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.

Пікірлер: 44

  • @ericsurf6
    @ericsurf613 жыл бұрын

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

  • @Finne57
    @Finne577 жыл бұрын

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

  • @ThatGuy-nv2wo

    @ThatGuy-nv2wo

    7 жыл бұрын

    He is young (?)

  • @AndyMossMetta
    @AndyMossMetta13 жыл бұрын

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

  • @singingbanana
    @singingbanana13 жыл бұрын

    @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...

  • @grobweiler
    @grobweiler8 жыл бұрын

    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
    @singingbanana13 жыл бұрын

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

  • @scotland7yard
    @scotland7yard13 жыл бұрын

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

  • @singingbanana
    @singingbanana13 жыл бұрын

    @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).

  • @singingbanana
    @singingbanana13 жыл бұрын

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

  • @elton1981
    @elton19814 жыл бұрын

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

  • @PEZenfuego
    @PEZenfuego13 жыл бұрын

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

  • @TyYann
    @TyYann13 жыл бұрын

    @nafativedec Nice to meet you too!

  • @boumbh
    @boumbh13 жыл бұрын

    @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)

  • @singingbanana
    @singingbanana13 жыл бұрын

    @TheHungarianCuber It is.

  • @Error081688
    @Error08168813 жыл бұрын

    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.

  • @boumbh
    @boumbh13 жыл бұрын

    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.

  • @Steven_Rowe
    @Steven_Rowe11 жыл бұрын

    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

  • @TyYann
    @TyYann13 жыл бұрын

    That was fun!

  • @mrtamborineman10
    @mrtamborineman1013 жыл бұрын

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

  • @superfluousness321
    @superfluousness32113 жыл бұрын

    @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
    @AllonsyRapunzel5 жыл бұрын

    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?

  • @nitrodavid
    @nitrodavid13 жыл бұрын

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

  • @pwed546
    @pwed54613 жыл бұрын

    lucas garron, as in the speedcuber?

  • @robin888official
    @robin888official11 жыл бұрын

    (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!

  • @Error081688
    @Error08168813 жыл бұрын

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

  • @WiseGuy508
    @WiseGuy50811 жыл бұрын

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

  • @aominaito
    @aominaito13 жыл бұрын

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

  • @GyanPratapSingh
    @GyanPratapSingh11 жыл бұрын

    This video does ring a bell.

  • @superfluousness321
    @superfluousness32113 жыл бұрын

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

  • @JohnSmith-ku1dr

    @JohnSmith-ku1dr

    6 жыл бұрын

    Yes they do.

  • @anneonimous9306
    @anneonimous93063 жыл бұрын

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

  • @addjewelry
    @addjewelry11 жыл бұрын

    That was tense.

  • @mrtamborineman10
    @mrtamborineman1013 жыл бұрын

    where is this? Is that Lucas Garron?!

  • @Forcalious
    @Forcalious13 жыл бұрын

    Hi people!

  • @austreneland
    @austreneland6 жыл бұрын

    FINALLY!!!!!!!

  • @Epamynondas
    @Epamynondas12 жыл бұрын

    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!!!

  • @Thatguy7109
    @Thatguy710913 жыл бұрын

    Is you name Jim or James

  • @musikSkool
    @musikSkool11 жыл бұрын

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

  • @AntiCliche
    @AntiCliche13 жыл бұрын

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

  • @WilliamRussell314
    @WilliamRussell31413 жыл бұрын

    You so crazy :P :D

  • @grande1899
    @grande189913 жыл бұрын

    first

  • @TheCrazyYoyo
    @TheCrazyYoyo13 жыл бұрын

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

  • @aominaito
    @aominaito13 жыл бұрын

    @TheHungarianCuber It is.