1 Based Math -- Bible Mathematics
Neither the original Hebrew nor Aramaic nor later Greek nor Roman counting systems have a digit for zero. Nothing was written nor counted using zero “0” in the Bible. The first item in lists of items is item number 1.
Obvious? Yes, but modern people don’t always count this way. Using zero based counting as an interpretive grid of time references in the Bible is a source of major errors.
For the rest of this discussion Roman Numerals will be used as a stand-in for the original language numbering systems. Roman Numerals are similarly ancient and they have identical features.
Readers will most likely be aware of Roman Numerals, and how counting works using Roman Numerals. Roman Numerals have the same expressive ability as ancient numbering systems. None of these systems have a digit for zero.
The topic of a Biblical chronology eventually reveals interpretive issues surrounding the problem of pure biblical mathematics. The Bible was written before most of the modern mathematical principles were widely adopted. This means that the Bible is built using techniques that will "trip up" a modern reader if that reader is not very careful.
Before stepping into the question of the historical order of events in the Bible we must look at the base question, "What math rules were followed when the Bible was written?"
1 Based Math
The first issue, the one that pervades this entire discussion, is the issue of 1 based math.
The digit 0 was introduced at the same time as Arabic Numerals. Arabic numerals began making appearances in western countries sometime in the 600s. By convention Arabic numerals were not adopted for certain things until the 1900s.
Dates, especially those on corner stones and monuments were widely stated on Roman Numerals until the 1900s. Bible chapter and verse numbers were also widely stated using Roman numerals until the 1900s.
Arabic numerals, and the ability to state the value "0" using Arabic Numerals did not happen until well after the close of the Christian canon. Any attempt to understand the text of the Bible, requires careful attention to the value "0" and any accidental use by readers of the value zero since it cannot even be expressed in the original languages.
Modern, Elementary School mathematics can drive a wrong conclusion about what various passages in the Bible actually mean because modern readers can so easily, accidentally, think in terms that involve zero.
Roman numerals as well as Hebrew, Aramaic and Greek counting systems have no digit for 0. To understand this problem try using Roman numerals to write down 0. You can’t because no Roman numeral exists for zero. Hebrew, Aramaic and Greek are also devoid of any way to write the number "0". This is in part what made Arabic numerals so powerful, fundamentally so. Before Arabic numeral adoption no one wrote, counted or thought using 0 as an idea, it was not expressible in any of the western languages, it was not part of mathematics as we know it today.
Ask a shepherd in Bible Times, "How many sheep have you?"
His answer, "15," to his good fortune.
What if, the shepherd had no sheep?
His answer, "none," to his shame.
Notice that his language does not give him a number for no sheep. The answer does not come from his understanding of mathematics, but from regular language. He has no sheep, the question is insane in this case where there are no sheep.
Instead of using counting, when there are no sheep, the ancient shepherd backs up, and instead of using counting, and primitive mathematics, as the system for providing an answer the shepherd moves to regular language and says, basically, there is no count for this. Mathematics, numbers, only provide an answer once the Shepherd has some sheep.
Lack of 0 drives the way counting in the Bible works. In the Bible all counting starts with the number 1, not the number 0 as modern people do so often today.
This is a pervasive idea, one that impacts most references to time given us in the pages of the Bible. There are a few references that reveal the use of 1 based math, references that support this idea. We will look at some of them shortly.
The Bible was written before the adoption of Arabic numerals, it is 1 based, not 0 based, as most modern counting is today.
The simplest place to see the way the writers of the Bible counted things is to look at a reference found in the Book of Jude.
14Enoch, the seventh from Adam, prophesied about these men: "See, the Lord is coming with thousands upon thousands of his holy ones Jude 1:14 NIV
14And Enoch also, the seventh from Adam, prophesied of these, saying, Behold, the Lord cometh with ten thousands of his saints,"de" and "kai" are uncertain. Jude 1:14 KJV
The keyword here is the word after, or from depending on English translation. To a modern ear this word suggests that Adam would not be counted in Jude’s list. Strange as it may seem today, Adam was counted in Jude’s list. The following table shows the names listed by Jude and then includes a number to indicate the position in the list.
|Genesis Supplied Name||Jude’s Count||Modern Count|
What is going on here? Something very important. Jude is counting Adam as his first in line behind Adam. Though this may seem odd to a modern ear this was not to Jude. He meant what he said. The list of names after Adam shows how Jude counted. Jude was using 1 based mathematics.
If the previous table represented a line of people, say a line queued to get into a movie, and we asked Seth what position behind Adam he was, his answer to us would be "I, Seth, am in the 1st position behind Adam." This is how modern counting works, and how the modern conventions work generally when it comes to counting.
Similarly everyone else in line behind Adam would answer in a similar way, revealing the numbers given in the Modern Count column above.
As we study the Bible this difference in counting, and what the counts actually mean becomes an issue. The mathematics of the Bible, must be understood before the quantitative aspects of the Bible can be properly understood, especially the topic of Bible Time.
Ages of People
The use of strict 1 based math has an important application in the ages of people.
Modern English speakers assign ages to people beginning with a year 0.
A modern mother, when asked the age of her child, would count the year number 1 of that child’s life as year 0.
This is why ages of new-borns are given in months and weeks and never in years because the modern child is not even 1 year old until the end of year 1 of life. Only after a birthday would someone say of that child "this child is 1 year old".
This strategy is implicitly assigning for the child a year of age 0. This is a result of the cultural adoption of 0 into the thinking of counting ages.
Irregular Use in Historical Sources
The change to 0 based age counting has happened within the past 150 years. There are several examples that are important for seeing this change in action.
New England Grave Stones
In the New England states of the United States there are colonial era grave yards. People were buried in these graveyards in the 1600s and 1700s. The tombstones in those graveyards often mark the death date and age of people when they died, especially if the birth date was unknown.
Without knowing any better, visitors to these graveyards often misunderstand the meaning of the ages carved on those stones. Instead of using modern age length calculations, where year 1 of life is today know as year 0, the people of colonial New England used the Bible’s system of measuring time. Someone who died in their first year of life has "aged 1" carved on their stone. Similar differences exist for all ages up from their first year of life. Finding the associated paper records is often impossible without knowing this detail about how people measured their own ages.
Even encyclopedias written 50 years ago use the old, 1 based, system of age counting, whereas more recent encyclopedias often translate the ages of individuals involved into the modern system.
I was first exposed to this problem with a reference in an old encyclopedia to the age of Alexander the Great at his death. He died young, not allowing him to consolidate his newly won kingdom. The encyclopedia revealed his age at death, using 1 based math. The math used by the historians of Alexandar’s era to record his life span.
A couple days later, while the memory of his death was still fresh in my mind I received my Church’s monthly newsletter. In the letter my Pastor cited the age of Alexander the Great’s age at death. In his account it was one year lower. Noticing the difference I asked my Pastor for his source.
He had used a newer encyclopedia that translated Alexander’s age at death to the newer, modern, 0 based age counting system. No longer in agreement with the historical sources for Alexander’s age at death, it did accurately reflect how a modern person would count the age.
Note, though, how this shift in stated age can cause considerable complications since readers must know which system is in use.
Asian Age Counting
Some cultures in the world today still count years of life where the first year of life is "age 1" the second "age 2" and so on. This is one year higher than conventionally used in the modern Western World.
In Korea, the transition was made in the mid 1900s. Korean elderly count their age using their years of life instead of the more conventional modern zero based system. They were age 1 when they were born. Years go up by 1 each year thereafter. An interesting twist in Korea is that the year of life changes at new years day. Everyone’s age counted on this system goes up by 1 year together at new years day. No questions like "how does it feel to be 1 year older?" since everyone feels their age increase together. This New Years day change in age is a convention that we will see again in the Bible.
When discussing age with someone from a distant culture, not only must the language barrier be overcome, the conventions on age length counting must be understood too.
Which System Was Used in the Bible?
The use of Roman numerals, Hebrew, Aramaic or even Greek numbering systems, all preclude the assignment of the first year of life to the count of "0". All of these systems build up from a common numbering system and that system does not express any count less than 1.
Ask a young mother in ancient times how old her child was and her answer would shock a modern reader. Consider the following dialog.
"Madam, how old is your infant?"
"Sir, he was born 13 days ago, and is age 1."
Our normal sense of language kicks in when following a dialog like this. It sounds wrong, because someone born 13 days ago is not yet aged 1 to a modern person, but clearly was in their first year of life and therefore to an ancient ear they were aged 1.
The modern, western, age counting system has changed from a system common across all mankind through all historical time.
In the Bible, the first year of life is known as "age 1" or "year 1." Life lengths are counted using 1 based math.
Jude’s example suggests that each time a person or item is counted in a list, and that person or item is last, that if that person or item starts a new list then the person or item would be counted twice.
Matthew chapter 1 provides an example of just such a list. In that chapter, the Book of Matthew recounts the genealogies of the time from Abraham to Jesus.
When finished, Matthew summarizes his list and says that there were 14 generations from Abraham to David, 14 from David to the Exile to Babylon and 14 from the Exile to the Christ.
Using modern math we would quickly count and incorrectly expect 3 * 14 = 42 names in Matthew’s genealogy. Instead what we find is 41 names. Considering that Joseph, the man at the tail end of Matthew’s Genealogy was not the Biological father of Jesus, the list only has 40 names that properly make up the genealogy from Abraham forward to Joseph. Jesus was not Joseph’s seed, as all the other names given in the list were.
There are several ways to understand what might be going on here. There are, of course, several names listed editorially in this list. Certain brothers, wives and mothers, important to the general flow of the old testament chronology are listed. A modern ear, trained to count with 1 based mathematics would assert that Matthew is probably counting some of these other names. Another possibility is that Matthew made a mistake. This answer is typically chosen by critics of the Bible generally.
Another possibility is that Matthew is using the same counting system as Jude, where the first item in a list is counted from 1, not zero. Since Matthew is providing 3 separate lists of 14, the two transition points are double counted, 14th in the list before and 1st in the list that follows. When taken this way, Matthew’s list works perfectly. The following table shows how the counts work out this way.
|Name||Rank||First 14 Counts||Second 14 Counts||Third 14 Counts|
As a check on the math: 14 * 3 = 42 expected names. Since 2 names, David and Josiah, are counted 2 times, the total number of names in the list is 42 - 2 = 40 names. This, of course, is what this list shows.
It may be that only one of the two names, either David or Josiah, is not intended to be both 14th and 1st as marked off here. If either of these were only counted one time then Jesus would be the 14th name in the 3rd set. In that case the ancient listing system would be ambiguous. Generally speaking the Bible is not ambiguous so this is an unlikely alternative. But, there are times when "butted" lists do occur. Take each list with care and watch for this overlapped case. Overlapped lists mess up modern math calculations.
There have been numerous studies done on the apparent early aging in the population today. People are aging quicker than they did even 200 years ago. This is the tail end of an acceleration of human life spans begun at Noah’s flood.
Much of the analysis of this trend disregards the change in how people’s ages are stated. This makes the situation worse than it actually is.
Reading the Bible for its quantitative stories, especially counting stories is difficult. The problem is the modern ability of most readers to mentally run complex math calculations against the text. Though this is an important skill, one that can be used to open up great areas of Bible study, care must be taken that the original meaning of the text is understood before running the math.
This article was first written years ago. I’ve since started learning original language issues and the grammar surrounding Matthew’s genealogy is in serious doubt relative to the overall list of names.
It is most likely the case that there are 42 names in the original list. If that is right, then Matthew is a case of a butted list and the overlap suggest here is not how Matthew works. Students should still be aware of the problem of overlaps like shown here since they do show up later in strongly provable ways.
1. Matthew 1:17
2. Matthew 1:2
3. Matthew 1:2
4. Matthew 1:2
5. Matthew 1:3
6. Matthew 1:3
7. Matthew 1:3
8. Matthew 1:4
9. Matthew 1:4
10. Matthew 1:4
11. Matthew 1:5
12. Matthew 1:5
13. Matthew 1:5
14. Matthew 1:6
15. Matthew 1:6
16. Matthew 1:7
17. Matthew 1:7
18. Matthew 1:7
19. Matthew 1:8
20. Matthew 1:8
21. Matthew 1:8
22. Matthew 1:9
23. Matthew 1:9
24. Matthew 1:9
25. Matthew 1:10
26. Matthew 1:10
27. Matthew 1:10
28. Matthew 1:11
29. Matthew 1:12
30. Matthew 1:12
31. Matthew 1:13
32. Matthew 1:13
33. Matthew 1:13
34. Matthew 1:14
35. Matthew 1:14
36. Matthew 1:14
37. Matthew 1:15
38. Matthew 1:15
39. Matthew 1:15
40. Matthew 1:16
41. Matthew 1:16
42. Matthew 1:16