The Mathematics of Bell Ringing

The mathematics of bell ringing. One thing bell ringers might want to do is ring out all possible combinations of their bells. For example, Plain Bob Minimus is a method that rings all 24 possible combinations of four bells. On the other hand, there are also 24 possible orientations of a cube - in fact underneath the mathematics is the same, and the sequences act as a bridge between the mathematical world of rotations of a cube and the musical world of bell ringing.

[@singingbanana]

@superfluousness321 No, the group of permutations of n bells is S_n, which I can't represent with rotations and reflections of a physical object beyond n=4. But I may do this again someday with something else...

[@ericsurf6]

Pretty cool Jim...I really respect the work that you do.

[@Finne57]

Fantastic fun. James looks so young (in a good way)! The best I've seen.

[@ThatGuy-nv2wo]

He is young (?)

[@AndyMossMetta]

That actually sounded lovely as a piece of bell ringing music in itself.

[@scotland7yard]

next instalment: the mathematics of beetles who can't turn around when they fall on their backs

[@grobweiler]

This is great theory. I very much enjoyed watching but no. 1 needs to be the highest in pitch if it is to help bell ringers.

[@singingbanana]

@superfluousness321 This shows that all permutations of four bells (and rotations of a cube) can be generated through repeated use of the permutations (12)(34), (23) and (34).

[@boumbh]

@singingbanana Oops, yes, with only these two permutations you could only make one third of the combinations (two opposite faces of the cube). (1,2,3,4) -> (1,2,4,3) every 8 moves. roll(90) x yaw(180)

[@elton1981]

Great to find one of your older videos. What was really annoying was 1 should be the treble not the tenor!

[@singingbanana]

@Thatguy7109 I use both. It always surprises me that some people find that confusing.

[@TyYann]

@nafativedec Nice to meet you too!

[@singingbanana]

@boumbh That's it :) Have a closer look for a third permutation.

[@boumbh]

There are only two permutations used, alternatively: (1,2,3,4) -> (2,1,4,3) which corresponds to a roll(180) of the cube (1,2,3,4) -> (1,3,2,4) which corresponds to a roll(180) x yaw(-90) of the cube And you get all the combinations.

[@singingbanana]

@TheHungarianCuber It is.

[@PEZenfuego]

I thought that was Lucas Garron. As others have pointed out, good cuber.

[@Error081688]

Was this at MathsJam? Ah, yes I've see the credits now. Well done! I was quite impressed with your abilities as a cubist. That would have been extremely difficult for me to remember, I think.

[@mrtamborineman10]

oh haha it is! sorry i hadn't watched the end. Lucas is an awesome Cuber as well!

[@Steven_Rowe]

That is very interesting , I know the full extent of 8 bells has been rung which is 40320 changes, but let not go to 12 bells as it would take over 38 years on a proper peal of bellls. The longest peal I have rung was 5152 changes of Yorkshire Surprise Major and it took 3hours 27 minutes

[@superfluousness321]

@singingbanana Oh I see so you get the whole of S_4, but can you ring the changes of not just rotational symmetry but the full reflection group?

[@AllonsyRapunzel]

I know this was 8 years ago but it bugs me so much that you start in reverse rounds as the lowest note ought to be the tenor and last bell. Otherwise great vid. Have you tried ringing two at once yet?

[@superfluousness321]

Cool. Do bell ringers not use any odd permutations then?

[@JohnSmith-ku1dr]

Yes they do.

[@TyYann]

That was fun!

[@pwed546]

lucas garron, as in the speedcuber?

[@Error081688]

I lied. I memorised the sequence with using my rubik's cube, haha. Still, well done!

[@robin888official]

(Two years late, sorry, I try catching up.) English "short" names are sometimes confusing to those who aren't familiar with them. (I'm from Germany.) They often seem not to be just abbreviations but completly other names that share the same first letter! Jim for James is not a bad example. :-) I actually got very confused reading "The picture of Dorian Gray" where Lord Henry was also referred to as "Harry" which isn't shorter neigther in speech *nor* writing! If you happen: Thanks for reading!

[@nitrodavid]

i notice they also have the same shirt colours as there bells, classy

[@mrtamborineman10]

where is this? Is that Lucas Garron?!

[@anneonimous9306]

0:35 I think you're actually talking about permutations, not combinations.

[@GyanPratapSingh]

This video does ring a bell.

[@aominaito]

@PEZenfuego second one from left looks same as Lucas so im pretty sure thats him.

[@WiseGuy508]

Actually in a Numberphile video she said her favourite number was 21.

[@addjewelry]

That was tense.

[@Thatguy7109]

Is you name Jim or James

[@Epamynondas]

it's easy, you gust grab a sphere and rotate it it's the same group because the sphere doesn't change, and the bug is stuck on its back so it can't change either MATHEMATICS!!!

[@austreneland]

FINALLY!!!!!!!

[@Forcalious]

Hi people!

[@musikSkool]

mm-hmm, you are mathematicians, then whats her number? (okay, bad joke)

[@AntiCliche]

I... I'm not entire sure I understand. -_-

[@WilliamRussell314]

You so crazy :P :D

[@TheCrazyYoyo]

i bet some people ask you this and you might have already awnsered, but what is your IQ?

[@grande1899]

first

[@aominaito]

@TheHungarianCuber It is.