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Gardens as Crypto-Water-Computers
Water Computer

I only recently found out about Google's reverse image search functionality. Since then I've been busy feeding its search engine some of the more mysterious images that have been littering my archives for years, hoping finally to figure out what they are actually pictures of, and why I even found them interesting enough to keep in the first place.

One of those images is the one you see above. According to a translation of this article published in the Russian magazine Science and Life in 2000, it shows one of the “monuments of science and technology” that “brought [the Soviet Union] to the forefront of the analog computer” — Vladimir Lukyanov's marvelous water computer.

Built in 1936, this machine was “the world's first computer for solving [partial] differential equations,” which “for half a century has been the only means of calculations of a wide range of problems in mathematical physics.” Absolutely its most amazing aspect is that solving such complex equations meant playing around with a series of interconnected, water-filled glass tubes. You “calculated” with plumbing.

To better explain how it works, here is a description by Steven Strogatz of what I'm assuming is a comparable device. Built in 1949, nearly a decade and a half after Lukyonov's, it's called the Phillips machine, after its inventor, Bill Phillips.

In the front right corner, in a structure that resembles a large cupboard with a transparent front, stands a Rube Goldberg collection of tubes, tanks, valves, pumps and sluices. You could think of it as a hydraulic computer. Water flows through a series of clear pipes, mimicking the way that money flows through the economy. It lets you see (literally) what would happen if you lower tax rates or increase the money supply or whatever; just open a valve here or pull a lever there and the machine sloshes away, showing in real time how the water levels rise and fall in various tanks representing the growth in personal savings, tax revenue, and so on.

“It’s a network of dynamic feedback loops,” Strogatz further writes. “In this sense the Phillips machine foreshadowed one of the most central challenges in science today: the quest to decipher and control the complex, interconnected systems that pervade our lives.”


To go back to Lukyanov, his water computer was built specifically to solve the problem of cracking in concrete, a “scourge” that slowed the construction of railroads by his employer. Doing so meant developing manufacturing regimes for concrete blocks that took into account the complex relationships between material properties, the curing process and environmental conditions. Existing “calculation methods were not able to give fast and accurate solutions.” Lukyanov's invention did.

Appropriating and altering Strogatz's text, we get:

Filling up not just a corner but the entire room, inside not one but several structures that resemble large cupboards with a transparent front, is a Rube Goldberg collection of tubes, tanks, valves, pumps and sluices. You could think of it as a hydraulic computer. Water flows through a series of clear pipes, mimicking the production line of concrete blocks. It lets you see (literally) what would happen if you change the type of cement used or increase the load capacity of the concrete or whatever; just open a valve here or pull a lever there and the machine sloshes away, showing in real time how the water levels rise and fall in various tanks representing material properties, curing time, temperature, and so on.

Changes to the water level in the “measuring tube” would be marked on a graph paper (“a kind of curve”), and “these marks build schedule, which was the solution of the problem.”

Because of the simplicity of their design and programming, subsequent models were “successfully used” in other fields such as geology, thermal physics, metallurgy and rocket engineering. The first and second generations of digital electronic computers could not match their computing abilities. In the mid-1970s, they were still being used in “115 manufacturing, research and educational institutions located in 40 cities” across the Soviet Union. “Only in the early 80s” were digital computers cheap, configurable and powerful enough to match the “possibility of [the] hydraulic integrator.”

Polytechnic Museum Moscow

Having briefly traced the history of water computers forward from Lukyanov to the rest of the 20th century, I can't help but thread the timeline backward to include some of the most elaborate hydraulic engineering schemes used in the sprawling aristocratic gardens of early modern Europe, such as the always indispensable Versailles, the hydro-acoustically drenched Tivoli, the masterworks of Salomon and Isaac de Caus, and one of my top favorite gardens, Pratolino.

Garden historians usually characterize the technical control of water in stately gardens as part of a system of social control. As an alternative, or at least to offer another layer of meaning, this augmented timeline presents a crypto-historical narrative of gardens as gigantic water computers.


All those water-screws, force pumps, water-lifting wheels, vents, wells and settling tanks, all those reservoirs, canals, aqueducts and pipes buried under mountains and rivers, and all those jets spurting out of vases and statuaries, creating water rainbows and sonic merriment, and all those fountains, water parterres, giochi d'acqua, automatas and damp grottos: those are the gurgling circuits, the programmable interfaces, the data storage devices and the visualization screens of landscape proto-supercomputers.

To operate it, you will have to consult an unpublished edition of Solomon de Caus's Les raisons des forces mouvantes, avec diverses machines tant utiles que plaisantes, auxquelles sont adjoints plusieurs dessings de grotes & fontaines, from which the following may have been excerpted:

Embedded in the earth is a Rube Goldberg collection of tubes, tanks, valves, pumps and sluices. You could think of it as a hydraulic computer. Water flows through a series of clear pipes, mimicking the way that money flows through the empire. It lets you see (literally) what would happen if you lower the price of bread or increase the construction of palaces or whatever; just open a valve here or pull a lever there and the machine in the garden sloshes away, showing in real time how the water levels rise and fall in various tanks representing colonial trade supplies, food riots, and so on.

Attached to the measuring tube is a series of fountains that gurgles the solution to the equation.

Jean-Baptiste Martin

Gardeners and their patrons would then walk around marking the fluctuating levels of these fountains on graphic paper. From fountain to fountain, they follow a set of programmed perambulations, gathering data at relevant nodal points, along the way not just picking up the solutions to the problem being computed but also gaining a greater understanding of the complexities of the natural and social worlds.

With these gardens as crypto-water-computers, they were taking measurements of the universe.

  • Anonymous
  • January 24, 2012 at 1:50:00 PM CST
  • This is my favorite blog. I love intellectual but subconscious flow of ideas that highlight how (dis)/connected we are to nature. power struggle

  • Anonymous
  • January 25, 2012 at 7:33:00 AM CST
  • I'm pretty sure I have seen the (a?) Phillips machine in the science museum in london....


  • adrian beaumont
  • January 25, 2012 at 7:47:00 AM CST
  • Ahm, yes....

  • Anonymous
  • January 25, 2012 at 8:09:00 AM CST
  • this would be much more readable if the font color were BLACK.

    that's #000 in your CSS.

    thank you very much.

  • Ellie K
  • January 25, 2012 at 9:29:00 PM CST
  • This is remarkably clever. What you wrote, that is, pulling together so many disparate themes and concepts, then gracing it all with vintage diagrams, and art (Tivoli, Versailles). I never even knew there was another Tivoli, the original one, apparently in Italy. I only knew of Tivoli Gardens in Copenhagen.

    Regarding technology, yes, it is true that the Soviet Union took analog computing quite far. I was told in my very first mechanical engineering class by a very elderly professor, that the U.S.S.R. chose the analog path, and the U.S, Europe took the digital one. It wasn't clear which would be better until the 1970's. But I never knew about the partial differential equation solving machine using water! That is wonderful! And so appropriate in a contextual, maybe even aesthetic sense, given the importance of PDE's (PDQ's?) for fluid dynamics and human biology e.g. osmosis.

    This was AWESOME! Thank you!

    P.S. I would vote for black font too. #000 or #000000.

  • jkuecklich
  • February 3, 2012 at 3:38:00 AM CST
  • In his fantastic novel "Ada, or Ardour", Vladimir Nabokov envisions a world in which water has taken on the role that electricity has in the real world. As Wikipedia puts it: "Electricity, however, has been banned since almost the time of its discovery following an event referred to as "the L-disaster". Airplanes and cars exist, but television and telephones do not, their functions served by similar devices powered by water."[1] Interestingly, the world of Ada also blends (pre-Soviet) Russia with North America, i.e. the places of Nabokov's childhood and adult life, respectively.


  • Michael
  • February 13, 2012 at 2:40:00 PM CST
  • this is soo freaky but Terry Prachette in his diskworld novel, "making money" describes an Igor and a crazy scientist who maintain such a "water" computer in the basement of the bank. The above description is like almost given verbatim in the book.

  • Unknown
  • October 3, 2012 at 3:42:00 PM CDT
  • Aahhh. Terry Pratchett. Turtles all the way down...
    He writes excellent social satire in a fantasy setting.
    I think he would like this blog very much indeed!

  • tudza
  • October 4, 2012 at 8:41:00 PM CDT
  • Rube Goldberg does not seem to be a good description of these machines. They are as complex as they need to be to do the job.

  • Anonymous
  • October 9, 2012 at 3:03:00 PM CDT
  • Agreed. I enjoyed the read but was irritated at the incorrect usage of the overused term rube goldberg.

  • Unknown
  • October 10, 2012 at 9:15:00 AM CDT
  • If a computer is a device to perform some arbitrary computation (i.e. the running of what could be termed software, though not nessesarily turing-complete), the Phillips machine was not a computer but a simulator, and an imperfect one and that, actually more of a simulator of how its designers thought something ought to work - but it was a fantasy. Adam Curtis actually mentions it in episode 3 of Pandoras Box. Lukyanov's marvelous water computer probably was on the cusp of performing arbitrary computations and similar patterns could probably have been used to create a hydraulic computer. But the hydraulics in water-gardens were certainly not, at least, no more so than traffic patterns arbitrarily traversing a cityscape perform computation, all they do is simulate (with exactly no loss of detail in the abstraction), water flowing through a garden or traffic flowing through a city respectively. But that got me thinking - how hard would it be to build logic gates using water? How hard would it be to design a hydraulic engine from a garden which performs turing-complete computations? Wolfram's 2- and 3-state Turing machines are paragons of computational simplicity as is his Rule 110 Celular Automoton. But they all require an infinitely-large 2-D surface on which to store their working memory. (Similarly, the Turing machine requires an infinitely-long 1-D ticker tape). I don't know how you'd get around that requirement - for an abstractly large working-memory area - for a Turing-complete water garden. I'm imagining something microscopic like a cellular organism which could turn any surface into a memory-storage substrate.. it wouldnt be hard.. The other problem is I'm not sure how to abstract a processor (tape head reader/writer in the original turing machine, the narrator in Randall's XKCD comic) into the design. So perhaps a parellell processing network - like a neural network - would be a much more appropriate design. Parallel processing networks can simulate Turing machines but do so in linear time, not polynomial time, so a hydraulic garden would actually be quite fast, relatively speaking. What a fantastic idea!

  • Anonymous
  • June 19, 2013 at 7:34:00 PM CDT
  • no partial diff eqs in 1615.
    it could have been implemented in the 1700's---what a great idea.

    logic gates in water : look up fluidics.

  • Alexander Trevi
  • June 19, 2013 at 8:04:00 PM CDT
  • Hey Anonymous,

    The backward threading garden historical timeline is a parallel world timeline.

    For fluidics, see the sequel to this post:


  • Anonymous
  • May 24, 2018 at 4:46:00 AM CDT
  • Great article but I must say the annoying repetition of "Rube Goldberg" in every single quote is... well... annoying. Especially when the quote is attributed to someone living 3 centuries before Rube Goldberg.

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