Crthuky

Several times within the Old and New Testament of the Bible there are notes pertaining to a long time as "40 days," as in 40 days of fasting, rain, traveling, etc. Why 40? Is there a factual association? The only thing I've noticed are references to 40 days needed for mummification in natron. Any insight? Thanks!

I believe it to be an euphemism similar to how today one might say something like gazillions for a large number.

In a society that is mostly innumerate as well as illiterate, where neither pencils nor paper exist and both slateboards and chalk are fragile and rare, the scale of numbers readily accessible to the common population are much smaller than today. The meaning of 40 to me comes across as: "longer than a month, and more days than one would care to count"; or as Wikepedia puts it in that link:

similar to "umpteen".

There seems to be a bit of pushback on Pieter's (correct) answer, so perhaps a bit more detail is in order.

It is not at all uncommon in languages to have words that, while technically a specific number, are usually used just to indicate an unspecified large amount. One of the technical terms for this is non-numerical vague quantifiers.

The most well-known of these is of course the Hebrew Bible's "40", but they also had a word for an even larger indeterminate number: רבבה. This word came into English (via Greek) as "myriad", but the technical literal value for it is 10,000.

Probably the next most famous for us English speakers is 1,001, which came into English from the Arabic work 1,001 Nights (which usually doesn't contain exactly 1,001 stories, unless you get an edition that purposely tried to edit to that amount for some weird reason). You can find all kinds of English-language books with titles on the theme "1,001 Uses For...", and nobody really expects those to contain exactly 1,001 of the thing in question.

Now most secular (and mainline Christian) Biblical scholars will tell you that the earliest written source for the Hebrew scriptures (including the story of Noah that prominently featured the indeterminate 40) committed the stories to writing around the 6th Century BC.

This was about 4 centuries before the Hebrews started using their distinctive Greek-borrowed numeric system (which resembles Roman Numerals a bit in implementation). At that time the numeric system in use would have been the old Babylonian Sexagesimal system. This survives today mostly in our units of time and angle "degree" (and thus Earth surface coordinate) measurements. This was technically a hybrid base 60 system, but represented with a weird base 10 tally system within the 60.

If that sounds complicated to you, you're probably still better off than the common Semite, who as Pieter pointed out, probably didn't really know how to read or use this system themselves beyond the bare basics required for everyday life. Doing reckoning under this system was much harder than what we have today, and there was no equivalent to the modern western education system, where every child gets basic mathematics instruction. Working with numbers that high was difficult, and very few in the audience of these stories would have been trained to do so.

You may notice that the superglyph for 40 specifically is the first one where there isn't enough space for all the 10's tallies on one line, so you have to start compressing them together into 2 lines in the same amount of space. Perhaps its a coincidence, but this is certainly the point where the writing/carving for numbers starts to look like a bit of a mess. Its a lot.

Biblically, Forty is a number associated with testing and trials
https://www.thoughtco.com/biblical-numerology-700168

Jesus wandered in the wilderness 40 days, Israel wandered in the desert for 40 years etc.

It's a number that indicates enough time passed for God to achieve a goal. Fullness of time.