The Root of Borscht

Andrei Vazhnov's blog

The Horn of Plenty: 3D Printers and the Future of Manufacturing

“It is possible to invent a single machine which can be used to compute any computable sequence. If this machine U is supplied with a tape on the beginning of which is written the standard description of some computing machine M, then U will compute the same sequence as M.”
— Alan Turing, 1936

Any sufficiently advanced technology is indistinguishable from magic.
— Arthur Clark, 1961

The Shape Shifter
The Magic Will Be Effective and Universal
Turing’s Genie Escapes the Digital Bottle
What Can They Do Now?
Fabrication Without Limits
Music, Painting, and the Vortex of Infinite Leverage

In classical mythology, Zeus, the ruler of Olympus, did not have it easy growing up. One could definitely say that he was one of the originals who “came up the hard way” since he spent most of his childhood hiding out in a cave because his father, Chronus (Time), had a decidedly ungodly predilection for devouring his own young.

The only food available to the future thunder-thrower was milk from the goat Amalthea who nourished him. Even at that early age, Zeus was a strong young fellow, and accidentally broke off one of Amalthea’s horns while playing around one day. The horn then acquired the magical power of providing its user with unending bounty and ever since has been the symbol of abundance that is still used today in holidays such as Thanksgiving.

Several thousand years had to pass before humanity took its first step towards getting us one of these. That step was made in 1936 by Alan Turing when he invented the concept now known as the Universal Turing Machine. His discovery has transformed and defined our lives so much so that we simply can no longer see it for the remarkable flash of genius that it was 75 years ago.

The Shape Shifter

To see exactly what it was that Turing had invented, imagine you were talking to Thomas Edison a 100 years ago, and you pulled from your pocket a device whose small screen said, “Thursday, August 25, 10:36am.” Without a doubt, Thomas Edison would be really impressed; he would probably say “Wow, such an amazing tiny clock!” And what would probably impress him most is that the clock numbers would change without the hum of any little built-in motor or any moving parts at all…

And yet that would be the least impressive thing about your pocket companion. At the flick of your finger, the same exact object would first turn into a Calculator, then into a Camera, into a Telephone, into a Music Player, into a Television and into dozens of other things. In fact, “dozens” does not even begin to scratch the surface — your Smart Phone can run hundreds of thousands of different programs — and each of them would look to Thomas Edison like a entirely different invention. “There is an app for that!” slogan of iPhone aficionados would leave him totally befuddled and depressed — he’d probably throw in the towel and just retire right then and there before you completely put him out of business with your digital witchcraft.

As we go about our day, we take it for granted that the same physical object can be thousands of different things at the same time — and that is the essence of Turing’s invention. In fact, every smart phone, every netbook, every desktop is a direct descendant of the Universal Turing Machine defined in his 1936 paper. To anyone who did not grow up with these things this ability to shape-shift the same object at the click of the button would be magic at its utmost — far more so than TV, or electricity, or cars were in their day. That we think this is the most natural thing in the world is only a sign of how the idea of Alan Turing forms the very foundation of our lives and our economy. But what was the idea that made it all possible?

The Magic will be Effective and Universal

Before Turing, logicians have long struggled to define the notion of “effective process” — a process by which a person could perform logical reasoning by blindly following simple rules that he or she does not have to understand. The reason this is important is that logic aims to be objective, and this goes to the heart of what “objective” means: if any person, regardless of training or education, could prove a theorem by following a series of simple rules that everyone agrees on, it is fair to say that the theorem has been “objectively” proven. It is objective because it does not rely on understanding by a specific visionary mathematician and can be verified by anyone for themselves. The word “effective” here has its original connotation that stems from the Latin efficere “to accomplish,” so the logicians were simply searching for a method in which person could reason through doing, through performing simple actions.

Turing reflected deeply about what humans go through when they think and when they do, and he found the solution whose simplicity belies its vast power and generality. He realized that the simplest action is one that changes the physical world in one specific location, and in the simplest possible way. He symbolically represented this simplest action as writing “0” or “1” on a tiny square of a paper tape. He represented the person following the rules — the doer — as a simple machine with a mechanical head that can erase the “0” and replace it with “1” and vice versa. The machine also could move the tape to the left or to the right, which was analogous to when a person moves to perform an action in a different part of the world.

Turing then proved that any set of actions, no matter how complex, can be represented by this type of simple machine as long as you fed it enough tape to write its 1’s and 0’s. In short, what Turing had discovered was — in a way of speaking — a quantum of action.

This by itself was an important breakthrough, but then Turing saw something else — he saw that not only the calculations but also the machine that is performing them can be represented as 0’s and 1’s on the same tape. This led him to a stunning realization that you do not need a more complex machine in order to perform more complex tasks — that it is possible to construct one single machine that could do absolutely any task regardless of its nature. It is worth spending a moment reflecting on how strange this discovery truly is since it runs counter to all of human experience. For example, if you want to write something down, you need a simple instrument, a pencil, but if you want to construct a building you need all kinds of complex tools — cranes, bulldozers, etc. Before Turing, it was clear to everyone that the more complex the task, the more complex the machine or the set of instruments had to be; today it is just as obvious to us that if I want stop play Solitaire and start editing family photos, I do not need to head to a photo supply store to get a different machine.

That this should be so, that the infinite variety can be grasped by a single finite machine has always been a source of mystery to me. This finite machine, technically known as the Universal Turing Machine, is the idea at the heart of any modern computer, and if we read the prophetic sentence of Turing’s 1936 paper translated into modern terminology we can see the inklings of our world — the glimpses of PCs, of smart phones with their endless variety of apps, of simulated environments in Video Games, and even the venerable pop-culture milestones such as the Matrix in which one reality was simulated in another.

1936 2012
“It is possible to invent a single machine which can be used to compute any computable sequence. If this machine U is supplied with a tape on the beginning of which is written the standard description of some computing machine M, then U will compute the same sequence as M.” “It is possible to invent a single machine which can be used to execute any software program. If this machine is supplied with a tape/hard disk with the the standard description of some software program M, then U will behave as if it were M.”

In Turing’s original model, the paper tape represented what we now call data storage, and the head that changes 0’s to 1’s served as the model of what would later become the CPU. Of course, the humble tape has now been replaced with multi-megabyte memory chips, and modern CPU’s change billions of 1’s and 0’s per second, but it is hard to overstate how the basic concept remains thoroughly identical to that of Turing. Through the discovery that one single machine could simulate countless others, Turing connected the finite and the infinite right here in our physical world. Today, we hear routinely about studies in which scientists used software to simulate the evolution of a hurricane over the next month, the changes to the ocean’s ecosystem for the next 100 years, the evolution of the galaxy over the next billion years or even the future of the entire Cosmos. Through the concept of one machine simulating another, Turing made very real the essence of William Blake’s famous line “To hold infinity in the palm of your hand and eternity in an hour”

Turing’s Genie Escapes the Digital Bottle

Today, three quarters of a century after Turing’s paper, many of the largest, most valuable corporations either make Universal Turing Machines (Apple, Samsung, Dell) or write programs for them (Microsoft, Oracle, Google, Facebook).

Yet, as amazing as the computer revolution has been, it is only half of the story that began with Alan Turing’s 1936 paper: In the 20th century, Turing Machines were mostly confined to working with information — your computer could display things on screen or write them into a file, but it could not create things in the physical world directly. Recently that has begun to change.

The second half of Turing’s story is the coming age of the 3D printer which will make the Horn of Zeus look like a rusty Lada next to a Lamborghini. For while the original Cornucopia only made food, Turing’s version will soon be able to provide not only nourishment but pretty much everything else: furniture, clothing, automobiles, and even a replacement for your kidney when you need one.

If you like a couch or a table at your friend’s house, one day you will be able to scan its bar code and have one just like it printed at a local fabricator office. If you like someone’s outfit in a TV show, you will be able to customize it from your Apple remote and have it sent to you from a fabricator down this street or just print it out right at home.

In fact, the name “3D printer” sounds so mundane as to mask the true importance of the technology. It is a combination of the now banal concept of “printer” with the “3D” prefix that is often evocative of various gimmicky technologies such as 3D televisions. Perhaps a better name would be The Universal Turing Fabricator to better reflect the magnitude of the change that will unfold in the next few years.

What can they do today?

I first read about the possibility of programmable fabrication around mid-nineties in Eric Drexler’s remarkably prescient 1986 book “Engines of Creation.” Ever since, news items regarding these technologies attracted my attention, but for a long time they never seemed more than curiosities that you would display in a science museum. In the last few years, however, practical advances started coming in rapidly. For instance, here is a gallery of user-created 3D objects at Right now you can digitally design an object on a computer and this service will print it out and mail it to you. Not only that, it can also mail to some else for a fee and deposit the money into your account the same way an iTunes purchase sends the royalties to P.Diddy.

Still, it is one thing to 3D-print funky costume jewelry or bookshelf knick-knacks, it’s a whole different ball game to be able to print a car, a kidney, a nice BLT sandwich. How long will it take for the technology to mature to that point? Will it even ever be possible to print things with complex interior structures such as living tissue or electronic components? The answer to this question is that in prototype form all this has already been achieved, and, as recent history proved on numerous occasions, what is possible in a lab today is commercial reality a few years down the road. Here is just a small sample of what you might expect to see at your local copier office towards the end of this decade:

Cars Watch Video PCWorld: 3D printed cars may be the way of the future
Kidneys Watch Video
TED where the surgeon prints a kidney on stage
Surgeon Prints New Kidney on Stage
Guitars Watch Video
Shows the process of printing the guitar to the soundtrack of that that guitar!
World’s First 3D-Printed Guitar
Teeth Watch Video Dental prosthetics market on the rise, boosted by 3D printing
Food Cornell Fabrication Lab Makes Edible Objects With 3-D Printer
Bikes Watch Video

Fabrication Without Limits

When you watch the videos of this technology in action, it is clear that it is a bit clumsy, still in its early stages. It also seems almost trivial — just as a regular 2D printer places ink dots on paper, a 3D printer deposits layers of material one upon another according to the instructions from the computer. Doesn’t really seem like a big deal. However, the power of this invention derives not from the printer itself, but from the Universal Turing Machine that animates its motion. And, as we have seen, there is no limit to the complexity of what a UTM can create.

Turing himself was aware of how difficult it is for the mind to accept this infinite potential. In his classic 1950s paper which remains one of the most cited works in philosophy, he commented as follows regarding objections that there are some things machines will never be able to do, wryly noting that they mostly stem from the unconscious use of “scientific induction.”

No support is usually offered for these statements. I believe they are mostly founded on the principle of scientific induction. A man has seen thousands of machines in his lifetime. From what he sees of them he draws a number of general conclusions. They are ugly, each is designed for a very limited purpose, when required for a minutely different purpose they are useless, the variety of behavior of any one of them is very small, etc., etc. Naturally he concludes that these are necessary properties of machines in general.

When it came to the future potential of what machines can do, Turing was mostly interested in creating Artificial Minds. He wrote a chess playing program when there were no computers that could run it and personally simulated the computer with pencil and paper, taking half an hour to calculate each move. At the time, it seemed like an eccentric academic exercise, and yet Turing remarked in his paper:

We may hope that machines will eventually compete with men in all purely intellectual fields.

His pencil-and-paper program lost, but 45 years later a real computer defeated Garry Kasparov, the highest rated player in the history of the game, and nowdays machines already successfully compete with humans in many fields: google does a passable translation from almost any language, email and SMS deliver most of our communications, Siri is taking over the secretarial jobs which were already in decline due to wordprocessing and groupware, Amazon and google books supplanted most functions that used to be performed by libraries, e-commerce is replacing traditional retail jobs — the list is quite long.

With the arrival of 3D printers, it seems that only one correction needs to be made to update Alan Turing’s quote above for 2012 — remove the words “purely intellectual” since it is rapidly becoming possible to build a single machine that can create any possible physical object and bring the unlimited power of the UTM into the world of manufacturing.

Music, Painting, and the Vortex of Infinite Leverage

In all ages past, up until the 20th century, if one had a gift for painting, he or she could earn a decent living making portraits for people who wanted to have a remembrance. In fact, many of the old masters we admire in museums today got their income mainly from commissioned portraits. With the arrival of the camera, the vast majority of these jobs disappeared almost instantly while the few who were left standing did so by reinventing the profession. It is not a coincidence that the 20th century art is drastically more abstract; it’s not that people all of a sudden became more creative — there was simply no value left in re-creating reality on canvass. In a cognate development, the “starving artist” is a relatively modern concept reflecting the fact the traditional economic basis of this profession had largely disappeared.

Similarly, there used to be good money in being a musician: you wanted to enjoy Chopin before turning in, you had to hire local professionals to come to your house and provide you with that service. With the development of a record — quite literally a 2D imprint of sound — no one wanted to be inconvenienced by having strangers over to perform music when you can have the same experience for a small fraction of the price.

The fact that portrait painting and musical performance have disappeared as a significant source of steady employment does not imply that the demand for these services has decreased — on the contrary, people take more portraits and listen to more music than ever before. It’s just that all the economic benefits of this value chain now accrue to the top 100-500 people in each profession (e.g. Elvis Presley, Brangelina), not to hundreds of thousands as used to be the case in the old times. This is a natural choice for most people — why would one want to hear the music or look at the paintings from the mediocre artists and musicians who live nearby if one can listen to the very best person in whatever genre that he or she happens to enjoy?

Every time marginal costs fall to nothing, a vortex of infinite leverage forms. The value chain that was heretofore distributed is now funneled to the people at the very top of the profession — almost everyone else becomes a hobbyist. This has already happened in the transition from painting to photography, from live music to radio and records, from theater to movies and television.

This is what Marc Andreesen referred to when he used the provocative phrase Why Software Is Eating the World. He argues that the lofty valuations of technology companies do not represent a bubble. According to him, not only there is no tech bubble, but some of the companies like Facebook, Groupon, Skype, if anything may be valued too low since they could end up vacuuming the value chain from entire industries as Amazon is doing with retail and publishing and Apple did with music. As an investor in these companies, Andreesen may be viewed as biased towards optimism, but I think his larger point is correct: Software represents a vortex of infinite leverage on an entirely new scale and it is only a matter of time before what happened to music, painting, and theater happens to all of manufacturing businesses.

Why must this be so? We can again look to Turing’s insights for the answer. Note that the terms “program” and “programmer” did yet not exist when he was writing it, and he used “instruction table” for what we now call “program” and “mathematician with computing experiences” for what we call “programmer.”

Instruction tables will have to be made up by mathematicians with computing experiences and perhaps a certain puzzle-solving ability. There will probably be a great deal of work to be done, for every known process has got to be translated into instruction table form at some stage.

The process of constructing instruction tables should be very fascinating. There need be no real danger of it ever becoming a drudge, for any processes that are quite mechanical may be turned over to the machine itself.

I think today the software is still regarded as an “industry” in its own right. But that is an incomplete view of the situation: Software is to business what mathematics is to science — it is a language of description and every known business process will eventually be translated. As Turing’s quote above suggests, software is stories we tell our machines so that they could liberate us from the work that is mechanical and mundane — i.e. from the type of activities that we generally call “work.”

It also reflects something else that is fundamentally different about software — you never need to build anything twice: If you have one bridge in your town and you need a second one in a new location, you have to hire the construction crews again. If you need Microsoft Word at a new location, you do not need need to hire programmers to build you another one.

This means that, once the 3D printing technologies are perfected, a giant vortex will form into which all of manufacturing will rapidly disappear, and just as happened to musicians, all the value in manufacturing will be funneled to star industrial designers who will be known by name like Jony Ive at Apple today. A residual amount will go to the manufacturers of 3D printing technologies and robotics, though like the CD-player makers of today they will eventually become low-margin businesses as the technology matures.

How will this transformation compare to its historical antecedents in music, theater, and painting?

Will take a look at this in the next few weeks.


1. Drexler, Eric 1986, “Engines of Creation: The Coming Era of Nanotechnology”
This book popularized the notion of nanotechnology and influenced a lot of science fiction writers. However, it also has a lot to say about many other interesting futuristic topics.

2. Turing, Alan 1936, “On Computable Numbers With Applications to Entscheidungsproblem”
This is Turing’s original paper that defined the concept of stored program computer and started the road to the digital age.

3. Turing, Alan 1950, “Computing Machinery and Intelligence”
In this paper, Turing examines the possibility of constructing intelligent machines and describes his now famous “Turing Test” whereby a machine should be considered conscious if it can convince a human judge that it is human. This is one of the most cited in philosophy because Turing was the first one to try to define rigorously the answer to the question “What is mind?”

4. New World Encyclopedia article on Alan Turing.

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Andrei Vazhnov


Written by Andrei Vazhnov

February 7, 2012 at 10:21 pm