Humans have probably been calculating since the moment that Paleolithic hunters first used a scorched stick to scratch a record of their kills on the limestone walls of a cave.

“Rrrr! Og kill four! More than Zog!”

Fast forward a few millennia to July 7, 1752, when Joseph Marie Jacquard is born. His automated loom, controlled by punch cards that encoded the complex fabric patterns it was to weave, led the way for many subsequent calculating and computing machines.

But Jacquard was hardly the first to conceive of using machinery to enhance the human brain’s computing power.

People have built calculating and computing tools for thousands of years. Let’s take a look at a few of the non-electronic predecessors to today’s silicon circuits.

This page: Babylonian clay tablets

In fact, archeologists still debate the meaning of cave paintings such as those at Lascaux. But there’s less dispute about the meaning of Babylonian clay-tablet writing, which was clearly used to record stores of grain and of beer, circa 2500 BC. It might be a stretch to call these clay tablets “computers,” but their role in tabulating and storing data is clear. Think of them as the ancient world’s first data banks.

This image, from the University of Chicago, is an administrative record of the payout of at least 600 quarts of an as-yet unidentified commodity at five villages near Persepolis in about 500 B.C.

Photo: University of Chicago

Abacus

Fingers may have been the first “digital” computers, but you need something a little more sophisticated than your hands if you want to work with numbers beyond 10. (That is, unless you want to use your fingers to count in binary, which lets you get as high as 1,023 on two hands.) Enter the abacus.

An abacus is essentially an array of beads threaded on string or held in grooves, with each row representing a different digit. The first abaci appeared in Sumerian and Babylonian times, were used by the Romans, but reached the height of their development in China from the 14th century AD onward.

Chinese abacus operators can use the gadgets to add, subtract, multiply and divide numbers with great speed, handling figures up to the tens of millions. Learn to use an abacus, and you might even be able to use the same techniques to do rapid-fire math in your head.

In this AP photo, a teacher helps a blind child to count with an abacus during a mathematics class at The Santa Lucia school, which has ninety-nine students at different stages of blindness in Guatemala City, Sept. 25, 2002.

Photo: Jaimie Puebla/AP

Antikythera Mechanism

A dictionary-size assemblage of 37 interlocking dials crafted with the precision and complexity of a 19th-century Swiss clock, the Antikythera mechanism was used to predict the movements of the heavenly bodies as well as the dates and locations of upcoming Olympic games.

It was made around 150 BC, then lost in a shipwreck. By the time it was recovered from the seafloor near the Greek island of Antikythera in 1902, it had been reduced to 81 rusted, clumped-together fragments.

Its purpose remained a mystery for decades. It is only recently, using X-ray and gamma-ray imaging and 3-D computer modeling, that scientists have been able to piece together the mechanism’s original components.

One enthusiast has even built a working replica of the Antikythera computer, enabling the celestial computer to run again, after more than 2,100 years.

Photo: Thanassis Stavrakis/AP

Jacquard Loom

Jacquard’s loom was the first to use pasteboard cards with holes punched in them to control the operation of a loom. The loom’s up and down motion is controlled by the positions of these holes, enabling the operators to, in effect, pre-program fabric patterns by laying them out on the cards.

The Jacquard loom didn’t actually do any computation, but it was an inspiration to later computing pioneers, such as Babbage and Hollerith, who would see the value of using punched cards to store procedural instructions as well as data.

Difference Engine

Charles Babbage’s Difference Engine No. 2 was a precursor of modern computers, capable of performing complex mathematical calculations with 31 digits of precision, all using Victorian-era rods, gears, levers and linkages.

But after designing it in 1849, Babbage never completed it. It took engineers and curators at London’s Science Museum almost six years of work to bring Babbage’s 20 pages of blueprints to life in 1991.

Babbage intended to use the Difference Engine to compute trigonometric tables, which sailors (among others) used to compute the results of trig functions. In Babbage’s time, such computations were laboriously completed by humans — usually women “computers” — working through tedious, repetitive calculations. Not surprisingly, errors were rife. Babbage envisioned a more accurate, labor-saving way of making such tables, and his Difference Engine was the result.

Although it took 150 years to complete, the Difference Engine No. 2 works exactly as Babbage planned, computing — and even printing — table after table of super-accurate data. That is, when its many wheels, gears and rods aren’t getting jammed.

Babbage had even grander aims than computation: after planning the Difference Engine, he went on to begin designing an “Analytical Engine” that would be a true computer, in the sense that it would be fully programmable to accomplish any number of different computing tasks. His Analytical Engine was never built, but it remained an inspiration to more than a century of computing pioneers — not to mention steampunk science fiction authors.

Above: The engine, built over a 3½-year period by engineers at London’s Science Museum, will open May 10, and stay in the museum in Mountain View for one year — after which it will take up residence in Myhrvold’s living room.

Photo: Jon Snyder/Wired.com

Hollerith Tabulator

Herman Hollerith was a statistician who helped the U.S. Census tabulate data. After some years of that work, he thought of a better way: Tabulating data using punched cards and a mechanical tabulator, which he patented in 1889. Perhaps he’d heard of Jacquard?

Hollerith’s tabulator was remarkably effective, enabling the government to complete its analysis of the 1890 census two years faster than the 1880 census — and for $5 million less than it would have cost with manual labor.

Hollerith’s Tabulating Machine Company would later merge with three other companies to form the Computing Tabulating Recording Corporation, renamed International Business Machines (aka IBM) in 1924.

Enigma Machine

The German Enigma machine was an electro-mechanical device used to encrypt and decrypt secret messages during World War II. It had a complex design consisting of rotors, electric relays, steppers and ratchets, which would translate the whatever was typed on its keyboard into or out of code. In this file photo, Luftwaffe troops use an Enigma machine. One man types while another records the enciphered or deciphered letters.

The Enigma code was broken by Allied cryptanalysts, helped in part by the capture of machines and code tables.

The first Enigmas were manufactured in the 1920s, and were heavily used by the German armed forces from the 1930s on. The army, navy and Luftwaffe each had specialized versions of the Enigma. Because the Allied codebreaking effort remained secret until the 1970s, Enigma machines were still used by some countries — including the Franco government in Spain — until the 1950s.

Photo: Helge Fykse, Norway

Curta Calculator

One of the devices most prized by gadget collectors, the Curta Calculator is a modern Difference Engine — an entirely mechanical calculating machine capable of great precision. In fact, it works much like Babbage’s Difference engine, except that its digits are arrayed along the outer surface of a cylinder instead of horizontally along a loom-like rack. You set your initial figures by sliding knobs along the side of the cylinder, then turn the crank to compute the results.

The Austrian inventor of the Curta, Curt Herzstark, designed his calculator largely in his head while imprisoned in a German concentration camp during World War II. After he was released he put the plans on paper and began producing his calculators in 1947. They remained in production for about 20 years, until they were finally made obsolete by the advent of electronic calculators like the HP 9100.

Photo: The CURTA Calculator Page