The paradox of the endless violin bow (VIDEO)
The violin bow has a problem: it ends. And with it, so does the phrase.
But what if the bow didn’t have to end?
Step into a parallel reality with me, one where no matter how long you draw a bow, you never reach its limit!
Zeno the Greek
In the fifth century BCE, Zeno (despite not owning a violin, as far as we know) thought about this very problem. He devised a series of “paradoxes” that challenged his listeners to perceive time and space in new ways. In particular, he proposed that motion is nothing but an illusion!
One of his most famous paradoxes features Achilles and a tortoise. And it holds the key to an endless bow, which in turn will give you endless phrases.
So if you’ve ever been frustrated by bow changes, watch my video and discover a brand new practice technique:
What did you think of Zeno’s paradox? And how are your bow changes? Let me know in the comments below.
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21 thoughts on “The paradox of the endless violin bow (VIDEO)”
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Love the article and the advice! I believe you are saying that when you feel you get your best sound, you can make the bow change?
I imagine Zeno’s Paradox doesn’t work in real time because Zeno considers distance and speed (speed or velocity is usually measured as distance/time, e.g., 65 miles per hour) but Zeno doesn’t throw elapsed time into the mix.
Thus, as time elapses, Achilles will soon overtake the tortoise. But, to finish second place to Achilles is pretty dang good!
Right on with the bow changes… bad bow changes result when you wait until you’re making a bad sound. Great ones happen when you’re making a great sound. And who knows about Achilles? I think he had a frustrating time of it under the watchful eye of Zeno!
Ugh, this paradox really messed with my mind! I think the paradox also works if you think of elapsed time, as in the tortoise and Achilles are always moving, and they don’t stop whenever they reach the same point like in the cartoon Nathan showed. Zeno thinks of distance and time as things that can be infinitely divided, so Achilles actually never reaches the tortoise, and both never reach the finish line! I was reading this article that was really interesting: https://plus.maths.org/content/mathematical-mysteries-zenos-paradoxes
Here’s an excerpt:
“By dividing the race track into an infinite number of pieces, Zeno’s argument turned the race into an infinite number of steps that seemed as if they would never end. However, each step is decreasing, and so dividing space and therefore time into smaller and smaller pieces implies that the passage of time is ‘slowing down’ and can never reach the moment where Achilles passes the Tortoise. We know that time doesn’t slow down in this way. The assumption that space (and time) is infinitely divisible is wrong”
But it’s a cool way to think about motion! It might help with fading away a long note, or making a bow change that happens through a diminuendo seem seamless because we are thinking of infinite little pieces of distance and time.
I like your train of thought about fading away a note! And nice link too, I look forward to giving it more than the skim I just gave it now.
Thanks! Great visualization and probably helpful for other types of bow work, such as up bow/down bow staccatos, Collé, etc., yes?
I think so, especially for chaining together strokes like you’re talking about with the staccato or perhaps linked martele.
Hi Nate! Love your post! After seeing your video, I got inspired and made a little recording of my own: https://www.dropbox.com/s/oavqgmf2x8oo6r4/Fun.aif?dl=0
Do you like my bow changes? Anything else you like/dislike? Thank you!!
Great Beethoven 9, thanks for sharing! Bow changes sound wonderful, so I’m happy if this inspired you. For an audition, I would get even pickier with the pitch as far as matching notes: all B-flats, Fs, etc the same. Sometimes I found that the vibrato was too wide for this excerpt, and that that was affecting the pitch perception. All around high quality though.
Ah, I see what you mean! Thank you. There is no hiding with these medium speed excerpts 😀
Also, the simplicity of this particular excerpt made me afraid of sounding too cold; hence the vibrato.
Definitely a warm excerpt! But go for that with the right hand, only adding a bit of left hand (vibrato) for color.
pronation and supination have something to see with the parameter of tilting the bow more or less – Pronating at the tip -down bow ) for a more flat bow and supinating at the frog (up bow) for a bow leaning towards the fingerboard – That’s what I understand here –
Yes, for a more even sound (with a few exceptions) it’s best to have flat hair at the tip, and a slight tilt at the frog. The exceptions would be when you need maximum sound, in which case you can keep flat hair all the time!
What did Zenon actually prove? (By the way, if you check the Greek spelling, you will notice that it will end by nu, but the English and the Americans neglect that for some reason unknown to me.) What Zenon actually showed was that there is an infinite number of instants of time when Achilles has not reached the tortoise. This is NOT the same as Achilles would never pass the tortoise, because this sequence of times converges to a specific limit. This limit is just the time when Achilles has reached the tortoise. Of course, this means that we assume time behaves in the same way the real numbers do (this is not obvious, but it seems to be a very good approximation at least). Zenon was a very clever man, indeed, but he did not know the mathematical concepts of real numbers and convergence (nobody knew at that time).
Good points! I hope that violinists will keep a sense of humor when applying this to the bow. If it helps people feel that they have more and more bow than they used to, it will be a useful paradox!
Also, I did not know that about the Greek spelling. Zeno is what I’ve always read, and what was familiar to me, but I’ll look out for Zenu!
Well, not Zenu but Zenon… The Greek spelling is Ζήνων. Here the last letter is not our v, but a Greek alphabet which we usually call ‘nu’ if we do not have Greek alphabets available. In transliteration we replace it by n.
By the way, you are doing a great job in telling people like me how to play the violin. The internet gives possibilities which were not available when I was young. Still, I try to improve with a variable success.
Your articles are so fun and helpful! 🙂 When you talk about the motion of turning the door knob, and how it’s not visible at bow changes, that confused me a bit. I think I can see your forearm rotating to your left a bit on the bow change at the tip. I think supination isn’t apparant at the frog because it’s more slight and counteracts the pronation that happens on the up bow, so the hand returns to a neutral position, where the weight of the arm is more balanced between the fingers. Is that a valid way to think of it?
Also, I was thinking about smooth bow changes in various parts of the bow, and believe the door knob turning motion happens as well, but usually to a lesser degree than at the tip or frog because the bow weights are less extreme in the middle 2/3 of the bow. Is that a valid thought too?
Yes, all your thoughts are right on! You can see the bow stick bending when I demonstrate the “doorknob” thing at the tip. The energy of the rotation (pronation) goes into bending the stick.
Awesome content thank you for sharing useful content
Thank you Nate, this is a wonderful lesson. I do all these instinctively, but it helps to know the mechanics.
Good “food for Thought”!
I did not find any observations on the bow’s speed at the tip or at the frog…?
Maybe I didn’t put that in here! Even though technically the bow must slow down and stop in order to change direction, the image I find helpful is that the bow maintains the same speed from one side of the bow change to the other. In other words, fast to fast, or slow to slow. That way the change is not noticed.