What's the largest number you could fit in a KZbin comment? Also, quick note: you would've had to stop at G63 when starting at G0. Graham's sequence usually starts at G1 = 3^^^^3 and ends at G64 = 3(g63 ^s)3. You ended up at 3(Graham's Number ^s)3 when trying to explain Graham's Number.

This is such an incredible explanation. 10/10

Iteral, which is {10, 10, 10, 10, 10, 10, 10, 10, 10, 10} with BEAF notation

The best and most complete explanation of Perlin Noise in the context of Procedural Generation. Only here i could see how this articulates with a pRNG. Looking at the Perlin (or Simplex) Noise source code i was not seeing nothing random about it, but now i get it

Tried to do 2^^^^3 but its something like 2^^65536 which is too huge of a number to go below tetration 💀💀

4 tetrated to the 4, the first non countable bi tetration, infact is unwriteable lol

Just maybe the TETRATION routine wouldn't get so unforgivably MONSTROUS if the exponent were SUB INTEGRAL ?

I'm up to 2,527,152

5:37

Huh?

What about non integer operations? If addition is 2 and multiplication is 3, what's 2.5?

Recoding this has made me lose my will to live somehow

What s next level of ordinals?

why are you using this function for smoothstep at 12:00 ? i normally just use 3x^2-2x^3 it looks almost the same but it is way faster to compute.

0:42 proppably the funiest gag you've seen this month

2:24 i literally LMAO to this picture 🤣👌

2:20 I almost jumped out of my seat

g(TREE(TREE3))^^^...(g googolplex ^^^^^^^^^^^^^^^^^^^^g (g googolplex))... g g g g g g g g(TREE(g64))

You dislike serifs. You disgust me.

It doesn't see as if you are continuing. That, if so, would be/is a real shame!!!

Imaginary numbers and tetration already exists. *328889😊 Find it to me out together to you whatever.

Call it "divide into 0" and it becomes really obvious what the question is asking.

Inverse is what you will call it superlog but i call it tetralog because it's tetration. slog x^^y = y slog x slog x^y = slog_x x^y (slog x) I found this rule because it's for fun. I might be wrong, please correct me if it is.

there is a logical flaw in the developement of the levels. Tetration should not be 3^(3^(3^(3^3))), but ((3^3)^3)^3)^3). The fact that you write a power tower for tetration for displaying purposes does not give you the "right" to calculate it as you would a "real" power tower. But dude, you are NOT alone with this flaw on YT

Great video!

Tierra Aria mentioned 🗣🗣

Actually, 5^5^5=1.9x10^2184 NOT 1.9x10^2185. So you were off by a order of magnitude. Also, the number name started with 191,101.... But it really starts with 1,911,01...

I thought you would actually play the game and get the maximum highscore

Your voice is perfect

why choose 6x^5-15x^4+10x^3? Are there more?

Tetration is also the end of human intuition Like 2 tetrated of 4 is 65,526. Which is already very big. And this is one of the smallest possibilities from tetratio

It isn't an overly complex concept, but I think it's mostly left out of curriculum due to limited practical application. It's fun to play around with it, but there aren't a ton of truly useful applications where this is a useful shorthand or where people need to work with numbers so astronomical.

There is one thing I don't understand concerning tetration. I'd think that the way you should repeatedly exponentiate would depend on where and whether or not you're writing down brackets. I know that tetration is done by repeatedly exponentiate from top to bottom, but the way the calculation is made doesn't make much sense to me. Let me explain. For example, I want to find the answer to 3^^3. How they'd type this is '3^^3 = 3^3^3' or '3^^3 = 3^(3^3)'. Why are both of these actually the same? The way I see it, if tetration must be repeated exonentiation from top to bottom, then I'd think we should be forced to do so by the inclusion of brackets, and calculate from bottom to the top instead if there are no brackets. Operations between brackets always come first, so why aren't we explicitly directed by brackets to calculate from top to bottom? The way I see it, '3^3^3' should be calculated from left to right, while in this case I ONLY interpret '3^^3' as '3^(3^3)', which forces me to calculate it from top to bottom. Why else use brackets with hyperoperations anyway? Why would it be normal to write down '3^^3' as '3^3^3', while it would be incorrect to write down '3^^^3' as '3^^3^^3' instead of '3^^(3^^3)'. It doesn't make sense to me. I understand how tetration works, but not how there can be that kind of 'freedom' to fully write down the calculation.

Would you use PTEMDAS?

the just in time 4's exist only at 4:41 when you have reached the very end of the game, where you have a snake of 2^17, 2^16, 2^15, and so on until you only then reach 2^4. You will have more room to spawn tiles in the start of the game, making half of the just in time 4's for every tile not needed. So by having just in time 4's for every tile, you lose the chance to get many points. Here, the score actually used just in time 4's in the correct way. I tried it as well, and I also got the "3,932,100 points" by just autoclicking a 1×16 board with 2's being guaranteed to spawn.

I dont agree fully about procedural generation is what is on the center of this. I think there are open games that are repeatable and enjoiable without procedural generation, the problem is that it is hard to make a game world build around an open idea, open world games sometimes work, sometimes dont work. There are other sort of challanges regarding a game being replayable and feel like new every time you start a new playthrough.

I don't know if anyone will be able to help me but I am a bit confused about the lerping part 11:15 since i noticed that the end of the red line segments always aligns with the start of the next yellow segments but I don't understand why they seem to align perfectly

11:00 You talk about lerping, which is linear interpolation, but then you demonstrate bilinear interpolation 12:00 "Smootherstep" is not smoother than smoothstep except that it has more continuous derivatives. Smoothstep is quick and cheap, EaseInOutSine is smoother but slower (unless you use LUTs), and EaseInOutExp is "infinitely smooth", insofar as all of its derivatives are continuous.

3^5 is not multiplying 3 by itself five times. it's multiplying 3 by itself four times. 3x3 is not multiplying 3 by itself twice, but once. 3x3x3 is not multiplying 3 by itself three times, but twice. etc.

Yeah, I was wondering why Terraria didn't have any coal in it... guess it's because every bit of it was shoveled into Red's Christmas stocking because of that daytime Empress fight.

I am trying to wrap my head around procedural generation for game production purposes and this was very helpful! Thank you!

There’s actually octotiation

not gonna lie I skipped through most of this because I didn't understand 99% of it.

Mans tried to calculate tree-3 on a ti 82 😂😂😂😂

how to 2^^1/2

I just wanted to add this comment because when you read the highest possible score it reminded me of my 5th grade teacher harping on “and” in numerical values. According to my teacher “and” is reserved for the decimal place. I appreciate someone using it for its general use in public instead of the technical purpose. Loved your video and thank you for a breakdown of 2048! 🙏

Hello! A while back, I stumbled upon an intriguing video where the creator analyzed the speakers' usage of filler words, I think the creator was in a conference and decided to count the frequency of these words. They applied mathematical techniques to the frequency of these words and concluded that it followed a Poisson distribution. I recall that Grant had some commentary on this. Does anyone happen to know which video I'm talking about?

Ao is there a calculator app that can calculate tetration?

Imbecile

So the fight operation is repeating the tetration a certain amount of times. Now those numbers would be bonkers. 3^^^5 would be going absolutely nuts. Maybe we could test if reality was a simulation by trying to force that calculation into reality somehow. Eventually you'd just overload any simulation's computing power.