What is the symbolic idea behind this number?
Also, what might be His intention behind the travel?
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The field of Biblical numerology can be a pretty mirky pond. There are some clear trends (three for completion, seven for perfection, a thousand for a really big number, etc.) and a lot of speculation and conclusions that may or may not be warranted.
In this case however, the answer is pretty much spelled out in another verse. The 40 years of wandering was an exact calculation, one year for one day, based on how long the spies spent looking around the land before they were originally supposed to enter.
Numbers 14:34 (ESV)
34 According to the number of the days in which you spied out the land, forty days, a year for each day, you shall bear your iniquity forty years, and you shall know my displeasure.’
The logical next question is, "Why did the spies spend 40 days on their quest"? To that we are not given any definite clues. It does seem like a reasonable amount of time to get around to a bunch of different places on foot and get an idea of the lay of the land without making your movements too obvious and getting caught.
There are actually quite a few references to 40 in the Bible. The flood. The spies. The wandering in the desert. The reigns of many of the Judges. Moses life has three periods of 40 years each. The temptation of Jesus. The surmised time between the resurrection and the ascension that Jesus spent back on earth. However the connections between these references is faint at best, and I think it is safe to say, since we are not told explicitly that there is any meaning to this number, that it is of no particular consequence that the spies took 40 days to get their spyin' done.
Numbers 14: 26-35
26 The LORD said to Moses and Aaron: 27 “How long will this wicked community grumble against me? I have heard the complaints of these grumbling Israelites. 28 So tell them, ‘As surely as I live, declares the LORD, I will do to you the very thing I heard you say: 29 In this wilderness your bodies will fall—every one of you twenty years old or more who was counted in the census and who has grumbled against me. 30 Not one of you will enter the land I swore with uplifted hand to make your home, except Caleb son of Jephunneh and Joshua son of Nun. 31 As for your children that you said would be taken as plunder, I will bring them in to enjoy the land you have rejected. 32 But as for you, your bodies will fall in this wilderness. 33 Your children will be shepherds here for forty years, suffering for your unfaithfulness, until the last of your bodies lies in the wilderness. 34 For forty years—one year for each of the forty days you explored the land—you will suffer for your sins and know what it is like to have me against you.’ 35 I, the LORD, have spoken, and I will surely do these things to this whole wicked community, which has banded together against me. They will meet their end in this wilderness; here they will die.”
God commanded Israelites to explore the land of Canaan. Indeed, the milk and honey was flowing in that land. However, the people of Israel did not believe in God's powers and refused to march into Canaan and claim the land, except for Joshua and Caleb. God multiplied the number of days the group of explorers took to explore Canaan and multiplied it by a year. Eventually, the entire disbelieving generation died out.
It was 40 years exactly, God does not do nearly or just about and it was a year for every day because of the Israelites disobedience and complaining about the land. They wanted out and away from the Egyptians to a better place and when they got it they were not satisfied and wanted more, so God gave them the run around as punishment.
God said that all those who had refused to believe his promise that he would give them the land of Canaan would die in the wilderness. Thus, they had to wonder long enough for all these people to die. That would require decades. "Forty years" seems to be a standard Old Testament period for "one generation".
I'm a Biblical literalist, but I wouldn't insist on the 40 years being an exact number. It may simply be a round number, and the exact time was 37 years, 4 months, and 12 days or whatever. If the writer is rounding off to the nearest 10 years, there aren't that many possible different numbers. It would pretty much hae to come to about 40 years give or take. Maybe 30 or 50. 20 would be too short; 60 probably too long.
So it may have symbolic significance. But I wouldn't make too much of it. Like that statement in John 21:11 that the disciples caught 153 fish. Did this number have symbolic significance? Or was it just that that happened to be the number?