I recently watched the 2015 documentary, Patterns of Evidence, which is about the historicity of the biblical Exodus.  See here for the trailer.  You can watch the movie on Netflix.
Before I offer some thoughts about the documentary, I would like to 
present some preliminary information about the proposed dates for the 
biblical Exodus.
Some scholars date the Exodus to the thirteenth century B.C.E., which
 was the time of Raamses II.  There are a variety of defenses for this 
particular date.  Exodus 1:11 states that the Israelites in Egypt built 
for the Pharaoh the treasure city of Raamses, and the time of Raamses 
was one of mass building projects.  Another argument in favor of the 
thirteenth century B.C.E. date is that, around the beginning of the Iron
 Age in 1200 B.C.E., we see in the land of Palestine new houses, which 
differ from the previous houses and which a number of archaeologists 
believe are Israelite.  In the documentary, James Hoffmeier was an advocate for the thirteenth century B.C.E. date.
Other scholars date the Exodus to the fifteenth century B.C.E.  This 
appears to coincide with I Kings 6:1, which states that the Israelites 
came out of Egypt 480 years before King Solomon started to build the 
Temple (which many believe dates to the tenth century B.C.E.).  In the 
documentary, Bryant Wood was
 an advocate for the fifteenth century B.C.E. date.  Wood argues, on the
 basis of archaeology, that the city of Jericho was destroyed in the 
fifteenth century B.C.E.  Archaeologist Kathleen Kenyon, however, dated 
the destruction of Jericho to the sixteenth century B.C.E.  In any case,
 the Canaanite cities pose a potential problem for those who date the 
Exodus to the thirteenth century B.C.E.  First of all, in the biblical 
narrative, the Israelites destroyed Jericho soon after leaving Egypt, 
and archaeology seems to indicate that Jericho was destroyed prior to 
the thirteenth century B.C.E.  Second, in the biblical narrative, there 
are indications that Canaanite and Transjordanian cities were walled and
 fortified (e.g., Numbers 13:28; Deuteronomy 1:28; 3:5).  That was not 
the case in the thirteenth century B.C.E. (see here),
 but it was the case during the Middle Bronze Period in Palestine 
(1950-1550 B.C.E., according to T.A. Holland’s article on “Jericho” in 
the Anchor Bible Dictionary).
A third approach is one that this documentary leans toward, and it 
states that the Exodus took place during the Middle Kingdom period of 
ancient Egypt.  The Middle Kingdom dates from 2000 B.C.E. to 1700 
B.C.E.  In the documentary, David Rohl is the main proponent of this view, and John Bimson
 seems to agree with him.  The documentary’s argument is that Egypt 
during the Middle Kingdom fits the biblical narrative better than the 
thirteenth century B.C.E..   According to the documentary, during the 
Middle Kingdom, we see the following: Semites were in the Egyptian area 
of Avaris (which later became the city of Raamses); there is a house of a
 Semitic high official that is surrounded by twelve tombs and has twelve
 pillars (the twelve tribes of Israel?); there is a tomb of a Semitic 
official who has a multicolored coat (Joseph?), and the body is missing 
(because the Israelites took Joseph’s bones to the Promised Land in 
Exodus 13:19?); the economic status of the Semites in Avaris 
dramatically declined from a state of prosperity (because the Pharaoh 
made them slaves?); there is evidence of high infant mortality for males
 in Avaris (the Pharaoh’s ordered slaughter of the male Israelite babies
 in Exodus 1?); Papyrus Ipuwer talks about events that sound like the 
biblical plagues; there are bones in Avaris that are tossed into the 
ground, and indications that people abandoned the site (the plague 
killing the firstborn, following by the Exodus?); and the slave city of 
Kahun shows signs of abandonment (the Israelites left Egypt?).
Rohl in the documentary, from what I remember, did not identity whom 
he believes was the Pharaoh during the time of the Exodus, but this article
 states that he thinks that it was Dedumose II, whom some Egyptologists 
(not all) date to the Thirteenth Dynasty of the Middle Kingdom.  (UPDATE: Actually, Rohl in the documentary refers to a statement by the third century B.C.E. Egyptian historian Manetho that, in the reign of Dudimose, God smote the Egyptians.)  The 
Thirteenth Dynasty is significant: according to this site,
 it was during the early Thirteenth Dynasty that Kahun was abandoned; 
John van Seters argues that the present form of the Admonitions of 
Ipuwer dates “no earlier than the late 13th Dyn.” (Ronald J. Williams, 
“Egyptian Literature (Egyptian Wisdom Literature),” Anchor Bible Dictionary);
 and the Thirteenth Dynasty marked extreme decline for Egypt (Ronald J. 
Lephrohon, “Egypt, History of (Middle Kingdom-2d Intermediate Period),” Anchor Bible Dictionary).  The Thirteenth Dynasty
 lasted for over one hundred years, so one could ask if it is 
problematic to Rohl’s position for the abandonment of Kahun to date to 
the early Thirteenth Dynasty, whereas the final form of the Admonitions 
of Ipuwer dates to the late Thirteenth Dynasty.  The Exodus was one-time
 event, right, not something stretching out for over a hundred years?  I
 have not read Rohl’s ideas on this, but he may have reasons for dating 
things as he does.  Dating is not an arbitrary exercise that lacks 
support (far from it!), but there are times when it can have 
uncertainties and can rest, at least in in part, on assumptions.
There is a challenge to this Middle Kingdom date for the Exodus, 
however, and that is that the Middle Kingdom ended about two centuries 
prior to the time that Kathleen Kenyon dates the destruction of 
Jericho.  How would dating the Exodus to the Middle Kingdom work, if the
 Israelites destroyed Jericho soon after leaving Egypt?  In the biblical
 narrative, the Israelites wandered in the wilderness for forty years, 
not two hundred years!  This is where the New Chronology enters the 
picture, in the documentary.  Rohl and Bimson are advocates for a New 
Chronology, one that deletes about three hundred years from the standard
 Egyptian chronology.  This New Chronology is controversial.  It allows for some conclusions that may strike people as pretty odd: According to this article,
 for example, Rohl identifies Shishak, the Egyptian king who invaded 
Jerusalem during the reign of King Rehoboam (I Kings 14), as Raamses II 
rather than Shoshenq I.  If true, that would mean that the Pharaoh whom 
many believe was the Pharaoh of the Exodus was ruling after the time of 
King Solomon of Israel, which was long after the time of the Exodus!  
The New Chronology does not necessarily exist to uphold the Bible: as 
John Bimson said in the documentary, there are Egyptologists who do not 
believe that the standard chronology holds up, who think that it has 
problems.  Still, there are people who believe that the New Chronology 
can allow for the Exodus to occur during the time of the Middle Kingdom,
 while moving the destruction of Jericho closer to the time of the 
Middle Kingdom.
I’ll stop here.  I may write a sequel, offering my thoughts on the documentary.
 
 
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