This lesson has some interesting music theory applications. Western music can be understood as a mod 12 system. And the intervals between pitch classes can cycle through all 12 pitch classes in only two ways: by half step, or through the circle of fifths--or their inversions. The other intervals make augmented triads, diminished seventh chords, whole tone scales and tritones, all of which are cycles that include only 3, 4, 6 and 2 pitch classes, respectively. Hearing these relationships might be helpful for some learners with musical inclinations.
@@ComboClass I'm excited to see that clock! There is also the tangential issue of factors of 2 and factors of 3 being coprime. Since intervals based in 5ths rely on vibrations of lengths based on 2/3 and octaves based on vibrations/string lengths of 1/2, the history of how to finagle this to something that SOUNDS good is pretty interesting. In other words if you cycle through 2/3 intervals you will only approximate an octave after 12 cycles...but we've tweaked this so no one actually is able to notice this discrepancy in practice.
@@jasmint6703 If you aren't already familiar with ViHart's videos then you definitely should check them out, I think you would find them fascinating. The one titled "Twelve Tones" in particular.
Make a grade -0.5 of you showing us cleaning up and get everything put together and setting out the fires, it wouldn’t do as well but that’d be interesting
I struggled with arithmetics before but since I discovered your channel I feel so much enlighted ! Thank you so much for sharing you passion for primes numbers, mods, and all the rest !
You have one of the coolest channels I have ever seen… you really point out some of my favorite aspects of math!! I am very grateful I found your channel
I’m going to be starting grad school in math soon and it’s so nice to have such high level concepts explained in these easily digestible videos! Thank you!!
Currently I’m a private teacher/tutor for some students. I’m also going to start offering online group classes in math and stuff which will be available on the patreon I’ll be launching at the beginning of December
second comment on your video but I love your physical comedy bits, they help the math bit so much by making math fun in any way shape or form; you're one of the only people I know who makes me feel like that, god work.
The artistic idea of this performance is 11 out of 10. For me it does in some sense represent how we try get focused on a problem inside our brain which is full of valuable throwaway thoughts. We can not clean it up completely but just grab the part we need and work with that. An then for a moment all the noise gets into background for the time you are in the thinking process.
If you went through the process multiple times and set the base to various highly composite numbers, could the ratio get any lower than 1/3? Because 6 and 12 had the best ratio and they are highly composite, would the trend continue or is 1/3 the lowest.
There are some mods/bases later with even smaller ratios (although if you were using them as numerical bases they might be less practical). For example, the only numbers coprime to 30 and smaller than it are 1, 7, 11, 13, 17, 19, 23, and 29, which is just 8 out of 30 numbers
The whole numbers less than and coprime to 24 are 1, 5, 7, 11, 13, 17, 19, and 23. Their squares are 1, 25, 49, 121, 169, 289, 361, and 529. Each of these are congruent to 1 mod 24. That means that for all primes greater than 24 (in fact, all primes greater than 3), the prime's square will be 1 greater than a multiple of 24.
Very interesting to see these as visual representations of cyclic groups and their generators. I am coincidentally self studying abstract algebra at the moment, so this is great!
So a base-prime system (base-3, base-5, base-7, base-11, base-13, … base-769, etc.) would actually be a major headache for prime hunters, since any number not ending in zero is potentially prime.
I love the comedy that's built into your videos what with everything falling and collapsing and stuff, but make sure that nothing hurts you super badly! 😆😆😆 And keep up the good work!!
Dimotro do you live in an area where its always pretty warm outside because otherwise I fear Combo Class may have to be moved indoors for the next few months
To check if number is prime I was divising it by numbers up to this number root, for obvious reasons. I believe that by making the mod checks, like in this video I could improve my prime checker alghorithm. It would be more code and memory complicated, but I believe it would be faster. 🤔
Is a 6 pointed star the only star with >= 5 points you can't draw (vertex to vertex obvs to avoid pedantry lol) without taking your pen off the paper? I believe it is the case but I don't have a proof (I believe it would be to do with Euler's Totient function though?)
3:19 an odd hour like 2 in the morning? really any time in the middle of the night would be an odd hour to film this. but i dont see how that would affect the math.
What's special about 12 that we use it for clock faces anyhow? My suggestion in a word: tides. Starting with low tide, a clock divided into 12ths could tell you successively what proportion of the tidal range had been reached at a given time until 6 at high tide, and while it recedes until 12 again. 1 o'clock tells you that 1/12 of the range has been reached, 2 o'clock that another 2/12 has been added (so increase in height and water flow is speeding up), at 3 o'clock that another 3/12 has been reached and we're now at maximum flow speed. By 4 another 3/12 has been added. The speed would be diminishing but the height would still be increasing till 6 when the tide starts to recede again. This change in flow speed is represented by the sequence 1 2 3 3 2 1, which of course sums to exactly 12. If the clock face were divided into 16 say, then the sequence would be 1 2 3 4 4 3 2 1 which sums to more than 16, and if 10 the sequence would be 12321 which sums to less than 10. The high tide to high tide cycle seems to roughly match the midday to midday cycle at 2:1, so 2 lots of 12 covers the latter. Tide, both high water and flow speed, must have been of immediate practical importance to early shore based and many riverine civilizations, enough to decide the number of time division units you were going to use over the tidal cycle.
Isn't there any number high enough to be used as a base for numbering big numbers but having few enough coprime numbers to help us hunt primes? 97 sounds like a good start!
So, this proves that infinity is prime and that a circle with infinitely many points would have all of those points hit by any and every prime number of skips.
Dude this is crazy Do you realize that any prime / 6 will have a .166 or .833 ?!?!?! Having those don't guarantee that the number is prime, but not having those guarantees that it's not prime... Mind blown
Hey, since a lot of people requested that I make a Patreon, here is it (with various cool rewards for different tiers) www.patreon.com/comboclass
This lesson has some interesting music theory applications. Western music can be understood as a mod 12 system. And the intervals between pitch classes can cycle through all 12 pitch classes in only two ways: by half step, or through the circle of fifths--or their inversions. The other intervals make augmented triads, diminished seventh chords, whole tone scales and tritones, all of which are cycles that include only 3, 4, 6 and 2 pitch classes, respectively. Hearing these relationships might be helpful for some learners with musical inclinations.
Yeah I love music theory and will be making some episodes about it in the future. I need to turn one of my clocks into a giant circle of fifths haha
@@ComboClass I'm excited to see that clock! There is also the tangential issue of factors of 2 and factors of 3 being coprime. Since intervals based in 5ths rely on vibrations of lengths based on 2/3 and octaves based on vibrations/string lengths of 1/2, the history of how to finagle this to something that SOUNDS good is pretty interesting. In other words if you cycle through 2/3 intervals you will only approximate an octave after 12 cycles...but we've tweaked this so no one actually is able to notice this discrepancy in practice.
@@jasmint6703 If you aren't already familiar with ViHart's videos then you definitely should check them out, I think you would find them fascinating. The one titled "Twelve Tones" in particular.
Make a grade -0.5 of you showing us cleaning up and get everything put together and setting out the fires, it wouldn’t do as well but that’d be interesting
fr
No way, this set up is perfect
Yes
base 12 and prime numbers? Dango this class is EXTRA combo'd
This man is an absolut legend.
Almost brole his leg for our entertainment
*for our enlightenment :D
...
bRoLe
Absolutely loving this backyard mathematics professor. So glad I found this channel.
I struggled with arithmetics before but since I discovered your channel I feel so much enlighted ! Thank you so much for sharing you passion for primes numbers, mods, and all the rest !
Domotro: gets hurt
Also Domotro: stay safe
😂
If every class is like a Combo Class, then the whole class would get an A,
I came here cause I was bored, came out amazed and excited for more
Professor Domotro getting himself injured in the pursuit of teaching knowledge. What a legend.
You have one of the coolest channels I have ever seen… you really point out some of my favorite aspects of math!! I am very grateful I found your channel
It’s amazing to find a channel that covers topics that are my niche interests!
every time i take a deeper look at the classroom i see something new and obscure i love it
I’m going to be starting grad school in math soon and it’s so nice to have such high level concepts explained in these easily digestible videos! Thank you!!
happy 16:16 video
god bless combo class the funniest math youtube channel out there
Man this is such a good channel, you're so unique!! Are you a teacher professionally lol?
Currently I’m a private teacher/tutor for some students. I’m also going to start offering online group classes in math and stuff which will be available on the patreon I’ll be launching at the beginning of December
Love your content and this is easily one of your best videos, I wish you had more subscribers, I recommend you whenever relevant
Be careful out there with that desk dude! We need more combo class!🤣🤣 great vid as usual guys!!
Thank you! This gave me some new perspective on a problem Im solving!
I love your vids! I’ve been showing my friends them because your energy is just *perfection*. Keep doing what you’re doing! :)
second comment on your video but I love your physical comedy bits, they help the math bit so much by making math fun in any way shape or form; you're one of the only people I know who makes me feel like that, god work.
Underrated channel, u just earned a new sub, I'm literally watching this at 3 AM
Hell yeah, new Combo Class video! :D
Just watched, RIP your leg LMAO
Rip leg 1201-2022
The artistic idea of this performance is 11 out of 10. For me it does in some sense represent how we try get focused on a problem inside our brain which is full of valuable throwaway thoughts. We can not clean it up completely but just grab the part we need and work with that. An then for a moment all the noise gets into background for the time you are in the thinking process.
If you went through the process multiple times and set the base to various highly composite numbers, could the ratio get any lower than 1/3? Because 6 and 12 had the best ratio and they are highly composite, would the trend continue or is 1/3 the lowest.
There are some mods/bases later with even smaller ratios (although if you were using them as numerical bases they might be less practical). For example, the only numbers coprime to 30 and smaller than it are 1, 7, 11, 13, 17, 19, 23, and 29, which is just 8 out of 30 numbers
The whole numbers less than and coprime to 24 are 1, 5, 7, 11, 13, 17, 19, and 23. Their squares are 1, 25, 49, 121, 169, 289, 361, and 529. Each of these are congruent to 1 mod 24. That means that for all primes greater than 24 (in fact, all primes greater than 3), the prime's square will be 1 greater than a multiple of 24.
It’s always a good day when Combo Class uploads a new video! 😄
Very interesting to see these as visual representations of cyclic groups and their generators. I am coincidentally self studying abstract algebra at the moment, so this is great!
So a base-prime system (base-3, base-5, base-7, base-11, base-13, … base-769, etc.) would actually be a major headache for prime hunters, since any number not ending in zero is potentially prime.
Dude, you're a gem on youtube.
I love the comedy that's built into your videos what with everything falling and collapsing and stuff, but make sure that nothing hurts you super badly! 😆😆😆
And keep up the good work!!
Love your class man! I made a poster looking at the 1st 144 numbers like this. I call it the 12x Spiral.
Which one had the lowest proportion of coprimes?
This video made my day! Great content!!
Dimotro do you live in an area where its always pretty warm outside because otherwise I fear Combo Class may have to be moved indoors for the next few months
No snow in my area so apart from when it rains my outdoor classroom should still be ok :)
@@ComboClass ok awesome, that's good to hear
this guy never ceases to amaze us
I've come to a really similar set of discoveries analyzing the twelve tone system in music! This is amazing!
Like the animations, good touch.
To check if number is prime I was divising it by numbers up to this number root, for obvious reasons. I believe that by making the mod checks, like in this video I could improve my prime checker alghorithm. It would be more code and memory complicated, but I believe it would be faster. 🤔
Do you know if there is a more efficient algorithm for searching for primes using other bases, such as 6 or 12?
you are simple amazing. Keep doing videos please, your content is unique :)
really glad the algorithm gods blessed us this time. love the quirkinesss of your vids!
Is a 6 pointed star the only star with >= 5 points you can't draw (vertex to vertex obvs to avoid pedantry lol) without taking your pen off the paper? I believe it is the case but I don't have a proof (I believe it would be to do with Euler's Totient function though?)
Is this what a mad scientist would be for math?
Either way, good stuff.
Great video as always
3:19 an odd hour like 2 in the morning? really any time in the middle of the night would be an odd hour to film this. but i dont see how that would affect the math.
Is there any way to make a base 1? because then that wouldn't have any primes
Imagine winning a messed up desk competition against scott the woz only to find out this guy is the final boss
OMGoodness
I went to high school with Scott the Woz! I didn't know him super well, but some of his friends in his skits I knew better.
Amazing.
Interesting how numbers that are coprime to n, that aren't 1 or n-1 make spiky intersecting shapes that touch every node.
love the credits scene
This is the one UA-camr I would want to meet in real life
Great stuff, also someone was pissed in a car :D So much honking going on!
lmao "mod 11 - just imagine these ones" cracked me up
What's special about 12 that we use it for clock faces anyhow?
My suggestion in a word: tides. Starting with low tide, a clock divided into 12ths could tell you successively what proportion of the tidal range had been reached at a given time until 6 at high tide, and while it recedes until 12 again. 1 o'clock tells you that 1/12 of the range has been reached, 2 o'clock that another 2/12 has been added (so increase in height and water flow is speeding up), at 3 o'clock that another 3/12 has been reached and we're now at maximum flow speed. By 4 another 3/12 has been added. The speed would be diminishing but the height would still be increasing till 6 when the tide starts to recede again. This change in flow speed is represented by the sequence 1 2 3 3 2 1, which of course sums to exactly 12. If the clock face were divided into 16 say, then the sequence would be 1 2 3 4 4 3 2 1 which sums to more than 16, and if 10 the sequence would be 12321 which sums to less than 10. The high tide to high tide cycle seems to roughly match the midday to midday cycle at 2:1, so 2 lots of 12 covers the latter. Tide, both high water and flow speed, must have been of immediate practical importance to early shore based and many riverine civilizations, enough to decide the number of time division units you were going to use over the tidal cycle.
Only 4 days late! good job UA-cam algo! Guess I'll keep dinging the bell until it gets the picture lmao
Show us on the chart: where did the coprime touch the mod?
Great topic ...
Isn't there any number high enough to be used as a base for numbering big numbers but having few enough coprime numbers to help us hunt primes? 97 sounds like a good start!
very spooky, the wilson's theorem
Cant wait till your entire fence is just clocks 🤝💯
A post! Good day lol
hey i know you!!
@@MayorVideo My channel, or do you know me from the comments on these videos?
@@Asterism_Desmos He has your IP address. 🫢
… 🤨🤨
@@unclegardener and family somewhere underground
His videos are perfect representation of my life, total mess but there's value if you wish to see ❤️
You need a stunt double!
So, this proves that infinity is prime and that a circle with infinitely many points would have all of those points hit by any and every prime number of skips.
9:36 we all know what this "sort of star shape" is actually called... Right?
Dude this is crazy
Do you realize that any prime / 6 will have a .166 or .833 ?!?!?! Having those don't guarantee that the number is prime, but not having those guarantees that it's not prime... Mind blown
Wounded in the line of duty 😭 but his pain is our gain!
There is a formula which will give you all results in the last column, testing any N.
You could represent it as ≡|X|
You're like one of those Berlin crackheads. love it
I think that that would looks modern Einstein
voted "professor most likely to contract tetanus while delivering a lecture," by 23k students currently enrolled
love ya, bro!
make your new shows with this stylee.....
Circle of 5ths
I am not going to stay safe. I am going to do drugs tomorrow.
Injury type: occupational
Occupation: mathematics
dude is just a maths lover like me lol
God i want to like the video but it has 456 likes
Tip watch this at 1.75x speed
With all physical effort just for us to learn about Modular Arithmetic and Primes! ❤
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