Π in the sky!

September 17, 2012 • 11:16 am

Now this is conceptual art that I like.  On Sept. 12, 5 planes printed out the first 1,000 digits of pi using skywriting and digital presentation.  The printing stretched over a 100-mile path (see below) encircling San Francisco Bay. According to Open Culture,

“. . . the Pi project was the brainchild of ISHKY, an eclectic collaboration of artists, programmers and scientists looking to explore ”the boundaries of scale, public space, impermanence, and the relationship between Earth and the physical universe.”

To hear more about it, see the top video at the Open Culture site, which I can’t embed.  Here are some photos:

Over Golden Gate some bridge (may be Photoshopped):

And the route:

Now if this appeared two hundred years ago, and I was living then, I would take it as provisional evidence for a deity.

Here’s a short video of the printing. Skywriting sure has improved since I was a kid!  But I hope some reader can explain how this is done.

Here’s what they printed:

3.1415926535897932384626433832795028841971693993751058209749445923 0781640628620899862803482534211706798214808651328230664709384460 9550582231725359408128481117450284102701938521105559644622948954 9303819644288109756659334461284756482337867831652712019091456485 6692346034861045432664821339360726024914127372458700660631558817 4881520920962829254091715364367892590360011330530548820466521384 1469519415116094330572703657595919530921861173819326117931051185 4807446237996274956735188575272489122793818301194912983367336244 0656643086021394946395224737190702179860943702770539217176293176 7523846748184676694051320005681271452635608277857713427577896091 7363717872146844090122495343014654958537105079227968925892354201 9956112129021960864034418159813629774771309960518707211349999998 3729780499510597317328160963185950244594553469083026425223082533 4468503526193118817101000313783875288658753320838142061717766914 7303598253490428755468731159562863882353787593751957781857780532 171226806613001927876611195909216420198

h/t: Matthew Cobb

75 thoughts on “Π in the sky!

  1. “Now this is conceptual art that I like.”

    You do? You’ve considered the greenhouse emissions of those planes, engaged in a wholly unnecessary task?

    1. Oh, for crying out loud. Most plane trips are wholly unnecessary too, as are many car trips. And you should tell people to stop eating all hamburgers so long as you’re being the moral police.

      1. I think it’s brilliant, and not just because it appeals to me as a letter artist and a land artist. Just off the top of my head, here are a few benefits:
        * piques an interest in maths to a very wide audience
        * repeats and reinforces the “pie in the sky when you die” criticism of the American Christian fundamentalist concept of salvation.
        * It is probably the most simultaneously widely seen work of art ever and as such will have a place in the hearts of a very large number of people across a very wide cultural, political and economic spectrum. This joint, interesting and enjoyable experience forms a bond.

        1. Would be great if it stimulated interest in math, but most people seemed to think it was a phone number or viral marketing of some kind. Won’t be long before it pops up in videos as “unexplained new world order chemtrails” or some bullshit.

      2. I don’t wish to be a poophead, but I had the same initial reaction as JG.
        Yes, it is a cool project, and is neat that it could be done at all, but that’s about it as far as it goes in terms of eliciting an emotional response from me. A lot of performance art (such as the orange fabric “gates” in NYC a number of years ago)does not require much talent.
        I grew up during the environmental movement and got a bio degree because of my strong feelings for the environment (am the same age as you, JAC), and I made a living for a couple decades as an artist. But honestly, it’s a bit difficult to consider this endeavor as wonderful–at least more than for a fleeting moment.
        This is really more of an endeavor of science and industry (industry in the sense of “industrious”). I don’t think there is necessarily much artistic skill that produced it. It is more like a demonstration of technology.

        1. Well, I have no trouble considering this as something pretty exciting. It was a cool experience to see those planes puffing out the digits in the sky.

          1. I’m astounded it’d occur to anybody to think there was a problem with this. Heck, I’m surprised there’re even those who wouldn’t merely get a groan at the pun and move on…but, apparently, there’s no accounting for taste.

            From the time the first passenger gets on an airliner to when it clears the airport, that airliner has already burned more fuel than most Americans will in an entire year of driving. By the time it reaches the gate at the destination, the airliner has probably burned more fuel than an entire private flight school will in a lifetime.

            A bit of skywriting like this? Most of those reading these words are going to burn more fuel on a single day’s commuting than the stunt took.



            1. I know what you mean about being astounded that someone would think of the downside.
              I have always been an atheist, but I must shamefully confess to being an environmentalist.
              This is almost an equally destructive belief system which affects my thoughts and actions too much. This belief system has caused me to think of the earth and of other people before thinking of myself, which is counter-productive to my well-being and to my instant gratification. I still have some ridiculous habits such as wanting to recycle aluminum but I will hopefully be cured of that before too long.

              1. The confusion isn’t over whether or not somebody would embrace environmentalism. My roof is covered in solar panels that generate half as much again electricity as I use; I’m burning under 200 gallons of gasoline per year (and in a car that’s older than I am); and I’m in the planning phase of putting in a garden that should more than amply give me all the produce I could ever hope to eat.

                The confusion is over how it could even occur to somebody that this has even a hint of a blip of an environmental impact.

                No, I’m not exaggerating when I state that the pilot quite possibly did more damage to the environment in driving to the airport than in doing the skywriting.

                If you’ve got a problem with a skywriting loop like this, then you’ve gone so far beyond environmentalism into such depths of insanity that I can’t even figure out why you haven’t committed suicide yet.

                Either that, or you’re so far out of touch with commonplace occurrences that you’re completely unequipped to make any sort of informed evaluation of the environmental impacts of…well, of anything.


              2. “I’m in the planning phase of putting in a garden that should more than amply give me all the produce I could ever hope to eat.”

                How big is that? I would have thought a garden like that would be acres in size and be a full time job to maintain. I assume you’re not talking about growing grain for your own bread and pasta, but still.

              3. How big is that? I would have thought a garden like that would be acres in size and be a full time job to maintain. I assume you’re not talking about growing grain for your own bread and pasta, but still.

                For the Victory Garden in the front I’ve got about 20′ x 50′ to work with. The area for the fruit orchard in the back is probably about twice that size.

                And, no, I’m not going to be growing (significant amounts) of grain. Nor will I have animals (except some koi in a pond in the back, and maybe a desert tortoise as well).

                There’ll certainly be times during the year when I’ll still have to buy produce, but there’ll also be lots of times when I’ll have so much stuff I’ll have trouble giving it away.

                I’ve already got one each orange and grapefruit trees, and there’s no way I can eat all the fruit they produce.

                It doesn’t take a lot of space at all to grow fruits and vegetables. Think of how much fruit you can get from a single tree, and think of how long it takes to go through a single head of cabbage. And leafy herbs like those in the mint family (oregano, basil, etc.)? A single plant in a single season might give you a lifetime’s supply.

                It’s going to take a lot of work to get started, but ongoing maintenance shouldn’t be too bad. I’ll be putting in an irrigation system to last a lifetime. The trees will mostly take care of themselves. The veggies will need a bit more work, but not too much — a bit of soil preparation, then planting, then weeding (quickly, with a rake) for some crops every week or so, maybe some fertilization (preferably with the muck from the pond filter), and then harvest (right before it goes on the table, of course).

                It’d be a hugely different matter if either my livelihood depended on this as a commercial venture or if my life depended on it for sustenance farming. But I don’t have to make a profit on this and it’s no big deal if I lose some crops for some reason. So long as I regularly get to eat good food from the garden, it’s perfectly fine if I still make trips to the butcher or the grocery store or whatever.



            2. My apologies. I somehow thought that flying a plane about a hundred miles (or five planes) would have used a good amnt. of fuel, but I was probably wrong.

              1. Skywriting is done by small, slow planes, preferably certified for aerobatics. A Citabria is perfect for the job. A Citabria is going to cruise at about 115 MPH and burn about 6 gallons per hour, which works out to about 19 MPG, and presumably about 6 gallons for the whole stunt. It’s definitely under 35 gallons, as that’s all that plane holds.

                (This is assuming a Citabria at cruising speed. Significantly slower speeds generally mean poorer efficiency, and some bigger planes might be less efficient. But even a four-passenger Cessna 172, serious overkill for skywriting and not suited for aerobatics, only burns 9 gallons per hour at a 150 mph cruise.)

                Depending on where the pilot lives and where the plane is hangared, it easily could have taken more than 6 gallons to drive to and from the airport, especially in the Bay Area.

                A 747, on the other hand, burns about a gallon per second. There’s a reason or three why they’re not used for skywriting, and operating costs would be right there at the top of the list.



              2. By the accounts I read, there were five planes.

                Also, one should indeed include the gasoline that every pilot used to get to the hangar, and back home again, as part of the footprint of this work of art.

                Just wanting to get the facts straight.

                And, on the Open Culture link that Jerry provided in the original piece, there were as of a few minutes ago only two comments, both of which reflected a concern similar to mine.

                Also, I do not think that casting aspersions to someone’s sanity just because one disagrees is the correct thing to do on fine website such as JAC’s.

                That is all I have to say on this matter.

              3. Jesse is correct, of course. There’s no way a single typical daily commute uses more fuel than six stunt planes each traveling 100 miles, plus the fuel used by the pilots to get to and from the airport, plus the fuel used by any other staff involve in the stunt. But no amount of facts or evidence will convince Ben Goren that he is wrong…

              4. So, since I left last night, I now see multiple references to five or six planes, along with gratuitous remarks that the additional planes somehow transforms the stunt into an environmental catastrophe.

                Cry me a river.

                Take my figures, multiply them by a hundred. That’s still far less than the environmental impact of a single day’s commute by a single small business’s employees, or about as much as an airliner burns in its first few minutes after takeoff.

                Big fucking deal.

                I mean, seriously people? All y’all’re so uptight about the arts that you want a goddamned environmental impact study that includes the miles driven on the road in order to justify it?

                Jesus Christ.

                What next? A ban on oil painting because of the heavy metals in the paints? A ban on musical instruments because of the lead in the solder joints?

                I’m sorry, but all this pretend environmentalism is pathetic and shameful — and hypocritical in the extreme.

                Clearly, it’s not the environmental impact y’all’re upset about, but, as with all Puritans throughout history, that somebody somewhere had some harmless fun.

                Let me steal a page from the A+ crowd and tell y’all to shove it.



              5. Hey, Ben, your points may be valid but your language is getting pretty intemperate (“shove it” et al.). How about being a bit more polite to those with whom you disagree?


              6. Damn, that rant gave me a good laugh! Funny how the foul language takes on a righteous character when when you’re so totally cogent and right. I’d like to disagree with you one day and have the honour of one aimed at me too.

              7. That’s still far less than the environmental impact of a single day’s commute by a single small business’s employees

                Now you’re moving the goal posts. You didn’t say “by a single small business’s employees.” You said, “Most of those reading these words are going to burn more fuel on a single day’s commuting than the stunt took.” And that claim is just obviously wrong. The average daily commute burns about one gallon of gasoline. There’s no way this skywriting stunt was done on one gallon of gas.

      3. Another thing: the way the numbers degrade into asemic-looking characters is interesting. Impermanence in art is not a very new thing but it has had a recent exponential rise which dovetails nicely with the rising concern over the human footprint. Art that is transient degrades naturally, recycles, undermines the self-importance which affects so much art and reinforces the idea that we and what we do is temporal and that it’s good that way. Who needs literal eternal life?

        1. Why is impermanence good? How exactly does it affect the quality of the artistic content?

          I really don’t know how I should apply the knowledge of a piece of music’s or visual art’s transience in evaluating it.

          If I knew that, somehow, all Bach’s works were to be wiped off the face of the Earth on Sep 30, I would do one thing, and wouldn’t do another:

          I would</i

        2. Why is impermanence good? How exactly does it affect the quality of the artistic content?

          I really don’t know how I should apply the knowledge of a piece of music’s or visual art’s transience in evaluating it.

          If I knew that, somehow, all Bach’s works were to be wiped off the face of the Earth on Sep 30, I would do one thing, and wouldn’t do another:

          I would panic like I’ve never panicked before; I wouldn’t decide that the quality of the musical content had suddenly and drastically increased.

          As a confirmed curmudgeon, I wonder if the recent trend in impermanence isn’t a subconscious acknowledgement by the artists that what they’re producing is not really worth saving.

          1. Good question.
            Art is a kind of dialogue and the impermanence is mainly about meaning, about what the art says by being impermanent. So if you had to apply the transient quality of a work when evaluating it, you’d have to ask what it adds to the meaning of the work (or subtracts!)

            For example, and to continue with the Bach analogy, suppose that one one day he invited everyone to a performance at which he was, before their very eyes, to compose a string quartet, have it performed once and then burned? That would be interesting but probably not very meaningful. However, if he were responding to some burning of books or dedicated the work to a son lost in infancy, the impermanence and the method of its passing takes on a whole new meaning.

            But it doesn’t necessarily depend on the deliberate use of impermanence. I am a calligrapher and my paid display work is geared at permanence – archival paper, ink, gold, etc – but I have a hobby of carving calligraphy into the beaches here. The cut is very much like the neat V one sees in letters carved into stone but my work is the exact antithesis of what it looks like precisely on the point of permanence and that gives it a layer of meaning, or at least a receptacle for meaning within a limited range, regardless of what my intentions are. For example, I once carved a woman’s husband’s name for her. He had recently died, and she stayed there with the carving for at least an hour until the tide took it. It was a meaningful experience for her and the impermanence of the work played a pivotal role in the meaning by providing an apt receptacle for what she was feeling about her husband.

            1. Hmm.

              I can understand the impact an experience like the widow’s would have. But I’m still not sure how much this vaunted impermanence plays in generating or contributing to such experiences. Surely the other circumstances play bigger roles in getting someone into that “emotional place.” If I’d seen the sandy inscription, but was unaware of the reason for its creation, its impermanence would probably not have figured at all in my reaction to it or evaluation of it.

              Many, many musicians, from ages before Bach up to the present, regularly engage in impermanent art: improvisation. My job requires that I improvise quite a lot. But I am keenly aware, as I must assume many other musicians are and have been, that thoughtful composition is a much better way to achieve fully satisfying results. Perhaps the most renown improvisateur, Beethoven, still took great pains working out the details of his written compositions. You can see all the revision and hard work in his sketchbooks. If spontaneity and transience really add to the quality of a work, why would he have bothered in that way?

              It seems to me that impermanence in art is another instance of the ever increasing premium artists and consumers alike place on concept, as opposed to execution. Which I think is because concept is the easy part.

              1. But — every live performance is impermanent!

                Even if it’s recorded, the recording is no different from a photograph of the sand sculpture — a mere representation, while the original has long since been lost to the ravages of entropy.


              2. @ b&

                Yes, that’s technically true, but you still have to make a distinction between art that is literally “one time only” and art that has been preservedin one way or another.

                And yes, recordings and sheet music are indeed mere representation. But as long as we have access to those representations, we have access to the abstract edifice which is the composer’s real creation.

                Impermanence of some kind is perhaps unavoidable. I’m just not convinced that it’s a contributing factor to the quality of a work.

                To paraphrase our illustrious host, I think Sophisticated Artists &trade are trying to turn practical necessities into artistic virtues.

        1. The skywriter isn’t making contrails.

          Contrails are mostly water vapor, and are the visible exhaust from jet engines at cruising altitude (generally several miles / 10 km). It’s no different, really, from when you see your own breath or exhaust from tailpipes in winter — except, of course, that they’re much higher and bigger in scale.

          That also means that they’re no different from other high-altitude clouds, and they function climactically the same way. What contrails can do is spread out and create a light high-altitude cloud cover on days that otherwise would be cloudless. That both reflects some incoming sunlight and traps some heat radiated from the surface.

          As we saw in the days after 9/11, they disperse as rapidly as any other cloud — which is hardly surprising, since that’s exactly what they are.

          What the skywriter is most likely doing is burning oil to make smoke. As anybody who’s ever had or witnessed a blown head gasket or the like knows, a little bit of oil creates a lot of smoke, and the whole project burned far less oil than it did gasoline.

          Oh — and the pilot probably burned as much gasoline driving to and from the airport as in flying the plane for the project.



          1. Thank you for the clarification. Although I’m not that old, I still tend to think of the bi-plane era. Not even sure what they used then, maybe an oily mixture injected into the exhaust manifold?

  2. I haven’t read the article, but you ask how it’s done – apparently the plane has five smoke nozzles, under computer control, and pulses them on and off like a dot-matrix printer.

    Is that picture over the Bay Bridge real? The numbers over it are from the first and second line of what you gave as what they’re printing, but that location is about halfway through their route according to their map.

    Maybe they went through that more than once.

    Anyone have any quick calculations to show that with this many digits of pi, you could calculate the circumference of a circle with diameter x, to y degree of accuracy?

    1. Anyone have any quick calculations to show that with this many digits of pi, you could calculate the circumference of a circle with diameter x, to y degree of accuracy?

      It’s been a long time since I’ve done that, but I’m pretty sure that what Jerry has above is more than you’d need to calculate the entire universe down to Planck length.

      It’s not that hard a calculation to do. And, yes, for masonry at the scale of tens of cubits, one significant figure is plenty. Three significant figures gets you anything you’re ever likely to encounter in your life unless you’re an engineer, and almost everybody has enough digits memorized for the engineers as well. Your calculator displays enough digits for precision engineering at terrestrial scales, and it just keeps getting more ludicrous from there.



      1. Agree, the original post SAYS it was 5 planes. as for HOW I can give a vague hand-wavy speculation: Most of us are aware that we can get incredibly high resolution elevation maps using LIDAR, which depends on knowing precisely where the source of the laser is at a precise moment in time, presumably using a combination of GPS, accelerometers, and gyroscopes (?). Once you have a smoke machine that knows exactly where it is, you basically just have a dot-matrix printer in the sky. Can anyone else flesh this out?

        Very cool, all greener-than-thou whining aside.

        1. There was an aerobatic team that had computer controlled smoke system… like said above, pulsing out squirts of oil into the engine exhaust pipe like a dot matrix printer. One plane has the controller and it times out the pulses via radio. As long as the planes stay in formation and fly a fixed speed, all is good. They definitely burned more fuel flying this route than driving, that is a long flight at probably 8gph for over an hour. Times 5. The oil is paraffin based made for air shows and injected a foot or so before the end of one of the exhaust pipes. I have a couple friends who have this on their planes. One guy uses used cooking oil from his restaurant but it isn’t as visible. I haven’t looked at who did it and what they were flying, looks like they were fairly high. Sorry I missed it, I was definitely under it. Nuts

  3. 2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427427466391932003059921817413596629043572900334295260595630738132328627943490763233829880753195251019011573834187930702154089149934884167509244761460668082264800168477411853742345442437107539077744992069551702761838606261331384583000752044933826560297606737113200709328709127443747047230696977209310141692836819025515108657463772111252389784425056953696770785449969967946864454905987931636889230098793127736178215424999229576351482208269895193668033182528869398496465105820939239829488793320362509443117301238197068416140397019837679320683282376464804295311802328782509819455815301756717361332069811250996181881593041690351598888519345807273866738589422879228499892086805825749279610484198444363463244968487560233624827041978623209002160990235304369941849146314093431738143640546253152096183690888707016768396424378140592714563549061303107208510383750510115747704171898610687396965521267154688957035035

    1. “Pi goes on forever,
      And e is just as cursed;
      I wonder which is larger
      When their digits are reversed.”

      I don’t know the source for this.

  4. That’s not the Golden Gate Bridge, it’s the Akashi Kaikyō Bridge in Japan. That picture appears to be a conceptual render.

        1. Yeah, it isn’t the Bay Bridge. It certainly isn’t the eastern span, as you’d be able to see the Bay Bridge’s replacement in that shot. And given the horizon and the sun, the only way that shot would make sense for the western span would be for the photographer to be facing SF directly. This can’t be because: 1) SF isn’t on an island; 2) San Francisco has building not evident in the photo.

          Moreover, the structure of the bridge (especially the top) is different than the Bay Bridge and the whole thing is COMPLETELY different than the GGB. Finally, what seems to be a train on the bridge isn’t a feature of any bridge in the Bay Area (though it could possibly, though unlikely, be a large bus on the lower deck of a double-decker bridge similar to the Bay Bridge).

      1. Looking at Wikipedia, it’s definitely the Akashi Kaikyō bridge. They are very similar, but the Akashi Kaikyō bridge has 4 “X” shaped crossbeams on the tower, while the Oakland Bay bridge has 3.

  5. – “Now this is conceptual art that I like.” –
    Yes, so do I! This is great. What about the human genome printed out in the sky?

  6. Any one want to check my sums?

    Planck length [P] =
    10^-35 metres

    Our comoving distance to the edge of the observable universe is [U] =
    10^26 meters

    U/P = 10^61

    Number of Plank-sized points in the Observable 3D universe [10^61]^3 =

    Pi value shown is approx 1,000 powers

    1. If the digits if pi are normally (in the sense that each successive 1 digit sequence of pi shows up 1/10 of the time, each 2 digit sequence of pi shows up 1/100 of the time and so on) and randomly distributed, which appears to be the case, then everybody’s credit card number is in there somewhere.

      And your PIN as well.

      1. And, as Carl Sagan pointed out in “Contact,” a block of 1,000 consecutive zeroes on the average every 10^1000 digits.

        Last time I checked, maybe five years ago, the digits of pi had passed all tests for normality. Not a proof, of course, but suggestive.

  7. I saw this in a ‘Conspiracy Theorists say the darnedest things” facebook group the other day with many posters claiming it was related to the numbers broadcasting from Cuba and counting down to a Korean Invasion by chemtrail spewing commercial airlines . . . no kidding . . . Whew, I’m glad to know that’s it’s mostly harmless!

  8. Why do I hear about the cool things I could have taken part in only after they’re done? I guess in this case I could have just looked UP. 🙁

  9. I do consider all of the ideas you’ve offered in your post. They’re really convincing and can definitely work.

    Still, the posts are very brief for beginners. May you
    please lengthen them a little from next time?
    Thank you for the post.

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