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I have been brainstorming a short-story idea about an advanced civilization that develops on earth 60 million years after humans go extinct. Said civilization discovers time travel and decides to meet up with the "precursors" to see what they can learn. While learning about real-world civilizations, I learned an interesting fact. The first time the number zero was used in Europe was in the 1200s! An interesting idea occurred to me. What would be the limitations of a civilization that never developed the mathematical concept of zero?

To make the scenario interesting, the following are true:

  • They still have the concept of "nothing," but they never developed the mathematical concept of zero.

  • They developed a mathematical system nearly identical to our own prior to the development of zero.

  • They can't develop a "placeholder" that has the same functionality as zero.

How would such a civilization develop? What would be its limitations? Would there actually be any positives in the development of a mathematical system that did not invent zero? How would their systems develop around the concept of zero assuming that they are still able to become significantly technologically advanced?

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  • $\begingroup$ Surprisingly this question has already been asked before. Here's another highly similar question based on the same theme. worldbuilding.stackexchange.com/questions/222874/… $\endgroup$
    – sphennings
    Mar 13 at 20:05
  • $\begingroup$ This really should not have a 'post-apocalypse' tag as the protagonists are not struggling with the remains of a collapsed civilization. They have built their own successful world and are only studying a previous one. $\endgroup$ Mar 13 at 20:06
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    $\begingroup$ Not having a symbol for zero in math (or, maybe just not a recorded one we know about) does not mean the concept of having nothing of something does not exist and isn't understood, that's your mistake, it's implausible to claim the 'concept' of zero was not well understood by every society that has ever existed, and even by any reasonably sentient individuals from long before our ancestors could even really call themselves human 🤔 I think you may have spent too much time listening to daft 'philosophy' types and giving their word salad 'extrapolations' far more credit than they deserve 😉🤗 $\endgroup$
    – Pelinore
    Mar 13 at 20:57
  • $\begingroup$ @sphennings Oh wow. I did not expect this question to be a duplicate. Sorry! $\endgroup$ Mar 13 at 22:55

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Romans did not have a zero at all

The zero actually predates the Roman Empire: Mesopotamia had a zero placeholder thousands of years earlier, and the Mayas invented zero in Roman times.

Romans lacked a good number notation and zero. But nevertheless, the Roman Empire was quite advanced and very viable. It existed nearly 500 years, leaving architecture, laws, iron technology, literature, chronicles, bath houses..

In the Roman case, the zero would probably not have saved them: the Roman Empire was also corrupt and vulnerable for invasion. In 472AD it ended. But it did have fleets.. and a strong army!

The main limitations of Roman numeral notation persisted until medieval times in Europe: not using zero hindered trade and finance calculation. There was no easy way to write and interpret Roman numerals quickly, or denote accounts in an intuitive way. Mesopotamian civilization had bypassed the Romans in accounting, thousands of years earlier.

https://science.howstuffworks.com/math-concepts/zero1.htm

https://www.ignitespot.com/accounting-money-in-ancient-mesopotamia

The Khalifate did discover the zero and a 10-based notation, a few hundred years later.

https://www.scientificamerican.com/article/what-is-the-origin-of-zer/

No physical modeling? zero is not needed

A technology level predating Isaac Newton will hardly experience limitations. A design can be done using a drawing. Then you make a parts list and build your architecture. A Roman, advanced construct is the Partheon dome mentioned by AlexP in the comments. An advanced medieval invention that predates the zero: eye glasses.

While Roman engineering focused on straight forward mechanics and skill, not needing models or graphs, or even tables, the modern way of engineering needs a design, and model calculations. These cannot be made without algebra and algebra cannot really exist without zero. Not having a model or underlying physics to rely on will put airplanes, steam engines, and most mechanization out of reach.

Use of Greek

A remark made below by AlexP required some research. In the Roman Empire, especially the late Roman Empire, often Greek language was used.

Latin was the official language of the Roman Empire, but other languages were regionally important, such as Greek. (..) After all freeborn male inhabitants of the Empire were universally enfranchised in 212 AD, a great number of Roman citizens would have lacked Latin, though they were expected to acquire at least a token knowledge, and Latin remained a marker of "Romanness".[5]

In the Eastern empire, laws and official documents were regularly translated into Greek from Latin.[42] Both languages were in active use by government officials and the Church during the 5th century.[43] From the 6th century, Greek culture was studied in the West almost exclusively through Latin translation.[44] Latin loanwords appear liberally in Greek texts on technical topics from late antiquity and the Byzantine period

https://en.wikipedia.org/wiki/Languages_of_the_Roman_Empire

Greek numerals

There is no positional (placeholder) zero in Greek numerals, only an absolute zero value,

Hellenistic astronomers extended alphabetic Greek numerals into a sexagesimal positional numbering system by limiting each position to a maximum value of 50 + 9 and including a special symbol for zero, which was only used alone for a whole table cell, rather than combined with other digits, like today's modern zero, which is a placeholder in positional numeric notation. This system was probably adapted from Babylonian numerals by Hipparchus c. 140 BC. It was then used by Ptolemy (c. 140), Theon (c. 380) and Theon's daughter Hypatia (died 415). The symbol for zero is clearly different from that of the value for 70, omicron or "ο". In the 2nd-century papyrus shown here, one can see the symbol for zero in the lower right, and a number of larger omicrons elsewhere in the same papyrus.

https://en.wikipedia.org/wiki/Greek_numerals#Zero

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    $\begingroup$ "Romans lacked a good number notation": Are you laboring under the mistaken assumption that what we call Roman numerals, which were used to represent numbers in text and only in text, were what they used in engineering, mathematical tables, and so on? For those applications where a good number notation was useful, they used the Greek system. And yes, that system even had a notation for an empty rank for use in those even rarer situations where a positional number notation was essential. (And saying that Roman engineering focused on straight forward mechanics is simply wrong.) $\endgroup$
    – AlexP
    Mar 13 at 22:35
  • $\begingroup$ Hi @AlexP ! I wonder what non-straight forward mechanics (requiring modeling ) did Romans develop ? Example ? And what's so difficult to understand about the pitfalls of using a 1,5,10 non-base numerals grammar consisting of IVXLCDM that used to be a nuisance to use for coin weighing all over Europe, until it was finally replaced by the Arabic/Hindu notation in the 14th century.. I read a lot of text in your comment.. but don't quite grasp your objections. Maybe you can work it out some more, in a separate answer? $\endgroup$
    – Goodies
    Mar 13 at 23:06
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    $\begingroup$ (1) In the Antiquity, the number notation used in mathematics and engineering was the Greek numerals. (2) In mathematical tables where they needed to use a positional system they even had a symbol for zero (or, really, an empty rank). (3) I am pretty sure that the Rotuna of the Pantheon (which is to this day the world's largest unreinforced concrete dome) was carefully planned and documented before they starting pouring concrete... $\endgroup$
    – AlexP
    Mar 13 at 23:20
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    $\begingroup$ ... Note how the composition of the concrete changes from bottom towards the top, and how the thickness of the walls changes. That is not something which happened by chance. Or just look at the perfect geometry. $\endgroup$
    – AlexP
    Mar 13 at 23:22
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    $\begingroup$ Everybody who was somebody in the Roman Empire spoke Greek, and many more who were nobody. Greek played very much the same role in the classical world as English does in the modern world. Every educated person had Greek; it was a foundational part of the curriculum. There was simply no way for a person to acquire and education and not learn Greek. $\endgroup$
    – AlexP
    Mar 14 at 9:14

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