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Parabolas (etc.)

Tuesday, January 13, 2009 - 10:24 PM

Special bonus of the week! A video inspired by the mathematician, Steve Strogatz. At the age of thirteen, Steve was astonished to find that pendulums and water fountains had a strange relationship that had previously been completely hidden from him.

Directed by Will Hoffman with Director of Photography Derek Paul Boyle.


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Comments [75]

Interesting graph of time-of-swing (period) versus the length of the pendulum, but I'm afraid that it does not constitute a great discovery. Instead of a parabola, the student would have graphed a straight line - if the angular displacement of the pendulum was SMALL, say less than 10 degrees. This has been shown by countless experimenters, starting with Galileo ~1600.

Dec. 10 2013 09:40 PM
Pistol from Manhattan

Not much content these days. It's a shame because when you use to offer more content I was an avid listener. I guess I'm unclear about the type of revenue stream it take to create a show, and stream it. And how much you need to make up the difference between what you collect on your own and what you get from NPR? And is this shortfall in revenues what's holding up the production of new content?

Dec. 09 2013 01:55 AM
Fred Kepler

Umm... Most of the curves in the video are NOT parabolas. The mathematician's moment of insight is inspirational, but the rest of the video kind of makes a mess of the concept. You've included golden arches, several random curves and at least one catenary, all without explanation.
So it's essentially an observation, without explanation, followed by a sequence of random curvy stuff. And it seems that many of the commenters are eating it up. I'm reminded of a famous quote by Barbie: "Math is hard!"

Dec. 08 2013 04:11 PM
Myron Graff

Although I did not (patiently) view all of the parabolic natural examples in your piece, I would like to add one for your consideration. For many years, orthodontic wire manufacturers have produced preform (parabolic-shaped) arch wires for use by orthodontists. These are appropriate due to the parabolic shape of dental arches.

Dec. 08 2013 03:26 PM


Dec. 06 2013 11:18 PM

This is a great video. I am an undergrad student in applied mathematics with a minor in physics, working toward an academic career in mathematical physics. I love to hear others speak of what sparked their passion. That one moment that others passed by, but not you. Something so significant and profound that it changes thought and lifestyle, yet these moments are still and quiet like. I think it is like seeing your reflection in the water. Most only see the surface reflection and think "that's what I look like"...but some of us see deeper. We think "how does the light reflect so detailed an image"? Then we fall in love, not with ourselves as did Narcissus upon seeing his reflection in the water, but with the light and our interaction with it. This is not what started me on my journey in mathematics, but it is one of the many experiences common to mathematical scientists and others in related fields. Thanks for the video.

Oct. 24 2010 12:49 PM

Uhhhhhhhh. . . What the hey?????? "Giving me an update?" OK. . . ?

May. 20 2010 09:46 AM
Austin & Blaze

Vanya222 we are infact not done. we have recently moved in with Logan and things are going great. We worked out an amazing arrangment with the bills. everything is fine. just giving you an update on our progress.

May. 19 2010 03:10 PM

Aaaaand. . . I think the author's done.

May. 15 2010 10:00 AM

Oh man, this is hilarious. . . I'm wondering how long the person writing for Blaze, Logan, and Austin will keep this up.

Yes, I've have decided that they aren't real people. This is actually a very common prank pulled by many kids on a PBS Kids GO message board. (They also 'imposter', which is posing as someone else to ruin their reputation, get them into trouble, ect)

May. 14 2010 07:01 PM

Austin i love hearing back from you. i would be flattered to spend a wild night with the both of you over dinner and drinks. i would have to look into things, but i believe we could possibly make things happen between the three of us. i asure you that you both would have plenty of privacy. also about the bills we could decide that at a later time. i hope to hear back from you both shortly.

-Logan<3 love,peace,laughter

May. 12 2010 03:31 PM

i would also like to say: Get a life Ben! Seriously! who stays up until 2 in the morning watching videos of parabolas!?!?!

May. 12 2010 03:30 PM

sorry about that. the computer here at the library crashed and i was unaware that my first entry was posted.

May. 12 2010 03:24 PM

Hello Logan. Being new in town, Blaze and i do not have many friends. We would love to meet up with you sometime and have dinner. We were also wondering, assuming that all goes well, if we could possibly move in with you. we decided that it would be a good decision to move out of our old appartment, because of the lack of privacy. if you would be so kind as to allow us to move in with you, we would be more than happy to pay rent. We hope to hear back from you soon.

May. 12 2010 03:22 PM

Hello Logan. being new in town, Blaze and I don't know many people. we would more than happy to meet up with you and hang out. we are also wondering, if things work out well, if we could possibily move in with you seeing as we no longer have our appartment. we would be more than happy to pay rent and some of the bills. we hope to hear back from you soon.

May. 12 2010 03:14 PM

How dare you Bill!! that's private information!!! Will be hearing from Blaze and my lawyer Shortly!!!!

May. 12 2010 03:07 PM
Ben Luckman

people should not be allowed to ruin this video with comments

May. 11 2010 02:01 AM

OMG so just because you haven't seen an 11-year-old with good grammer doesn't mean there aren't any. And for your info I'm technically in 6th grade, but I'm doing 7th-and-8th grade Language courses. And BTW I live in a liberal family who's vegan and has many non-hetero friends! SERIOUSLY, people, PLEASE be just a LITTLE more open-minded! Especially if you're going to preach open-mindedness!

May. 10 2010 07:55 PM

You two live in C-Town Montana? we should all meet up sometime, i've been looking for a few good fellows to hangout with. you can't find respectable people like you two very often, im hoping to seize this oppertunity of meeting you to. have a pleasant day
-Logan<3 love,peace,laughter

May. 10 2010 03:33 PM
Austin & Blaze

why thank you vinkmann. actually the two of us are not the same preson. we are living together in the same appartment. it is in the small town of corvallis, Montana. we are, however, planning to move to San Fransisco where people of our sexual preference are not looked down upon or shuned by the rest of the community. for your information vanya, we contacted eachother via email on a differnt blog. we were very sorry to hear about your podcasts being canceled. however look on the bright side, now you can get off your computer and get a real life. we highly doubt that you are 11 years old. we have never heard a 5th grader use such good grammar. we am tired of all you homophobic people telling us what we can and can't do!!! its people like you that make this world such a cruel and dangerous place to live! we hope you have a short and miserable life ending in a long and painful death!!!

May. 10 2010 03:10 PM

It is ridiculous, but sadly, these are real people, as far as I know. Although I must say their dialogue sounds totally impossible. It wasn't even a particularly intelligent comment and they have exchanged no personal information on here. I do not see how they could have met each other, particularly the getting an apartment together part.

May. 06 2010 06:39 PM

This repartee between Blaze, Austin and Vanya is hilarious. It's so ridiculous I suspect all three to be the invention of one innovative writer. If so, well done.

May. 04 2010 10:03 PM

I'm 11. Don't blame me, I'm just doing what my parents and teachers taught me. Which, I know, sounds whiny, but I'm in a horrid mood today (they canceled two of my favorite podcasts for a week). Also, I do put my real name on this website, but there was another Vanya here previously, so I put 222 at the end randomly. Excuse me for being eleven. I didn't know I could control what age I am. Maybe you should think a little before posting. Ugh.

May. 04 2010 03:18 PM

I agree Blaze. this Vanya lady has no ieda what she is taling about. she is probably really a 45 year old man trying to pick up teenage boys. "she" brings shame to this site and everyone who has read the words she has written is a little dumber for doing so!!

May. 04 2010 03:02 PM

You mind your own buisness Ms. Vanya. Our personal lives have nothing to do with you. it just so happens that we, unlike you, are not afraid to put our real names by our comments. some people are such cowards. Austin and I have become marvoulous friends. were are planning on renting an appartment together. so, you just keep your nose out of our business!!!

May. 04 2010 02:56 PM

if you look at the building that is 2:23 minutes into the video i would guess that even thouth that building has a parobolic shape if you look at the two end they start to curve back in and not only that it would not be able to contine onward because of the ground or a axis you might think

Apr. 30 2010 10:28 PM

. . .

Wow. You guys don't even know each other's ages or real names. My God. I didn't realize that this epidemic spread to Radio Lab.

Apr. 30 2010 09:49 AM

Ha Ha. Austin you flatter me!!! i cannot wait to meet you!! are you by any chance, single?

Apr. 29 2010 11:40 PM

Why thank you Austin. I would also like to meet up with you sometime. i also have a son, his name is Winston. Im sure that he and Pedro would be amazing friends.

Apr. 29 2010 03:34 PM

His name is Pedro

Apr. 29 2010 03:32 PM

Well said Blaze. I couldn't agree more. You know what, you said such a intelligent comment I want to meet you. Lets have lunch together sometime, I want you to meet my kid

Apr. 29 2010 03:31 PM

I Agree with Austin. i dont believe that there are any true real world applications of parabolas, because nothing in the real world goes on forever. however i did enjoy this video.

Apr. 29 2010 03:30 PM

none of these are even parabolas, in the definition the parabola state that it has to go on forver

Apr. 29 2010 03:25 PM

The first rule in teaching ought to be "Do no harm". If this clip is supposed to serve an education function, proper identification of the curves shown should be given. It's obvious great harm has been done already; many of your viewers have gotten the mistaken idea that they are all parabolas.

Mar. 30 2010 02:31 AM

O.K., interesting resolution to the catenary/parabola debate: as it turns out the period of a pendulum is not quadratically related to the length, that is just the first term in the Taylor approximation. Similarly, the catenary is also a parabola to first order approximation. In that sense, almost any shape that changes direction (u shape) can be approximated as a parabola, a fact with important physical consequences.

Feb. 26 2009 06:53 PM

What was the background music used? Was it your own creation? Very soothing...

Feb. 11 2009 02:19 PM
Daniel Barkalow

Oddly, I found the catenaries annoying, but I liked the things that were parabolas or were neither. Of the things that were neither, I was most pleased by the conic sections.

I'd like to see a picture with a fountain and a lamp under a slanted ceiling such that the line from the filament through the edge of the shade furthest from the ceiling is parallel to the ceiling.

Feb. 01 2009 03:45 AM


"Comment from benadair
Date: January 16, 2009, 10:14 am
You guys might also like this video about discs."

Ben, I just realized you're the Pacific Drift guy! I still think about that show 3 years later. It was way too short-lived.

Jan. 29 2009 02:12 PM

I loved this. I was a math nerd myself in high school (still am), and am always fascinated by numbers, seeing it as some kind of absolute truth unaffected by us, exists without condition.

This was exactly like me back then. I was looking around my high school campus after school one day and saw this shape pattern in the walls. I saw the shape in different perspectives all around me. I finally ran into my former geometry teacher's classroom, drew the shape on her chalkboard, and asked her to remind me what that shape is. She pretended to be annoyed that I forgot, but happily informed me that it is a trapezoid. Parabolas served this video as trapezoids have served me.

As for the comments that not all the shots featured parabolas, they are true, but missing the point. Not just parabolas, but arcs and curves of all kinds exist in nature. And things that are man-made reflect our natural attraction towards incremental trends.

Jan. 29 2009 07:18 AM

The curve from the lampshade is a hyperbola, not a parabola. I agree with other comments that it was a shame to call the video 'parabolas' if so many of the curves were nothing of the sort. There are examples you could have used - the shape of a jet of water rising and falling, or the convave surface of a stirred cup of coffee.

Jan. 25 2009 04:12 PM

I really really enjoyed the video. I can't say that I even cared about what the shapes technically where and where not, I think it is nice to get some visual to go along with the amazing audio of the show. It very much made me think of TAL's television series. Bravo.

Jan. 25 2009 03:15 PM

... by the way - the video was inspiring. For me, the exact attention to mathematics carries up to the fading of the graph paper. The rest was a very clever, artistic display of parabolas, truncated parabolas, and suggestions of parabolas that occur all around us. This video bridges the spoken descriptions to open our eyes to mathematical shapes occurring everywhere. Euclid, Archimedes, Galileo, and Baldessari are smiling.

Jan. 24 2009 02:04 PM

The walkway next to the elevated road is at Newark Liberty Airport - yes?

Jan. 24 2009 01:25 PM

Did y'all watch "The Ring"? After watching the video I can't help but feel something terrible will happen in seven days.

Jan. 21 2009 07:16 PM
ben ho

Like others, I came here to complain that most of the curves weren't parabolas. which seriously for me detracted from its aethstics. Though i do appreciate that it made me think hard about what shape each of those curves were.

Like the light from the lampshade was a good example of parabola. The true example of a conic section which is how we first learn what a parabola is.

Jan. 20 2009 06:24 PM

Beautifully done, Will and Derek. I also noticed that they were not all parabolas and wondered what Steve said about that decision... but it is beautiful nonetheless. The music provides a poignant, perfect companion for the video.

More please!

Jan. 20 2009 12:50 AM

yes, the water tower is from the Bell Labs Holmdel building. See:

Jan. 19 2009 06:44 PM

Gotta agree with the others above who were irked that the video featured so many non-parabolas. The whole point of the piece with Steve Strogatz was the sudden recognition that the same abstract mathematical pattern lies beneath a diversity of physical phenomena. Illustrating that with a plethora of examples that DON'T conform to the same mathematical pattern undercuts the thesis -- it restores plurality and differentness and loses altogether the sense of "sameness" that underlies the notion of a natural law.

More succinctly and bluntly: it drives me freaking nuts when my high school and college math students use the word "parabola" to describe anything that's U-shaped. Precision is important, especially when the message is so subtle and profound as the one being expressed here.

On purely artistic grounds the video was lovely, of course. But I wonder what Steve thought of it?

Jan. 19 2009 04:32 PM

I am entranced by the visual expression of the curve/parabola theme, and I love the video. However, when I listened to the podcast I was excited by the mathematician's verbal exploration of natural parabolas (drinking fountains, rockets launched) whereas in the video, almost all of the instances were human-made or incidental. While the video was gorgeous, I would have liked to see some more examples of parabolas found in nature because of the underlying math and physics that cause their behavior.

Jan. 19 2009 01:58 PM

Beautifully done and more interesting I think because they were not all parabolas.

Note how he made the mistake of believing that there are laws of nature. Mathematics is a wonderful creation of man, a tool that helps us describes nature and a powerful predictor of the natural world. Nature continues to confound the physicists and mathematicians though, so as we peer deeper into its mysteries, we are greeted by more and more complexities.

Videos like this make me happy to be alive.

Jan. 19 2009 12:18 AM

I just watched the video and also noticed the thing about the catenaries, and rushed over to this blog so I could be the first asshole to point this out, only to find that radiolab listeners are such a mathematically savvy bunch ;)

and btw I hope you have more video tidbits in store, but urge that in keeping with the experimental sound editing of the radio show, you strive for more experimental forays into video--like if Bill Viola were a high school physics teacher or Carl Sagan was a devotee of Jack Smith.

Jan. 18 2009 11:05 PM
Annie Rudnik

Great video! But, please do not think about going into television. Do not become Ira Glass!

Jan. 18 2009 05:56 PM
nate beaty

really beautiful short film, as beautiful as the visuals i get from your purely audio output! thanks for sharing it.

now i'm going to see parabolas everywhere, THANKS! haha. (and/or hyperbolic cosines, yeesh.)

Jan. 18 2009 05:30 AM

I didn't think the video was TRYING to show parabolas, but more how nature and the world we live in are full of mathematics and laws. That's what I took from it. Honestly, I think the RadioLab folks are smarter than to simply get it wrong, like some of you are suggesting.

Hats off, RadioLab!

Jan. 18 2009 02:52 AM

I have to say that I agree with the above. Maybe it's the scientist in me, but I was slowly more annoyed by the number of images that didn't describe a parabola at all. I love the idea of the occasional short video piece on the feed, but Terry's got it right -- there is a standard for rigor that I have come to expect from RadioLab, and this video made me just the tiniest bit sad inside. Keep trying!

Jan. 17 2009 11:46 AM

As a visual person continually fascinated with the mysteries of our world and NOT being a mathematician, I simply GET IT; the video captured the "sensation" of the mystery that we can all view if we look around us, as in pay attention. I wasn't in need of a lesson in the specifics of curves, though fascinating in itself, don't think that was the crux of the video.
Thanks for always throwing thoughts and ideas out there to inspire and conversate about Radio Lab!


Jan. 17 2009 10:38 AM

Mmmm... I learned to enjoy poetry more when I realized it doesn't HAVE to rhyme... thank you WH, DPB and the RadioLab guys!

Jan. 16 2009 10:15 PM

Beautiful. More, please.

Jan. 16 2009 10:50 AM

Oops. Couldn't imbed. Here's the link:

Jan. 16 2009 10:14 AM

You guys might also like this video about discs.

Jan. 16 2009 10:13 AM

The water tower is (I think?) in Holmdel, NJ, at the now closed Lucent Technologies building. The playground looks like one in Rumson, NJ, near the Navesink River. Anyone know for sure? I enjoyed seeing some nearby sights.

I enjoyed the short film. Great job, Radiolab!

Jan. 15 2009 07:17 PM
Terry Robinson

I was also disappointed that a lot of the parabolas were hyperbolic cosines. One of Radiolab's powers is to investigate curious differences. "You thought these were all alike, well they're not and they're each beautiful" describes many radiolab episodes like reproductive organs in Sperm and the human brain in a handful of episodes.

Not a condemnation of the pretty episode but a warning that Radiolab has a high standard for rigor to be reached.

Jan. 15 2009 06:14 PM

moving and beautiful. i love radio lab for the poetry and simplicity it brings to science, especially for those of us that are science-minded but not necessarily science-trained. i like wrapping my mind around the complexities. this is a nice start, but exploring the full picture is better.

Jan. 15 2009 04:41 PM

I loved that video. By the end of the movie I was hearing in my mind, "parabola. parabola. parabola," each time a wave touched the beach.

Jan. 15 2009 12:06 PM
Julie Wegner

Well, first off, this was a wonderful and pleasant surprise.

I think there's a huge potential here, and the quiet, high-speed footage really suits the narrative tone of Radio Lab.

But, though I'm not a math buff, it irked me that few of the images shone were parabolas. That said, I think the images were beautifully put together and artfully chosen. I at first didn't realize what they were there for, and kept waiting for more narration, but as I saw the icicle I realized what it meant. And, the mix of natural and man-made curves was very interesting, especially with the contrast between the sharp lines and deliberate curves versus the soft natural curves and occasional jagged patch.

Overall, really great idea here, but not the best execution for the particular subject.

I really look forward to seeing more like this, though, since even while inaccurate the images were simply beautiful.

Jan. 15 2009 05:33 AM
Daniel Roberts

So super. Thanks Radio Lab! You guys never let me down.

Jan. 15 2009 04:00 AM
James Caldon

Outstanding! I really enjoyed the photography in this.

I think Katie and Rebekah are, in a way, missing the point here. Going along with those comments, since catenaries and hyperbolas are beautiful mathematical patterns as well, I feel the filmmakers were trying to extrapolate from Steve's monologue. Who cares if all the images aren't parabolas? I think they did a fantastic job of creatively visualizing the segment.

I'd like to see more visuals from Radiolab myself. Well done!

Jan. 15 2009 12:24 AM

Excellent, and congratulations to director Will Hoffman.

The images, however, include catenaries and hyperbolas, along with parabolas. Perhaps a sequel can distinguish the physical interpretations that define these three curves.

Jan. 14 2009 11:11 PM
Veronica Vazquez

I LOVE Steve Strogatz! He's amazing and also a super nice guy. More Steve, more Steve, more Steve...yay!

Jan. 14 2009 10:06 PM

I hate to repeat what others have already said, but the only reason I clicked on "comments" was the catenary issue that Katie and JBL mentioned. Just wanted to put my vote onto the side of those who are actually inspired by the manifestation of mathematics in the world. Maybe the video should have been about the catenary instead!

Jan. 14 2009 09:43 PM

Beautiful. This was a nice surprise in the feed.

Jan. 14 2009 06:40 PM

Like jbl, I noticed that few of the curves in the film are parabolas. Unlike him, I was distracted and bothered by this. Rather than riffing on the powerful idea of "natural law" raised in the interview excerpted, this piece seems impressed by the fact that there are curved things in the world. More attention to mathematical patterns, and less to vaguely similar shapes, would have been much more striking.

Jan. 14 2009 06:36 PM
james betz

i think the hair on the bar of soap is probably the funniest.

great video

Jan. 14 2009 01:20 PM

Though it looks a lot like a parabola, many of the curves are (probably) catenaries. The catenary is a curve described by a function called a hyperbolic cosine (abbreviated cosh), and is the actual shape of any hanging length of chain. It is also the best shapes used by architects for free-standing self-supporting arches. The gateway arch in St Louis is a catenary.

On the other hand, the cables of suspension bridges follow a parabolic curve.

An interesting connection between the parabola and the catenary is that if you roll a parabola along a straight line, its focus will trace out a catenary.

None of this detracts from the beauty of the film.

Jan. 14 2009 03:35 AM

I love this short film. I would love to see more subtle instances of an idea. The guy's hat and the water on the beach were my two favs.

Keep up the great work Radiolab!

Jan. 13 2009 11:22 PM

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