The Taylor Series is helping people love math.
Mathematics is a subject people are often very passionate about. I'm Derrick Taylor, and I want to share the things that energize me: the beauty, the mystery, the challenge and the joy of discovery. I do this by making videos on KZread with clear explanations, enthusiastic presentation and a lighthearted sense of humor. Whether you're a student or a mathematician, you'll get something out of my videos.
My release cycle is approximately one video a month right now because I'm a one-man show, in that I do all of the equipment setup, lighting, curriculum, script writing, recording, editing, special effects, producing and publishing. Hopefully as I grow in experience I can increase this pace!
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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! 🙏
Also now I’m conditioned to not use “and”when verbally discussing a numerical value unless it contains a decimal.
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.
What about RAYO'S number? Isn’t this the largest known number? Btw, infinity is not a number. It's an idea.
could've skipped the first 3 minutes. we're here for tetration, not the other obvious stuff.
It's awesome to describe the relation between physical applications and math inventions. That's the mysterious link between the world and mankind.
It's important to realize that more sophisticated numbers are built from primitive ones AND operations. And the most primitive numbers are natural numbers, which is kind of based on our instinct and unexplainable. And remember that, God create natural numbers, all the others are human artifacts.
Thanks a lot
The music is distracting and obnoxious
just like making tiramisu is not taught in school - don't really need it haha
Tetration videos are suddenly trending now
bro got the Dream music before Dream 💀
I remember years ago doing practice mode for months redoing 4s to never appear until I needed them for the maximum tile values. I actually managed to get the maximum score and felt weirdly proud of it.
One thing I would mention, is that infinity isn't a number, it's an idea. And you can't have a number or equation equal to an idea, that's not mathematics either.
Just learned some more about super roots and square super roots aka super square roots aka 2nd order super roots. Super roots for any one wondering is reverse tetration and square super roots is reverse pentation.
Someday, I hope there is a super duper root.
Because it is not useful.
Just happened to bump into you IRL, earlier today. Sorry I didn't know what to say, I absolutely blanked because I was on my way to a concert. Thank you for saying hello and sorry if I was intruding.
That's totally fine -- It's litereally the first time it's ever happened, so I had no idea what to say either! :) And my apologies; I'm bad about checking my comments too. I hope you enjoyed the concert. :)
I don't understand why pentation is following tetration. Why not call it quatrotion?
because "tetra" itself means 4 so it should be followed by something for 5 (hence penta)
Tetration? Did that in Chemistry claas, but we spelled it with an i not an e. 😊 .
I see what you did there :)
I'm 50 and I never got sigma until now. thanks!
how do even code or make a application that can compute and store that much number ??
I don't think it's possible, at least not with where we are currently (and perhaps not ever)
3:25 I'm writing that down
To bad this computer noise seems to think that distorting his narration with the annoying music is helpful.
Maybe i'm not the first to come up with this, but i think this Taylor Series is convergent only to a function that transcends any and all simple expectations of a math content creator. Well done. Keep it up. #Free Palestine!
I love what you’re doing with your channel. Is it also possible without (far too loud) background music? After 3 minutes watching, it had absorbed all attention and I saw your lips moving, but didn’t get any longer one word.
I have been getting that kind of feedback a lot as of late :) Yeah, I put in less music in my most recent vids.
@@TheTaylorSeries Hint: get rid of that music thing totally. It’s a tutorial, not a dance party 👯 🎉. Everything what distracts from the intended information isn’t good. In blockbuster movies is zero music in conversation scenes. That has a good reason. The Millennium Falcon flying into space, then there is music to fill/distract from the boring silence.
You can have fractional exponents, eg 4^.5, which is the second root of 4, ie 2. So what happens with fractional operation numbers?
Okay, it's cute, but because someone devised an exponentially powerful way of multiplying numbers, what does one do with tetration? Since ^4 (10) is a number already larger than all the ATOMS in the known universe, what can you calculate with it!
That's why tetration is hardly ever taught in school, the numbers go out of control quickly
Question: If tetration (the word doesn’t spell check BTW) results in numbers that quickly get out of hand and computers can’t calculate why bother? 😂
Why do I keep getting this? 😂
2:52 - "Begs the question" - you meant to say "raises the question." To "beg the question" is to give a circular justification for a statement. "Chocolate tastes good because chocolate tastes yummy." There is no justification there, just using the argument stated in a different way as reasoning why the first statement is true. 3:25 - "Because reasons." Yow, what HORRIBLE grammar! "Because <noun>" is a construct to be actively avoided. Always use a complete sentence after the word "because" if it is not immediately followed by the word "of." "Wear suntan lotion when you lie on the beach because the sun can burn your skin" or "Wear suntan lotion because of the sun," not "Wear suntan lotion because sun." Note how badly the second sentence sounds when written improperly. Always use a complete sentence or the word "of" after the word "because."
I refuse to believe this isn't satirical. No one can actually be this much of a loser.
My dear ol' dad, who was taking an accounting course at the time, taught me the square root algorithm which resembles long division when I was in elementary school. I've been fascinated with numbers ever since.
Just found your channel. It's a shame you don't post more often, friend. In the 90s I bought a book called, "Mathematics for Nonmathematicians." Really helped shape my view of how to look at math. That said, while patterns came naturally for me, the language did (does) not. This lead to many weird places. I've always thought that the reason math was difficult (well, one reason, at least) was because those that understood it (i.e., made a profession of it) had a difficult time understanding (and thusly teaching) those who found it more difficult. Like anything else that comes easier, be it art, music, basketball, etc.; while those talented enough to understand the complexity of it, the basics are so simple it almost boggles the mind how others can not understand how to do certain easier, basic concepts. With math, unfortunately, the notion of practice is absolutely true while also hated for the same reason. Most people find it so obtuse (hehe) and "unneeded" that they could care less. When you think of it like a puzzle to be figured out, it is exponentially more motivating. And call me old-fashioned, but I also think calculators take away some of the fundamental understanding (and beauty) of how things work. And I'm not talking about "plug and chug" things that can be used as cheat codes on a test; I'm talking about the algorithms themselves. Besides the language, I was lost in the calculator. Eventually my philosophy was if it could not be worked out on a chalkboard, I didn't want to understand because the purpose was already defeated. Tech has its place, for sure, but it can't replace the fundamental operation and thought processes. Professors do this too much. Anyway, great channel. I'm binging on your knowledge and wit. Breath of fresh air.