Sojourn of Israel in Egypt
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Main Article: Evidence for the Israelite Sojourn in Egypt
How long were the Israelites living in Egypt?
The Bible says that the Israelites sojourned in Egypt for 430 years. Exodus 12:31-42
"the length of time that the Israelites lived in Egypt was 430 years". Exodus 12:40
The New Testament also refers to this 430 years. Galatians 3:17 says “ The law, introduced 430 years later, does not set aside the covenant previously established by God and thus do away with the promise.“ Because of this it is traditionally believed that the 430yrs commenced with the promise being given to Abraham (Genesis 15:12-16 ) about 215yrs before Jacob and his family moved to Egypt.  
Other scholars believe that the Jacob's descendants lived in Egypt for 430 years before the Exodus (The Long Sojourn).
Not withstanding this, it is obviously important to know whether the Israelites were in Egypt for 430 years or 215 years so that we know in which dynasty to look for Joseph (taking the Exodus as a reference point).
It appears that there were only 3 generations after Levi (who was in the original group that went to Egypt) until Moses (who was 80 years old when he lead the Israelites out of Egypt). Four Generations in Egypt would make a Long Sojourn unlikely (although their ages do add up to more than 400 years and they may have had children at an old age as did Abraham). It is hard to see how the Israelites would come to number 2 million in 4 generations unless the tribes of Israel had shorter generation times than the Levites. Exodus 1:1-6 Exodus 6:13-26 Numbers 1:1-54 Numbers 2:1-34
Looking at the promise God made to Abraham (Abram) it would appear that God was telling Abraham (Abram) that his children would serve as slaves in a foreign land for 400 years and then God would bring them out of that land with great wealth and give them the promised land. Genesis 15:12-16 Acts 7:6-7
The place where Abraham (Abram) received the promise was Canaan. This is where Jacob was born and returned to before moving to Egypt. In Genesis 15:12-16 & Acts 7:6-7 it is clear that the foreign land where the Israelites would serve as slaves for 400 years did not include Canaan.
It is also clear that the 400 years did not begin at the point that the promise was made. It was Abraham's (Abram's) descendants who would be enslaved and mistreated as strangers in a country not their own; not Abraham (Abram) himself. Abraham would enjoy peace and would die at an old age! Genesis 15:15
The Israelite Oppression only lasted 400 years Genesis 15:12-16 . The Israelite Oppression ended when the 12th dynasty ended. The Exodus did not take place until 30 years later when Neferhotep I was ruling towards the end of the 13th dynasty.
400 Years or 430 years?
Yet the Bible also tells us that the Israelites lived in Egypt for 430 years to the very day. Exodus 12:40-41
The Israelite Oppression ended when the 12th dynasty ended, about 10 years after Moses / Amenemhet IV went into exile at the age of 40 years. This was 400 years after Jacob and his family came to Egypt. The Exodus did not take place until 30 years into the 13th dynasty when Moses / Amenemhet IV returned to confront Neferhotep I at the age of 80 years.
The Israelite oppression lasted 400 years - it ended when the 12th dynasty ended. No more pyramids were built after the 12th dynasty. The 13th dynasty was very chaotic and the Pharaohs did not focus on oppressing the Israelites because their thrones were not stable enough and maybe their attitude towards the Israelites was slightly more sympathetic than that of the 12th dynasty pharaohs. The Exodus occurred 30 years into the 13th dynasty during the reign of Neferhotep I who was the longest ruling pharaoh of that dynasty (11 years).
Amenemhet III would have reigned for 2 or 6 years after Moses' exile to Midian began and Sobekneferu would have reigned for 4 or 8 years after her father Amenemhet III's reign (Sobeknefru reigned for 4 years according to the Turin King List and 8 years according to Manetho). When Sobeknefru died, the 12th dynasty ended as there was no heir to the throne. The result was that Egypt fell into chaos. There was a rapid succession of Pharaohs in the 13th dynasty and as a result, the Israelites were not oppressed during this time. They were able to keep multiplying and prepare to leave Egypt.
What difference does it make?
People who believe in a 430yr sojourn in Egypt look for Joseph in an earlier dynasty and given the similarities between Joseph and Imhotep, have tended to place Joseph in the 3rd dynasty serving Pharaoh Djoser (Netjeriket).
If the Israelites were in Egypt for 430 yrs as suggested by Exodus 12:40-41 , then the date of Joseph's entry to Egypt can be determined to be around 1885BC. According to the chronology of David Down, this would place Joseph very close to the 3rd dynasty of Egypt where the most likely candidate for Joseph, namely Imhotep, is located.
People who believe in a 215 yr sojourn in Egypt look for Joseph earlier in the 12th dynasty and have nominated Mentuhotep as a possibility.
One of the problems of placing Joseph in the 12th dynasty means that the flood of Noah would most likely have occurred during during one of the earlier dynasties (2450BC) and this is not only out of keeping with the Bible but there is no archaeological evidence of a worldwide flood during any Egyptian dynasty.
Even Manetho, whom most archaeologists regard as the most authoritative source of information on the chronology of Egyptian history, believed that Mizraim and Menes (the first Pharaoh) were the same person (although the authenticity of the source of this information is disputed).
A complete revision of the Egyptian chronology is required to allow for parallel dynasties running concurrently in the North and the South and also for the common practice of co-regency. The result would be a considerable reduction in the time frame of the Egyptian dynasties.
This would allow historians to look in the right dynasty for archaeological evidence for the Israelites.
If it is true that Joseph and Imhotep were the same person, then the first pyramid (the Step Pyramid in Saqqara) was designed by an Israelite at the begining of Israel's Sojourn in Egypt and if the last of the great pyramids (those of the 12th dynasty) were constructed with a core made from mud bricks which were made by Israelite slave labour, then the Israelites were in Egypt while all of the great pyramids were being constructed. After the Israelites departed from Egypt in the 13th dynasty, lead by Moses (Amenemhet IV), there were not enough slaves left in Egypt to construct pyramids any more. No more large pyramids were built after Moses (Amenemhet IV) lead the Israelites out of Egypt in 1446BC. The Pyramid Age would coincide with Israel's sojourn in Egypt. The pyramids would, therefore, have been constructed over a period of around 400 years.
The Egyptian Chronology
In order to correlate Egyptian history with the Bible, it is also important to know how the Egyptian dynasties are ordered.
A number of archaeologists such as David Down have suggested that Egyptian history should be revised as it is now known that many Egyptian dynasties ran in parallel and some have been counted twice! What's more, it was common practice for pharaohs to co-reign for a while so the incoming pharaoh could be trained up and be tested.
The traditional chronology with sequential dynasties and sequential pharaohs was derived from the list of pharaohs and the lengths of their reigns left by Mantetho who was a priest in Egypt who had access to the Alexandrian library before it was destroyed. Manetho lived during the time of Alexander the Great about 1000 years after the Exodus. All his original work has been lost and we only have the notes of people who saw his works. The Turin King list was recorded on the back of another document and is very fragmented. Like Manetho's it is a list of pharaohs and how long they reigned. There are some discrepancies between the Turin King list and Manetho's list (eg the length of Sobeknefru's reign). These documents do not give dates or places and do not allow for parallel reigns or co-regency.
Archaeologists are in agreement about the dates when Solomon started building the Temple (966BC) and hence the date of the Exodus is generally agreed to be around 1445BC (480 yrs before the building of the Temple 1Kings 6:1 ). There is mounting archaeological evidence to suggest that Moses was born in the 12th dynasty of Egypt when Sesostris III was pharaoh (co-reigning with his son Amenemhet III). Moses was born during the first 4 years of Amenemhet III's reign. Moses would have grown up during the reign of Amenemhet III which lasted 46 years. It is quite likely that Sobekneferu (the daughter of Amenemhet III) was the Princess who found Moses in the Nile. Moses would have become the next Pharaoh (Amenemhet IV) if he had not killed an Egptian official and had to flee from Amenemhet III. He may even have co-reigned with Amenemhet III for about 9 years. When Sobeknefru died, 10 years after Moses' exile to Midian began, the 12th dynasty ended (as there was no heir to the throne). When Moses returned to Egypt 40 yrs after fleeing from Egypt, in the 30th year of the 13th dynasty, there was a different Pharaoh in charge of Egypt (Neferhotep). Neferhotep was the Pharaoh of the Exodus.
Answering the Atheists who claim that the Bible is a collection of myths
Placing Joseph in the 3rd dynasty and Moses in the 12th dynasties not only fits very well with the archaeological evidence, it fits very well with the Biblical account. It is the Egyptian chronology that needs to be revised.
What we know about Biblical characters from the historical records can be used to fill in the gaps in the Biblical record revealing how miraculous, amazing and glorious the Hand of God has been in dealing with mankind.