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The number 40 occurs many times in the Bible but what is the significance of 40 as opposed to another number such as 30 or 60?

I hope I will not offend too many people if I suggest that the significant numbers in the Bible may be derived from the previous cultures of the Middle East.
There were certain numbers that were significant to the ancients - to the Babylonians and Sumerians which I think were inherited by the people of Israel.

It was mainly about what they had access to observing.
These fall into 3 categories:
1. Astronomical - eg they could see 5 planets that did not twinkle and "wandered" in the sky, plus the Sun and the Moon
2 Biological eg most basic measures are hands feet or cubits and we most of us have 10 fingers
3 Agricultural - there were time periods that were important because they told farmers when to plant harvest or when the rains would come

The lunar month and its quarters, I think led to the 29/30 day lunar month and the seven day week;
The number of digits on the hands [5, 10] and the number of fingers bones of one hand [12]
probably led to counting in 10s and in 5 sets of 12 ie using base 60, which was the Babylonians method of doing arithmetic.

But where does the number 40 get its significance?

I found a number of possibilities:
A) Astronomical observation
1)looking for astronomical occurrences of the number 40 I found that the "retrograde of Venus"
[ie the time the planet appears to go "backwards" in the sky] takes approximately 40 days.
I have confirmed with a Professor of astronomy that the ancients could have observed this, though the middle section of Venus' retrograde motion would have been hidden by the sun, they would have had clear sight of the beginning and the end.
While I have not found any clay tablets in Cuneiform recording this so far, there is a famous cuneiform tablet of observations of Venus over a 21 year period
https://en.wikipedia.org/wiki/Venus_tablet_of_Ammisaduqa
- which at least shows the Babylonians took a keen interest in observing the planet.

2) An alternative quite interesting theory found here: https://web.archive.org/web/20081207153305/http://paganizingfaithofyeshua.netfirms.com/40_days_wilderness.htm
posits that 40 days was a period of the Sun passing through the constellation of Cancer - though I do not understand how that would have been observable? The author also appears to have had to "fiddle the figures" a bit to get 40 days rather than the 30 days that each constellation normally lasts suggesting this cannot be a primary source for the number 40.

B)Three other ideas I came across was an association with childbirth:
1) There are 40 weeks a pregnant woman can count from her last period to the expected date of birth
2) In many cultures eg Indian, Biblical and Eastern orthodox 40 days was the traditional time a woman took care of herself to recover from giving birth.
3) There is a comment by Rashi on Genesis 7:4 "For yet seven days, and I will cause it to rain upon the earth forty days and forty nights; and every living substance that I have made will I blot out from off the face of the earth.'" which reads
"FORTY DAYS — corresponding to the period of a child’s formation... (Genesis Rabbah 32:5)."
[Genesis Rabba 32~:5] ' Rabbi Yochanan said "They spoiled the shape that was given at 40 days" ';.
See http://www.sefaria.org/Rashi_on_Genesis.7.4.3?lang=bi&with=Bereishit%20Rabbah&lang2=en
He seems to be referring to the 40 days for the fetus to take an identifiable shape with organs visible.
At 6 weeks - The baby's nose, mouth and ears are starting to take shape, and the intestines and brain are beginning to develop.

C) Finally there is also an association with death and mourning customs:
It occurs in the Bible and in Indian culture the Greek rites of Persephone[?] and in Islam and in Eastern orthodox Christianity as a period of mourning after death.
[Genesis 50:3 states that it required 40 days for embalming, in Egypt].
Interestingly 40 days did not become the mourning period for the Jewish people
- Moses and Aaron were mourned for 30 days and Jewish practice still reflects this.

I think however, that if we assume the number 40 came from astronomical observations of Venus,
the third most significant object in the sky for the ancients [after the Sun and Moon],
then all these associations come together.

The Babylonians associated the goddess "Ishtar" with Venus.
The Babylonian Culture was inherited in large part from the Sumerians
The Sumerian name for Ishtar was Innana.
She was the goddesses of fertility which ties in with the connection with childbirth.
But she was not just associated with fertility but also with war.
She was connected both with birth and death.
[Perhaps because Venus is both "Evening star" and also "Morning star" and
because its retrograde motion includes a fading away followed by a "rebirth"]

Some of the Sumerian tablets referring to "Innana" are not unconnected to floods and destruction:
"She stirs confusion and chaos against those who are disobedient to her, speeding carnage and inciting the devastating flood, clothed in terrifying radiance. It is her game to speed conflict and battle, untiring, strapping on her sandals."
and "Her wrath is ……, a devastating flood which no one can withstand. A great watercourse, ……, she abases those whom she despises. "
Inanna also was associated with rain and storms.
See "The literature of Ancient Sumer" by Jeremy A Black https://books.google.co.uk/books?id=a1W2mTtGVV4C&pg=PA93

So from the ancient Mesopotamian links to the significance of Venus, and the connection of Venus to the number 40, out comes a relationship to death and to birth and a connection to the catastrophic destruction of the flood, as well as to the womb-like rebirth of humanity and all living creatures coming out from the Ark.
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