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This article is divided into two main sections. The first is an appropriate background for those readers who may not be aware of the similarities and differences between the synoptic gospels, Matthew, Mark and Luke. If you understand this already, and are aware of the Q hypothesis, you are welcome to continue to either to a description of detecting the order of plagiarism through jumps in content or continue to the main content. Please note, there are three aspects to this document:

  1. The first is a presentation of a graphical means of demonstrating the relationship between the order of pericopes between the synoptic gospels.

  2. The  second is an argument to suggest that it is very unlikely that while the authors of Matthew and Luke definitely had access to Mark, they did not have access to each others texts, and thus suggests the existence of a 'Q' document.

  3. The last is to see if there is a suggestion of a single 'Q' document, or multiple such documents. I am suggesting there might be evidence to indicate that there may in fact have been multiple documents or pamphlets that were circulating in the early Christian community, and that the authors of Matthew and Luke had used such documents when compiling their gospels.

The last aspect is based on the methodical copying of the authors of Matthew and Luke from Mark, and this is contrasted with the much more chaotic relative ordering of the pericopes that are alleged to have been taken from a Q source. 

For those interested, this document shows what I understand to be the common pericopes between the synoptic gospels. This was collated from a number of sources, and I tried as much as possible to confirm some and reject others. The most common pericopes that seem to be conflated are those discussing that divorce is forbidden, except that Matthew copies both from Mark and from Q while Luke only copies from Q.

 

 Background 

It is clear that the authors of Matthew and Luke used the text of Mark as a source, and there are entire pericopes that were copied verbatim or close to verbatim. For example, 

Καὶ εὐθὺς ἐκ τῆς συναγωγῆς ἐξελθόντες ἦλθον εἰς τὴν οἰκίαν Σίμωνος καὶ Ἀνδρέου μετὰ Ἰακώβου καὶ Ἰωάννου. ἡ δὲ πενθερὰ Σίμωνος κατέκειτο πυρέσσουσα, καὶ εὐθὺς λέγουσιν αὐτῷ περὶ αὐτῆς. καὶ προσελθὼν ἤγειρεν αὐτὴν κρατήσας τῆς χειρός· καὶ ἀφῆκεν αὐτὴν ὁ πυρετός, καδιηκόνει αὐτοῖς.

Καὶ ἐλθὼν ὁ Ἰησοῦς εἰς τὴν οἰκίαν Πέτρου εἶδεν τὴν πενθερὰν αὐτοῦ βεβλημένην καὶ πυρέσσουσαν· καὶ ἥψατο τῆς χειρὸς αὐτῆς, καὶ ἀφῆκεν αὐτὴν πυρετός, καὶ ἠγέρθη καὶ διηκόνει αὐτῷ.

Ἀναστὰς δὲ ἀπὸ τῆς συναγωγῆς εἰσῆλθεν εἰς τὴν οἰκίαν Σίμωνος. πενθερὰ δὲ τοῦ Σίμωνος ἦν συνεχομένη πυρετῷ μεγάλῳ, καὶ ἠρώτησαν αὐτὸν περὶ αὐτῆς. καὶ ἐπιστὰς ἐπάνω αὐτῆς ἐπετίμησεν τῷ πυρετῷ, καὶ ἀφῆκεν αὐτήν· παραχρῆμα δὲ ἀναστᾶσα διηκόνει αὐτοῖς.

Mark Goodacre also uses editorial fatigue to demonstrate that the authors of the latter two gospels copied from Mark and not vice versa. Two examples of this include the death of John the Baptist, where in Mark, it is clear that Herod admires John the Baptist:

But she could not because Herod stood in awe of John and protected him, since he knew that John was a righteous and holy man. When Herod heard him, he was thoroughly baffled, and yet he liked to listen to John.

When Herod Antipas was tricked into beheading John, it is clearly stated that he was frustrated:

 

Although it grieved the king deeply, he did not want to reject her request because of his oath and his guests.

In Matthew, however, Herod Antipas feelings towards John the Baptist are opposite those expressed in Mark:

 

Although Herod wanted to kill John, he feared the crowd because they accepted John as a prophet. 

Matthew, however, quickly forgets his edits and when tricked into beheading John:

 

Although it grieved the king, because of his oath and the dinner guests he commanded it to be given.

 

Comparing these two verses, an entire phrase is copied verbatim: 

καὶ λυπηθεὶς ὁ βασιλεὺς διὰ τοὺς ὅρκους καὶ τοὺς συνανακειμένους ἐκέλευσεν δοθῆναι, 

καὶ περίλυπος γενόμενος ὁ βασιλεὺς διὰ τοὺς ὅρκους καὶ τοὺς ἀνακειμένους οὐκ ἠθέλησεν ἀθετῆσαι αὐτήν·

Note also that Matthew copies the error in Mark where Herod Antipas is described as a king (βασιλευ or basilen), a title not given by the Romans to any of the sons of King Herod. When King Herod died in 4 BCE, Herod Antipas was given authority over approximately one quarter the lands of King Herod, and was thus titled a tetrarch together with his brother Phillip who was also given authority over one quarter. The remaining half (Samaria, Judea and  Idumea) went to Herod Archelaus, who was named ethnarch and who was later deposed by the Romans in 6 CE.  

As an example of editorial fatigue by the author of Luke, in Mark, we have the following introduction to the feeding of the five thousand:

Then the apostles gathered around Jesus and told him everything they had done and taught. He said to them, “Come with me privately to an isolated place and rest a while” (for many were coming and going, and there was no time to eat). So they went away by themselves in a boat to some remote place. But many saw them leaving and recognized them, and they hurried on foot from all the towns and arrived there ahead of them.

In Luke, however, this occurs at the town of Bethsaida--hardly an isolated and remote place:

When the apostles returned, they told Jesus everything they had done. Then he took them with him and they withdrew privately to a town called Bethsaida. But when the crowds found out, they followed him.

Yet, both authors give the same reason for the crowd's hunger:

When it was already late, his disciples came to him and said, “This is an isolated place and it is already very late. Send them away so that they can go into the surrounding countryside and villages and buy something for themselves to eat.

Now the day began to draw to a close, so the twelve came and said to Jesus, “Send the crowd away, so they can go into the surrounding villages and countryside and find lodging and food, because we are in an isolated place.

In Luke, Bethsaida is no longer an isolated place, and if they were next to Bethsaida, would not some, if not all, simply go to that town to purchase food and, perhaps, find lodgings (although, why would they need to find lodgings if they do not seem to have travelled the distance they did in the telling of the story in Mark)?


There are, however, also pericopes that are common between Matthew and Luke that do not appear in Mark, so there must have been a third common source that the two authors of these gospels had:

Ἰδὼν δὲ πολλοὺς τῶν Φαρισαίων καὶ Σαδδουκαίων ἐρχομένους ἐπὶ τὸ βάπτισμα [a]αὐτοῦ εἶπεν αὐτοῖς· Γεννήματα ἐχιδνῶν, τίς ὑπέδειξεν ὑμῖν φυγεῖν ἀπὸ τῆς μελλούσης ὀργῆς; ποιήσατε οὖν καρπὸν ἄξιον τῆς μετανοίας καὶ μὴ δόξητε λέγειν ἐν ἑαυτοῖς· Πατέρα ἔχομεν τὸν Ἀβραάμ, λέγω γὰρ ὑμῖν ὅτι δύναται ὁ θεὸς ἐκ τῶν λίθων τούτων ἐγεῖραι τέκνα τῷ Ἀβραάμ. ἤδη δὲ ἡ ἀξίνη πρὸς τὴν ῥίζαν τῶν δένδρων κεῖται· πᾶν οὖν δένδρον μὴ ποιοῦν καρπὸν καλὸν ἐκκόπτεται καὶ εἰς πῦρ βάλλεται.

Ἔλεγεν οὖν τοῖς ἐκπορευομένοις ὄχλοις βαπτισθῆναι ὑπ’ αὐτοῦ· Γεννήματα ἐχιδνῶν, τίς ὑπέδειξεν ὑμῖν φυγεῖν ἀπὸ τῆς μελλούσης ὀργῆς; ποιήσατε οὖν καρποὺς ἀξίους τῆς μετανοίας· καὶ μὴ ἄρξησθε λέγειν ἐν ἑαυτοῖς· Πατέρα ἔχομεν τὸν Ἀβραάμ, λέγω γὰρ ὑμῖν ὅτι δύναται ὁ θεὸς ἐκ τῶν λίθων τούτων ἐγεῖραι τέκνα τῷ Ἀβραάμ. ἤδη δὲ καὶ ἡ ἀξίνη πρὸς τὴν ῥίζαν τῶν δένδρων κεῖται· πᾶν οὖν δένδρον μὴ ποιοῦν καρπὸν καλὸν ἐκκόπτεται καὶ εἰς πῦρ βάλλεται.

If there was a common source, which case was it:

  1. Matthew had access to the text of Luke,

  2. Luke had access to the text of Matthew, or

  3. both authors had access to a common source.

We can begin by ruling out that Matthew had access to Luke. First, it is understood that Matthew was likely written before Luke, but also, there is another example of editorial fatigue is a pericope that tells the story of a master giving his slaves money while he is away, and they are expected to invest that money.

  1. In Matthew, there are three (3) slaves, each given money, and the first two double their money while the third does not, and the first two are rewarded, but the third fearfully says ‘Master, I knew that you were a harsh man, reaping where you did not sow, and gathering where you did not scatter seed; so I was afraid, and I went and hid your talent in the ground. Here you have what is yours.’ The master responds with You wicked and lazy slave! You knew, did you, that I reap where I did not sow, and gather where I did not scatter? Then you ought to have invested my money with the bankers, and on my return I would have received what was my own with interest. So take the talent from him, and give it to the one with the ten talents. For to all those who have, more will be given, and they will have an abundance; but from those who have nothing, even what they have will be taken away. As for this worthless slave, throw him into the outer darkness, where there will be weeping and gnashing of teeth.’

  2. In Luke, the narrative now begins with ten (10) slaves, each is given money, and they are expected to invest that money; however, when the master returns, we are only told of the works of the three slaves, in parallel with the story told in Matthew, and the third fearfully says ‘Lord, here is your pound. I wrapped it up in a piece of cloth, for I was afraid of you, because you are a harsh man; you take what you did not deposit, and reap what you did not sow.’  The master replies ‘I will judge you by your own words, you wicked slave! You knew, did you, that I was a harsh man, taking what I did not deposit and reaping what I did not sow? Why then did you not put my money into the bank? Then when I returned, I could have collected it with interest. Take the pound from him and give it to the one who has ten pounds. I tell you, to all those who have, more will be given; but from those who have nothing, even what they have will be taken away.

One may see the author of Luke starting the story by thinking that he will significantly embellish the story he is copying, intending to tell of the exploits of all ten slaves, but upon copying the consequences, he only includes the same three that were told in Matthew. It is unknown what happened to the remaining seven slaves: did they make money for the master, or were they, too, punished?

Given the parable of the talents or pounds, and the editorial fatigue shown by the author of Luke, one may suspect that Luke may have copied from Matthew; however, there are good reasons to suspect that both the authors of Matthew and Luke had, instead, access to other sources. The first two are unlikely given that Mark says nothing about the life of Jesus prior to his baptism, and similarly says nothing about the events that occurred after his resurrection. This is likely that the author of Mark had an adoptionist attitude towards Jesus: Jesus was a human born of human parents and adopted the Son of Yahweh at his baptism. By the time Matthew and Luke were written, these authors appear to have believed that Jesus was born the Son of Yahweh, and neither gospel suggests that Jesus preexisted his birth. It is only John who appears to believe that Jesus pre-existed his birth, and Paul, who seems to have envisioned Jesus as an angel or other being lesser than Yahweh, for

who though he existed in the form of God did not regard equality with God as something to be grasped,
but emptied himself by taking on the form of a slave, by looking like other men, and by sharing in human nature.
He humbled himself, by becoming obedient to the point of death—even death on a cross!
As a result God highly exalted him and gave him the name that is above every name,
so that at the name of Jesus every knee will bow—in heaven and on earth and under the earth—
and every tongue confess that Jesus Christ is Lord to the glory of God the Father.

This poetry is nonsensical of one is to maintain the common belief that Yahweh, Jesus and the Spirit of Holiness are somehow one and the same since the beginning: if Jesus was Yahweh, why would Yahweh be exalting himself?

However, none of this appears to have been on the mind of the author of Mark, and it was only his ministry between his baptism and resurrection that mattered. It was only subsequently that other followers began to believe that Jesus needed to come from Bethlehem, and so it was necessary to get this Jesus of Nazareth somehow to Bethlehem for his birth. Note, however, that the author of John didn't seem to see this as important::

Philip found Nathanael and told him, “We have found the one Moses wrote about in the law, and the prophets also wrote about—Jesus of Nazareth, the son of Joseph.” Nathanael replied, “Can anything good come out of Nazareth?” Philip replied, “Come and see.”

However, with it being common knowledge the Jesus was from Nazareth, it was necessary to introduce a narrative that somehow had him born in Bethlehem. The issue is, however closely Matthew and Luke followed Mark, they provide mutually incompatible birth narratives:

  1. Matthew has Joseph and Mary living in Bethlehem. Luke has the family living in Nazareth.

  2. Luke has the family travel to Nazareth for a census. Matthew has no need of this journey, as they are already there.

  3. Matthew has Jesus born before the death of King Herod (4 BCE). Luke has Jesus born after the deposition of Herod Archelaus (6 CE), who was King Herod's son.

  4. Matthew has the family flee to Egypt to escape the wrath of King Herod. Luke describes a family at peace, describe Jesus's circumcision, and the family's journey to Jerusalem for the ritual sacrifice of a pair of doves.

  5. Matthew has the family return from Egypt upon hearing of the death of King Herod, and they seem to want to return to Bethlehem, but fear Herod's son, Herod Archelaus (the one who was deposed before Jesus was even born according to Luke), and only seem to end up in Nazareth almost by chance: After being warned in a dream, [Joseph] went to the regions of Galilee. He came to a town called Nazareth and lived there. Luke simply has the family return to Nazareth from Jerusalem with no hint of any threat.

It is important to note that in Luke, the family starts in Nazareth and returns to Nazareth. In Matthew, the family starts in Bethlehem, seems to want to return to Bethlehem but feared returning there (But when [Joseph] heard that Archelaus was reigning over Judea in place of his father Herod, he was afraid to go there.), and only seems to have come across Nazareth by chance: He came to a town called Nazareth and lived there. There is no suggestion that either he or Mariam had previously lived there and that they were simply returning to their home. It's also interesting to note that Luke makes no mention of a star: a star that no other astronomers in Greece, Rome or China seem to detect, but of course, did this star appear in 5 or 6 BCE or 6 CE?

Similarly, the narratives of what happens after the resurrection equally diverge:

  1. In Matthew, the angel at the tomb says to the women: “...he is going ahead of you to Galilee; there you will see him.’ This is my message for you.” Then, after the disciples are told, Jesus never-the-less tells them again “Do not be afraid; go and tell my brothers to go to Galilee; there they will see me.” The narrative continues: Now the eleven disciples went to Galilee, to the mountain to which Jesus had directed them and concludes with Jesus giving what is called the great commission.

  2. In Luke, no such instruction is given to the women to tell the disciples to go to Galilee, and Peter returns to the tomb to find it empty. Jesus then meets two followers on the road to Emmaus in the vicinity of Jerusalem, although they do not recognize Jesus, and when they reach Emmaus, Jesus reveals himself and disappears. They then return to Jerusalem to meet with the disciples and other followers. Oddly, they tell the disciples and other followers that “he has appeared to Simon!” when no such meeting is recorded. Jesus then appears amongst them, speaks to them, and instead says “...so stay here in the city until you have been clothed with power from on high.”--no mention of Galilee. Jesus then leads them to Bethany (near Jerusalem) and ascends into heaven. It is understood that book Acts of the Apostles, also addressed to Theophilus, is a continuation of Luke, and all subsequent events take place in and around Jerusalem. Indeed, the only reference to Galilee in the first few chapters of Acts is to refer to the disciples as men of Galilee, and it is only next referenced in Acts 9 in relation to [m]eanwhile the church throughout Judea, Galilee, and Samaria had peace and was built up, and no subsequent events involving the disciples occur in Galilee. 

So, did Jesus give instructions for the disciples to go to Galilee, or were the disciples told to stay in Jerusalem? Did Jesus meet the disciples in Galilee or did he meet them near Jerusalem? If the author of Luke had access to the text of Matthew, given how closely the author of Luke followed Mark (as we will see), one would think that he would also, at the very least, attempt to take at least some cues from the birth narrative and post-resurrection narrative of Matthew, as opposed to authoring a text that is irreconcilable with that of Matthew in both cases. Of course, most congregants are likely unaware of these discrepancies, and most ministers will simply deliver sermons that piece together different non-contradictory aspects of each narrative into a shared narrative. For example, prepending the narrative of Joseph and Mary in Nazareth to before the events in Matthew, interpolating the story of the shepherds and their flocks as an event immediately after the birth of Jesus, blending the stories of the return journey to Nazareth and appending the stories of Jesus as a youth onto the end of the birth narrative in Matthew. Any contradictory details, such as Jesus being born before King Herod dies or after King Herod's son and successor as ethnarch is deposed ten years later, are ignored. Similarly, the giving of the great commission can be told without reference to the location where it occurred, and it would not be necessary to comment that the author of Luke and Acts never once describes the disciples as returning to Galilee to meet Jesus, and it would not be necessary to contrast this meeting in Galilee told in Matthew with the observation that all interactions between Jesus and the disciples in Luke and Acts occurred in the vicinity of Jerusalem.

As an aside, to comment, this author no longer believes that any of the synoptic gospels (Matthew, Mark and Luke) in any way present a chronological order of events in the life and ministry of Jesus, apart from each beginning with his baptism, and ending with his entry into Jerusalem, execution and resurrection. Most of the stories in Mark start with phrases that would be associated with a person telling an independent story; after all, very few of the pericopes refer back to previous events or teachings of Jesus or even depend on previous events; instead, each is an individual story, as if the author of Mark was writing down one story at a time as they were recited to him. Individual stories as told by an oral tradition would necessarily need to be self-contained, and would not necessarily rely on the audience being aware of other narratives, and forty years had passed since the execution of Jesus. There is, however, one interesting contrast between Mark and Matthew, and Luke in relation to the timeline of Jesus's ministry: the reason for Jesus beginning his ministry. In all three gospels, Jesus returns to Nazareth following his baptism, and Mark and Matthew tell that the reason began his ministry is that he hears that John the Baptist has been arrested, which may very well be the truth. This strongly suggests that Jesus was himself a disciple of John the Baptist, and this perhaps did not mesh well with the idea that Jesus had his own purpose. After all, if Jesus was Yahweh incarnate, why would he wait until John the Baptist is arrested before starting his own ministry? Instead, a pericope found in Mark and Matthew where Jesus returns to Nazareth and is subsequently chased out, and forms part of the narratives in the middle of these gospels is copied to the very start of Luke where it becomes the driving reason for Jesus beginning his ministry.

This first section has just demonstrated with examples the fact that Mark, Matthew and Luke have common pericopes. Next, we will want to try to detect such plagiarisms by looking at the changes in the order of the pericopes. We will do this by considering how much the pericopes in on gospel change with another based on jumps from where they are copied.

Detecting plagiarism through jumps

Suppose Author A told twenty stories in the order

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Suppose now Author B copied them; however, Author B decided to reorder them, but Author B is lazy, so that author starts by copying the first five stories, jumps to Story 13, copies 13, 14, 15, 16 and 17 then returns to Story 6 and continues through to Story 12, and the concludes with Stories 18, 19 and 20:

1 2 3 4 5 13 14 15 16 17 6 7 8 9 10 11 12 18 19 20

There are three jumps in this sequence when contrasted with the original:

1 2 3 4 5|13 14 15 16 17|6 7 8 9 10 11 12|18 19 20

Suppose now that Author C decides to copy these stories. It is very unlikely that independently Author C would make the same jumps, so suppose that Author C copied Stories 1, 2 and 3, then jumped to Story 9 and copies to Story 15, then returns to Stories 4 through 8 and concludes with Stories 16 through 20. If this author was copying from Author A's source, we would see:

1 2 3|9 10 11 12 13 14 15|4 5 6 7 8 9|16 17 18 19 20

Again, there are only three jumps; however, suppose Author C copied Author B's stories with this same order of breaks. The order of the stories now becomes:

1 2 3 16 17 6 7 8 9 10 4 5 13 14 15 11 12 18 19 20

If we now flag the jumps compared to the order of the stories in Author A, we now get:

1 2 3|16 17|6 7 8 9 10|4 5|13 14 15|11 12|18 19 20

There are six jumps instead of only three, so assuming random placements of jumps, the number of jumps with Author C reorders Author B's stories, and Author B reorders Author A's stories, is additive. If Author C is working independent of Author B, it is unlikely that, given sufficiently many stories being copied, that both authors will choose the exact same place at which to jump to copying elsewhere in the text that they are copying from.

Note that jumps are symmetric, so if you were to were to reinterpret the order of that of the second author, the same number of jumps would appear.

We will therefore define jump(AB) to be the number of the number of jumps between two documents, and thus, jump(AB) = jump(BA). Also, if A was the original author, then jump(BC) will be approximately jump(AB) + jump(AC).

Now, suppose we did not know who the original source was, be it Author A, B or C. The number of jumps between two documents is symmetric, so if we determined that jump(A, B) = 2, jump(B, C) = 3 and jump(A, C) = 5, then we have slightly less information: Either

  1. Author B was the original, and Authors A and C independently copied from Author B,

  2. Author A was the original, Author copied from A, and Author C copied from Author B.

  3. Author C was the original, Author B copied from C, and Author A copied from Author B.

Fortunately, other evidence gives us that Mark is the original author.

This example shows only a single jump within the ordering of the stories: jumping ahead for a while, and then returning to copy any of the missed materials. As Matthew and Luke copied from Luke, if we count the number of jumps in Matthew and the number of jumps in Luke relative to Mark, if Luke copied from, or at least had reference to, Matthew, then the number of jumps should be significantly higher when contrasting Luke versus Mark as when contrasting Matthew versus Mark. Please keep this in mind, as we will use this to demonstrate that it is reasonable to believe that the author of Luke did not have access to the text of Matthew, and as well, neither author had access to a common source "Q", but rather, likely had in their hands collections of narratives, each of which came to the authors through independent sequences of other authors copying and reworking stories in turn.

Jumps
Graphical comparisons of the pericopes 

Thus, we will return to the main point of this article:

  1. To demonstrate graphically the relationship between the pericopes in the three gospels Matthew, Mark and Luke.

  2. To demonstrate graphically that it is likely that both Matthew and Luke had access to Mark, and copied from that text in a reasonably lazy manner,

  3. To demonstrate graphically that it is unlikely based on the common pericopes shared by all three gospels that the authors of Matthew and Luke did not have access to each others texts.

  4. To demonstrate graphically that it is unlikely that the common source was a single document labeled Q, but rather, likely a collection of written narratives that were likely shared within the Christian community at the time, but where in most cases, neither author had access to the same document, just having access to narratives that shared some of their pericopes.

It is easy enough to tabulate the pericopes described in the three synoptic gospels and indicate the relative orders; however, I chose to display this information graphically. To begin: what pericopes were included and which were excluded. I excluded all teachings of Jesus and all parables, and focused only on descriptions of events that occurred in the life of Jesus where there were identifiable persons and events.

We will begin with the common pericopes as described between Mark and Matthew. This is shown in Figure 1. Each verse occupies the same vertical distance so the length of the pericope as far as the number of verses is concerned is shown visually. In some cases, it is quite clear that common pericopes never-the-less are described in greater or lesser extent. For example, The two pericopes making up Mark 5, the casting out of demons at Gerasene and the performance of a resurrection, appear at the end of Matthew 8 and in the middle of Matthew 9, respectively, although much more abbreviated. The birth narrative, comprising Matthew 1 and 2, do not appear in Mark, and Matthew 5, 6 and 7 recall the Sermon on the Mount. You will note that the post-resurrection narrative in Matthew only comprises half of the last chapter of Mark. What is most interesting, however, is that initially the author of Matthew, while nominally following the order in Mark, does make numerous deviations; however, after Matthew 13, the author of Matthew seems to succumb to editorial fatigue--it is just easier to follow the lead of Mark with the occasional injection of material from elsewhere. Figure 1 emphasizes that approximately 94% of Mark appears in Matthew. In this figure, the pericopes in Mark that appear either in Matthew or Luke or both are colored in red or cyan in an alternating pattern. A block of verses that is colored but does not have a link to Matthew does have a link to Luke (see Figure 2).

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Picture1.png

Figure 1. Common pericopes between Mark and Matthew.

Next, we look at Mark and Luke, which is shown in Figure 2. Like Matthew, the birth narrative does not appear in Mark. The Sermon on the Plain occupies most of Luke 6 and 7, but unlike Matthew who copies a much greater proportion of Mark, it is clear that the end of Mark 6 and most of Mark 7 and 8 did not make it into Luke. This absence is often described as the Great Omission. The author of Luke also includes much more additional material then Matthew, including most of Luke 10, 12, 13, 14, 15, 16 and 17 and approximately half of Luke 18 and 19, as well as a much larger post-resurrection narrative. However, like Matthew, Luke succumbs to editorial fatigue, and while initially including many changes to to the order of the pericopes in Mark, by the time the author gets to Luke 18, the author more-or-less faithfully follows the order of the pericopes in Mark. You will note in Figure 1, the author of Matthew begins to more-or-less faithfully follow the order of Mark once we get to Mark 6, while Luke only begins to more-or-less faithfully follow Mark after Mark 10.

Picture2.png

Figure 2. Common pericopes between Mark and Luke.

 

Finally, we look at the common pericopes between Matthew and Luke. Those pericopes that are shared by all three synoptic gospels maintain their red or cyan color shown in Figures 1 and 2. Those other pericopes that are common only between Matthew and Luke are shown in other colors. What is immediately apparent is while those pericopes that are copied by both authors of Matthew and Luke do have many sequences of pericopes that continue to be in the same order, there appear to be, also, significantly more jumps. From the previous section, if Authors B and C copy independently from Author C, then jump(B, C) = jump(A, B) + jump(A, C), at least, approximately. We will investigate this later one; however, what is much more apparent is that there are significantly more jumps in that material common to Matthew and Luke (the Q source) than with that material common with Mark. We will suggest that this leads to the conclusion that while the authors of Matthew and Luke had Mark as a source, there was not a single document "Q" that was a common source for the authors of both Matthew and Luke. Instead, we will posit that there were many collections of documents that were circulating, and these collections must have been copied and recopied and collated by other authors and editors first. We will, however, one observation: there is a significant overlap of the teachings of the Sermon on the Mount and the Sermon on the Plain; however, once the author of Luke finishes the Sermon on the Plain, he includes material unique to his gospel and then includes what appears in the first half of Matthew 11: the tale of the disciples of John the Baptist visiting Jesus. You will note that Matthew 26, 27 and the start of Matthew 28 closely mirror Luke 22, 23 and the start of Luke 24. This sequence of pericopes begins with, in both cases, a description of the plot to kill Jesus.

  ​

Picture3.png

Figure 3. Common pericopes between Matthew and Luke.

We will now look at the Matthew and Luke and their relationship to Mark, but we will in each case exclude what I will call sporadics. These are pericopes copied from from Mark in a place distant from any pericope before or after it in Mark. We will start with Matthew. In Figure 4, with the removal of only five common pericopes.

 

Picture4.png

Figure 4. Common pericopes between Mark and Matthew with five sporadic common pericopes removed.

Lookin at this, it is quite straight-forward to observe how the author of Matthew copied from Mark. Apart from sporadic pericopes:

  1. After finishing his birth narrative, the author copies most of Mark 1 into Matthew 3 and 4, in generally the same order.

  2. The author then inserts the Sermon on the Mount.

  3. With the start of Matthew 8, he returns to copying what remains at the end of Mark 1.

  4. He then jumps to copying the end of Mark 4 and the first half of Mark 5.

  5. He then returns to continue copying from Mark 2 up until almost the end.

  6. He returns to the balance of Mark 5.

  7. After inserting mostly new material at the end of Matthew 9, most of 10 and all of 11, he then returns to continue copying from end of Mark 2, and continues copying up until almost the end of Mark 4.

  8. Finally, the author jumps to and starts copying from Mark 6 and faithfully follows the order of pericopes in Mark, occasionally inserting new material.

This is a total of only four jumps. Next, we will look at Luke, where I have excluded six sporadic pericopes, as shown in Figure 5.

Picture5.png

Figure 5. Common pericopes between Mark and Luke with six sporadic common pericopes removed.

Lookin at this, it is clear that Luke made even less of an attempt to do anything other than copy the pericopes of Mark, and generally faithfully followed the order in Mark and only either:

  1. Skipped pericopes in Mark, or

  2. Inserted new material

Apart from the six sporadically copied pericopes, there are really only two exceptions to this seen in Figure 5:

  1. In Luke 5, a pericope from Mark 1 that was skipped is included again.

  2. In Luke 11, the author seems to copy over three pericopes that were previously skipped.

That is it, there are no real significant jumps: Luke faithfully followed the lead of Mark. Only a handful of pericopes are significantly out of order.

There is, however, a much more critical observation: any place where the author of Matthew jumped, even if we go back to including the sporadic pericopes, the author of Luke did not, and of course, vice versa: there are no common jumps what-so-ever. If the author of Luke did have access to to the text of Matthew, he must have never referred to it except to compare and contrast the choice of text.

We will continue by showing the orderly relationship between Mark and Matthew, and Luke and Mark, but between Matthew and Luke, we will only show the pericopes common to each other and not appearing in Mark. This is shown in Figure 6.

Picture6.png

Figure 6. Common pericopes between Mark and Matthew on the left, between Luke and Mark on the right, and those only common between Matthew and Luke in between.

What is immediately obvious in Figure 6 is the more-or-less faithful copying of both authors of Matthew and Luke from Mark, and this is contrasted with very little order between the pericopes shared only between Matthew and Luke.

If we were to assume that the author of Luke had access to Matthew, this would mean that the author of Luke was jumping back and forth between the pericopes in Matthew, in complete contrast to the orderly copying from Mark. Even when adjacent pericopes in Matthew are copied, they are occasionally copied in the reverse order, the most obvious of which is the question as to whether or not Satan first took Jesus to the Temple in Jerusalem, and then to the mountain, or vice versa. Also, even if the author of Luke was referring to the text of Matthew, he never inserted a common jump from Matthew, even if you consider the sporadic pericopes. It is therefore highly unlikely that the author of Luke had access to Matthew directly, and it is more likely that there was a common source. Recall that if two sources copy independently from another, then the jumps are also likely going to be independently chosen, so if we are just contrasting the top copyists, there will be additively more jumps.

This common source has been suggested to have existed since the early 1900s, and this common source is described as the Quelle or spring or source, and is often abbreviated simply as "Q". B.H. Streeter has suggested that it is likely that the author of Luke more closely preserved the order of the pericopes in Q than did Matthew, and given that we have seen that Luke more closely followed the order of Mark, this is not unreasonable. If both Matthew and Luke copied from Mark, and both copied from a single document Q, then one may expect a similar number of introduced jumps when we compare those pericopes that are common between Mark, Matthew and Luke, and those common only between Matthew and Luke. This is shown side by side in Figure 7.

Picture7.png

Figure 7. Pericopes in common between Mark, Mathew and Luke on the left, and those in common only with Matthew and Luke on the right.

What you see on the left is more chaotic than either Figure 1 or Figure 2, but because there were not that many jumps in either Matthew or Luke, apart from eleven sporadic pericopes, there should not be too many jumps between Matthew and Luke: independent jumps are additive. Again, we are now looking at all common pericopes between the three synoptic gospels without excluding any sporadic pericopes, and so by our above description of the number of jumps when contrasting two sources that copied independently from a common source (Mark), we do expect additively more jumps. ​This is why the left-hand image is more chaotic than Figures 1 or 2.

Unfortunately, when we look to the right, there is significantly more chaos than on the left. Both authors would have needed to decide to treat the source Q as much more copy-from-here and then copy-from-there, in complete contrast to their reasonably orderly (and lazy) copying from Mark. Even when the authors ultimately succumbed to editorial fatigue and more-or-less copied the balance of Mark essentially in order, they still would have been energetic enough to make more significant changes to Q.

This author will suggest that instead of there being a single common Q source, a much more plausible scenario that more closely fits what we see above is:

  1. The authors of Matthew and Luke had access to multiple documents (which I will call pamphlets) significantly shorter than Mark.

  2. It is likely that each such pamphlet had a specific theme associated with its contents.

  3. While the authors of Matthew and Luke likely had similar copies of Mark, most of these other pamphlets, even if commonly shared, may have still been different. For example, being shorter, when copying a pamphlet, there is no reason to not make additional small changes, such as adding related sayings or pericopes, or leaving others out. Additionally, intermediate editors may have combined two or more pamphlets into one. On the other hand, if you have a recognized document like the gospel of Mark, it is more likely that it would be reasonably and faithfully copied as a whole.

Sequences of verses (pericopes and sayings) that may have have come from a common pamphlet may possibly be deduced visually by the appearance of fans within the above images. This is a sequence bundle of lines between the two documents that are either parallel or form a fan-shape. For example, consider Figure 8 and look at the first few pericopes in Luke 17.

Picture8.png

Figure 8. A fan between Matthew 17 and 18 (left) and the start of Luke 17 (right).

At the start of Luke 17 are four sayings of Jesus that are copied in approximately the same order in Matthew, but interspersed with new material or pericopes copied from Mark, including the parable of the lost sheep, which appears instead at the start of Luke 15. This may have been a pamphlet which the author of Matthew occasionally referred to while authoring Matthew 17 and 18, which the author of Luke copied as a single block, or perhaps some of the intermediate material in Matthew was not copied by the author of Luke: for example Matthew 18:15-20 are sayings of Jesus, so could have been included at the start of Luke 17, but perhaps the author chose not to include them from this common pamphlet.

 

Another common fan appears in the first half of Luke 10, and these same verses appear in the same order throughout the end of Matthew 9 and throughout Matthew 10 and 11, with one more appearing in Matthew 13. This fan is shown in Figure 9.

Picture9.png

Figure 9. A fan between the end of Matthew 9 and Matthew 10 and 11 (left) and Luke 10 (right).

Luke 10 begins with the mission of the 70 to various towns, the consequences of those towns that reject his message, and the return of the 70 followed by Jesus rejoicing. In Matthew, there is a reference to the harvest that appears also in Luke, but this is now followed with a mission of twelve (12) (recall how Luke exaggerated the number of slaves in the parable of the talents or pounds?), Jesus then seems to discuss details not in Luke 10 referring to the difficulties ahead, and then later continues to discuss the consequences of those towns that reject his message. Both sequences end with “I thank you, Father, Lord of heaven and earth, because you have hidden these things from the wise and the intelligent and have revealed them to infants; yes, Father, for such was your gracious will. All things have been handed over to me by my Father; and no one knows who the Son is except the Father, or who the Father is except the Son and anyone to whom the Son chooses to reveal him.” or words to that effect.

Now, one reason this author doubts that there was just a single Q document is that inside the fan shown in Figure 9, there is a second fan, but going in the opposite direction. If you look at the end of Matthew 10, there is a sequence of verses that appear later on in Luke, but still in the same relative order. This is shown in Figure 10, although, this may be a more tenuous example.

Picture10.png

Figure 10. A fan between the end of Matthew 10 (left) and Luke 12 to 17 (right).

Here, the fan goes in the other direction: a tight cluster of verses and pericopes at the end of Matthew 10 is spread out, but still in approximately the same order, throughout many chapters in Luke. Again, this could have been a separate pamphlet accessed by both the authors of Matthew and Luke. 

 

There is one final example of a fan within a fan, which perhaps suggests multiple sources. This is the Sermon and the Mount (Matthew 5, 6 and 7) and the Sermon on the Plain (most of Luke 6), shown in Figure 11. The story of Jesus healing the Centurion's servant appears immediately after both sermons, so this story may have been an addenda to the common pamphlet; however, given that the two stories of the Centurion's servant are so different (in Matthew, all communications is between the Centurion and Jesus, and in Luke all communication is through intermediaries--the Centurion and Jesus never meet, not even once), and consistently different (and given how much both authors are subject to editorial fatigue), this suggests that the common sermon pamphlet may have been edited between it being received by the author of Matthew and it subsequently being received by the author of Luke. However, this is clearly only speculation.

Picture11.png

Figure 11. A fan between the Sermon on the Mount and the Sermon on the Plain, but with a second fan within the Sermon on the Mount spread mostly throughout Luke 11 and 12.

The sayings and pericopes that appear in the Sermon on the Plane in Luke appear in approximately the same order as they do in the Sermon on the Mount in Matthew; however, in Matthew, there is a sequence of verses and pericopes not shared with the Sermon on the Plain. Instead, these verses appear in approximately the same order but throughout the balance of the gospel of Luke starting with Luke 11 and 12, with perhaps a few other pericopes appearing later. This would make more sense if there were two pamphlets available to both authors: one that contained what is summarized in the Sermon on the Plain in Luke, but which the author of Matthew started copying, but then copied a second pamphlet inbetween. This second pamphlet may have been also available to the author of Luke, but the author of Luke simply referred to it on occasion during those chapters where he was not explicitly copying from Mark. Alternatively, there may have been a shorter source which Matthew received directly, and Luke received an expanded edition that had those sayings and pericopes together with other fresh information. After all, it is understood that Luke was authored after Matthew, so a pamphlet that Matthew had access to could easily have gone through further revisions by the time it reached the author of Luke.

A final observation on sporadics

One question that may be of interest is are there any examples that might indicate that some of the pericopes that are in common with all three gospels were also included in the Q document or documents? The only definitive way that this could be ascertained is if a pericope in Mark appeared out of order in both Matthew and Luke, and both Matthew and Luke had similar pericopes from Q surrounding it. Unfortunately, that does not seem to be the case. Instead, it does seem that there was text in Q that was sufficiently similar to what was in Mark that on at least one occasion, one of the authors used only the Q source and not the source in Mark. Specifically, I refer to the verses that forbid divorce while occasionally providing an exception:

  1. He said to them, “Whoever divorces his wife and marries another commits adultery against her; and if she divorces her husband and marries another, she commits adultery.” Mark 10:11-12

  2. And I say to you, whoever divorces his wife, except for unchastity, and marries another commits adultery.” Matthew 19:9

  3. “Anyone who divorces his wife and marries another commits adultery, and whoever marries a woman divorced from her husband commits adultery. Luke 16:18

  4. But I say to you that anyone who divorces his wife, except on the ground of unchastity, causes her to commit adultery; and whoever marries a divorced woman commits adultery. Matthew 5:32

The exception, on the grounds of unchastity, only appears in Matthew, and awkwardly enough, appears twice in Matthew. This may seem to be an example of the authors of Matthew and Luke copying from Mark, and the author of Matthew copying that text twice; however, that doesn't appear to be the case. Instead, it seems that Luke's source is from a Q document, while Matthew takes and modifies both the text from Mark and the Q document. This is most easily seen when examining the surrounding text:

  1. The setting in Mark is in Judea beyond the river Jordan and pharisees are questioning him regarding when divorce is allowed.

  2. The setting in Matthew 19 is, again, in Judea beyond the river Jordan and again the pharisees are questioning him.

  3. The setting in Luke is also amongst pharisees, but Jesus was simply teaching: there was no questioning involved.

  4. The setting in Matthew 5 is where Jesus was simply teaching as part of the Sermon on the Mount.

If you look at Mark 10 and Matthew 19, you will see immediately following this teaching, we see that Jesus blesses some children and tells the story of the rich man asking what must be done to come to heaven. Thus, this was copied by the author of Matthew while copying the balance of Mark 10. If you look at Luke 16 and Matthew 5, both are surrounded by other text that does not appear in Mark. Unfortunately, the text in Luke does not appear in the sermon on the plain, so it is necessary to look elsewhere for evidence that this was copied from the same source, so returning to the Greek:

  1. καὶ λέγει αὐτοῖς· Ὃς ἂν ἀπολύσῃ τὴν γυναῖκα αὐτοῦ καὶ γαμήσῃ ἄλλην μοιχᾶται ἐπ’ αὐτήν, καὶ ἐὰν αὐτὴ ἀπολύσασα τὸν ἄνδρα αὐτῆς γαμήσῃ ἄλλον μοιχᾶται.

  2. λέγω δὲ ὑμῖν ὅτι ὃς ἂν ἀπολύσῃ τὴν γυναῖκα αὐτοῦ [μὴ ἐπὶ πορνείᾳ] καὶ γαμήσῃ ἄλλην μοιχᾶται καὶ ὁ ἀπολελυμένην γαμήσας μοιχᾶται.

  3. Πᾶς ὁ ἀπολύων τὴν γυναῖκα αὐτοῦ καὶ γαμῶν ἑτέραν μοιχεύει, καὶ ὁ ἀπολελυμένην ἀπὸ ἀνδρὸς γαμῶν μοιχεύει.

  4. ἐγὼ δὲ λέγω ὑμῖν ὅτι πᾶς ὁ ἀπολύων τὴν γυναῖκα αὐτοῦ [παρεκτὸς λόγου πορνείας] ποιεῖ αὐτὴν μοιχευθῆναι, καὶ ὃς ἐὰν ἀπολελυμένην γαμήσῃ μοιχᾶται.

While the phrase ἀπολύσῃ τὴν γυναῖκα αὐτοῦ is common to all four passages, the text surrounding that found in Mark matches that found in Matthew 19, and the text that is found in Luke matches that found in Matthew 5. Given that Matthew was copying from Mark, one must wonder what local pressures forced him to impose the exception to getting a divorce. Did the author himself get a divorce, or did an influential member of the the author's community get a divorce and required justification, or wanted a divorce? As the author of Luke had already copied this verse from the Q source, when it came to copying a similar verse from Mark, the author skipped over that verse--no requirement for duplication. Matthew, however, copied and modified both sources, so perhaps instead wishing to reinforce not the rule, but rather the added exception ("Look here, Jesus twice said this was justification for a divorce!"). Another possibly interesting observation is that the exception clause existed primarily in the community of the author of Matthew: Mark was written before Matthew, and the author of Mark did not have the exception clause, and Luke was likely written after, and yet, the copy of Q that was passed to him also does not appear to have had the exception clause included. However, it could have been that the author of Matthew was simply copying the Q source, and then inserting the exception clause into the text copied from Mark, while Luke was copying the Q source but then removed the exception clause, as the author of Mark did not include it. This author would suggest this second case is less likely. 

Changes as evidence of a common source

Another ​means of detecting a common source is that copyists invariably make changes. If A and B copied from C independently, then both may make changes independent of each other, just like independent copyists will jump between texts at different points in the original (as shown above).  If A also had access to B, then if B made an occasional change, then A may potentially choose that change over what appeared in the original. Thus, if A and B were indpendent, then while A and C may differ from B (when B makes a change) or B and C may differ from A (when A makes a change), it is unlikely that both A and C will make changes at the same location, and it is even less likely that they will both make the same change. One fascinating narrative that appears in all the gospels, however, makes it quite clear is the women coming to the tomb Sunday morning.

All three gospels agree on these points:

  1. Mary Magdalene and Mary the mother of James (and Joseph, one may presume) went to the tomb.

  2. The stone was moved aside.

  3. There were linens inside the tomb.

Beyond this, there are many points where Matthew agrees with Mark, but Luke differs:

  1. Are the individual or individuals the women speak to standing or sitting: Matthew and Mark say he is sitting, Luke has them standing.

  2. Matthew and Mark have the women approach the individual, while Luke has them suddenly appear after they entered the tomb and found it empty.

  3. What do the individual or individuals say to the women: Luke has the individuals say “Why do you look for the living among the dead? He is not here but has risen…” while Matthew and Mark are similar with

    • “Do not be afraid, for I know that you are looking for Jesus who was crucified.

      “Do not be alarmed; you are looking for Jesus of Nazareth, who was crucified.

    • He is not here, for he has been raised, as he said.
      He has been raised; he is not here.

    • Come, see the place where he lay…”
      Look, there is the place they laid him…”

  4. In Matthew and Mark, the individuals tell the women to tell the disciples to meet Jesus in Galilee. In Luke, the women are given no such directions and later Jesus explicitly tells the disciples to wait at Jerusalem.

  5. In Matthew and Mark, the women simply return, while in Luke, Peter returns to the tomb to examine it.

There are also points where Luke agrees with Mark, but Matthew differs:

  1. Neither Luke nor Mark describe how the stone was moved, but Matthew states the angel moved it and this subsequently caused a second earthquake (the first being when Jesus died, an earthquake not recorded in Luke or Mark).

  2. Neither Luke nor Mark indicate anyone else is present at the tomb, while Matthew has guards who are frozen with fear present.

  3. Luke and Mark both say that the women are bringing spices, while Matthew leaves this out.

  4. Luke and Mark have the women see Jesus only after they enter the tomb, while Matthew has the angel sitting on the stone.

  5. Luke and Mark indicate the individuals are men, but Matthew describes his as an angel.

  6. Luke and Mark do not describe the women as having met Jesus, but Matthew has such a story where Jesus speaks directly to the women.

There are situations where all three disagree:

  1. Mark says that Salome went to the tomb, while Luke mentions Joanna, but Matthew only mentions the two already mentioned in Matthew and Mark.

  2. In Mark in the oldest ending has the women flee and say nothing, in Matthew it seems the women told the disciples, as they meet Jesus in Galilee, while in Luke the women are disbelieved, although Peter goes to the tomb.

There is exactly one change that is common between Matthew and Luke:

  1. Mark says the women visited the tomb after the sun has risen, while Matthew and Luke say they went there at dawn (before sunrise).

Given that these events span a small chapter in Mark, and less than a chapter in Matthew and Luke, such changes strongly point to very different understandings of why no one believed that Jesus had been resurrected, and why likely some followers did not believe, either, but the above variations indicate again very strongly that Matthew and Luke copied from Mark independently.

Summary

To conclude, this graphical presentation of common pericopes and sayings of Jesus between the synoptic gospels is a much more clear presentation of the commonalities of these gospels. Together with editorial fatigue, the increase in the number of jumps between pericopes in common with all three gospels suggests that both Matthew and Luke copied from Mark. This also suggests that the author of Luke did not have access to Matthew when authoring this third gospel. When we compare only those pericopes and sayings common to Matthew and Luke, we get a much chaotic picture than we do even when comparing those pericopes in common with Matthew and Luke that also appear in Mark. Consequently, this suggests, at least initially, that there was not a single Q document. Instead, this author is suggesting there may have been multiple documents or pamphlets available to both authors, and this is supported by the existence of numerous fans throughout the common pericopes and sayings. A fan may indicate a shared pamphlet, and the fact that there are fans within fans, given how lazy and faithful the authors were to Mark, that these authors, instead, had access to a number of common pamphlets containing sayings and pericopes of Jesus.

Similar works

While I was not aware of this other attempt to graphically show the relationship between the synoptic gospels, there was one such attempt by Thomas J. Mosbo. While his graphics are more stylish, he is attempting to claim that Luke combined the gospels of Mark and Matthew, and to do so, he only chooses verses as coming either from Matthew or Mark, but not both, even if the text appears in both. He claims other links are similarly not explicitly drawn so as to not obfuscate the claims of the author. Here is another such attempt by Richard Salisbury. Finally, here is a much more professional example.

References

The only aspects of this discussion that are mine are the graphics and the observation of what I'm calling fans. The concept of editorial fatigue is described by Mark Goodacre, and a good reference is his article Fatigue in the Synoptics. A nice blog post is How Editorial Fatigue Shows That Matthew and Luke Copied Mark by Paul Davidson at his blog Is that in the Bible?  Bart Ehrman also discusses the relationship between the gospels in many of his books. From his blog post, Paul Davidson also references works by 

  • Michael Goulder, Midrash and Lection in Matthew, 1974.
  • Mark Goodacre, “Fatigue in the Synoptics”, New Testament Studies 44 (1998).
  • Mark Goodacre, The Synoptic Problem: A Way Through the Maze, 2001.
  • G. A. Wells, Who Was Jesus? A Critique of the New Testament Record, 1989.

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