Roots: The Difference An Analyzer Makes

The Differential Analyzer was a game-changer in the history of computing. This machine was able to perform differential equations, which look at the relationship between physical attributes and their rate of change. These calculations are vital for dynamic operations that are essential to computing. 

If you wish to understand where technology is going, it is important to take a look back at where we’ve been. In the series Roots, we trace the history of computing: from the very birth of the digital age, through networking, all the way to the current era of smart devices, and beyond. This month, the precursor of the digital computer: the mechanical computer.

Most stories about the birth of computing look back at Charles Babbage, whose work predated the machines to perform differential equations that are mentioned here in this article. Babbage designed the very first mechanical devices to execute those equations, Difference Engine Number 2, in the late 1840s. That device was, sadly, never built during his lifetime, but replicas are – rightfully so – often one the main attractions in computer history museums.

Difference Engine Number 2 was the development one can view as the first of the general-purpose mechanical computer. Babbage’s design for his later Analytical Engine functioned a lot more like a modern computer, and in many ways it was vastly more advanced than the machine discussed below. Just imagine how computing history would have evolved if the world had made the leap it made in the 1930s almost a hundred years earlier. But for the purpose of moving from human computers to analog mechanical computers, it is probably less useful to look at this alternate history that never came to be. Instead, let’s look at the creation of the interconnect that made it possible for mechanical integrators to use the outputs of others as inputs for subsequent integrators: Vannevar Bush’s Differential Analyzer.

More and more complex machines

Human computers in the 19th and 20th centuries had their skills augmented by tools that helped them perform calculations faster. The slide rules that they used, over time, became complex and useful to quickly get at the results of parts of repetitive math problems that beforehand they had to calculate on a piece of paper. These tools are not by any stretch of the imagination the first mechanical computers. These computers that would perform calculations done by humans required a different kind of math that simply wasn’t possible with earlier tools.

However, the mechanical computer, like all technology, didn’t just simply came into being in a vacuum but was created as an evolution of earlier tech. Several trends were leading to more and more complex machines that built on each other’s basic concepts. American inventor Vannevar Bush is widely credited with building the first mainstream mechanical computer. His invention was the culmination of several technological evolutions that were leading him to his first Differential Analyzer.

One such evolution was the arithmometer of the 19th century. These used a Leibniz wheel, a design that stemmed from the 17th century. This weel was a device that counted the teeth of a spinning wheel. The first arithmometers used this concept to quickly do additions and subtractions, but not much else. For more advanced functions, human computers still turned to slide rules. 

Cranking dials

Arithmometers turned to an advanced version of this concept, the pinwheel design, with an adjustable number of teeth. A human computer pulled levers to get at the desired input values and then cranked a wheel to spin the drum to produce a result. These devices were also able to perform division and multiplication, so they were should have been much more useful for computers. But those operations were cumbersome. They involved pulling several levers, cranking multiple dials, and keeping count of the desired inputs.  

Arithmometers are basically advanced versions of the ancient abacus. The devices used a rudimentary system to perform static calculations. The real innovation would be a more adaptable device: a machine that could be set to perform a complicated calculation and then reset for a completely different action. In other words, a machine that the operator would program and reprogram as needed. What was needed was a way to perform dynamic math operations instead of the static operations that tools like arithmometers brought to the table.

Integral magic

At the basis for dynamic calculations are differential equations, mathematical formulas where functions represent quantities, and the derivatives contained in the function express rate of change. A differential equation defines the relationship between the two. What computers needed to be able to do was to use antiderivatives and derivates of functions to execute some integral magic. Integral calculus was calculated mechanically with ball-and-disk integrators. These devices had an adjustable rotation speed and operated two parts of the integral: the number of spins of the ball (in later devices such as Bush’s mechanical computer a disk, but the same principle applies) and a connected sliding carriage that moved at a rate directly related to the spin cycle of the ball.  

At MIT, Vannevar Bush used these devices to build the first mainstream mechanical computer in 1931. It was a machine that used plotting tables to input data and record the outputs, six wheel-and-disk integrators, and an interconnect of mechanical shafts. The interconnect was the real secret sauce here: it provided a way for any subsequent integrator to use the outputs of the previous integrator as an input. 

Attempts at these interconnects had been made earlier but the outputs did not properly propagate from one integrator to the next. Bush’s interconnect solved that problem. He applied belts to rotating drums and spun them with servos. The loosening and tightening of bands around the drums based on the inputs provided a way to amplify the outputs in order to propagate them to the next integrator. 

Automated dynamic calculations

Bush had built an engine to perform differential equations and had thus built the first general-purpose mechanical computer, known as the Differential Analyzer. These machines became popular in record time in academic centers around the world to perform dynamic calculations in an automated way, which had not been possible before 1931. 

However, these devices still required manual reconfiguration. They utilized tape (and, because of the inherent problems with such a fragile component, most models opted for punch cards) to feed inputs and record outputs, but scientists were looking for a way to automate this process even further: a machine that would record the outputs and re-use them as inputs to do further calculations, again and again. Such a universal machine would be another leap forward in computer history.

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