The History: Finding a 1

“If I have seen further it is by standing on the shoulders of Giants.”

Isaac Newton, 1675

“The journey of however many miles starts with a single cliche”

Anonymous

We’re starting our journey into the “art of code” with a brief history of computing up to the first written evidence of humans encoding something resembling a bit, with or without the context of a full-blown computer. A bit is the smallest unit of data in a computer, which can only have two values: 0 or 1 (false or true). The plan is to scan documented history and get to that point in time in at most three posts including this one.

Early Symbols

The word code carries a few meanings depending on the context. One of the meanings has to do with transmitting a message in a synthesized or transformed form (sometimes called an encoding of the message), often in the interest of keeping the message secret. Consider Morse Code and its assignment of dots and lines instead of letters. Someone who knows Morse Code can easily encode or decode a message using the code’s substitution table.

By definition, speech is (an) encoding because it servers the purpose of conveying information (words, context, meaning, thought, emotion) through the careful arrangement of sounds. There are some estimates and speculation around the timeline of the appearance of speech. For this story, we’ll only consider being “code” or “encoding” that which can be seen or touched.

As early as 50-60 thousand years ago, early humans (and Neanderthals?) have created cave paintings depicting recognizable stylized animals, notable events, and places. I imagine that these creations had the purpose of mementos, capturing and communicating emotion, and perhaps community building. I speculate that this early form of mimesis, using the world as its canvas, contains the earliest known form of encoding. Cave building has to have been an essential step towards the birth of letters and digits as we know them today.

I find it mesmerizing and comforting that so many years ago, our species (I wish “specieses” were a word) had this need for communication and connection. I do imagine other forms of art and code have manifested without resisting the test of time as long as cave paintings did. As it could probably be the subject of a whole book, I am not mentioning astrology, star gazing, and calendar making as forms of “coding.” Of course, the best method to do that is to mention it, as observed here.\

Should we discard the different numbers of objects present in cave paintings as an understanding of numbers? It feels like there’s some inherent intuition on numbers in all species. We’re looking for that proven intuition that goes beyond animal instinct, beyond fight or flight, beyond purely imitating the world around. We’re looking for the first use of numbers as an abstract concept, some evidence of giving them a name or a description.

The first 1

At around 3-6000 BCE, there’s evidence of Sumerians (overly simplifying the involvement and advances of other civilizations in this story) having invented a sexagesimal (base 60) numerical system, probably a necessity in managing their administrative needs. So, to anyone wondering, the decimal (base 10) system was not always “the norm”:

This table is remarkable. Remember, the table contains what we would call digits today. In other words, the first two-digit number would occur for them while counting when they reached 60. These digits followed a pattern that made digits “look like” their respective “real-life” “numbers.” In other words, not only their numbers but also their digits followed the same rules and principles as our numbers do. They seemed to have symbols for 1 and 10 together with a rule for composing them into their symbols for “digits.”

You might also observe that there is not something resembling 0 in this table, which probably made for much confusion. Imagine not being able to tell the difference between 5 and 50; 101 and 11; 1 and 10000; and many others.

The Babylonians later on tried to work around this shortcoming of this system by and even later a slanted double wedge symbol for “nothing.” (circa 3rd-6th century BCE ) They understood “nothing,” but they did not see “nothing” as a number; instead, they saw it as the absence of something. Another quirk in this workaround was that they only used the “nothing” symbols in the middle of the number. Thus, there was no way other than the context for them to differentiate between 1 and 60 and 3600; and so on.

To keep things brief, I’m skipping detailed depictions of their use of a single-hand 12-counting system, ties to base 60, and why base 60 was so thriving for them in general.

Let’s get back to numbers. Imagine you see a number like 637 (magic, right?); you immediately know the scale of it and, well, that it’s 637. That’s because your brain’s wiring is for base 10. You don’t have to consciously calculate (in any given order): 7 ones plus 3 tens plus 6 hundreds.

102	101	100
6	3	7

Now let’s do something similar in sexagesimal. I’ll use numbers instead of the symbols in the table above since I found no easy way to use them in this text at this time. Similarly to our example above, in the Sumerian system, a number like 357 would mean to them: 7 ones plus 3 sixties plus 6 thirtisixhundreds.

602	601	600
6	3	7

Their brains wiring was for (their) base-60, maybe it was just as natural to them as it is to us to interpret decimal numbers? Things that keep me up at night ?

There’s plenty of material out there about Sumerian, Babylonian, and Egyptian math. Fire up google and look it up if you want to. For now, I’ll mention one more thing very relevant to the birth of computing but not necessarily to our story: the Sumerian abacus (est. 2700-2300 BCE).

An abacus is a “manual” calculator, with columns or rows of beads typically strung on wires representing the digits of the number: ones, tens, hundreds, thousands, etc) – or in the case of Sumerians: ones, sixties, thirtysixhundreds, etc). The operator of these early computers would calculate subtractions and additions by sliding the desired number of beads on each of the corresponding digits rows or columns. To my knowledge, the abacus is the earliest form of deliberate computing: devising a set of symbols and rules and then designing tools to operate on that set of symbols and rules.

This was a very roundabout way to say: the earliest form of “1” appeared in written form as part of a mathematical system somewhere around 5-8 thousands of years ago.

In our next post, we will continue our search for the first clear signs of “0” as a number or digit.