# Who Invented the Computer? The Differential Analyzer

*Who Invented the Computer?** This is the fourth installment in our ongoing series.*

A Differential Analyzer is a mechanical analog computer designed to solve differential equations. OK. So what?

Let's just say that it's the sort of thing without which we'd still be stick way back near the beginning of the developmental road to the modern computer. For those not versed in calculus, a bit of background may help explain the uses and importance of a differential analyzer.

**Differential Equations: A Superheoric Story**

A differential equation is a complex equation in which a variable and its derivative are related. For example, suppose that Iron Man takes a hit while flying around in battle, shorting out his suit and sending him plummeting to earth.

Tony likes to cut his odds close and look like a hero, so he decides to find out how much time he has to fix his suit before winding up at the bottom of a modest impact crater. The first step to solving this problem is calculating his velocity, or speed and direction toward the earth. Easy, right? Not so much.

For simplicity's sake, we will say that to find his speed he needs to know how fast gravity is dragging him down minus how the degree of air resistance pushing back in the other direction. Being Tony Stark, he knows the gravitational constant, so that's covered.

The air resistance depends on variables such as the density of the air, the surface area of his suit that air is pushing against (whether he's in a nosedive or sprawled out), and of course his current velocity as he falls. But wait: It seems that in order to determine his velocity he needs to � already know his velocity?

Suddenly Tony's head starts to swim, and not just with hypoxia. This type of seemingly endless circular equation is the scourge of many an undergrad and the great gatekeeper of that torturous realm they call calculus.

The good news is that Tony, being a super genius and a student of the grand old American education system, remembers his calculus. He manages to fix his suit milliseconds before hitting the ground, earning the awe of onlookers, and soars back up into the sky to grapple with the forces of evil.

**A Device to Do the Heavy (Mathematical) Lifting**

The surprising thing is that differential equations pop up a lot more in our lives than we even realize. From superconductors to cancer treatment, the development of many of the technologies and advances we currently enjoy have been dependent on our ability to solve differential equations.

Often the deeper into science we go, the more complex the equations become, and the more computing power we need to solve them. Thus, the glory of machines like the differential analyzer.

Viewed as a standalone device, the differential analyzer is an impressive looking piece of machinery. Constructed of a lot of gears, axels and chains, it looks like Rube Goldberg went nuts with an Erector set. Behold:

*Differential analyzer constructed by Dr. Bonita Lawrence of Marshall University*

**The Brothers Thomson**

The concept that underlies the differential analyzer originated in 1876 with Scottish engineer James Thomson, the elder brother of William Thomson. William is better known to history as Lord Kelvin, inventor of the tidal prediction machine. Though less well known than his little brother, James Thomson also possessed a brilliant mind. As an expert in water transport he made his own significant contributions to theoretical and mathematical engineering.

An unusually bright child, William Thomson began studying at Glasgow University at age of 10, impressively graduating two years later. By the time he was 17, he had completed a master's degree with honors in mathematics and natural philosophy.

As brothers often do, James Thomson gave William a helping hand in the process of developing his tide predicting machine. A key factor was the inclusion of a ball-and-disk integrator that enabled analysis of random tidal patterns.

The integrator consisted of three components, a disk, cylinder, and ball, all made of brass. The disk and cylinder were connected to shafts that controlled their rotations and the ball would roll along the cylinder with the turning of a gear shaft, enabling William Thomson to record tidal projections. **Click here** to see a model of the integrator.

While James Thomson initially saw his creation as an improvement on an existing mathematical instrument, the platometer � a device used for determining the area of an arbitrary two-dimensional shape � William Thomson imagined it as much more.

William reasoned that if the disk and cylinder were mechanically connected to shafts, and several integrators linked to each other, then the result of one complete revolution of an integrator would become the input of another thereby enabling the modelling of complex differential equations.

**Guns Blazing**

This ball-and-disk integrating machine would eventually be incorporated by the British Navy as a firing control system. Prior to the integration machine, ships fired salvos utilizing the artillery spotting technique where an observer would estimate how far off target a shell had landed (and in what direction).

The spotter would inform the crew and the crew would make adjustments for their next shot. This method worked well when ships got close to one another in a fight, but became increasingly ineffective as the range for naval guns increased and enemy ships kept their distance.

The integrating machine concept made weapon fire more effective as crews could now adjust for variables like wind speed, the pitch and roll of the ship, and temperature. They could even adjust for the minute rate of change in the size of gun bores as they heated up and expanded with repeated firings.

*Note:** Sorry for the abrupt ending. At this point in the history of the differential analyzer, Lord Kelvin hands off the baton to Vannevar Bush ... who you'll meet in our next installment.*