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In the movie, they (Cobb and his partners) are drawn into multiple layers of dreams, and they said that if you're going further/deeper you'll find the time in real world or previous layer is multiplied, thus allowing you to do more in the dream world.
Is there any actual calculation for this?
The calculation is on a 1:20 ratio between each layer of dream on strong sedative. And 1:12 on normal sedative.
This is a bit weird though. When the van is falling in the first layer of the dream, the passengers are weightless and time is flowing 20 times slower. The van falls in ... maybe 5 seconds? That means in the second layer, the character must do the following in approx 1 minute 30 seconds:
Which is a little short, I'd say.
In the film, Nolan gives his character a pseudo-scientific speech on relative temporality about dream states (to which "Eames" said he doesn't like math).
This time ratio is constant between states. This make Cobb able to calculate the "when" of the kicks to get back awake in real life.
x = ½ g t² that's about 125 meters, which is even rather high for an average bridge... So either Arthur was really quick, or the ratio was simply underestimated, maybe in the upper levels the sedative was even stronger. Or the Adrenaline due to the van pursuit had some influence...
Yusuf: Brain function in the dream will be about 20 times of normal. When you enter a dream within that dream, the effect is compounded.
The only calculation is multiplying by 20.
The flight lasts for 10 hours, so in the first dream you have (10 x 20 =) 200 hours. In the script, however, they quote one week which is only 168 hours, so we might need to assume a bit of time at the start of the flight to drug Fisher and get set up, and time at the end to clear the gear away.
In the second dream, we multiply again, giving us 20 weeks - again someone in the script didn't get their maths right because the script talks about six months, whereas 20 weeks is only about 5 months.
In the third dream, six months multiplied by 20 is indeed 10 years.
I just came up with an equation. I might be wrong, but in the movie, it is said that 5 minutes is equal to an hour. This means for every 1 minute in the real world is 12 minutes in the dream. So you take x, being the time in the real world, and multiply it by 12. This will get you a so-so amount of hours. You then divide this by 24 to come up with days. So 10 (hours) * 60 minutes is 600 minutes. So (600 * 12) ÷ 24 would come to 5 days. That is nearly a week. My formula is 12x ÷ 24.
Also, if you just wanted to know how long you would have to sleep to get a certain number of days, you set that formula equal to how many days in the dream you want. Ex. You might want to spend a year in a dream. 12x ÷ 24 = 365. This is roughly 730 hours, which is about 31 days being asleep in the real world. Maybe I'm right, maybe I'm wrong... You guys decide.
