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randomlingSo one of the things I'm fannish about is the movie Inception. It is a very enjoyable film, full of thinky thoughts, big guns, explosions, and beautiful people.
This afternoon as I was on the bus, I was thinking about my beloved Mr Eames and how he says, "Maths was never my strong point," when they're figuring out how much time they will have on the various dream levels. And I was thinking that maths was never my strong point, either, clearly. Because I can't figure out how the hell they get from 10 hours to a week to six months to 10 years.
The net result of this train of thought was that I decided to start thinking it through and seeing if it can make sense.
(Some caveats at this point. One: I'm only on the fringes of Inception fandom really, so this topic may well have been done to death. Two: I've only seen the movie twice, so if I'm wrong on the details, forgive me.)
So.
The thinking it through part.
The first piece of information we get is that "five minutes in reality is an hour in the dream world". (We're talking about Level One, here, obviously.)
This piece of maths is quite simple. There are 12 lots of 5 minutes in an hour, so time passes 12 times faster on Level One than it does in reality. (I'm guessing that the brain is imprecise, these are all ballpark figures, and that this can vary widely in shared dreamspace and even more widely in personal dreamspace - but we need a little specificity [thanks, Arthur] in order to be able to do the maths.)
So on the Fischer job, they're going to be asleep in the real world for 10 hours. 10 x 12 = 120, so on Level One, they have 120 hours, or 5 days. That's a week, more or less! So how they get from "10 hours in reality" to "a week on Level One" is pretty clear and obvious.
What's next? According to the team (I forget who has which lines) a week on Level One equals six months on Level Two.
We don't get told that there is (or isn't) a change in the multiplier, so I'll start by trying the maths for figuring it all out as x12.
If you're saying this is "a week", it should be 12 weeks (that's three months).
If you're looking at the answer of 5 days, 5 x 12 = 60, so it should be 60 days (two months).
Still a long time, but the figure we get is six months - so clearly the multiplier changes.
Six months is (roughly) 24 weeks or (roughly) 180 days. So if you're counting that first result as a week, that multiplier is probably x24. If you're taking it as 5 days, you're looking at x36.
We've either doubled or trebled the multiplier to get to Level Two, then.
Interesting.
So... might we expect the multiplier to increase again for the jump to Level Three? I think we might. I think we might be able to bank on some consistency here.
Except.
The next jump is from six months on Level Two to ten years on Level Three. And this is where my assumptions and expectations fall to pieces.
Any which way you slice it, ten years is only twenty times six months.
So whether you multiplied by 24 or 36 to get to Level Two, you're decreasing the multiplier to get to Level Three.
If you kept the multipliers the same all the way through (x12), you'd be looking at:
10 hours in the waking world = 5 days on Level One = 60 days on Level Two (two months) = 720 days on Level Three (two years).
If you doubled the multipliers, it'd be more like:
10 hours in the waking world x12 = 5 days on Level One x24 = 120 days on Level 2 (4 months) x48 = 5,760 days on Level 3 (15 years and change!).
And if you treble the multiplier:
10 hours in the waking world x12 = 5 days on Level One x36 = 180 days on Level 3 (6 months) x108 = 54 years (!!!) on Level 3.
(Yes, I used a calculator for some of that!)
Any way I slice it, I can't seem to make the maths work out for ten years (or even roughly ten years). If Ariadne is saying "5 days is a week and 24 weeks is 6 months", she'd then have to be multiplying her figure of 6 months by only 20 to get ten years. And if she's doing that, then the multiplier's surely doubling for each level you go down, so she should be coming up with a figure that's more like 24 years.
(And from above, the actual result from that model would be more like 15 years. Which maybe isn't a huge difference in the ballpark-ey world of dream-level maths, but I bet if you were living through it, those extra 5 years would make some difference.)
Some parts of Inception, it's true, are brilliantly and beautifully thought-out. The plot is very well-structured indeed and the emotional and psychological content is compelling. But I don't blame Eames for not being able to grasp maths, because apparently the maths of dream levels is beyond us both!
I'm pretty sure that either the audience just isn't given all the information (Inception does leave you to infer an awful lot, which I like very much in a movie!), or that the "10 hours - a week - 6 months - 10 years" thing was just put in there because it sounded good and not because it made any mathematical sense.
I still love the movie. But apparently, I shouldn't think about the maths too hard.
This afternoon as I was on the bus, I was thinking about my beloved Mr Eames and how he says, "Maths was never my strong point," when they're figuring out how much time they will have on the various dream levels. And I was thinking that maths was never my strong point, either, clearly. Because I can't figure out how the hell they get from 10 hours to a week to six months to 10 years.
The net result of this train of thought was that I decided to start thinking it through and seeing if it can make sense.
(Some caveats at this point. One: I'm only on the fringes of Inception fandom really, so this topic may well have been done to death. Two: I've only seen the movie twice, so if I'm wrong on the details, forgive me.)
So.
The thinking it through part.
The first piece of information we get is that "five minutes in reality is an hour in the dream world". (We're talking about Level One, here, obviously.)
This piece of maths is quite simple. There are 12 lots of 5 minutes in an hour, so time passes 12 times faster on Level One than it does in reality. (I'm guessing that the brain is imprecise, these are all ballpark figures, and that this can vary widely in shared dreamspace and even more widely in personal dreamspace - but we need a little specificity [thanks, Arthur] in order to be able to do the maths.)
So on the Fischer job, they're going to be asleep in the real world for 10 hours. 10 x 12 = 120, so on Level One, they have 120 hours, or 5 days. That's a week, more or less! So how they get from "10 hours in reality" to "a week on Level One" is pretty clear and obvious.
What's next? According to the team (I forget who has which lines) a week on Level One equals six months on Level Two.
We don't get told that there is (or isn't) a change in the multiplier, so I'll start by trying the maths for figuring it all out as x12.
If you're saying this is "a week", it should be 12 weeks (that's three months).
If you're looking at the answer of 5 days, 5 x 12 = 60, so it should be 60 days (two months).
Still a long time, but the figure we get is six months - so clearly the multiplier changes.
Six months is (roughly) 24 weeks or (roughly) 180 days. So if you're counting that first result as a week, that multiplier is probably x24. If you're taking it as 5 days, you're looking at x36.
We've either doubled or trebled the multiplier to get to Level Two, then.
Interesting.
So... might we expect the multiplier to increase again for the jump to Level Three? I think we might. I think we might be able to bank on some consistency here.
Except.
The next jump is from six months on Level Two to ten years on Level Three. And this is where my assumptions and expectations fall to pieces.
Any which way you slice it, ten years is only twenty times six months.
So whether you multiplied by 24 or 36 to get to Level Two, you're decreasing the multiplier to get to Level Three.
If you kept the multipliers the same all the way through (x12), you'd be looking at:
10 hours in the waking world = 5 days on Level One = 60 days on Level Two (two months) = 720 days on Level Three (two years).
If you doubled the multipliers, it'd be more like:
10 hours in the waking world x12 = 5 days on Level One x24 = 120 days on Level 2 (4 months) x48 = 5,760 days on Level 3 (15 years and change!).
And if you treble the multiplier:
10 hours in the waking world x12 = 5 days on Level One x36 = 180 days on Level 3 (6 months) x108 = 54 years (!!!) on Level 3.
(Yes, I used a calculator for some of that!)
Any way I slice it, I can't seem to make the maths work out for ten years (or even roughly ten years). If Ariadne is saying "5 days is a week and 24 weeks is 6 months", she'd then have to be multiplying her figure of 6 months by only 20 to get ten years. And if she's doing that, then the multiplier's surely doubling for each level you go down, so she should be coming up with a figure that's more like 24 years.
(And from above, the actual result from that model would be more like 15 years. Which maybe isn't a huge difference in the ballpark-ey world of dream-level maths, but I bet if you were living through it, those extra 5 years would make some difference.)
Some parts of Inception, it's true, are brilliantly and beautifully thought-out. The plot is very well-structured indeed and the emotional and psychological content is compelling. But I don't blame Eames for not being able to grasp maths, because apparently the maths of dream levels is beyond us both!
I'm pretty sure that either the audience just isn't given all the information (Inception does leave you to infer an awful lot, which I like very much in a movie!), or that the "10 hours - a week - 6 months - 10 years" thing was just put in there because it sounded good and not because it made any mathematical sense.
I still love the movie. But apparently, I shouldn't think about the maths too hard.
