TWOS-DAY 22-2-22 - The Saga Continues 

The original video starts on Stand-up Maths: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Ffa8-S_71xo.html ... And then transitions to Steve Mould Shorts: ru-vid.com267MQF1z2PU ... Before landing HERE... then going back to the original Stand-up Maths

Honestly not even surprised that Tom can travel between dimensions.

"Everest is the mountain of 2s" K2: "Am I a joke to you?"

Tom finishing this off was priceless

It's appropriate that they make two timelines running parallel with these videos

we love the implication that tom is just, taking a trip to another reality as if it's just another cool thing to make a video about "Amazing Places: Outside The Universe"

"import math as maths" is now going to be my thing. Thank you for these videos - they made my day!

Let digons be digons was one of the best jokes ever. You can tell everyone else was sad they didn’t come up with it

Nicely fitting to see this on numberphile 2

I love the digon tattoo. That's the perfect mix of very nerdy yet obscure enough that you have to be a super nerd to even know that it IS nerdy =)

Seeing the recusion joke twice makes it even more funny 😄

19:50 It's not just about the order of the day-month pair, but about consistency in the day-month-year triple, where the American `month/day/year` is absolutely confusing. I remember shortly after the millennium, when the year was also just a low number, American dates were impossible to decipher, unless it was the end of month. I don't like my country's `day.month.year` date-format either (although, it is at least consistently increasing, as opposed to the seemingly random American format), and I prefer to use `year-month-day` instead, as described in ISO-8601: decreasing order of "magnitude" separated by dashes, as in 2022-02-22, which is also consistent with the decreasing `hour:minute:second` time-format, which - when combined - naturally results in date-time-stamps being sortable lexicographically.

This is the content I signed up for. My fav mathematicians geeking out over silly facts for more than 20minutes. Way to go!

Ah, so Tom Scott is a Time Lord and was out in his TARDIS. That explains his poor attempts to look like he's aging.

If Tom doesn't restart the universe, there will be nothing for him to use in order to practice his parkour.

2^20 = 1,048,576

That was a cool piece of improvised mathematics if that was really as on-the-fly as it looked

Tom Scott having to fix what Matt has done in the end is a mood, honestly.

Matt is 2. James is 4. Katie is 8. Steve is 16. Ayliean is 32. Ben is 64. Grant is 128.

Surprised that nobody comments about "My God, it's full of twos!" XXXD Big fan of Steve Mould.

For Grant: About representing dates and times: This is why YYYY/MM/DD is the only appropriate way to write dates. We don't write the time as mm:ss:hh or hh:ss:mm, do we?

Import math as maths is an excellent language joke.

The amount of effort that went into such a silly cyclical composition joke... I would expect nothing more nor less from Matt, who I have to assume was the mastermind behind the idea 😂 If he wasn't... then I certainly expected more from you, whoever you are! 😁

Looks like this is a Part 2!

Tom Scott is the MVP as always

I love this! To me, this is the culmination Phase 6 of the superhero multiverse ❤

9:10 Two feet on the Mount Everest 😂

2:54 - You don't need to walk underwater, or anything like that. Just go with a friend to Digon Alley, and there you have it.

19:20 the disgust in matts voice gave me a proper laugh

It is oddly satisfying that the video is EXACTLY 23 minutes. So exact I can barely believe it...

Alright, Watching both one after the other was worth it. Nicely set up Love to see all working together over so many years

I have my calendar marked for threes-day Thursday. Let's Goooooooo!

19:22 if you're looking for the date with the most 'e's in it, december and september seventeenth both have seven, and the year can be any combination of seventeen, seventy-three, and seventy-seven, all of which will have eight, for a total of fifteen the most recent e day was december seventeenth, seventeen seventy-seven (12/17/1777) the next e day will be on september seventeenth, seventy-three seventeen (9/17/7317) If you want to include the day of the week, wednesday has the most with 2 Both dates in 1777, 7377 and 7777 are wednesdays, totaling 17 e's. All the other dates are fridays. the most recent was wednesday december seventeenth, seventeen seventy-seven (12/17/1777) the next will be on wednesday september seventeenth, seventy-three seventy-seven (9/17/7377) You could also add 1 e to all of these by saying "the _ of _" instead of the normal way

Loved this! Great to see you all together.

Her tattoo is VERY satisfying! Quite exceptional!!!

Pure joy. What a beautiful, beautiful collaboration!

I watched the other video when it went live... I just discovered this now... This is great! Kinda

I love this channel so much!!! Massages my brain internally and it feels so good!

"let digons be digons" hahaha

Destin's unexpected cameo was the hot fudge on top of this sund...well Tuesdae, but Tom's outtro was the cherry. 🤣

I enjoyed tuning this in.

I don't think I've laughed this hard at a video in my life. A subtle "I'm here at the outside of the universe" joke by Tom after everyone gets sucked into a recursive black hole. Love it

What a fantastic journey through reality itself. Marvellously composed.

For some reason it makes perfect sense to me that Tom is an interdimentional traveler

"For the love of God, surely there's a better way to do this" Grant's notes to himself in Desmos are great. That sentence feels very Grant-like, too, somehow.

I love this unplanned format of you asking follow-up questions amongst yourselves which lead to a discussion! Moar!

Have you ever watched a bunch of musicians just jamming? This was a math jam. And just as fun to watch.

2 is the only even prime number

happy 22/2/22

They got into the sqrt(2) to powers, but they neglected to state that since (sqrt(2)^sqrt2))^sqrt(2)=2 (so not power tower, but nested powers), there is an irrational number which raised to an irrational power is rational- but we don't know whether the base is sqrt(2) or sqrt(2)^(sqrt 2)!

Priceless

Another fact involving 2: In binary, if you write 11, you get 3. Now put 2 0s in between the 1s, you get 1001, which is 9. Keep increasing the number of 0s by 2 and write the result. You get the sequence 3, 9, 33, 129, 513, 2049, etc. They are all multiples of 3. Now, if you divide all of these results by 3, you get the sequence 1, 3, 11, 43, 171, 683, etc. if you take each term and subtract the previous term from it, you get 0, 2, 8, 32, 128, 512, etc. this could also be written as 2^1, 2^3, 2^5, 2^7, 2^9, etc. the power is 1 higher than the number of 0s in the original binary number that yields the result. I’ve tested this with a python function and it works for all numbers below 514, and the only reason 514 doesn’t work is because the value exceeds the size limit for floats. If the above explanation didn’t make sense, put the function below into a Python editor and test: def function(n): return math.log2(((2**(2*n-1)+1)/3)-((2**(2*(n-1)-1)+1)/3)) print(function(n)) It should return the exponent of the power of 2, not the power of 2 itself, as it’s easier to test if it’s a power of 2 by getting the log2 of it. It should return increasing odd numbers, starting at -1 when n is 1. If you would like me to explain the function in greater detail, let me know.

thank you at all who participated!

As a reward for discovering irrational numbers like √2, the Greek Hippasus was drowned.

The fact that video is 23 minutes long on Twosday is just triggering.

I can't believe they talked about Mt. Everest on Twos-Day and didn't mention the 2nd highest mountain in the world, K2!

This was fun to watch

Good thing Tom brought a warm jacket on his interdimensional journey.

Thinking back on 11/11/11 Numberphile was a simple channel and only had James doing something about the date. Wow, has the decade changed.

This would've been so incredibly difficult to coordinate, wow. Great job everyone involved!

Matt didn't listen to publishers when they said "that's not how you do marketing"

In general for f(x) = b^x, if b = x^(1/x) you will find f(x) = x. However, 1 and 2 are the only whole numbers for which the recursive part works (and 2 is the only interesting case). If you do it for 3 or 10 or 20, you will find that the recursion does not converege to that number. The reason is that they are "unstable" solutions. The recursion converges if the derivative around the solution is smaller than 1. In this case, f'(x) = log(b) b^x. Plug in x^(1/x) and you get log(x^(1/x)) (x^(1/x))^x (1/x) * log(x) x log(x) and log(x) < 1 gives only two whole number solutions: 1 and 2!

this is amazing

I investigated the tower of powers for a class decades ago. It does cool things if you let x < 0 and graph the complex numbers that the value oscillates between as you add powers. 🙂

this is great

You guys are absolutely crazy and i really love that! It feels a bit like "Big Bang Theory - Advanced" 😂😂😂

Love it 🦸‍♀️

Nice work Matt.

19:00 the way that I understood this is that you have n ^ (1/n) to the infinitely stacking powers of n^(1/n). So here we have sqrt 2 ^ sqrt 2. The powers will alternate between 2 and 1/2 down to the base. So you really have 2 ^ 1/2 ^ 2 ^ 1/2... So you could say that it (sqrt 2) ^ 2 ^ 1/2 ^ 2 ... And you could collapse the exponents with fancy multiplication and go (sqrt 2) ^ 1 ^ 1 or 2 ^ 1/2 ^ 1. But! If you steal the first 1/2 and multiply it by the next 2 you can go 2 ^ 1 ^ 1 but the last exponent in the chain will be 1/2. So as your chain gets infinitely long, you can keep collapsing the exponents until you get 2^1 =2

Loved this video 😂

"There's no such thing as 2" - Phillip J Fry. It had to be said.

Ending was truly amazing. Or should I say "two-ly" amazing...

these two videos were too much fun

Of course i had to go and check.... Turns out the third of march 2033 will indeed be a thursday. You guys better deliver for threesday video :p

This was the best one to start with

I enjoyed that square roots of 2 section way too much, it was a joy to see you all get really into that one! ^_^

7:32 "some fine toones" laughs

Great interlinked Videos 😎😎😎👍

Well this was two-riffic!

Brilliant. 2 fun.

lol, this pair of videos was great

There was something about the intonation of digons at 2:55 which instinctively made me think of the phrase, "let digons be digons," and sure enough, 9 seconds later...

22/2/22 22:22 Tuesday here in Nepal

I expected someone to sign off with "2-dles!"

love the UK/US time date convention rivalry!

I'm watching this exactly 22 days after it first uploaded

Genius!!

The best joke is the recursion of each Tom referring to "every time" referring back to the other one referring back to the other one, etc... etc...

I have both of the Twosday videos in my recommendations, so I am clearly in the best possible RU-vid

I never thought I'd say this on a Numberphile video but: What The Fuck Just Happened

15:11 Did you seamlessly cut out Grant's struggle with setting up Desmos or did he have this power tower notebook on hand xD?

My contribution: I recently defended my dissertation, and the result I proved relied heavily on the fact that function fields over F_2 behave very differently than other function fields.

Loved this chaotic Saga!

Very cute and nicely done.

The similarity between the infinite fraction and infinite powers is that... You can write 2=sqrt(2)^2, where you actually have another 2 on the right side, so just like the fraction construction, you can "plug in the exact same thing", and now you get 2=sqrt(2)^{sqrt(2)^2}, and you can go on forever again.

This video is a minute too long bc in the other video, the point where they transfer to this channel to the end of that video and the length of this video differs by one minute. Plus, the length of this video would be 22:00 which would've been perfect.

Ladies and gentlemen, the Matt Parker Cinematic Universe.

You don't celabrate e's day. You celebrate e's eve.

awesome

I just *had to* watch it twice.