branches are little and big, (which I'll abbreviate into L
- and B,) then there are only 8 possible sequences of 3 letters, all of which are identical to their inverses.
- Obviously, any sequence shorter than 3 letters, is also identical to its inverse
- so we'll need to go longer than 3 to find it. A brute force solution would just be to check all sequences of longer and
- longer lengths until we found one that is apalindromic, but that feels lazy and wouldn't give us an
- understanding for why the solution is what it is. So let's think a little harder. My first key observation
- was that a cluster of consecutive letters that are all the same is always the same backwards.
- Let's call this a chunk. If we want to reverse a sequence consisting of three chunks,
- we don't actually have to reverse the whole thing,
- we just have to reverse the order of the chunks. Chunks are actually a big deal because here's point two:
- Every sequence is made entirely of chunks. Even a single letter is a chunk of length 1.
- The number of chunks a sequence has is just the number of similarly lettered consecutive regions within it, but hold on!
- There's only two types of letters,
- so when one region ends we know what the next region must consist of,
- meaning every chunk of B's must be followed with a chunk of L's and every chunk of L's must be followed with a chunk of B's.
- If two adjacent chunks contain the same letter then they just be the same chunk,
- so now we know the number of chunks is just the number of times the letter alternates plus one.
- But hold on! So far,
- we've been considering these sequences as if they have a beginning and an end, but as we proved with our "Detective Work," earlier,
- they don't. They're cycles.
- That means that if the chunk at the beginning contains the same letter as the chunk at the end,
- then they're actually in the same chunk. Cool, right? Now, imagine you start at any point along the cycle and you go around once.
- You will witness the letters alternating a certain number of times,
- but since you end up on the same letter you started on, that number of times must be even.
- Since the beginning of each chunk is defined when the letter changes,
- we have reached our next breakthrough. Every sequence has an even number of chunks.
- For example,
- these have two, while these have four, while these have six. Notice that there's one exception:
- When the sequence consists of entirely one letter and that has one chunk.
- Although, I'd argue it has zero chunks because if you cycle around it infinitely many times,
- there's still one chunk spread across infinitely many iterations and one over infinity is zero
- but we can see that this type of sequence will always be palindromic so we can ignore them. Recap!
- We're trying to find the shortest cyclic sequence such that when it's reversed, it's different, and now we know two things:
- Reversing a sequence is the same as just reversing the order of the chunks and
- every sequence has an even number of chunks. Instead of sorting sequences by a letter length,
- let's sort them by chunk length. As I said before, 0 and 1 are out of the picture
- so the lowest number of chunks we should check is 2. We must ask ourselves, "Can sequences of two chunks be
- apalindromic?" Lets check!
- Now, the length of these chunks is arbitrary, and as you'll see soon, it's actually irrelevant.
- But to simplify things, let's substitute the first chunk with an X, and the second chunk with a Y.
- Don't forget this equivalence. It's also nice that all these symbols are the same reversed,
- so we don't need any more notation than this.
- So, every single two chunked sequence can be written as, "X, Y, X, Y, X, Y, X" and so on, right?
- Well, what is, "X, Y, X, Y, X" reversed? Still "X, Y, X, Y, X", which means this sequence is unchanged and
- palindromic. That means, every two chunker fails. [stock baby crying sound'
- Next, we'll move up two sequences with four chunks. For this one, we can replace the four chunks with the labels, "X1,
- Y1, X2, and Y2" but remember that if this chunk and this chunk are the same length
- then they're identical and in that case we should represent them both with the same symbol that divides the four chunker's into three
- categories those where both pairs of chunks are identical
- Those where one pair of chunks is identical, but the other is different and those where both chunks are different analyzing the first category
- it's pretty obvious that this is just a two-chunk sequence doubled up
- so every beanstalk in this category fails. (Crying) The second category isn't as clear cut.
- But if we define X1 and X2 to mark the two chunks with the same letter
- but different length and Y to mark the ones that are the same letter and the same length
- then every four-chunker of this category can be written as X1 Y X2 Y and so on.
- Reversing it and using the X1's as anchor points to realign the sequence
- we see that everything still matches up and this sequence is palindromic as well.
- (Crying)
- The issue here is that the Y's are just acting as delimiters that don't give us any more
- information. Like glue. So even though the x's are differentiable when they flip around
- we don't know which one belongs with which other one so we can easily shift the chunks around to get a 100% match.
- Rest in peace. As you probably guessed the third category is where it gets interesting.
- Now we have to mark all four chunks with different symbols. When we reverse this boy, and align the x ones as anchor points
- sure,
- the X2's also line up by virtue of being two away from the X1's. But the Y's have
- flipped positions! Meaning that this sequence is different from its reverse.
- So we can in theory say that this is a success!
- Yaaay!
- But I think it's time to show you an example of this. So like we said the third category
- consists of four chunker's where both pairs of chunks are different
- and the only way to differentiate two chunks is with a different length
- so to achieve minimum total length
- we'll make one of the X
- chunks have one B and another x chunk have two B's (as two and one aren't the same)
- and we need one Y chunk to have one L
- and the other Y chunk to have two L's it actually doesn't matter which way we put it in
- So let's plop them in. Our final beanstalk is big little big big little little.
- When we reverse it
- we get little little big big little big
- and there is no way to make the reverse line up with the original.
- Looking at the sequence we can kind of see how it works: having different lengths allows us to say,
- "Hey only pay attention to the chunks with one letter because those are our
- flags when reading it forward the flag with the big branch is in front,"
- Since these two consecutive one chunker's are surrounded by stuff
- We don't care about when the whole thing is reversed and the two consecutive one chunker's are still surrounded by stuff
- we don't care about we can then see that the flag what the little branch is now in front and something has changed.
- So there's our answer
- the giant has to grow a beanstalk with a cycle length of at least six if he wants Mickey Mouse and his
- Posse to be forced to recite a different mantra when going up versus down.
- But what if it wasn't a beanstalk?
- (DRAMATIC STING)
- But a bean TRELLI S?
- (EXTREMELY INTENSE DRAMATIC STING, followed by darkness...)
- Yeah, I gotta stop it with the Inception sounds.
- Anyway, hello again, and how dare you watch such a stupid video!
- But first of all, can I just say that this upcoming December 23rd is scaring me?
- That's because, once we hit that date, I will have been on YouTube for half my life, and that makes me feel old.
- Hmm... actually,
- I take that back.
- Because, I've been telling IRL friends that I do YouTube for so long,
- that it's hard for me to imagine that fact NOT being true.
- But, I wasn't a YouTuber for the majority of my life? What did I do with all my time? Whatever. Oh second thing,
- thanks for 300k subs (that's one step closer to impressing my parents
- And I could make a dumb Sparta joke, but I won't.)
- Okay, I hit 200,000 last September. And 300,000 this September. Oh!
- Okay. It happened!
- It happened! Oh my god, I didn't even finish my sentence! What the heck guys? You were interrupting me! How rude.
- Lastly, while I was gone, I got a Instagram and no, I was not born in 1994,
- I was just the 94th Cary Huang to sign up for Facebook, ok?
- Also, you just know I'm active on that platform because the number of my Instagram posts is a power of ten!
- *inhale*
- WOW Ok, I gotta go finish some take-home midterm exam now.
- Actually though, that's what I have to do right now. So BYE.

Nobody asked for this.

yay instagram yay instant grandma

https://www.instagram.com/cary.huang.94/

Music:

"Branchless", "Widge", and "Chapter Complete" by Sippie Jepper (my brother Michael!!!)

https://soundcloud.com/sippie-jepper

•••••••••••• Music By •••••••••••••

'Into Uncertainty'

Jay Man - OurMusicBox

http://www.youtube.com/c/ourmusicbox

••••••••••••••••••••••••••••••••••••••••

"Childhood Memories of Winter" from: Music4YourVids.co.uk

Fredji - "Happy Life"

/watch?v=KzQiRABVARk