10 Restructured and bolstered
source | link

Motivation for the answer

In this answer I'll take a literary approach, aiming less at the surrounding historical context and more at an internal analysis of what "significance" the document's authors intended to convey.

However, rereading your question and David Robinson's comment, I see that you're not asking about this significance so much as the motivation to use "40" specifically. Thus, this answer doesn't directly address your question. But I do believe it provides an important foundation for an answer, because understanding the purpose a tool was used for helps understand the choice of tool.

Both Pieter and T.E.D. offer explanations of the choice of tool, and in that regard the answers will be more satisfactory. But the implied or stated purpose they are based on almost certainly misses the mark. I submit that both traditional and modern biblical scholarship would say it's unlikely that the purpose, the force of using "40" is to have an indeterminate number on hand. It certainly is not a euphemism (there is no social taboo to soften); it certainly is not due to the impossibility or awkwardness of inexpressing bigger numbers with precision or with vagueness (both are done often enough); and the biblical authors were not interested in de-nerding what is in fact a very nerdy document replete with specific numbers both large and small, particularly in the Pentateuch, where we find many of these same narratives that strategically use "40".

Some answers have suggested mathematical reasons for "40", computing percentages or aligning the numbers with other (supposedly) significant values. I find these anachronistic and atypical of biblical narrative structure.1

Pieter's and T.E.D.'s suggestions of a number system cutoff (or significant change) and of averaging out months or lifespans are more likely, more interesting, more basic motivations. But why did the writers (or the speakers of the language they used) look to natural or manmade phenomenon of around that size? Hopefully the discussion below concerning the function of "40" from the perspective of the document helps clarify what the tool is for for any other answerers.


Interderminate number

We can make one observation in line with the previous answers, namely that it is almost certainly not a literal but a symbolic number. There are at least three numbers that come up too often and at too useful a time to be coincidence: 7 / 70 (completeness; the root is related to "satiate"), 12 / 144 (traditional number of tribes of Israel, frequently recurrent), and of course 40value.2 In that sense, it is indeed an "indeterminate" number in that one is not interested in the exact value.

But we can also make the observation that though it may stand for an indeterminate number, it's not exactly an "indeterminately large number" in the sense of "more than one would care to count". The Bible is well aware that 40 is too small a unit for such purposes, and for big, vague numbers it prefers rounded-off hundreds, thousands, tens of thousands, or even hundreds of thousands (Deut 32:30, Josh 23:10, 1 Chron. 12:14, Judges 15:16, Psalm 91:7, 1 Sam. 13:2, 2 Sam. 18:3, Lev. 26:8, 1 Sam. 15:4, Num. 11:21, NT Rev. 7:4, etc.). Hence, reading "gazillions" or even "umpteen" for the biblical 40 seems to miss the mark.23


Significant block of time

One important note is that it'sthis number almost alwaysuniformly counts a period of time. (One rare exception is the number of se'ahs in a mikvah; note that this correspondence is only established by extrabiblical tradition.)4

When speaking of years, some instances: The Israelites wandered in the desert 40 years, with the explicit effect being that a whole generation died off (Num. 32:13). Moses fled Egypt at 40 years old (Acts 7:23) and returned 40 years after that (Acts 7:30). Some patriarchs married at 40, including Isaac (Gen. 25:20) and Esau (Gen 26:34). More than one king is said to have ruled for 40 years (e.g. 1 Sam. 4:18). In Jewish tradition, a person is allowed to study the Kabbalah at 40.35

Meanwhile, for "40 days" we can extend and miniaturize that meaning: it's a significant block of time within an average lifespan. We might say that 40 days is to a person's lifetime what 40 years is to a nation's history: a unit of time big enough to mark a change or a significant event.46


Interpretive context

Wikipedia tells me this reading is corroborated by Michael Coogan.57 

Other commentators, such as Ellicott in the 19th century, identified the number as one indicating "trial and patience", which fits well with the idea of a significant event (but doesn't agree with my focusing on a generation). 

Meanwhile, the Pulpit Commentary (also 19th century) cites Trench that it's sometimes a "signature of penalty, affliction" and confession of sin, and other times a sign that "work is completely [and thoroughly] done".

These are widely accepted, established readings, in line with other commentators (except literalists who take "40" to be a precise value). I don't believe there are many who would say that the force or purpose of using "40" is to select an indeterminate number or to suggest that the exact value doesn't matter in a given context. Sure, it doesn't — but that's not the reason they chose "40". 

To me this reinforcesthese interpretations reinforce the idea of communicating a whole "unit" of time, whether that unit is characterized by trial or by simple "fullness".

Footnotes

1 Without anyWhen I talk about what the Bible "means" by the number I make no reference to "hidden"supposedly hidden significance, i.e. such as numerological or mystical interpretations.

2 There are at least three numbers that come up too often and at too useful a time to be coincidence: 7 / 70 (completeness; the root is related to "satiate"), 12 / 144 (traditional number of tribes of Israel, frequently recurrent), and of course 40. Some other lists include more, but the wider the net cast, the less compelling the explanation of function seems to become.

3 As someone who reads Biblical Hebrew daily, I should note that T.E.D.'s explanation comes closer, but seems to miss the point makes a mistake when citing the word רְבָבָה revavah. This word stems from the root רבב r-b-b meaning "to multiply, to become many", and is a good candidate for "indeterminately large number". Wiktionary and other dictionaries' gloss "10,000" does not refer to the "technical, literal value" of revavah but to precisely the figurative value "10,000" carried in early translations such as the KJV.

34 One exception is the number of se'ahs in a mikvah; this correspondence is only established by extrabiblical tradition.

5 Although, as the linked article notes, this appears to be only ambiguously supported by the Talmud.

46 In sacred matters, the Bible does sometimes use the metaphor of a person for a nation, particularly the Israelite nation.

57 Michael David Coogan, A Brief Introduction to the Old Testament: The Hebrew Bible in Its Context, Oxford, 2008, p. 116.

In this answer I'll take a literary approach, aiming less at the surrounding historical context and more at an internal analysis of what "significance" the document's authors intended to convey.1

We can make one observation in line with the previous answers, namely that it is almost certainly not a literal but a symbolic number. There are at least three numbers that come up too often and at too useful a time to be coincidence: 7 / 70 (completeness; the root is related to "satiate"), 12 / 144 (traditional number of tribes of Israel, frequently recurrent), and of course 40. In that sense, it is indeed an "indeterminate" number in that one is not interested in the exact value.

But we can also make the observation that though it may stand for an indeterminate number, it's not exactly an "indeterminately large number" in the sense of "more than one would care to count". The Bible is well aware that 40 is too small a unit for such purposes, and for big, vague numbers it prefers rounded-off hundreds, thousands, tens of thousands, or even hundreds of thousands (Deut 32:30, Josh 23:10, 1 Chron. 12:14, Judges 15:16, Psalm 91:7, 1 Sam. 13:2, 2 Sam. 18:3, Lev. 26:8, 1 Sam. 15:4, Num. 11:21, NT Rev. 7:4, etc.). Hence, reading "gazillions" or even "umpteen" for the biblical 40 seems to miss the mark.2

One important note is that it's almost always a period of time. (One rare exception is the number of se'ahs in a mikvah; note that this correspondence is only established by extrabiblical tradition.)

When speaking of years, some instances: The Israelites wandered in the desert 40 years, with the explicit effect being that a whole generation died off (Num. 32:13). Moses fled Egypt at 40 years old (Acts 7:23) and returned 40 years after that (Acts 7:30). Some patriarchs married at 40, including Isaac (Gen. 25:20) and Esau (Gen 26:34). More than one king is said to have ruled for 40 years (e.g. 1 Sam. 4:18). In Jewish tradition, a person is allowed to study the Kabbalah at 40.3

Meanwhile, for "40 days" we can extend and miniaturize that meaning: it's a significant block of time within an average lifespan. We might say that 40 days is to a person's lifetime what 40 years is to a nation's history: a unit of time big enough to mark a change or a significant event.4

Wikipedia tells me this reading is corroborated by Michael Coogan.5 Other commentators, such as Ellicott in the 19th century, identified the number as one indicating "trial and patience", which fits well with the idea of a significant event (but doesn't agree with my focusing on a generation). Meanwhile, the Pulpit Commentary (also 19th century) cites Trench that it's sometimes a "signature of penalty, affliction" and confession of sin, and other times a sign that "work is completely [and thoroughly] done". To me this reinforces the idea of a whole "unit" of time, whether that unit is characterized by trial or by simple "fullness".

1 Without any reference to "hidden" significance, i.e. numerological or mystical interpretations.

2 T.E.D.'s explanation comes closer, but seems to miss the point when citing the word רְבָבָה revavah. This word stems from the root רבב r-b-b meaning "to multiply, to become many", and is a good candidate for "indeterminately large number". Wiktionary and other dictionaries' gloss "10,000" does not refer to the "technical, literal value" of revavah but to precisely the figurative value "10,000" carried in early translations such as the KJV.

3 Although, as the linked article notes, this appears to be only ambiguously supported by the Talmud.

4 In sacred matters, the Bible does sometimes use the metaphor of a person for a nation, particularly the Israelite nation.

5 Michael David Coogan, A Brief Introduction to the Old Testament: The Hebrew Bible in Its Context, Oxford, 2008, p. 116.

Motivation for the answer

I'll take a literary approach, aiming less at the surrounding historical context and more at an internal analysis of what "significance" the document's authors intended to convey.

However, rereading your question and David Robinson's comment, I see that you're not asking about this significance so much as the motivation to use "40" specifically. Thus, this answer doesn't directly address your question. But I do believe it provides an important foundation for an answer, because understanding the purpose a tool was used for helps understand the choice of tool.

Both Pieter and T.E.D. offer explanations of the choice of tool, and in that regard the answers will be more satisfactory. But the implied or stated purpose they are based on almost certainly misses the mark. I submit that both traditional and modern biblical scholarship would say it's unlikely that the purpose, the force of using "40" is to have an indeterminate number on hand. It certainly is not a euphemism (there is no social taboo to soften); it certainly is not due to the impossibility or awkwardness of inexpressing bigger numbers with precision or with vagueness (both are done often enough); and the biblical authors were not interested in de-nerding what is in fact a very nerdy document replete with specific numbers both large and small, particularly in the Pentateuch, where we find many of these same narratives that strategically use "40".

Some answers have suggested mathematical reasons for "40", computing percentages or aligning the numbers with other (supposedly) significant values. I find these anachronistic and atypical of biblical narrative structure.1

Pieter's and T.E.D.'s suggestions of a number system cutoff (or significant change) and of averaging out months or lifespans are more likely, more interesting, more basic motivations. But why did the writers (or the speakers of the language they used) look to natural or manmade phenomenon of around that size? Hopefully the discussion below concerning the function of "40" from the perspective of the document helps clarify what the tool is for for any other answerers.


Interderminate number

We can make one observation in line with the previous answers, namely that it is almost certainly not a literal but a symbolic value.2 In that sense, it is indeed an "indeterminate" number in that one is not interested in the exact value.

But we can also make the observation that though it may stand for an indeterminate number, it's not exactly an "indeterminately large number" in the sense of "more than one would care to count". The Bible is well aware that 40 is too small a unit for such purposes, and for big, vague numbers it prefers rounded-off hundreds, thousands, tens of thousands, or even hundreds of thousands (Deut 32:30, Josh 23:10, 1 Chron. 12:14, Judges 15:16, Psalm 91:7, 1 Sam. 13:2, 2 Sam. 18:3, Lev. 26:8, 1 Sam. 15:4, Num. 11:21, NT Rev. 7:4, etc.). Hence, reading "gazillions" or even "umpteen" for the biblical 40 seems to miss the mark.3


Significant block of time

One important note is that this number almost uniformly counts a period of time.4

When speaking of years, some instances: The Israelites wandered in the desert 40 years, with the explicit effect being that a whole generation died off (Num. 32:13). Moses fled Egypt at 40 years old (Acts 7:23) and returned 40 years after that (Acts 7:30). Some patriarchs married at 40, including Isaac (Gen. 25:20) and Esau (Gen 26:34). More than one king is said to have ruled for 40 years (e.g. 1 Sam. 4:18). In Jewish tradition, a person is allowed to study the Kabbalah at 40.5

Meanwhile, for "40 days" we can extend and miniaturize that meaning: it's a significant block of time within an average lifespan. We might say that 40 days is to a person's lifetime what 40 years is to a nation's history: a unit of time big enough to mark a change or a significant event.6


Interpretive context

Wikipedia tells me this reading is corroborated by Michael Coogan.7 

Other commentators, such as Ellicott in the 19th century, identified the number as one indicating "trial and patience", which fits well with the idea of a significant event (but doesn't agree with my focusing on a generation). 

Meanwhile, the Pulpit Commentary (also 19th century) cites Trench that it's sometimes a "signature of penalty, affliction" and confession of sin, and other times a sign that "work is completely [and thoroughly] done".

These are widely accepted, established readings, in line with other commentators (except literalists who take "40" to be a precise value). I don't believe there are many who would say that the force or purpose of using "40" is to select an indeterminate number or to suggest that the exact value doesn't matter in a given context. Sure, it doesn't — but that's not the reason they chose "40". 

To me these interpretations reinforce the idea of communicating a whole "unit" of time, whether that unit is characterized by trial or by simple "fullness".

Footnotes

1 When I talk about what the Bible "means" by the number I make no reference to supposedly hidden significance such as numerological or mystical interpretations.

2 There are at least three numbers that come up too often and at too useful a time to be coincidence: 7 / 70 (completeness; the root is related to "satiate"), 12 / 144 (traditional number of tribes of Israel, frequently recurrent), and of course 40. Some other lists include more, but the wider the net cast, the less compelling the explanation of function seems to become.

3 As someone who reads Biblical Hebrew daily, I should note that T.E.D. makes a mistake when citing the word רְבָבָה revavah. This word stems from the root רבב r-b-b meaning "to multiply, to become many", and is a good candidate for "indeterminately large number". Wiktionary and other dictionaries' gloss "10,000" does not refer to the "technical, literal value" of revavah but to precisely the figurative value "10,000" carried in early translations such as the KJV.

4 One exception is the number of se'ahs in a mikvah; this correspondence is only established by extrabiblical tradition.

5 Although, as the linked article notes, this appears to be only ambiguously supported by the Talmud.

6 In sacred matters, the Bible does sometimes use the metaphor of a person for a nation, particularly the Israelite nation.

7 Michael David Coogan, A Brief Introduction to the Old Testament: The Hebrew Bible in Its Context, Oxford, 2008, p. 116.

9 deleted 150 characters in body
source | link

Although I think History SE is a decent place to askIn this answer I'll take a literary approach, I thinkaiming less at the surrounding historical observationscontext and surrounding data will yield good educated guesses around the target, but not necessarily address the questionmore at an internal analysis of what "significance" the document's authors intended to convey. That to me is a literary question that would be better suited to Biblical Hermeneutics SE. But I'll attempt it here anyway.1

1 Not referringWithout any reference to "hidden" significance, i.e. numerological or mystical interpretations.

Although I think History SE is a decent place to ask this, I think historical observations and surrounding data will yield good educated guesses around the target, but not necessarily address the question of what "significance" the authors intended to convey. That to me is a literary question that would be better suited to Biblical Hermeneutics SE. But I'll attempt it here anyway.1

1 Not referring to numerological or mystical interpretations.

In this answer I'll take a literary approach, aiming less at the surrounding historical context and more at an internal analysis of what "significance" the document's authors intended to convey.1

1 Without any reference to "hidden" significance, i.e. numerological or mystical interpretations.

8 added 88 characters in body
source | link

Although I think History SE is a decent place to ask this, I think a better answer would come from Biblical Hermeneutics SE. Educated guesses based on historialhistorical observations can be made hereand surrounding data will yield good educated guesses around the target, but I think this is morenot necessarily address the question of what "significance" the authors intended to convey. That to me is a literary question concerning the Bible's use of the numberthat would be better suited to Biblical Hermeneutics SE. But I'll attempt it here anyway.1

For example, weWe can make one observation in line with the previous answers, namely that it is almost certainly not a literal but a symbolic number. There are at least three numbers that come up too often and at too useful a time to be coincidence: 7 / 70 (completeness; the root is related to "satiate"), 12 / 144 (traditional number of tribes of Israel, frequently recurrent), and of course 40. In that sense, it is indeed an "indeterminate" number in that one is not interested in the exact value.

Although I think History SE is a decent place to ask this, I think a better answer would come from Biblical Hermeneutics SE. Educated guesses based on historial observations can be made here, but I think this is more of a literary question concerning the Bible's use of the number.1

For example, we can make one observation in line with the previous answers, namely that it is almost certainly not a literal but a symbolic number. There are at least three numbers that come up too often and at too useful a time to be coincidence: 7 / 70 (completeness; the root is related to "satiate"), 12 / 144 (traditional number of tribes of Israel, frequently recurrent), and of course 40. In that sense, it is indeed an "indeterminate" number in that one is not interested in the exact value.

Although I think History SE is a decent place to ask this, I think historical observations and surrounding data will yield good educated guesses around the target, but not necessarily address the question of what "significance" the authors intended to convey. That to me is a literary question that would be better suited to Biblical Hermeneutics SE. But I'll attempt it here anyway.1

We can make one observation in line with the previous answers, namely that it is almost certainly not a literal but a symbolic number. There are at least three numbers that come up too often and at too useful a time to be coincidence: 7 / 70 (completeness; the root is related to "satiate"), 12 / 144 (traditional number of tribes of Israel, frequently recurrent), and of course 40. In that sense, it is indeed an "indeterminate" number in that one is not interested in the exact value.

7 added 190 characters in body
source | link
6 added 190 characters in body
source | link
5 deleted 2 characters in body
source | link
4 added 5028 characters in body
source | link
3 deleted 113 characters in body
source | link
2 added 1 character in body
source | link
1
source | link