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 😂

[@aa01blue38]

not gonna lie the editors' visualizations are insanely helpful here

[@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

[@BenjaminBlackParker]

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

[@benjaminanderson1014]

Months? How about ever

[@BenjaminBlackParker]

@@benjaminanderson1014 inscryption was pretty good though

[@benjaminanderson1014]

@@BenjaminBlackParker 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

[@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

[@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

[@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

[@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

[@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-“

[@lorenzosegoloni]

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

[@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.

[@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.

[@TKNinja37]

1:19 -- Editing perfection

[@cineblazer]

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

[@callie1205]

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

[@DWal32]

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

[@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

[@baerthegamer3366]

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

[@Thiefwriter]

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

[@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.

[@BinaryArmorOnline]

This is my favorite game on this channel since Baba

[@itsmhtaab6922]

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

[@dackid2831]

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

[@aemorion]

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

[@pablorepetto7804]

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

[@salmonbamminfish2925]

Amazing start. Give in to the impulsive thoughts

[@terdragontra8900]

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

[@Cubicaltothepowerof3]

8:19 I think it folded in on itself

[@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

[@Map71Vette]

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

[@SonorianBnS]

this is such a mesmerizing game to watch

[@klapekzagady2078]

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

[@DukeChameleon]

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

[@aba3220]

So satisfying! Would love to see more of this!

[@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.

[@mercymakesmemoist8560]

Absolutely incredible editing, thank you BenBen

[@Scratchydoesmusic]

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

[@seanshepherd1071]

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

[@TheBobmBoy]

THAT CUT IN THE INTRO 🤣

[@echoes6092]

This game is AMAZING i love it

[@WhatsAGoodName42069]

Great editing again to convey Tyler's mysticism

[@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.

[@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.

[@christinejoyreyes1767]

That beginning though

[@cynicalmoose19]

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

[@boblobgobstopper13214]

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

[@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.

[@qschroed]

Low dimensional topology the game, this is so cool

[@lillianruiz9474]

It goes in the square hole… 2:26

[@garvgupta3567]

I already love this game

[@lanceriossss]

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

[@Hlebuw3k]

This game is amazing

[@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.

[@ppgang9151]

love this game! keep the videos going

[@Note_Creator]

Wow the last puzzle. 🤯

[@JustAnotherCommenter]

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

[@Bogdan100pink]

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

[@mehdi5575]

Loved it! Would love to see more it!

[@zacharycates5485]

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

[@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

[@notbraytonnottran9143]

The intro caught me off so bad lmao

[@spazzydog100]

2:26 it goes in the square hole

[@Schwanton]

Im just imagining this being useful for my engineering classes.

[@remz94]

great game was fun to watch

[@danser_theplayer01]

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

[@enzo2.2]

1:18 why did u blurr it?

[@dylandepetro4187]

Honestly, just watching this is satisfying. Lol.

[@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!

[@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

[@Awesomekraken677]

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

[@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.

[@ryano654]

2:25 that's right, square hole!

[@akosijj8330]

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

[@Zero102811]

Can't sleep without your videos

[@arandomgamer66gamez69]

1:17 this is why i watch aliensrock

[@HalfBoyHalfGod]

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

[@AirmanTerror180]

The return of glasses Tyler!

[@ExplodingWaffle101]

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

[@jamiesnow8190]

Thanks for the content!

[@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

[@XiaoMingXing]

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

[@john_cool42]

unrelated but i just busted my lip on my metal waterbottle and its bleeding

[@networkofneurons]

is it still bleeding

[@zamasoom.]

we hope you didn’t die

[@thefunny1250]

are you ok

[@daffa_fm4583]

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

[@Fluid-combo]

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

[@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

[@RealXpro0000]

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

[@ronanh.9261]

love it

[@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.

[@rupert_1491]

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

[@little_unicorn5455]

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

[@lewispowell575]

6:30 Mac and cheese

[@mstarOnYT]

I am now really interested in the internals of that game

[@toastonry435]

I can’t believe I’ve been had like this in the opening