The Growth of Knowledge

There are two sides to knowledge: Acquiring and assimilating it and thus forming your own ideas and disseminating it and thus helping others to form ideas. So, reading and writing and arithmetic.

It may seem obvious, but you have to invent writing, before you can learn to read. So, you write down the words of a Homer poem, show it around and everybody laughs. “What are those funny marks you have made?” Writing was invented slowly, over many thousands of years. It started off as pictures, painted on cave walls, using some natural clay pigments, ground with a stone and mixed with water or spit. Mainly, they used their hands to paint, but hairs from an animal’s tail, tied in a bundle made a primitive brush, and bits of animal hide were used as swabs. These paintings were a direct representation of what the painter was seeing. What we now needed to do was to slowly turn that real representation into the abstract representation of life that is written language.

The first stage in in that process was creating spoken words to represent things around us. Once we had a spoken language, we could settle down and try to write it. Our first attempt at writing was pictograms and we have a treasure trove of Egyptian and Mesopotamian pictograms.

Pictograms could represent an object, an idea, or just part of a word, but we needed more abstraction, so we turned to cuneiform. Cuneiform symbols were developed over much of the Middle East, from the early Bronze age right through till the common era. Cuneiform is halfway between pictograms and an alphabet, in that each symbol usually represented a syllable and the syllables could be set next to each other to form words. The basic unit of cuneiform is a wedge shape, created by pressing a sharpened read into damp clay. So, you might put together the syllables PA and AN to make the word PAN. Cuneiform developed over a period of some 2,000 years.

The first writing code close to being a modern alphabet, was the Phoenician Abjad. An Abjad is an alphabet with no vowels, only consonants. The vowels would, apparently, be inferred by the reader and I have no idea how that was achieved. Over time, vowel markings were added, and these later codes are called impure Abjads. Abjads are still in use today, in languages like Arabic and Hebrew. Finally, we reach probably the first true alphabet, that of ancient Greece. This alphabet is recognisably modern, containing all the consonants and vowels you need to spell the words of Homer or Shakespeare. Now, we just need something to write with and something to write on.

Making sense of the words

In the early days, reading followed the development of writing. We gazed at cave paintings, understanding the images of animals, without possibly having any word to name them. We understood pictograms, as they were very visual. We then learnt the meaning of scratches on clay tablets and finally, after many thousands of years we understood an alphabet.

I say we, but there were only a few of us who could read. Royalty, priests, scholars and some rich merchants. The great leap forward in reading came when Martin Luther published his 95 theses. One of the things he argued for was the use of common language, rather than Latin, for church writings. The use of a common language was aided by the invention of the printing press in the fifteenth century, which was simply a heavy flat piece of wood that could be lowered and raised via a screw. A wooden block, with words laboriously carved into it, would be smeared with ink and the press would be screwed down to transfer the ink to the paper. This worked fine for printing price lists for indulgences, but for a 300-page bonkbuster, or the adventures of a boy wizard, you need a more efficient process. Fortunately, around 1540, Johannes Gutenberg had invented moveable metal type. Needless to say, the Chinese had invented moveable type already, somewhere around 1045CE, and made of porcelain. Word of this never reached Europe so Johannes gets the nod as the enabler of mass reading.

To make moveable type you need a mould which is constructed by hammering an image of the letter into a piece of copper. Pour heated liquid alloy of lead, tin, and antimony into the mould and voila, you have a piece of moveable type. For the next 400 years, this is how type used for printing books, magazines, and newspapers is made.

Now line your type up in a wooden frame the size of your page and you are ready to print. You may have noticed that this block will print the word “read” backwards. O.K., there is a bigger problem. What size do you make your shiny new moveable type. Any printer can decide to make his type in whatever size and style he feels like. Moveable type was standardised into typefaces, an alphabet in a particular style, and fonts, typefaces in a particular size. The size of fonts is measured in points, and a point is 1/72 of an inch, or 0.35mm. So, a 12-point Calibri font is roughly 4.2mm tall. I say roughly, because points do not actually measure letters, but an invisible box which surrounds the letter. There are now thousands of typefaces available in a myriad of different fonts. What about this, an available typeface but, perhaps, a little flamboyant for your next CV.

We now have moveable type, a printing press and loads of sheets of paper, so we print our bestseller. Book production rises by leaps and bounds. Here are some figures for Western Europe, from the World Economic Council.

As well as producing books, we also need to produce readers, and how do we do that? We educate them in reading, writing and arithmetic. Like many other human measurements, literacy rates are very rough and ready, but here are some British literacy rates for you to consider, taken again from the World Economic Council. There are a couple of things worth noting. A leap from 16% literacy to 53% literacy after the invention of the printing press and then a hiatus, before another jump to 76%, as a result of Victorian social reformers like Charles Dickens. Mind you, he had a vested interest in people being able to read.

Today, there are at least as many words read from a computer or phone screen as are read from a book or newspaper. You may well be reading this as an eBook, or on my web site. However, some 2.2 billion paper books are sold per year – over 17% in the U.S., China and the U.K. – so I think that my favourite activity will still be catered for in the near future.

Adding it all up

The first calculation aid was, of course, fingers. A finger up is one and a finger down is zero, so we can now count to ten. There are many steps on the long road from fingers to the iPad. Marking of bones or stones, and tally sticks to improve computing memory and extend our ability to count beyond 10. However, such artifacts cannot easily be changed. It was the use of a pointed stick to make marks on wet clay in Mesopotamia, some 5,000 to 6,000 years ago that really moved computation forward.

Of course, for any computation you need a numbering system, and the Sumerians had one. Well, they had lots. Their main numbering system was based on 10 and 60, but they had different numbering systems depending on what was being counted. The use of different numbering systems for counting different things, we still use today. You can buy eggs by the dozen, measure 360 degrees or so many feet and inches, measure a horse in hands and measure wind-speed in kilometres per hour. There was an odd measuring unit in Mediaeval England called a Baker’s dozen, which was thirteen. Bread was nominally sold by weight, but the weight of baked goods could vary, so the baker gave you an extra one in case the weight of a dozen was less than expected.

The next step is something which allows repeated calculations of different amounts. Whilst chalk on slate will do the trick, the Chinese have come up with an ingenious tool for mathematical calculations, the abacus.

A variation on the abacus was invented by the mathematician John Napier (1550 – 1617) and called Napier’s bones, or Napier’s rods, Napier used something called lattice multiplication for his bones and set values onto a set of flat lengths of wood, inside a frame. Napier also invented natural logarithms. Logarithms allow you to multiply and divide large numbers using addition and subtraction. Find the logarithms of two numbers, add or subtract them and the look up the antilogarithm of the result.

To progress in mechanical calculation, we had to shoot a lot of elephants. We needed the ivory. It would have been possible to use wood, but ivory is much more dimensionally stable in all different climatic conditions. The first ivory calculator is the Sector – also called a proportional compass. This is made of two ivory strips, hinged at one end, with scales marked in brass.

The next step in calculation was the slide rule, which depends on John Napier having invented logarithms. This allows you to do some quite complex calculations, just by sliding scales past each other. Mechanical calculators were the next step, and had a surprisingly long life, from the 1500s right through to the middle of the twentieth century. There are two types of mechanical calculator, keyboard or pepperpot. The keyboard calculator, sometimes called a tabulator, was used for simple addition and subtraction, whereas the pepperpot could do more complex maths, multiplication, division, and even exponential calculations.

The first electric tabulator was the Hollerith machine, used to process data for the 1890 U.S. census. The Hollerith company was merged with three other companies to form what was to become IBM. The electric tabulator was a bridge between mechanical calculators and computers. It used data input and output but could not be programmed for anything other than adding and subtracting.

The first electronic computer was ENIAC (Electronic Numerical Integrator and Computer). It used 17,468 vacuum tubes and spread itself over 548.64 square metres (1800 square feet). In order to get from ENIAC to a modern smartphone or tablet, we first had to invent the transistor, which happened in 1947. Then we just had to keep making the transistor smaller. From a size of 20 micrometres in 1968 we were down to 2 nanometres by 2025 and expect to be down to 1 nanometre by 1027. We now have ten times the power of ENIAC’s 548 square metres in a smartwatch.