Ferocitus
Deity
So, before Sumerians arrived on the scene, could people only count up to one?
For the Mathematicians
- Thread starter Berzerker
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So, before Sumerians arrived on the scene, could people only count up to one?
Hygro
soundcloud.com/hygro/
They'd just exclaim "by the gods, more than one!"
Why yes they could. The progression went like this:
Tallies – Simple counting (the addition of one more unit of something) that shows up in Paleolithic finds as notches in a stick or bone. The notches represented the total, but it was not expressed as a number, just notches.
Concrete counting using clay tokens– One to one correspondence. A token that represents “one jar of oil” or “one measure of grain” illustrates this concept. In modern society “twins” and “quartet” are examples of modern concrete counting. These tokens show up in the Fertile Crescent as early as 6000 BCE. Over time they get more and more complex. One jar of oil was represented by a specific token. One bag of grain was represented by a different token. Multiple tokens were used to represent larger amounts.
Abstract counting – Numbers separated from objects. “Twoness” is independent of any particular object and may be associated with many items and used mathematically. 2+4 = 6. This is one step beyond concrete counting where twins cannot be added to quartets. This is the number system we are used to. It happened in Sumeria about 3100 BCE. This was the first known instance where numbers were separated from objects.
Tribes outside of the ME that counted often used their body parts and then went to "many". Here is an example of a counting system that doesn't use body parts. The Weddas of Sri Lanka had only a few number words: a single, a pair, one more and many. When they counted coconuts they collected a heap of sticks and then assigned a stick to each coconut as they counted "and one more". At the end they would point to the pile of sticks and say they had that many coconuts.
Berzerker
Deity
I believe prehistoric people had names for larger numbers, the bone notches may have been (Alexander Marshack?) a lunar sequence with the notches added over the course of a cycle.
how many enemies did you see?
IIIIIIIIIIII or twelve (or whatever they called it)
I suspect the Sumerians had trig before the Babylonians, the latter inherited so much of their culture as did we all
how many enemies did you see?
IIIIIIIIIIII or twelve (or whatever they called it)
I suspect the Sumerians had trig before the Babylonians, the latter inherited so much of their culture as did we all
The problem is that there is no evidence of the use of large numbers in the Middle East prior to the invention of abstract counting about 3100 BCE. In fact, without the notion of abstract counting, you cannot have large numbers.
|||||||||||| tally marks equaled |||||||||||| They didn't have any name for it other than "look at my marks". The number twelve as a number didn't exist.
Senethro
Overlord
Ehhhhhh, that doesn't sit right with me. When did people start having herds of sheep, because as soon as that happens then one person has a need to count to 40 or more.
I remember my grandfather having some kind of sheep speedcounting system that began it, dit, da and counted in 12s or something. You counted individual sheep on one hand and once it completed the other hand raised a finger and that was how many 12s you had, so it was good for 60.
I remember my grandfather having some kind of sheep speedcounting system that began it, dit, da and counted in 12s or something. You counted individual sheep on one hand and once it completed the other hand raised a finger and that was how many 12s you had, so it was good for 60.
In the Middle East the earliest clay tokens that were used to record economic transactions appeared about 8000 BCE. These earliest tokens were linked to accounting for quantities of cereal crops and animal herds. Over the next 4000 years these tokens evolved and became more complex and directly led to the invention of abstract counting.
Keep in mind that the system used by your grandfather was post the the use of abstract counting so he and his predecessors had the benefits of such thinking. It has been 5000 years since the Sumerians invented abstract numbers.
https://blogs.scientificamerican.com/roots-of-unity/dont-fall-for-babylonian-trigonometry-hype/
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Berzerker
Deity
I cant look, tell me the total
Certainly people counted the days in a year and named the total rather than show 365 marks to anyone wanting to know how many days were in a year. How many days will I live? How many years? I suspect people kept track of that stuff, maybe not everyone, but I cant imagine the builders of Gobekli Tepi were ignorant of basic math and timekeeping.
Senethro
Overlord
People have been people for thousands of years. When they don't have much to do then they shag, get high, play music or engage in mathematics according to their predilictions. It seems really unlikely to me that shepherds with little to do other than sit watching ovines crap everywhere and wonder if someone was going to bring them a drink didn't come up with a way to check they had the same number of sheep at the end of the day as they did at the start.
Ugh, I'm off to read about concepts of numbers among uncontacted tribes now.
Gobekli Tepi was active around 9000 BCE at its earliest. that may be even before the first sedentary agricultural communities. there is no record of agriculturre or animal domestication there. But at nearby Cayonu Tepesi which dates from about 7200 BCE we see very early plant and animal production. It is there that we find some of the earliest clay tokens that are the beginnings of agricultural accounting and 4000 years later the invention of numbers.Given our facility with numbers and math it is easy to assume that people always used abstract counting, but the evidence clearly points to its invention in Sumer at about 3100 BCE. We take lots for granted and easily fall into the trap that people in the distant past had the same tools we did. The earliest tally sticks are thought to have been used to keep track of the moon which has a frequent cycle that repeats through distinct phases.Prior to 3000 BCE there are no records of people counting the days in a year. They may have noted annual events ((midsummer and midwinter), but they did not have abstract counting. You certainly don't need abstract counting to build things.I cant look, tell me the total
The earliest tokens (about 8000 BCE) "counted" grain and sheep. that coincides with the first agriculture communities and increased raising of livestock by sedentary communities. It was the need for accurate record keeping of goods that developed from 8000 to 3000 BCE that created the token system and as economics became more complex some thing better was needed. The result was abstract counting with writing as a spin off. The problem they solved was an accounting one. If abstract counting existed prior to 3100 BCE, there wouldn't have been any need for 5000 years of using a token system. Why would tally sticks exist?
My Weddas example several posts above is an example of a primitive counting system.
Some sources:
https://en.wikipedia.org/wiki/History_of_ancient_numeral_systems
https://www.barnesandnoble.com/s/"Denise%20Schmandt-Besserat"?Ntk=P_key_Contributor_List&Ns=P_Sales_Rank&Ntx=mode+matchall
