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--- numeric [2025/03/09 15:27] – [Division] ken
+++ numeric [2025/05/16 19:30] (current) – [Number System] ken
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 =====Numeracy in ancient Yeberi culture====
-The ancient [[Yeberi]] culture and the associated Ancient [[Hebrew]] language did not use the same number system that we are familiar with today.
+In the ancient world, many cultures developed or borrowed several different number systems. It is misguided to simply assume that the ancient [[Yeberi]] culture and the associated Ancient [[Hebrew]] language used the same number system that we are familiar with today.
-Yeberi culture was heavily influenced by the superpowers of the day, primarily the long series of Mesopotamian cultures including Sumer, Babylon, and Akkadia. These cultures used a base 60 "sexagesimal" number system. The second major influence was Egypt, which used a simplified version of sexagisimal based on the number 12. However, Egypt **also** used a base 10 system.
+Yeberi culture was heavily influenced by the superpowers of the day, primarily the long series of Mesopotamian cultures including Sumer, Babylon, and Akkadia. These cultures used a base 60 "sexagesimal" number system. The second major influence was Egypt, which used a simplified version of sexagisimal based on the number 12. However, Egypt **also** used a base 10 system, so it is not far fetched to think that the [[yeberi]] may have also, particularly considering that the Israelites immigrated from Egypt.
 With these influences in mind, we'll explore the numbers that appear in the ancient Hebrew texts and try to determine what these numbers meant to the original authors.
-Depending on which number system was used, [[yeser]] could mean either "ten" or possibly "twelve" or "a dozen". Similarly, although [[mah]] is typically translated as "hundred", it might mean "sixty". These meanings would be in keeping with the number systems of their historical time period. (Speaking of time, the passage of time is one of the most frequent uses of numbers within the text. This important concept is examined at [[time]].)
+====Base Numbers====
+Understanding the base numbers is important because depending on the value of the base numbers, the intended value of all compound numbers can vary quite dramatically.
+  *[[yeser]] could mean either "ten" or possibly "twelve" or "a dozen".
+  *[[mah]] is typically translated as "hundred", but it might actually mean "sixty".
+  *[[alep]] is typically translated as "thousand", but other values are possible, including "100", "144" or even "360"
+  *[[sebeyetim]] seems to be a special case base number for multiplication by seven, possibly used as a figurative device only.
+Twelve and sixty as base numbers would be in keeping with the number systems of their historical time period.((Speaking of time, the passage of time is one of the most frequent uses of numbers within the text, and its interpretation is greatly impacted by the base numbers. This important concept is examined further at [[time]].))
+The number 12 is an important concept in [[yeberi]] culture. It goes far beyond a symbol numeric value, "as part of the Israelite national founding myth: the number 12 was not a real number, but an ideal number, which had symbolic significance in Near Eastern cultures with duodecimal counting systems, from which, among other things, the modern 12-hour clock is derived."((Glassman, Ronald M. (2017). //The Origins of Democracy in Tribes, City-States and Nation-States.// p. 632. ISBN 978-3-319-51695-0))
+The [[wp>Twelve_Tribes_of_Israel]] were the fundamental political, geographical and cultural subdivisions within ancient [[yeberi]] culture.
+From this standpoint it would make sense to assume that the numeric system would also reflect this importance, and therefore there is a strong basis for interpreting [[yeser]] as "twelve".
+Theoretically, this assumption should be testable. All we would need to do is find a passage in the text that include the number [[yeser]] within an enumerative list. In other words, is there a verse in the text where we actually count to twelve? FIXME try to find one
+Most instances of [[yeser]] are not helpful in this regard, for they are simply references to groups in general. For example, in Genesis 18 Abraham pleads with [[ihoh]] to spare the city if "ten" good men can be found. This is a hypothetical situation and the exact number is irrelevant. The argument works equally well whether Ihoh and Abraham meant 10 or 12. The important point is that they both agreed on the meaning.
+Similar ambiguity is found in Genesis 24, Genesis 31, Exodus 18, and many times throughout Exodus in the context of the Tabernacle. In each of these cases, a number is specified, but the text does not give us any indication of what numerical value that number implies.
+Luckily, this is not always the case. There are a few instances where [[yeser]] does seem to correlate with a numeric value which can be substantiated.
+Several instances occur where [[yeser]] appears in conjunction with what appears to be a day of the month. In these cases [[yeser]] seems to function like the suffix "-teen" does in English.
+|Genesis 7:11|hedes senim sebey yeser iom hedes|in the month second on the seven and tenth day of the month|
+|Genesis 8:4| hedes sebeyit sebey yeser iom hedes |in the month seventh on the seven and tenth day of the month|
+Note that the word "and" in the English translations does not appear in the Hebrew. This raises some doubt as to the veracity of this interpretation. If the Hebrew text was supposed to mean "seven and ten", we would expect it to read 'sebey **[[yed]]** yeser'. The missing 'yed' is suspicious and allows for other possible interpretations. Maybe "and" is not the intent. Could it be "seven times ten"?
+These examples do appear to reference a specific day of the month. A month is based on the cycle of the moon which takes a certain amount of time, one lunar month or around 29.5 days. By this assumption, the days of the month are limited to a certain range, between one and 30. The interpretation of 'sebey yeser' as "seven and ten" does fit into the allowable range. If one were to assume a "seven times ten" interpretation, the value falls well outside the range of days in a month. Or at least it does if one assumes that yeser equals ten. Which we are NOT assuming. Remember, this is the point of this exercise.
+Genesis 42 is one case where we can align [[yeser]] to an actual known value. Here we read that the "ten" brothers of Joseph went to Egypt to purchase grain. We can correlate this passage against Genesis 35, where we see the sons of Jacob listed: Reuben, Simeon, Levi, Judah, Dan, Naphtali, Gad, Asher, Issachar, Zebulun, Joseph, and Benjamin. Twelve sons in all. Joseph had eleven brothers. Genesis 42 specifies that [[yeser]] of Joseph's brothers went to Egypt, but that Benjamin did not go to Egypt with his brothers. The math adds up, and in this case seems to indicate that [[yeser]] = 10.
+Genesis 35:22 indicates that Jacob had 'senim yeser' sons. This is even more confusing, given the typical usage of [[im]] to indicate [[#multiplication]].
+Another example is Exodus 34:28, which ostensibly refers to "the ten commandments". However, this is far less cut and dry than it may appear.
+This supposed list of ten commandments is never enumerated clearly. The book of Exodus includes a very long list that covers 4 chapters. A reference is later made back to the in Deuteronomy 5:6–21, where only the first few are explicitly stated. The feeling here is that of remembering, "Remember A, B, C etc..."
+Some scholars interpret the passage as giving only eight separate commandments, while others count as many as thirteen.
+//Traditions differ in numbering the Ten Commandments. In Judaism the prologue (“I am the Lord your God, who brought you out of the land of Egypt, out of the house of slavery”) constitutes the first element and the prohibitions against false gods and idols the second. Medieval Roman tradition, accepted by Martin Luther, regards all these elements as one and preserves the number 10 by separating the prohibitions against coveting another’s wife and coveting another’s possessions. In the Greek Orthodox and Protestant Reformed traditions, the prologue and the prohibition against false gods are one commandment and the prohibition against idols is the second.//((Encyclopedia Britannica)) Unfortunately, this is not helpful in determining a numeric value for [[yeser]].
+Ezra 6:17 refers to 'ter yesher' relating to the number of the tribes of Israel. This is typically translated as "two and ten", however, the word [[ter]] is not well attested and speculative at best particularly considering the number of words that supposedly mean "two". The most common translation of [[ter]] is "remaining", so the Ezra passage could be interpreted as "yeser remained according to the tribes of Israel" this seems to imply that one per tribe remained and therefore yeser = 12.
+====Counting====
+There are quite a few passages in the text which enumerate a list of objects. Many of these instances consist of a list of children born to a certain person, with their birth order explicitly stated. Another example is the first instance and perhaps the most famous. It occurs in Genesis 1, where a list of events is delineated and counted.
+The phrase "[[ahih]] [[beqer]] [[iom]] <counter>" occurs seven times in Genesis 1. The <counter> indicated is increased by one each time. This gives us a template for understanding counting in Hebrew.
+^Phrase ^Interpretation|
+|ahih beqer iom **ahed**| dawned the first day|
+|ahih beqer iom **seni**| dawned the second day|
+|ahih beqer iom **selisi**| dawned the third day|
+|ahih beqer iom **rebiyi**| dawned the fourth day|
+|ahih beqer iom **hemisi**| dawned the fifth day|
+|ahih beqer iom **hesesi**| dawned the sixth day|
+|iom **hesebiyi**|seventh day|
+Comparing this list to all the other uses of what appear to be the same root words, we are able to generate a more general list of numbers, and extend it past seven. Note that there are some spelling variations. The follwing table captures the most commonly used spelling of the ancient Hebrew root word.
 ^Hebrew Word^Probable Value^Note|
 |[[ahed]]|1 |
-| [[seti]] or [[seni]] or maybe [[hex]]|2 |this is a bit tricky, we'll come back to it|
+| [[seti]], [[seni]], [[hex]], [[ter]]|2 |FIXME this is a bit tricky, we'll come back to it|
 |[[seles]]|3|
 |[[arebey]]|4|
@@ Line 20: / Line 75: @@
 |[[tesey]]|9| |
 |[[yeser]]|10 or 12|(depending on which base system was used) |
-|[[selesim]]|30|seles & [[im]]|
+| |20| |
-|[[arebeyim]]|40|arebey & [[im]] |
+|[[selesim]]|30 (or maybe 36)|seles & [[im]]|
-|[[hemesim]]|50|hemes & [[im]] |
+|[[arebeyim]]|40 (or maybe 48)|arebey & [[im]] |
-|[[sesim]]|60|ses & [[im]]|
+|[[hemesim]]|50 (or maybe 60)|hemes & [[im]] |
-|[[sebeyim]]|70|sebey & [[im]]|
+|[[sesim]]|60 (or maybe 72)|ses & [[im]]|
-|[[semenim]]|80|semen & [[im]]|
+|[[sebeyim]]|70 (or maybe 84)|sebey & [[im]]|
-|[[teseyim]]|90|teseh & [[im]]|
+|[[semenim]]|80 (or maybe 96)|semen & [[im]]|
-|[[mah]]|100| |
+|[[teseyim]]|90 (or maybe 108)|teseh & [[im]]|
-|[[alep]]|1000 or "a lot" | |
+|[[mah]]|100 (or maybe 144)|probably not 60, since that seems to be covered already |
+|[[alep]]|1000 | |
+|[[alepim]]|ten-thousand|alep & [[im]]|
-FIXME - analyze and compare the uses of 'mah' vs. 'sesim' to assess whether an interpretation of "sixty" for 'mah' is even remotely feasible. Then, based on those findings, assess 'alep'.
+Numbers traditionally interpreted as "teens" are formed by adding two numbers.
+  *ahed yeser is typically interpreted as "11" (see Genesis 37:9)
+  *sebey yeser is typically interpreted as "17" (see Genesis 37:2)
+It should be noted that this is not the only possible interpretation of these phrases. FIXME We need to examine more examples in context.
 ====Affixes as Mathematical Functions====
@@ Line 36: / Line 96: @@
 ===Multiplication===
-The use of suffixes indicates mathematical functions. As seen in the above table, the [[im]] suffix on numbers indicates multiplication (although the assumption that it is multiplication **by ten** might not be substantiated. It is probably more accurate to assume that the multiplication is **by yeser**, and to  keep in mind that 'yeser' might equal 10 but more likely equals 12.
+The use of suffixes indicates mathematical functions. As seen in the above table, the [[im]] suffix on numbers indicates multiplication (although the assumption that it is multiplication **by ten** might not be substantiated. It is more accurate (but less precise) to assume that the multiplication is **by yeser**, and to  keep in mind that 'yeser' might equal 10 or 12.)
+===Sevenfold===
+An interesting exception to the normal pattern of multiplication is embodied in the word [[sebeyetim]].
 An interesting example is Genesis 4:24. Traditionally, the verse is rendered "//If sevenfold shall be avenged Cain, then Lamech seven and seventy//"
@@ Line 74: / Line 136: @@
 ====Number System====
-By now you may have noticed a pattern:
+We can now consolidate the above information into a system:
 ^Root^Root Value^With 'im'^With 'it'|
@@ Line 85: / Line 147: @@
 |[[tesey]]|9| [[teseyim]] = 90 |[[teseyit]] (or teseyi) = 1/9 |
 |[[yeser]]|10 |[[yeserim]] = 100 |[[yeserit]] = 1/10 |
+|[[mah]]|100| not used | mahit = 1/100 (theoretical) |
+|[[alep]]|1,000 |[[alepim]] = 10,000| alepit = 1/1000 (theoretical) |
+====Checking the System=====
+If this system is correct, we should theoretically be able to use the data in Numbers chapter 2 and add up the numbers in each verse to get the grand total in verse 32.
-|[[hexi]] |half | |
+The NIV lists the total number of the census as 603,550.
-|[[mah]]|100| |
-|[[alep]]|1000 or "a lot" | |
+We disagree. Based on our rendering, the number given in Numbers 2:32 is:
+//ses mah alep seles alepim hemes mah hemesim// which transliterates to "six hundred thousand, three [x] ten-thousand, five hundred fifty". Clearly there is a three with a ten-thousand in our rendering. This results in a total of 630,550.
+FIXME - cool now do all the other verse and add them!
+====More Math====
+The ancient [[yeberi]] culture had a fairly accurate understanding of the geometry of circles. 2 Chronicles 4:2 estimates pi to within an error margin of 3% by indicating that the circumference of a circle is 3x the diameter.