Origins of information — from signs to records

Ask what a mark lets someone do

A message, a record and a number are related but different things. A spoken instruction can coordinate an immediate action. A durable mark can preserve a claim for someone absent when it was made. A numerical notation can make quantities easier to compare and calculate with. Studying these differences provides a starting point for computing history without calling every ancient sign a computer.

This chapter follows selected evidence from the ancient Near East and later numerical traditions. It is not a worldwide inventory of writing systems or an account of the origin of human language. The surviving records discussed here cannot date the beginning of speech. Language and writing must not be treated as interchangeable: a writing system represents aspects of a language, while a symbol system may communicate a restricted message without recording a spoken sentence.

Counting goods before recording sentences

Archaeologist Denise Schmandt-Besserat interprets Near Eastern clay tokens as an accounting technology. In her account, shapes represented different kinds or measures of goods and token counts represented quantities. Her reconstruction connects these practices to later written accounting. This is an interpretation of a particular archaeological tradition, not a universal sequence through which all societies passed.

The distinction between category and quantity is useful. In an original teaching model, suppose a triangle represents one grain measure and a disc one sheep. Three triangles and two discs stand for three grain measures and two sheep. Counting five objects after mixing the tokens loses the category information. Reading the record requires knowing both the shape convention and what counts as one unit.

That model is inspired by accounting systems; its triangle and disc code is invented for this lesson. It is not a transcription of an excavated tablet. No binary encoding is implied by its use of two object shapes.

Writing expands the possible message

The Met's account connects late-fourth-millennium BCE Uruk tablets with administration and discusses the complexity of writing's origins. It describes early pictorial and abstract signs, followed by increasing use of signs for sounds as well as things. Its examples of tablets dated approximately 3100–2900 BCE are objects with estimated dates, not a precise birthday for writing.

A phonetic use lets a sign participate in spelling a name or expressing an utterance beyond a stock inventory. In a rebus, a pictured thing can stand for a similar-sounding word. The point is a change in what the representation can express, rather than the claim that pictures were simply replaced everywhere by alphabets.

The record also depends on material and institutions. A mark must survive, conventions must be learned and someone must preserve or circulate the object. The archive we can inspect therefore reflects what was produced, retained and recovered. An administrative tablet is evidence of a recording practice, not evidence that administration was the only thing its makers could communicate.

Number systems choose what position means

A quantity and its notation are distinct. In an additive notation, repeated marks may contribute repeated amounts. In a positional system, a digit's contribution also depends on its position. Different conventions support different written procedures; none is a measure of its users' intelligence.

Use modern decimal notation for an original worked example:

205 = 2 × 100 + 0 × 10 + 5 × 1
25  = 2 × 10  + 5 × 1

Erasing the middle zero does not merely shorten the first record: it moves the 2 to another place and changes the value. In a base-sixty teaching notation written as a pair (2, 5), two positions would mean 2 × 60 + 5 = 125. This pair notation is ours, not a facsimile of Babylonian signs. It makes the need to specify a base visible.

MacTutor describes Babylonian positional notation and later placeholder signs. Context could supply distinctions that a written numeral did not make explicit. A symbol convention should therefore be interpreted within its historical use, rather than judged only against a modern printed number.

Zero has more than one history

MacTutor distinguishes a placeholder for an empty position from zero as a number used in arithmetic. These roles cannot be collapsed into one discovery by one person on one day. Its account discusses Babylonian placeholder practices and Indian mathematical work, including Brahmagupta's seventh-century rules involving zero and negative numbers.

A placeholder answers a representational question: which position has no contribution? An arithmetic zero participates in statements such as x + 0 = x and x - x = 0. A particular drawn sign, a name and a mathematical concept can travel and change on different timescales.

The same source notes difficulties in early rules for division by zero. For ordinary real-number arithmetic, 6 / 0 has no value: if it were a number y, multiplying back would require 0 × y = 6, which cannot hold. Treating zero as a number did not automatically settle every operation involving it. This explanation uses modern arithmetic to clarify the issue; it is not a claim that historical authors used this exact argument.

Encoding is not the whole message

Consider a second original code: G means grain, S means sheep, and a record has the form category:quantity. G:3;S:2 preserves the two categories in our token exercise. Replacing G with the bits 00 and S with 01 would change its encoding, while leaving its intended meaning unchanged if both readers share the new codebook.

But the codebook alone does not tell us whose grain, what size a measure is, whether the goods were delivered or merely promised, or whether the record is trustworthy. Those require context and conventions. A physically preserved message may still be ambiguous; an exactly copied message may still be false.

This distinction leads toward information and representation. Much later, Shannon's communication work asks a specific engineering question about message selection and transmission. Its mathematical notion of information should not be silently substituted for every earlier use of a sign or record.

Reading checks and answers

1. Why cannot an early tablet date the origin of language? It records a surviving written practice, not the first spoken interaction. Evidence for one is not a date for the other.
2. In the invented token model, what survives if you record only the total five? The number of tokens survives; the split of three grain measures and two sheep does not.
3. Decode decimal 304 and the invented base-sixty pair (3, 4). They mean 3 × 100 + 4 = 304 and 3 × 60 + 4 = 184. The base and positions matter.
4. Does zero's appearance as a placeholder establish that all arithmetic rules for zero were already accepted? No. Representation, mathematical operations and terminology need separate evidence.
5. Does the clay-token interpretation prove a direct line from an ancient account to a modern database? No. There is a useful comparison of recording problems; a documented chain of transmission would require further historical evidence.

Next, the origins-of-logic chapter asks a different question: how can the form of an argument help us judge whether a conclusion follows? Recording a statement and justifying an inference are separate achievements.