The Unusual Mathematics of Modular Division

In the land of "mod 60" (which works like minutes on a clock) "1 divided by 7" is 43, while "1 divided by 6" is impossible! Let me show you the strange patterns of "modular division", a deep mathematical concept which we can visualize through clocks and calendars....

I had hoped to have this episode out a couple days ago, but my computer broke over the weekend. I got a new one, but had to re-edit this episode. Now things should be back on track with another new episode this weekend. And make sure you're also subscribed to my @Domotro channel which has lots of shorts, livestreams, and bonus videos in between the main episodes here.

Special thanks to Evan Clark and to all of my Patreon supporters:
Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, and Michael Friemann.

Domotro
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If you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)com

In case people search any of these words, some topics mentioned in this video are: clock math, modular arithmetic (particularly mod 60 and mod 7), modular addition, modular subtraction, modular multiplication, modular division, coprime (also known as relatively prime) numbers, which operations have the property of being "closed" in which realms of numbers, and more!

If you're reading this, you must be interested in Combo Class. Make sure to leave a comment on this video so the algorithm shows it to more people :)

DISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this series. These videos are for educational (and entertainment) purposes.

[ComboClass]

I had hoped to have this episode out over the weekend, but my computer broke. I got a new one but had to re-edit this episode. Now things are back on track and I'll have another new episode this weekend. And make sure you're also subscribed to my @Domotro channel which has lots of bonus content in between these episodes.

[cookiequeen]

I can not express how cool it is to have found this channel. This particular video covers exactly what I think about all day and this is so cool!!

[themightyripples]

I loved the gag with the white boards. First time you pulled the one up just to have it fall and pull out a new one. Second time you tried writing on one and it fell so you just started writing on the other, lmao

[soninhodev]

Great video as always, grade -2 is already shaping up to be awesome

[mohammedalimuddin]

I thought i've checked out every cool educational channel on youtube.. Then I found this one.. You guys have earned a fan..

[readjordan]

I like the candor and positivity of the instruction here

[harriehausenman]

Wow! Great production quality! You really upped your filming and editing game. Love it! 🤗
Thank you for this very fascinating and intriguing intro to mod-math (not to be confused with the infamous math-mod 😄!).

[cookiesversuscream]

Elementary school math: We're going to learn about division! Yes, not all numbers divide evenly into each other, but you don't need to worry about that! We'll just use remainders!

Middle school math: It's time to learn about decimals and how to do *real* division, not that remainder cop-out nonsense.

College-level math: Actually, remainders are the defining aspect of modular mathematics, which is super important for many mathematical fields.

I may have forgotten nearly all the trig I learned in high school, but life truly does work in cycles.

[stephenjames]

Lovely. (7)(43) - (60)(5) = 1 and (2)(4) - (7)(1) = 1. For me, moves around the clock give the clearest intuition of the Euclidean algorithm.

[skeptica]

Nice, I was just wondering about this!

[tothemax]

There is an application of this principle in Vernier scales. Within the same distance, one scale will have N markings and another will have either N+1 or N-1 markings, which guarantees that the two are coprime so the intersection of the two covers the whole range.

[peter.]

spilling the birdseed was a perfect metaphor to learning math. as the seed is falling there's total chaos, but they always settle themselves down to the lowest common denominator;)

[aethrya]

Bro you're weird and I love your channel.

As a cryptography nut, it's good to see modular arithmetic.

Keep it up homie, thanks for sharing the knowledge.

[potatodawin]

calling the congruent sign "modular equals" makes it a lot easier to understand. Thanks for that! :)

[rhandhom]

I feel like I'm learning advanced mathematical concepts at my late grandmother's house, which is a bit comforting if not strange.

[sandpiperbf]

Love the implication that you're just like a crazy homeless math man living in a tent somewhere

[helixkirby]

Is it merely a coincidence that when you talked about consistent systems that you were holding a RING, which fields like Z/pZ are? Are you going to do bezout's lemma next, as I imagine that's what you were hinting at at the end for finding multiplicative modular inverses?

[Tletna]

I put a hint/simple solution to the 3 squares with 2 angles adding up to the 1st angle proof under the name KGG in puzzle discussion. I hope that was the correct place to put that.

[gottadomor]

Haven't watched yet but saved for later. Just want to say believe modular division how the Rainman - "guessing" the weekday any birthday fell on - calculation derived. Another method but much slower, an algorithm based on the perpetual calendar. Looking forward to viewing & t/y the YT.

[BooBaddyBig]

I dimly remember once I was testing some software written by a colleague and it worked fine, but then suddenly some huge numbers popped out. That's why, it was using modular arithmetic internally.