Mathematical Construction of a Viking War Horn! - Tandis

[@Axelantic]

Before watching Tyler I had zero interest in puzzle games, but this has been some of the most interesting content I’ve ever seen.

[@aynonymos]

I like puzzles but it's fun seeing how others use logic.

[@Nevir202]

Before watchin his Demon Crawl series I was NEVER able to understand Mine Sweeper. Now I've beaten that game on even the hardest difficulty, albeit with some lucky loot.

[@masonengel1928]

@@Nevir202 I miss Demon Crawl those streams were so good

[@Nevir202]

@@masonengel1928 Never watched the streams, I prefer edited content, as I'm not really good at "watching in the background." so watching someone else play a videogame for 6 hours is significantly less interesting to me than playing a game myself. However, watching a tightly edited, 20-60 minute video that may represent 6 hours of gameplay? That's right up my alley lol.

[@obeliusx]

I play completely different game genres to tyler but enjoy his content still, its calming 😂

[@Mysterious7352]

I like watching Tyler play this type of game because I know I am not smart enough to do it myself

[@alexbarnes5359]

Same here

[@masonboone4307]

Yeah

[@noahkendrick]

Agree

[@LoerisOtter]

That's the reason I watched Tyler's Cosmic Express playlist

[@JamesTDG]

Agreed, feels nice having a break from solving the puzzle in my head faster than the creator

[@aa01blue38]

not gonna lie the editors' visualizations are insanely helpful here

[@anorbinspace51]

use ctrl to use a grid to get things more perfectly. just a quick note

[@Not_mera]

Are you shitting me? I 100% the game today... I read through the little launcher thing to make sure I wasn't missing any of the controls.

[@gametalk3149]

@@Not_merahe is in fact, shitting you

[@BBPdot96]

This is probably most UNIQUE game I've seen in the past few months!

[@benjaminanderson1014]

Months? How about ever

[@BBPdot96]

@@benjaminanderson1014 inscryption was pretty good though

[@benjaminanderson1014]

@@BBPdot96 Oh absolutely, Inscryption is an awesome game. It takes a lot of inspiration from other card games though, so wouldn't call it as unique as this game. (not saying it's worse, just less unique)

[@pewpewpiedipie2673]

In terms of creativity, I loved can of wormholes

[@nluu8132]

The editing is immaculate on this one, especially at 14:00

[@palokyu9891]

I feel like every other comment is about the editing, and for good reason because *damn* his editors have been so good this past year

[@Leveronicus]

I scrolled down and saw this comment at exactly this moment. Wow.

[@IdoN_Tlikethis]

also 11:23

[@kianasheibani1708]

This game's design is very cool because it causes you to essentially invent mathematical and geometric concepts in your head as you familiarize yourself with the rules of the game. A lot of the more interesting examples of this were introduced in the last video (polar coordinates; circles, hyperbolas, and the fact that they are "opposites"; hyperboloids; construction of the torus (aka donut) by gluing the opposite sides of a square; the sphere as a degenerate case of a torus; and doubtless many more that I didn't even think to make the connection to) But this video has some cool examples of this too!

[@kianasheibani1708]

Some notes I have while watching this video: - In the first puzzle, Tyler ends up stretching out a cylinder by a factor of 4, applying the waviness transformation to it, then reversing the stretching. This is an example a group theory concept called _conjugation;_ to be more specific, the waviness transform is being conjugated with the stretching transform to result in a new transformation that (to put it informally) "combines" the effects of both original transformations. - The square transformation (not the regular square one, the new square one) is homeomorphic to the circular one, but with the points on each radial line scaled by a factor of min(|sec θ|, |csc θ|). - Theoretically speaking, this entire game can be mathematically modeled as taking place within a space M x ℝ, where M is an arbitrary 2-manifold. Each of the tiles represents a coordinate chart on M, and the game involves applying the transition maps of these coordinate charts (with the third dimension not involving M being left unchanged). Combined with the rotations that the player can perform, this set of transformations forms a subgroup of the automorphism group on ℝ^3; the puzzle is then to find an element of this group that, given two subsets of ℝ^3, images one onto the other. - The target shape at 8:39 is called a helix. Or rather, to be more specific, it's a cylinder that is deformed into the shape of a helix.

[@FinnishArsonist]

​@@kianasheibani1708 something that I noticed is that a lot of the procedure is very similar to using calculus to find a solid of revolution - you can see the thought process at 4:45. it's interesting to see a game that subtly use those sorts of concepts.

[@kianasheibani1708]

@@FinnishArsonist Yes, many of the shapes constructed in this game are solids of revolution. That comes from the fact that moving from the regular square tile to the circular tile turns a straight line into a circle. If you take into account that the vertical dimension is unchanged, performing that transformation is equivalent to constructing a solid of revolution where the axis is vertical.

[@terdragontra8900]

Very true (though there are no technical hyperboloids in this game, just surfaces with negative curvature with circular cross section, that is, the inner half of a torus)

[@jenniferdunstan5065]

I like your funny words magic man

[@LitNothin]

This game has a similar vibe to origami, where you can get shapes from a single piece of paper that you never thought were remotely possible.

[@Mushboom37]

I’m addicted to the puzzle man

[@Zaniahiononzenbei]

I just wish he put his videos out a little earlier, so I'm not staying up so late. 😅

[@AskTheMasked]

​@@Zaniahiononzenbeiit's literally 2:30AM rn and I'm like "alright, Tyler dropped, I NEED to watch this before sleeping"

[@jozimastar95]

​​@@AskTheMasked don't think you need sleep after this

[@lorenzosegoloni]

Once you understand how the transformations work, this game is so good to watch

[@butter_0021]

I’ve been watching for 3 seconds. Oh god Tyler what are you saying.

[@maximumxposuremarketing829]

Your profile picture shows that so we’ll tho 😂

[@stanley279]

he’s saying “tan this d-“

[@Joseph125]

That last puzzle was incredible. Aspects of the square transformation feel a bit less elegant, but nonetheless a brilliant exercise in getting a complex shape through a series of simple transformations.

[@ragequazar]

this game is genuinely incredible, i have no words to describe the feeling of awe i get from watching the process.

[@citratune7830]

Ok- Other people say they can’t keep up. Theyre right. I can’t. But holy moly, its so fun to pause for like 30 seconds, find a solution that works theoretically, and then watch you figure it out via a very similar thought process. For 5:37, I was thinking you could make a triangle with a right angle by using the bottom right 4 squares on the top right square. Then, just make it a circle and elongate. You just found a different way of making a triangle.

[@citratune7830]

I think a huge help for me is experience with stuff in 3d modelling, like extrudes and revolutes and lofts. Maybe not.

[@cineblazer]

Ben is killing it with those visualizations while you're explaining your thought process. Also, this game is so amazingly cool.

[@TKNinja37]

1:19 -- Editing perfection

[@callie1205]

honestly an amazing way to thing about some of these levels are to just hink about them in terms of doughnuts

[@hydration4333]

every video I think the editing's the best so far and then the next video makes it better, amazing stuff

[@agent_blarpy9730]

The puzzle game for if conventional puzzle games dont melt your brain enough

[@williamthomasmi10]

The editing at 3:50 was very clever; Felt like a hint built into the game or from games like Monsters Expedition etc. Insightful but not too revealing.

[@DWal32]

honestly the most impressive part is the fact you dont need to get perfectly exact replicas of the goal shape

[@Thiefwriter]

The editor is the absolute GOAT, incredible work helping visualize Tyler's thought process

[@baerthegamer3366]

This was very satisfying to watch! Screw those KZbin "satisfying" videos, this is peak satisfaction!

[@dackid2831]

Wow. It's seriously impressive to see you work through these puzzles.

[@pablorepetto7804]

Wow, this game looks amazing! And even seeing the solutions I can't quite follow them, it feels like a magic trick!

[@trueblueflare]

Being really good with visual thinking I think I'd be hella good at this. Just watching it the solution usually clicks in my head very quickly.

[@aemorion]

3:08 Is the fact that tyler can Understand how the checkerboard patterns relate To another pattern, lends credence to his intelligence

[@salmonbamminfish2925]

Amazing start. Give in to the impulsive thoughts

[@Scratchydoesmusic]

4:17 "it's a little small" i'm sure it has a good personality

[@klapekzagady2078]

8:35 So that's how PB2 springs are made!

[@GenTheFurredArtist]

Woah. Whoever edited this, they did a great job. And damn that game looks satisfying.

[@raymondarrington5339]

It’s in the description: BenBenRanger

[@GenTheFurredArtist]

@@raymondarrington5339 I didn't say I didn't know. I was simply complimenting their editing work.

[@pictureplanet1]

Time for some more cursed topology.

[@lwcky8929]

Had to go and watch the first episode of this series i somehow missed, this seems like a really cool game! Excited for more

[@Gihntemos]

I've done a couple years of 3d modeling from a more engineering perspective, like AutoCAD, SolidWorks, and FreeCAD. It's strange how similar this game is to some of those concepts, mainly the idea of projecting a shape across a line. I.e. to get a cylinder you project a circle across a line, as this adds depth to a circle. To make a spring you just coil the line, to make a donut you coil it on itself (or make a circle project down a bit then cut a hole in the middle then fillet because you're more of a chaotic neutral sort) Having said that it's also weird because a lot of the time my brain is just going "I know how to make this shape, but the tools doesn't exist"

[@Gihntemos]

To be clear, a lot of the concepts from this game are indeed used to make real complex parts, as well as simulations for them to be tested. Of course it's a fair bit easier in reality, thankfully. Also I never ended up going into the field, but I do still have a fair bit of skill in FreeCAD.

[@itsmhtaab6922]

this game is absolutely amazing please make more videos of this one

[@DukeChameleon]

Shoutout to mr Editor for helping us understand Tyler's thought process

[@SonorianBnS]

this is such a mesmerizing game to watch

[@mercymakesmemoist8560]

Absolutely incredible editing, thank you BenBen

[@terdragontra8900]

thanks for showing this game to me, i love it. if you beat all the extra levels too, id be impressed!

[@aba3220]

So satisfying! Would love to see more of this!

[@ardabaser1349]

This is very interesting. It feels as if Tyler is trying to solve the puzzles like sort of professional puzzle solver instead of trying to imagine how the transformations would actually work but when the puzzle is very challenging, he starts visualizing the transformations.

[@Map71Vette]

This is great exercise for CAD as well. Teaches you how to make complex shapes from primitive ones.

[@BinaryArmorOnline]

This is my favorite game on this channel since Baba

[@TheBobmBoy]

THAT CUT IN THE INTRO 🤣

[@WhatsAGoodName42069]

Great editing again to convey Tyler's mysticism

[@Cubicaltothepowerof3]

8:19 I think it folded in on itself

[@FrancoisTremblay]

I imagine programming the algorithms that figure out if your shape is "close enough" to the target was the hardest thing to do.

[@XxdevlinxX]

It probably uses photographic processing to give it a percentage of how close the players' output is to the real thing

[@be7256]

i imagine you could overlay slices of the shape you made and the target shape yeah then just check how well it overlays to get a % and boom there's your algorithm easier said than done obviously

[@DanLivings]

I don't think you'd actually need to compare the shapes directly to tell if it's close enough. How I'd implement this is that I'd store the target shape as a list of transformations rather than the mesh for the shape itself. Then to do the comparison, the game would have to: 1. Simplify the list of steps that the player performed. For example, stretching a shape and then immediately shrinking it again with no intermediate transformation can be considered the same as doing nothing. 2. Compare this simplified list to the list for the target shape. Each individual step can have a tolerance for "good enough", which can be as simple as checking the distance between the target shape's position on the grid for that step to the player's shape's position is less than some value (say 0.1 units). 3. If all steps taken are the same, and each step is within the tolerance, the player passes the level. I don't know for sure, but I suspect the actual game does something like this, as it seems to know immediately if you've done it wrong, and only if it's successful is there a delay, which I assume is done for suspense.

[@enzo2.2]

1:18 why did u blurr it?

[@abellematheux7632]

For the puzzle at 6:30 : I'm a maths student with a passion for maths (so it's cheating) and I immediately recognized the homeomorphism with a torus and the associated deformation, knowing that a torus is the cartesian product of two circles, which gives the solution.

[@boblobgobstopper13214]

2:26 that's right. it goes in the square hole.

[@cynicalmoose19]

This game is such a trip to watch. I can only imagine what went into coding it

[@christinejoyreyes1767]

That beginning though

[@seanshepherd1071]

Having taken many calculus classes, I really should understand this game a lot better than I do.

[@JustAnotherCommenter]

7:01 Binocular-looking shape looking like Apple's Vision Pro 💀💀💀

[@echoes6092]

This game is AMAZING i love it

[@lillianruiz9474]

It goes in the square hole… 2:26

[@Awesomekraken677]

lmao tyler was so excited to make that joke in the intro

[@ExplodingWaffle101]

tyler: “this doesn’t feel like something i can get just with a cross section” also tyler: ends up making the cross section

[@Bogdan100pink]

We need to bring back the timer for puzzle games, it just makes the whole experience better

[@danser_theplayer01]

Yep that confirms it, topography people are actually agents of the matrix, they can probably turn a doughnut into a shotgun.

[@ppgang9151]

love this game! keep the videos going

[@garvgupta3567]

I already love this game

[@GarrettHoward22]

Day 975 of telling Tyler that he never finished his minecraft series and that he should finish it.

[@NStripleseven]

Day 935 of agreeing

[@j4m7s]

almost 3 years wow-

[@GarrettHoward22]

@@j4m7s my guy you have not seen recent one lol, just did day 1484

[@qschroed]

Low dimensional topology the game, this is so cool

[@XiaoMingXing]

“Rotation of a donut” Me with my 2 braincells: sooo a rotated donut?

[@isudin]

I'm amazed on how you make these shapes, imagine someone like xqc playing this, don't think he'd get over the first two

[@aatwob]

Hey tyler! I know you don't usually play more factory-based games but I'd love a Satisfactory playthrough. It's really fun, hope you see this!

[@Note_Creator]

Wow the last puzzle. 🤯

[@L4Vo5]

This game hurt my head when I played it. It's interesting to see the differences between how I reasoned about some shapes vs how Tyler does it.

[@Strongestintheuniverse0]

No longer are we doing puzzle shapes for children, we’re doing advanced puzzle shapes for children! Game is really ramping it up now

[@saltyowl3229]

This game feels like if a math grad did research to prove what different, non-equivalent shape “functions” result in the same effective shape, or even some more complex thing related to what sets of 2d transforms to a shape result in the same end “shape” making function, and then made a computer program to test it, then said “man this is satisfying to mess with the numbers for, actually seeing the shapes would be even cooler” then just added a bit of a game on top of their favorite tests

[@spazzydog100]

2:26 it goes in the square hole

[@RealXpro0000]

4:28 is that shape still classified as a pyramid?

[@mehdi5575]

Loved it! Would love to see more it!

[@Hlebuw3k]

This game is amazing

[@little_unicorn5455]

Wait a second is that welcome to hell again ? 7:23

[@Schwanton]

Im just imagining this being useful for my engineering classes.

[@lanceriossss]

This games just melts my brain, it's too much for me, loving it tho ❤

[@arandomgamer66gamez69]

1:17 this is why i watch aliensrock

[@akosijj8330]

The donut binoculars made me scream at my screen when I realized it before Tyler did

[@Zero102811]

Can't sleep without your videos

[@HalfBoyHalfGod]

Can't wait to buy my very own AliensrockTM cups and glasses

[@rupert_1491]

As someone who's an ⅛ norwegian I approve of this video

[@remz94]

great game was fun to watch

[@AirmanTerror180]

The return of glasses Tyler!

[@vinnykitty1983]

Tyler casually creating a möbius strip while making macaroni

[@dylandepetro4187]

Honestly, just watching this is satisfying. Lol.

[@jamiesnow8190]

Thanks for the content!

[@notbraytonnottran9143]

The intro caught me off so bad lmao

[@Fluid-combo]

Tyler looks like a teacher with glasses on. I think he looks good with them on and without them on.

[@Machinex11]

Not gonna lie, but in my 10 years or so of watching Tyler this was probably the first intro I didn't understand.

[@halfprince]

For 12:28, I wonder if this could be used for video games. What's more intensive on the computer, a transformation of a flat sheet or separate models for cups/bowls/etc? I wonder if it's something we can exploit for better framerate... because if a flat sheet can be transformed into multiple shapes like this and all the game would need to do is paste a texture, surely this would be world-shattering for developers.

[@AGENTX506]

This already exists actually, but it's not the time-saver you think it is. Rather, it's the opposite, it's a space-saver. A traditional model is essentially a list of vertexes and their positions. The position of the vertices are essentially 'pre-computed' by the 3D modelling software, like Blender, used to create them. All the user has to do is put the vertices where they say to go and that's it, but of course they have to store the position of each vertex, which takes up quite a lot of space. So what you end up with is good performance, but a large file size. (The same logic can also be applied to textures and pixels). In this opposite case you start with a blank slate and some transformation functions. The transformation functions are orders of mangitude easier to store (especially when your models/textures have tens or hundreds of thousands of vertices/pixels), but of course before the computer can render them they have to actually apply the transform to each vertex to find it's correct position. What you've essentially done is traded time for space. Unfortunately, space is cheap and time is money, hence why traditional rendering wins out. A small corner of the internet is obsessed with making small self-contained programs, often called 'demos'. They often use this second approach to generate all their models and textures and store them in RAM while the game is running, resulting in ridiculously small file sizes. The game .kkrieger is a good example as it only takes up 97kB, but looks incredible. Have a look at 'kkrieger: Making an Impossible FPS' by the Nostalgia Nerd if you're interested.

[@halfprince]

@@AGENTX506 Thank you for the suggestion!

[@daffa_fm4583]

i wonder when he will find out that you can use control to align the shapes

[@RedCMonkey]

He made a flat half donut before 8:34

[@RickMattison314]

Has Tyler ever played Bejeweled? He’s been playing a lot of puzzle games. Granted, Bejeweled is not a long series, but he could get some videos out of it.

[@AexisRai]

godly editing

[@No_My_Sodas_Gone]

I love this channel

[@angeloid_]

Tyler I typically love following along with the puzzle games you play, it's really fun to try and think on my own and wonder where you'll take it but i cant follow this game at ALL i mean HOWW DOES YOUR BRAIN DO THISS

[@goldlizard9270]

New Aliensrock video!

[@zacharycates5485]

Anyone else getting Dr. Mario “Chill” vibes from the music around the minute mark of the video?