in the ##juggling irc channel tonight, Varkor asked an interesting question.
It's occasionally claimed that the most number of balls it is theoretically possible for a human to (toss) juggle (on earth) is 14.
Is that true, and if it is, who first said it? (and did they back it up with any evidence?)
After much rummaging around on the internet, the closest I've got to finding the origin of this claim is a paper Jack Kalvan wrote in 1997 https://www.juggling.org/papers/limits
This paper lays a lot of groundwork, and includes some experimental data relating to hand acceleration and applies that to a notional 13 ball pattern - but doesn't *quite* manage to define a theoretical upper limit. Jack does however say "I believe that eventually someone will juggle 13 balls, and flashing 15 doesn't seem too unlikely."
So I suppose it's a strong candidate for the origin of the "14 ball limit" idea.
Does anyone have any better candidates for the origin of the 14 ball limit claim? I seem to remember Joost Dessing was doing a phd(?) related to the kinematics of juggling, but I can't find any useful references to that either, let alone a copy of any papers he wrote on it.
Does anyone fancy revisiting Jacks experimental data, perhaps strapping accelerometers to the hands/wrists of some of the current generation of numbers jugglers? (Peter Bone or Alex Barron for example) to see how they compare to Jacks data from 15 years ago?
Some 'phones have accelerometers and apps to display and export the data. These might give better (=more optimistic) data than Kalvan '97. However he found the average person was fast enough to juggle 16 and the record was 24. Accuracy is clearly an issue. Holding and releasing the first time is also.
I've never accepted the science in Jack Kalvan's paper. There are so many variables that aren't taken into account by simply measuring hand acceleration.
I think the 14 ball claim just comes from the experience of numbers jugglers in general. For example, Ben Beever and I are quoted by Colin at the top of this article as saying that we think that a 14 ball flash is possible, but not 15.
However, if you ask Alex Barron, he'll say that he thinks a 15 ball flash will be achieved some day - so maybe Ben and I are just not good enough to really know.
Would it be possible to flash 15 balls just out of luck? In that case, once the day is there that there are 10 13 ball flashers on the world (which seems realistic to me), a few of them could just give it a couple of tries every day and chances are there that all balls happen to go in the right direction.
I think it would be too frustrating for me to wait between each attempt, picking up balls and getting focussed again.. And how are you going to launch ball nr 8? Putting it on your feet? :p.
I read the accelerometer article a long time ago and it seemed vague to me too, although probably if you give infinite attempts to juggling 24 balls and you have the ability of catching 12 balls in one hand I bet it will be possible.
Would it be possible to run 100m in under 9 seconds just out of luck by giving it enough attempts?
With enough attempts at 15 balls you may be able to get round the accuracy problem, but you still have the physical problem of needing to be strong and fast enough to launch that many balls.
'the physical problem of needing to be strong and fast enough'
Obviously, and for that I said 24 based on the paper (although it does not even take in account that you start with a full hand and end with an empty one right?), but I bet someone can make a better calculation.
Truth to be told, I will be happy if I will reach a 9 ball flash one day, for the rest I like to stick to 3ball tricks that are not scientifically proven ;)
I agree that Jacks paper is incomplete in its analysis (it doesn't take into account the problem of how to accurately launch the required balls from a hand, which has to limit things to some degree) but as an attempt to quantify things rather than just estimate a number based on "experience" I think it's probably usefully thought provoking.
That might be an interesting avenue of investigation actually. How many objects can you hold in a single hand, and still retain the ability to launch them individually?
I think you're probably right about the popularity of the 14 ball claim coming from that compendium article.
Accuracy isn't the only thing that I think's missing from the paper. Other more physical things that should be considered are air resistance on the balls/hands and the weight of the other balls in the hands during the launch, which greatly reduces acceleration.
I think you start running into other physical limits before the limit of how many balls you can hold and release from the hands.
I think the 'limit' is higher than 15 & will be pushed back further when someone reaches it.
Jack's hand acceleration data was taken from a sample of "over 100 people ranging from non-jugglers to some of the best jugglers in the world". We know nothing of the muggles but most people, even those that go to the gym, don't spend their time waving their forearms up & down as fast as they can. The best jugglers in the world have spent years work in on safe, controlled, stable patterns, not waving their forearms up & down as fast as they can.
I've watched some really high end martial artists & they showed that with training it is possible to achieve hand speeds far greater than any juggler that I have ever seen. Jet Li, a former Wu Shu champion who is a bit quick himself has said in an interview that he doesn't like the forms being performed in the modern Wu Shu championships because everything is done too fast.
A few friends at a place where I used to work was talking to me about his Tae Kwondo class. One guy demonstrated his skill by throwing a punch which depressed the skin of my nose but never went as far as the bone/cartilage. They were really impressed because I didn't flinch. I didn't flinch because I never saw it.
I do believe that if jugglers trained as hard as the top martial artists both the speed & accuracy required is there for the taking.
For me the best bit about Alex Barron's 11 ball qualify video is the bit at the end when he talks to the camera, & his voice cracks when he says he has been trying for 2 years to qualify 11.
To me 2 years is not a long time!
I see your point about martial artists being quick, but they're normally doing one quick movement and then maybe other quick movements with different parts of their body. With numbers juggling you're using the same muscles repeatedly for several repetitions. Also, martial artists are normally accelerating from zero velocity, whereas in juggling you're accelerating your arm from going quickly in one direction to quickly in the opposite direction. With juggling you're really talking about hand frequency rather than hand speed.
15 balls may only be 7.1% more than 14 balls numerically, but 9.58s is only 6.4% more than 9s and I think it's unlikely that we'll see anyone run 100m in under 9s in the future (research suggests around 9.44s may be close to the limit). I know that a lot more people train for running compared to juggling, but don't underestimate how far the limits of numbers juggling have already been pushed, or the huge difference in difficulty between 14 and 15 (much more than between 13 and 14 since the numbers tend to come in pairs of similar difficulty).
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