I'm not a juggler, but watching this has inspired me to relate these principles to my own interests. I feel that this is extremely useful to curious persons with disparate interests to discover a crossover between them. Thank you Allen Knutson.
Re: checking for invalid patterns (around 46:00), check the pattern average. 442 adds up to 10, 10/3 isn't an integer and the number of balls must be an integer. Similarly for anything that adds up to a prime number the pattern must be invalid.
yes, juggling is allways an ongoing process. there are almost (i believe...) an infinite number of combinations of patterns, throws, catches and styles. And as long as you feel good doing it, dont stop practicing. it improves peripheral vision, reflexes, and is realy fun!
Technical gripe (good lecture though): It is possible to compute the validity of vanilla siteswaps in linear time: Simply calculate each throw's "landing slot" and then look through landing slots to make sure that no slot has 2 different throws landing in it. This is one computation per throw which is significantly more efficient (and easier to do manually) than one computation per throw pair.
he was talking about different throws making more noise in general (the one was the loudest and the zero and two the softest) but, in anything, this would make finding the pattern easier, so yes, that would work.
in my oppinion the real beauty of it, is being able to juggle. when you try, try and try a new trick, and then you start being able to do it. the feeling of achieving that is far more rewarding to me then making a good show and people telling how cool it is... don't you remember when you were a little kid and you learned to ride the bicycle?
Actually, I just learned to juggle this past week (well, it's an ongoing process, but I can juggle 3 balls pretty well now). It's a lot of fun. For something that's so simple to do, it really impresses people. Looking at someone else, it LOOKS like it's difficult, but I was really surprised at how easy it was once I got the muscle memory down. I started with tennis balls, but I'm to the point where I can juggle most things I pick up, which is neat and makes practicing very easy.
That's what "average" means. Sum up all individual values and divide by the number of values. However, for juggling, we need to divide by the number of beats. Multiplex throws (e.g. [54]) are always a single beat and between synchronuos throws (e.g. (4,4)(4,4)) there always exists an additional beat where nothing happens by convention and which is not notated. He also talked about decomposing a pattern into orbits and then calculating the number of balls for each orbit individually. The decomposition in itself can actually be usefull, but to just get the number of balls, do it directly. When I script a small juggling act, most often with glowing juggling balls, it is really helpful to understand how patterns decompose into orbits. E.g. 531 decomposes into 501 (2 balls) and 030 (1 ball), so it looks nicest with two balls of the same color and one ball of a different color. However, for simply communicating or learning the patterns, orbits are mostly irrelevant. Well, for harder patterns like 661515, you could leave out an orbit and just practice 661500 first.
Cornell lectures on the events involving Ursa Major Jester on June 6, 2021. Juggling balls is super cool, houuever houu to access a solar system through its central sun and change the positioning of the solar system adjacent to it in that asterism. This is fascinating. Thank you.
Interesting question: Would it be possible to determine the pattern based only on sound if one hand was gloved and made a different sound or would any of the balls have to make a distinct sound as well?
It's a masterful performance, because he's giving a mathematical lecture in its own terms but all the while breaking into skilled juggling - and it all flows so well. The juggling supports/motivates the ideas and the ideas then makes the juggling even more watchable. It's like when teachers use 'affect'. Shame he can't cram it into 18 minutes eh?
This is awesome! my high school physics teacher Dave Morton went to college with this guy and held a world record for 5 years in passing 12 balls with this guy. I thought he was just lying to us but I guess its true
at 41:10 minute mark Allen is asked about the rhythm of a pattern. Some throws will sound different, loud 1's etc, but the rhythm is always even. The pattern shouldn't speed up or slow down. Each throw should occur evenly timed from the previous one. Some patterns are easier to juggle uneven, 51 for example, but from a siteswap point of view they should all be even.
Ok you could do 3,3,3 in a manner where you throw all the balls before the first one lands but later for example in the 661515 the first 6 does not land after the other throws have been made
Speaking in codes and mathematics of juggling about realigning planets and universal systems to make the desired mark of love and union a success and not disaster.
Mathematics of juggling: 1) Hold all balls 2) Start throwing balls in the air 3) If and only if no balls in your hand you may catch a ball 4) If one ball is in either hand throw it in the air 5) Repeat 3) and 4) as needed.
@daltonjuggles Even though I feel like I know 99% of this stuff, it's nice to hear it in the form of Q&A as well. This video really makes me want to record my upcoming 4 ball sync-siteswap video as soon as possible.
I dont understand. He keeps telling that the number means how many throws happen before it lands. But actually in a 3, 3, 3 pattern when you throw first ball in the air then only one throw happens before the first ball lands. Shouldnt it be that the number is the number of throws after which the first ball is thrown again.
Can someone please built a juggling robot who performs different patterns while calculating new ones according to site swap rules? Plus the robot should be able to do the "random juggling" Cornell is talking about in the end.
you just missed out what the x means in patterns like (6x, 4)(4 6x) and also the notation for numbers higher than a nine. If you'd've done that it'd've been comprehensive.
At 37:35, why did he start the 53 with simultaneous throws from both hands. (I'm having trouble getting to the point where I can juggle 53 and I'm wondering if that's an expedient I should be trying.)
Becasue thats the right way to d oit. Its the 4-ball halfshower and you start it from synchronous 4 ball fountains. Just search for a 4 ball halfshower tutorial online.
He basically starts with a (4x,3) throw and then continues into a 53, which is in theory a "hurry", as his right hand has to throw in consecutive beats. What he does: _ _ (4x,3) 5 3 5 3 .... He could have just done: _ 5 3 5 3 5 3 ... So pull the 4x throw forward by one beat, thus requiring a higher 5 throw and avoiding the need for both hands to throw at the same time and avoiding the need for his right hand to throw in consecutive beats. You could also interpret his first throw as a (5,4x), turning his pattern into _ _ (5,4x) _ 5 3 5 3 5 3 ... This removes the "hurry". Thats basically up to your interpretation, whether there happened an actual beat in between the synchronous throw and the first 5. Also, be aware, that in (4x,3) and in (5,4x) both throws cross hands. When you transition from synchronous to asych patterns back and forth, it is possible to encounter crossing even-value throws (denoted by x as in purely synch patterns) and non-crossing, straight odd-value throws (denoted by s).
Ok. So anyone who knows me well knows that this time of year especially I become obsessed with a livecam of a pair of Red Tailed Hawks at Cornell University. But I've always wondered what it was like to sit in on a class at Cornell. I found this video and I was reminded that God gives us each great gifts and mine isn't math, but I applaud the use of a real life example in teaching math. I have always said that doing so is the key to teaching math and science in particular. And for a visual learner in particular this is a great approach! Thanks for this cool glimpse into an Ivy League classroom! P.S. I loved the use of the old school chalkboard.
+Mary Wilbur Reed This isn't an example of a class at Cornell. This is a guest lecture for Math Awareness Month. This is something students go to in their free time. Math isn't a "gift," it's something you work at. Unless you suffer from dyscalculia, you can do math just fine if you put your mind to it. "Visual learning" and the other "learning styles" were debunked a while ago. www.psychologicalscience.org/index.php/news/releases/learning-styles-debunked-there-is-no-evidence-supporting-auditory-and-visual-learning-psychologists-say.html
i dont think someone who doesnt juggle with 10 boll can figure it out so easy, i had a pretty hard time trying to figure it out... often you use the 5ball pattern and multiplex throws
Juggling Theory is strange. a 5 in a 3 ball trick is much higher than a five in a 5 ball trick. take 531 for example. The 5 goes approx 2.1m to keep the same throwing pace. In the 5 ball cascade the throws are much lower. (I have somewhere calculations for this...)
A 5 throw isn't a defined height, you can juggle five balls at varying heights and the siteswap would still be five, the number is defined by the amount of beats under it as opposed to the height.
A 5 throw isn't a defined height, you can juggle five balls at varying heights and the siteswap would still be five, the number is defined by the amount of beats under it as opposed to the height.
It's actually easier than reading music. Each number directly corresponds to a throw height. And numbers are far easier to recognize than black ovals sitting on an array of lines. If you walk up to any sufficiently proficient juggler (understands siteswaps, can juggle 5 balls) and tell him a pattern that he never juggled, let's say 6316131, his main struggle will be the execution, not the understanding.
This was a well spent hour. Even after 3 1/2 years of juggling, I still learned some new things. Thanks Allen!
I know Im kinda off topic but do anybody know of a good place to stream new tv shows online?
@Cooper Dakota Flixportal
@Cristiano Romeo Thank you, I signed up and it seems like a nice service :) I appreciate it !!
@Cooper Dakota glad I could help :)
@@cooperdakota6626 wow that is some wild advertising
_That's a lot of balls._
-Cornell math department chair, 2010
I'm not a juggler, but watching this has inspired me to relate these principles to my own interests. I feel that this is extremely useful to curious persons with disparate interests to discover a crossover between them. Thank you Allen Knutson.
Re: checking for invalid patterns (around 46:00), check the pattern average. 442 adds up to 10, 10/3 isn't an integer and the number of balls must be an integer. Similarly for anything that adds up to a prime number the pattern must be invalid.
yes, juggling is allways an ongoing process. there are almost (i believe...) an infinite number of combinations of patterns, throws, catches and styles.
And as long as you feel good doing it, dont stop practicing. it improves peripheral vision, reflexes, and is realy fun!
Technical gripe (good lecture though): It is possible to compute the validity of vanilla siteswaps in linear time: Simply calculate each throw's "landing slot" and then look through landing slots to make sure that no slot has 2 different throws landing in it. This is one computation per throw which is significantly more efficient (and easier to do manually) than one computation per throw pair.
This is fascinating!
Awesome ! I learned alot about site swap and might start learning some patterns.
Fantastic video!
Doctor: You have 1:05:03 to live
me:
Mathematically, it's even MORE beautiful than it is visually. Something I would have never guessed, or even thought about!
Great video
MY SISTER GOES TO CORNELL AND I LOVE JUGGLING! AWESOME!
he was talking about different throws making more noise in general (the one was the loudest and the zero and two the softest) but, in anything, this would make finding the pattern easier, so yes, that would work.
Wonderful introduction to a fascinating subject. Thanks for sharing.
in my oppinion the real beauty of it, is being able to juggle. when you try, try and try a new trick, and then you start being able to do it. the feeling of achieving that is far more rewarding to me then making a good show and people telling how cool it is...
don't you remember when you were a little kid and you learned to ride the bicycle?
Actually, I just learned to juggle this past week (well, it's an ongoing process, but I can juggle 3 balls pretty well now). It's a lot of fun. For something that's so simple to do, it really impresses people. Looking at someone else, it LOOKS like it's difficult, but I was really surprised at how easy it was once I got the muscle memory down. I started with tennis balls, but I'm to the point where I can juggle most things I pick up, which is neat and makes practicing very easy.
감사합니다, 신선한 깨달음이네요~♡
He made it look so hard. Shouldn't we only add the numbers and divide the result by the number of throws to find out the number of balls used?
That's what "average" means. Sum up all individual values and divide by the number of values. However, for juggling, we need to divide by the number of beats. Multiplex throws (e.g. [54]) are always a single beat and between synchronuos throws (e.g. (4,4)(4,4)) there always exists an additional beat where nothing happens by convention and which is not notated.
He also talked about decomposing a pattern into orbits and then calculating the number of balls for each orbit individually. The decomposition in itself can actually be usefull, but to just get the number of balls, do it directly. When I script a small juggling act, most often with glowing juggling balls, it is really helpful to understand how patterns decompose into orbits. E.g. 531 decomposes into 501 (2 balls) and 030 (1 ball), so it looks nicest with two balls of the same color and one ball of a different color. However, for simply communicating or learning the patterns, orbits are mostly irrelevant. Well, for harder patterns like 661515, you could leave out an orbit and just practice 661500 first.
Excellent video. Makes me wonder what the mathematics of joggling is....
Cornell lectures on the events involving Ursa Major Jester on June 6, 2021. Juggling balls is super cool, houuever houu to access a solar system through its central sun and change the positioning of the solar system adjacent to it in that asterism. This is fascinating. Thank you.
This was great! Although the only bit I didn't already know about was the juggling states at the end.
@tsukiini It's based on the number of balls thrown before a ball is caught from the same hand it was thrown from
Mind BLOWN
Thank you so much for sharing this lecture so we can all benefit from it.
Interesting question: Would it be possible to determine the pattern based only on sound if one hand was gloved and made a different sound or would any of the balls have to make a distinct sound as well?
He did this in class today, best Linear Algebra class ever
amazing
Fantastic presentation Allen! I may have to share this with our audiences so they can appreciate the math behind the performance. :) Cheers! - Nick
SO Clear...this IS AWESOME.
@MichaelCDardant I dont think this possible either way since 333 and 55500 would sound the same if we record the second pattern after the "break".
It's a masterful performance, because he's giving a mathematical lecture in its own terms but all the while breaking into skilled juggling - and it all flows so well. The juggling supports/motivates the ideas and the ideas then makes the juggling even more watchable. It's like when teachers use 'affect'. Shame he can't cram it into 18 minutes eh?
This is how they are going to program robots how to juggle.
Are they 'they' or are we robots? Wait.. was that the same?
+Eri Q There were juggling robots well before this video was put up
To my knowledge the first juggling robots were built by Claude Shannon, father of information theory.
This is awesome! my high school physics teacher Dave Morton went to college with this guy and held a world record for 5 years in passing 12 balls with this guy. I thought he was just lying to us but I guess its true
Wow! Amazing video, now I can really understand what actually goes on during a juggling pattern
at 41:10 minute mark Allen is asked about the rhythm of a pattern. Some throws will sound different, loud 1's etc, but the rhythm is always even. The pattern shouldn't speed up or slow down. Each throw should occur evenly timed from the previous one. Some patterns are easier to juggle uneven, 51 for example, but from a siteswap point of view they should all be even.
I think this person is the best in explaining the juggling mathematics.
I sure hope he is applying his skills and talent outside of the world of juggling.
Being an awesome teacher in one lesson
quite nice, thank you
Ok you could do 3,3,3 in a manner where you throw all the balls before the first one lands but later for example in the 661515 the first 6 does not land after the other throws have been made
Speaking in codes and mathematics of juggling about realigning planets and universal systems to make the desired mark of love and union a success and not disaster.
Very, very nice! Which balls are being used?
Working on it!
Mathematics of juggling:
1) Hold all balls
2) Start throwing balls in the air
3) If and only if no balls in your hand you may catch a ball
4) If one ball is in either hand throw it in the air
5) Repeat 3) and 4) as needed.
I assumed Weiliang Khoo was talking about the professor that introduced you to the class. Sorry for the confusion.
Nice to meet you!
Giving me a pattern like 561 and not telling me it's exited state. What a trickster!
how does he keep track of all of them?!?!??
:) Thank you SOOOOOOOOOO MUCH!
Wow.................................
@daltonjuggles Even though I feel like I know 99% of this stuff, it's nice to hear it in the form of Q&A as well.
This video really makes me want to record my upcoming 4 ball sync-siteswap video as soon as possible.
His pants were really Juggled 🔥
I dont understand. He keeps telling that the number means how many throws happen before it lands. But actually in a 3, 3, 3 pattern when you throw first ball in the air then only one throw happens before the first ball lands. Shouldnt it be that the number is the number of throws after which the first ball is thrown again.
I'm not that great at math, but holy crap I almost understood that! :) mainly because I can juggle... I just never equated it with math until now.
where is the juggler?
Can someone please built a juggling robot who performs different patterns while calculating new ones according to site swap rules? Plus the robot should be able to do the "random juggling" Cornell is talking about in the end.
That took some balls
that's called an algorithm.
I learnt quite a bit! :D
@daltonjuggles Thanks for mentioning this on facebook, this is so cool :)
yes he did
What kind of ball is that
If you search for my name and the paper's title, "Juggilng Probabilities", then you should find a copy of the paper at my web page.
Lol you just turned siteswap into a 1 hour university lecture. You da man!
love ur juggling. didn't really get the math part.
Alan has a doctorate? Hi Alan. Josh from NYC.
question: Do you ever have time to drink or smoke because you spend all your time doing math and juggling?
The video he talks about at 27:06 in this video where he uses a small baby in the juggling pattern is here: youtube. com/watch?v=x8WBhLZDrhM at 4:17.
you just missed out what the x means in patterns like (6x, 4)(4 6x) and also the notation for numbers higher than a nine. If you'd've done that it'd've been comprehensive.
Entertainment is not useless.
I cannot find the baby juggling pattern. With the baby.
I don't get it? It's a picture of Hitler?
***** exactly ; )
*****
La matematica dei giocolieri - Allen Knutson - Parte 7/7 is the name of the video. From 4:20.
Who is the teacher???
@diabolodude000 "geek" is generally preferred
there's a juggling convention??!!!
Alas, I don't have that as an excuse.
There're green ones, red ones, orange ones, and silver ones. ;)
What about it?
At 37:35, why did he start the 53 with simultaneous throws from both hands. (I'm having trouble getting to the point where I can juggle 53 and I'm wondering if that's an expedient I should be trying.)
Becasue thats the right way to d oit. Its the 4-ball halfshower and you start it from synchronous 4 ball fountains. Just search for a 4 ball halfshower tutorial online.
He basically starts with a (4x,3) throw and then continues into a 53, which is in theory a "hurry", as his right hand has to throw in consecutive beats.
What he does: _ _ (4x,3) 5 3 5 3 ....
He could have just done: _ 5 3 5 3 5 3 ...
So pull the 4x throw forward by one beat, thus requiring a higher 5 throw and avoiding the need for both hands to throw at the same time and avoiding the need for his right hand to throw in consecutive beats.
You could also interpret his first throw as a (5,4x), turning his pattern into _ _ (5,4x) _ 5 3 5 3 5 3 ...
This removes the "hurry". Thats basically up to your interpretation, whether there happened an actual beat in between the synchronous throw and the first 5.
Also, be aware, that in (4x,3) and in (5,4x) both throws cross hands. When you transition from synchronous to asych patterns back and forth, it is possible to encounter crossing even-value throws (denoted by x as in purely synch patterns) and non-crossing, straight odd-value throws (denoted by s).
I didn't know that juggling is such a wiiiiiiide open mathematical topic
How many possible tetravex are there?
It's very normal for some accents to have that "eh" or "um" interjection in them. English isn't his first language.
Pᴀʀᴀsᴇʟᴇɴᴇ Tᴀᴏ
He has a very strong French accent.
Really nice, except he didn't talk about passing siteswap or made it clear that there were other forms of notation.
Do you know where i can find the article on random juggling, or his email adress?
thanks
Ok. So anyone who knows me well knows that this time of year especially I become obsessed with a livecam of a pair of Red Tailed Hawks at Cornell University.
But I've always wondered what it was like to sit in on a class at Cornell. I found this video and I was reminded that God gives us each great gifts and mine isn't math, but I applaud the use of a real life example in teaching math. I have always said that doing so is the key to teaching math and science in particular. And for a visual learner in particular this is a great approach!
Thanks for this cool glimpse into an Ivy League classroom! P.S. I loved the use of the old school chalkboard.
+Mary Wilbur Reed This isn't an example of a class at Cornell. This is a guest lecture for Math Awareness Month. This is something students go to in their free time.
Math isn't a "gift," it's something you work at. Unless you suffer from dyscalculia, you can do math just fine if you put your mind to it.
"Visual learning" and the other "learning styles" were debunked a while ago. www.psychologicalscience.org/index.php/news/releases/learning-styles-debunked-there-is-no-evidence-supporting-auditory-and-visual-learning-psychologists-say.html
His pants are fucking SWAG!
i dont think someone who doesnt juggle with 10 boll can figure it out so easy, i had a pretty hard time trying to figure it out... often you use the 5ball pattern and multiplex throws
Juggling Theory is strange. a 5 in a 3 ball trick is much higher than a five in a 5 ball trick. take 531 for example. The 5 goes approx 2.1m to keep the same throwing pace. In the 5 ball cascade the throws are much lower. (I have somewhere calculations for this...)
A 5 throw isn't a defined height, you can juggle five balls at varying heights and the siteswap would still be five, the number is defined by the amount of beats under it as opposed to the height.
A 5 throw isn't a defined height, you can juggle five balls at varying heights and the siteswap would still be five, the number is defined by the amount of beats under it as opposed to the height.
Fear me... I can juggle pi!
i like his pants
And what you're saying is incorrect.
It's a pattern, an algorithm, a rule to follow to get a particular result.
Math is more than just numbers.
read the description
El ocho ... el ocho con tres
el ocho con cincooooooo !!
Alan, what does "NYU Witchcraft" mean? Is that a trick? Sincerely, Josh.
the fact that you misspelled "watched" kinda explained why..... just joking!!
really interesting. made me bring out my diabolo and my juggling balls. really.
lol no in spanish the cascade is called cascada xD
El ocho.... El ocho con 3
I feel like I have dropped something...
Understandable, but complicated. You would have to picture the pattern in your head before attempting, its not like reading music!
It's actually easier than reading music. Each number directly corresponds to a throw height. And numbers are far easier to recognize than black ovals sitting on an array of lines. If you walk up to any sufficiently proficient juggler (understands siteswaps, can juggle 5 balls) and tell him a pattern that he never juggled, let's say 6316131, his main struggle will be the execution, not the understanding.
ma è un incapace questo...ahahha e insegna anche!
my German friend says that your pants are sooo nice
Incorrect. Equations need equals signs, but mathematics is more than just equations.