KZfaq: Are you a musician? Me: No KZfaq: Are you a mathematician? Me: No KZfaq: Do you use Excel? Me: No KZfaq: You wanne see a guy synchronizing virtual metronoms in Excel? Me: Sure

6:23 "that's pi, so 1 is a third of the way along" Engineers: *smile*

I find the "mistake" to be much more of a fascinating result than the proper synchronization result. I love how it just goes to the maximally divergent phases.

The botched function of that first spreadsheet should be called the Parker-Kuramoto Model. :)

"What's your favorite programming language?" Normal people: C, C++, Python etc Matt Parker: Excel Tom Wildenhain: Power Point

Mathematically perfectly out-of-sync? The Parker Sync.

9:20 I imagine the (former) student watching this video now, seeing that his paper (from 2005) is getting mentioned and even receives some praise from Matt Parker...

The Kuramoto-Parker coupling model you first did is the equivalent of a negative K, which is an inverse feedback, which in turn ends up pushing the phases apart instead of pulling them together. It's easy to model it for N=2 but not sure there is a generic solution for it for arbitrary N. I can imagine Bryan's (article author) view on this video. "How many references have you got to the article?" "Just two. But in 2019 I suddenly got ten thousand likes!"

I love the file name of the Excel document is "n-sync" 😂

The "out of phase" one looks like a 3-phase AC transformer where each of the 3 phases is 120 deg out of phase with each other.

man makes video about metronomes - forgets he has 0 tolerance for clicking.

"we'll get back to that" matt: never gets back to that

i fell asleep in a metronome factory, lost all sense of rhythm.

Now get Steve Mould to make a spreadsheet out of metronomes.

Reversing the order of subtraction of the phases exactly corresponds to the Kuramoto model with a negative summation. This has the effect of driving the phase of the oscillators away from the mean phase of the system. This can be seen by introduction of the 'mean-field variables' which decouples the oscillators so they satisfy the Adler equation (with some scaling). As for a physical model, nothing comes to mind as this also corresponds to negative coupling strength (K

The sign-switched graph reminded me of a juggler, starting off slightly out of phase before everything coming into perfectly synched balance.

“Evenly distributed phases” might be the better description.

Matt: US edition of Humble Pi is coming out in January! Me: *sitting at home in the US holding my UK edition... "Was I supposed to wait?"

Imagine the mathematicans back in the old days had some powerful tool like excel to play around with numbers and formulas.

As I listen to this on my noise canceling headphones, I wonder more and more about the ‘wrong way around’ maths, and their practical application.

This doesn’t capture the fact that in reality sometimes the metronomes end up 180 degrees out of phase. It seems in your excel model they always end up perfectly in phase. Why is that?

The columns on your spreadsheet in the video are labelled wave "A", "B, and "B".

i've loved the RI christmas lectures ever since i was a kid, it's so cool that you got to be involved, what an honour

Matt, you've outdone yourself yet again! So many videos report the phenomenon, but no-one I'm aware of works out the physics. Your channel is undisputedly one of KZfaq's finest. Do keep up the awesome work! Cheers, mate!

Place some spheres on the table and a round dish on top of them. Set the metronomers placed 120 degrees apart, all pointing outwards. Like a clock, at 12, 4 and 8 o'clock. So let's see if they behave like your first example!

2:56 Cambridge engineering student here. I walked on this in one of my first year labs. It was fun.

I love how you investigated the Kuramoto model using just Excel. Even though you said Excel is way under-powered for this sort of analysis, it highlights nevertheless just how powerful Excel is for prototyping, investigating, and even full models. And I was surprised at just how simple the Kuramoto model is as I was expecting some complicated solution to a PDE. Anyway, I have done this with innumerable kinds of models. And when the clunkiness of a spreadsheet is not adequate, I will quickly jump into VBA and bang out a custom function. One could easily create a custom function in VBA for the Kuramoto model that would enable the input of more than three coupled oscillators and output the results as an array. Furthermore, it would be interesting to see the Kuramoto model extended to more dimensions because in your example with the five metronomes, they weren't perfectly in sync which I hypothesize was due to the metronomes not being lined up perfectly.

So happy to see Humble Pi Audiobook finally available in the US! Thank you and Happy New Year!

0:38 Parker Metronomes on sale now

This guy loves spreadsheets more than Christmas 🎅🎅🎅

Got your book for Christmas and have been absolutely loving it!!!

I absolutely love this video, the way he shows his process. Its so much fun watching him work through each step and even discover something new! He doesn't have all the answers, he's here to find them and ask questions!

BTW Matt, it looks like the model that you accidentally first used would be called the "Repulsive Kuramoto Model" and it's apparently interesting enough to get published in PRL!: biocircuits.ucsd.edu/lev/papers/repulsive.pdf They define the model in the form you show, but with a minus before the sum of sin(theta)'s. But it has the same effect as reversing the indices like you did, since sin(x) is an odd function so -sin(x)=sin(-x). EDIT: And for those interested in physical systems that this could model, here you go -- "It may serve as a paradigm for many biological networks in which different elements compete against each other. The best known example of such networks are neuronal ensembles with inhibitor coupling [5]. It is well known that in such systems, nonuniform synchronized oscillation patterns may emerge."

Parker Coupling: perfect out of phase :D

The bridge thing was so amazing to watch! Amazing!

Matt, omitting the ω term left out a very interesting feature. In this case, if the platform the metronomes rested on was acted upon by a constant force, that force could be represented as ω. The interesting part is that this constant force would cause the metronomes to go in and out of phase at regular intervals, and if ω/K is rational, then the system is considered phase-locked. Phase-locking is incredibly fascinating and is fundamental to determining the stability of chaotic systems.

The antikuramoto would be useful in sound engineering on any chorus, flanger or phaser effect. You could implement it with a kuramoto for another interesting effect.

13:15 a wild Parker square appears

I love the way you are fascinated by what you are doing and eventually get to see there.

Great video! It felt soo good watching those sines syncing together. Thats why i LOVE maths.

The physical model for them being perfectly out of phase can be represented by a bad drummer - aka myself.

on the spreadsheet the names of the sin waves were A,B,B also really appreciated the name of the spreadsheet being n-sync

A lovely set of lectures for the bbc! Great job

This was cathartic. I did my final project in high school years ago on this subject. I used the kuramoto model as well in my paper. I reference that paper you used as well! The sound of those metronome brought back some memories of my own testing.

The evenly distributed phases cancel each other out, leaving out a null wave if you summed them. It's like the 3 phase system in AC, all of them some degrees apart from each other so they sum to 0.

1:50 AM Parker upload schedule

a new video is the best christmas present i could ask for

I'm so looking forward to around the beginning of February when the awesome Lectures will be available to watch around the world :)

Having the phases equally spaced would be amazing for building a walker. Maybe somehow measure the position of the occilators and couple it to the position of servos attached to legs. The leg motion could be the coupling force.

The inverted version is actually really useful :) we have a game where a bunch of things happen at random times but at a constant frequency after that and using the parker-kurumoto model, they could be spaced out over time so that the load on the server is constant and not bursty

that was delightful to watch as you worked it out

I'm so glad the sound of those metronomes irritates you. If it didn't we would have had it through the whole video so *thank you so much for stopping them* every time after only a short while. Some people can really learn from you that once you have made your point you don't have to "hammer" it in. This right there is why I love watching your videos!

Matt we love you 💕 and I can’t wait to watch the Christmas lectures as soon as they’re available in the US! Good work out there

This chanel helped me find love for math

RI Christmas Lectures are about the only thing I ever watch on TV at christmas

I decided to learn more (beyond just GCSE) about maths and computing at 33, I'm currently taking a proper run at learning excel fluently as a stepping stone to learn more elsewhere - thanks for giving us a fun brief/scenario to explore the tools!

12:49 "Oh! What has it done?"

The clickity clack is kind of calming

Enjoying the Christmas lectures so far. Seeing my favourite youtubers Hannah Fry, Matt Parker and Tom Scott on the same TV show made my Xmas, and makes me realise we've reached the point now where on-demand culture now dictates what is on traditional TV, rather than the other way around. All three of these people should have their own shows on TV anyway!

I absolutely love you. Your idiosyncrasies match my idiosyncrasies and I feel less strange. Also, you explain things well and I appreciate that.

Three-sided coin pls

The real question is, at what value of K does the kuramoto equation appear in Tupper's self-referential formula?

This is interesting. I was looking for a way to code a simulation and the best I found was this. Great job.

"Noone wants a label on their chart..." that one really got me :)

I would preorder the US release but i couldn't wait and got the UK one. Had to go through the whole thing and cross off all the extra U's but totally worth it.

I saw this in my sub feed. It said it had been posted "14 seconds ago." I found that a bit odd. It is the earliest I've been to a newly posted video (since I clicked on it right away). It currently has no views and 3 likes, which is also odd. It also has five comments... but none have appeared on the screen. Another odd thing. Well, Happy New Year!

The “even-spaced out-of-phase” plot is an example 3-phase AC power (US) and how it looks.

I think this is my favourite KZfaq video ever!

You could have just made K negative. Also would be interesting to see how much you could perturb the angular frequencies before the synchronisation stops working

I will get the spreadsheet, complete with the A, B, and B sine waves.

What an interesting video. I still have to watch the first two of Hannah's lectures, so will probably do that now on iPlayer. I wonder if I could have done this in Algol, back in the day when I could still remember how!

Congratulations on the half million subscribers 👍😉 Looking forward to your 2^19 subscribers video...

Would this also work in 3 Dimensons? Like pendulums swinging in different directions while hanging on a board that's also hanging? Or would this just lead to a Chaotic pendulum ?

What happens if you, instead of putting the oscillators on a "linear coupling board", put them on a "circular coupling board", like on the tips of a huge fidget spinner/ball bearing?

Really cool video. This may be obvious to many, but I had to think about it for a second: The equation given for the model is an "equation of motion" (a differential equation that defines d(theta)/dt), but doesn't give you theta(t) outright. So Matt is just doing Euler's method to solve theta(t) and plug that into x(t). Euler's method is the simplest way of numerically solving an ODE when you know theta(0) and d(theta)/dt, by approximating theta(t+dt)=theta(t) + dt*(d(theta)/dt). Of course, there is no factor of dt used here when solving theta(t), but I guess all the scaling here is basically arbitrary.

In July 1980, I took a riverboat from just south of Singapore into the heart of Sumatra. We entered the Siak River just around sunset and all along the riverbank, about every 10th tree was covered in fireflies - and they were all blinking in sync. Quite an astounding sight - and no noise either.

Hopefully we on youtube get to see the lecture Hannah did with you. Also, digging the scruff. 😍🔥

Read "Spreadsheet", clicked instantly

This is the second video where you have talked about your book (humble pi) at 3:14. It is a good book I have enjoyed reading it

Calls it Stand-up maths office Furnishes it with a chair

Now I'm really interested to see what would happen if you made them coupled but with different frequencies. What would the end result be

Are we going to talk about the fact that he named the spreadsheet n-sync

This demo with metronome and Excel model also illustrates how laser oscillators work. The phases couple from mutual feedback.

12:01 That's what my compiler said. Cheers for the video Matt, all the best for 2020 and quick question : Is there something you can't capture in a spreadsheet ?

"Excel is super underpowered for what I'm trying to do." These works have been spoken by everyone who's ever used excel.

looks like a Parker beard has grown :)

I loved this. I love putting math models in Excel to explore them, just like was done here.

Hi, Matt! I’m not much of a mathematician in any way, but I do find mathematics fascinating, especially as a musician and have always really enjoyed your videos! This particular one has gained my interest because of my familiarity to a similar topic in music. You should check out Steve Reich, a minimalist composer who uses the compositional technique of “phasing” in some of his music. Having played one of these pieces, “Drumming,” I became very familiar with the concept and was excited to see it in mathematics. In music, two (or more) players play the same rhythm, whether in unison or offset, and one player stays steady in tempo while another gradually speeds up, going out of phase, and through that eventually lines up on a different partial of the rhythm to create different interlocking patterns using the same rhythm through this process of “phasing.” This also often achieved using electronics and was how it was discovered, and was originally thought to be almost impossible for a single musician to do on their own. It’s a really awesome thing to listen to and creates an extremely satisfying moment when all the voices eventually sync back up in unison. You can find this in other works of his like “It’s Gonna Rain,” “Violin Phase,” “Piano Phase,” and more. He also takes this gradual process and makes it immediate in a process called “phrase shifting.” This takes out the gradual speeding up and at a certain moment a voice changes where exactly the rhythm starts like in his piece “Clapping Music.” You should definitely check out his music if you found this metronome phase cool!

Why do you do this to me Matt? I was about to go to sleep and now I have to stay up another 20 minutes!! (Not complaining though!)

Parker Synchronizing: doesn't exactly sync, in fact it makes stuff as out-of-sync as possible, perfectly out of sync!

What an awesome video!

Something you didn't touch on: The Kuramoto model allows for each oscillator to have their own increment/frequency/omega parameters. That's quite useful for real-world models where there is going to be some expected variance in the frequency of oscillators. For example, your metronomes will likely move in/out of phase on their own over long periods of time, despite your attempts to set them identically.

just for my curiosity: WHAT happens if the metronomes aren't synchronized perfectly? how would that graph look like? is it exponentially more difficult to "code" in excel?

A little disappointed that you went for “tweak freq” rather than modelling the forces directly to see the effect come out of the physics.... Also, modelling if metronome freqs are close bu slightly differ

Im mostly impressed by your excel skills :o I do C# in Visual Studio all day but this is amazing.

Nice few beers there too, from here in Melbourne (Colonial Brewing). Cheers Matt!

Didn't Mythbusters try syncing loads of these on a board wayyyyy back as well?

Least interesting video title award for 2019 goes to Matt Parker

Awesome video !

love the segue at the end... reminds me of the awesome insanity of Matt's FOTSN recursive intro video