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In modern scientific and technical notation, numerical values are routinely written together with explicit abbreviated unit symbols (for example, 3 ft, 2 mi, 5 lb), forming a single semantic object that combines magnitude and unit.

However, when looking at ancient sources, it seems that numbers and units were often treated separately, with the unit either stated verbally, indicated by a distinct symbol, or simply inferred from context.

My question is specifically not about the origin of units themselves, but about the history of notation:

When did it become common to write numbers together with explicit unit markers as part of the written expression?

In which historical contexts (administrative, commercial, scientific, engineering) did this practice first appear?

Did ancient civilizations (e.g. Egyptian, Mesopotamian, Greek, Roman) explicitly mark units in written records, or were standard units generally implicit?

At what point did abbreviated unit symbols (such as ft, mi, lb) begin to function as stable, conventional elements of numerical notation?

I am particularly interested in sources that discuss this shift from context-dependent units to explicit unit–number notation, especially in relation to the development of early science, engineering, or metrology.

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  • $\begingroup$ Concerning “ancient sources” that “stated units verbally���: isn’t this essentially the same as writing “2 miles”, which you at the same time call “modern”? Even writing “3 ft” is essentially the same as writing “3 feet”, except that “feet” is abbreviated. $\endgroup$ Commented Jan 22 at 13:39
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    $\begingroup$ Maybe you could list some explicit examples of what you consider "ancient" $\endgroup$ Commented Jan 22 at 13:41
  • $\begingroup$ @MichaelBächtold,Thanks, that is a helpful point. I’m indeed interested in cases where the unit behaves as a conventional written symbol (often abbreviated, like “ft”, “lb”, “km”) systematically attached to the numeral, not just as a word in running prose. I’ll edit the question to clarify this distinction and to add some explicit ancient examples. $\endgroup$ Commented Jan 22 at 15:07
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    $\begingroup$ Can you give at least one example of "number and unit treated separately" from an ancient source? It is not clear what you are asking about. $\endgroup$ Commented Jan 22 at 15:19
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    $\begingroup$ You may want to look at the Wikipedia page for the Rhind Mathematical Papyrus and the use of units (cubits etc.) in there. $\endgroup$ Commented Jan 23 at 11:56

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This is not an answer, but two remarks.

  1. As far as I am aware, almost all mathematical symbols, such as +, =, √, and %, originally began as written words. For a long time, people would write, for instance, 3 plus 3 rather than 3 + 3. Only later were these words abbreviated or turned into symbols, mainly to reduce writing effort or to present statements more clearly. From this perspective, there is nothing fundamentally special about abbreviating unit names such as "foot" or "mile".

  2. You write: “[…] written together with explicit abbreviated unit symbols (for example, 3 ft, 2 mi, 5 lb), forming a single semantic object.” I am not sure what is meant by “explicitly abbreviated” (as opposed to “non-explicitly abbreviated”). I am also unsure what is meant by a “single semantic object”, especially since an expression like “2 miles” does not seem any less a semantic object. But I would like to add that 3 ft (or 2 miles) can still be seen as composed of two parts with distinct meanings. It is the product of the number 3 and the length ft. To my mind, this is entirely analogous to writing $3\vec{v}$ to mean three times the vector $\vec{v}$.

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  • $\begingroup$ Intersting recall. $\endgroup$ Commented Jan 22 at 19:36

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