Wednesday, August 4, 2010

Inception movie review

Rating: 60/100

TLDR: Nice but too many inconsistencies in the script spoil the fun.

Nice idea (though not original, there have been other pieces with main plot revolving around people sharing dream), and fast paced. The movie keeps you engaged throughout. It also succeeds in making you talk about it while you are leaving the hall, but mostly because of questions that were left open.

The script has many holes however, which result in many inconsistencies throughout the movie -
1. Why does the effect of gravity not flow through levels of dreams?
2. How come the infinite staircase sometimes suddenly become disconnected? (This was probably thrown in just to show how a staircase may look infinite from a certain angle in real world - but is completely inconsistent with the storyline.)
3. Fine, they have invented a machine through which you can connect people together in a dream. How come the dreamed 'dream sharing machine' works, when you are already in a dream?
4. How does the 'limbo' retain what was built there before, may be by a different person?? (Cobb's creations are there in dream initiated by someone else.)
5. Why does the top fall when the old man spins it when the movie begins?
6. Why couldn't Cobb's wife simply spin her top to test if it is real life or a dream?
7. How did Cobb wake up from limbo?
8. Why does Arthur not wake up by the Van's freefall (the 'kick') but instead simply start experiencing zero gravity in the dream?

The movie also seems to throw a lot of ideas just for the effect, most of which are irrelevant or have no consequence to the story. Eg. Penrose staircase, and bending of the road in the constructed dream world by the student.

I liked a few of them though - for example the puzzle of creating a maze in two minutes that cannot be solved in one minute, or the idea that someone thinks the real life is a dream and wants to wake up from it.

Lots of room for improvement. At most this is comparable to Matrix 2, but not anywhere near as perfect as Matrix 1. With the concept, I feel they could have done a better job if they thought it through.

Leo's role was pretty much the same as Shutter Island. For others too, there was hardly any scope of showing acting in the movie, as it was mostly a chase.

I was actually debating whether to rate it 50% or 60%. I decided with 60% since it atleast kept me engaged, and the acting did not completely suck.

The movie was essentially a bunch of things thrown together to confuse people. This serves two purposes - people talk about it, and also people may watch it again in case they missed something, in the hope of some getting answers (which are not there).

Chris Nolan's imagination falls plain short of the idea of a dreamworld. If I were to implement it, it would not be lucid and perfect world with guns, explosions and zero gravity etc - it should be more like something that makes you feel you are dreaming. May be with a lot of computer generated images, imaginative creatures.

The reason it is being compared to Matrix is that clearly the intention was to copy Matrix. And it manages to fail in all levels in doing so.

Monday, July 5, 2010

Do you have a son born in a Tuesday?

Here's a very nice probability puzzler -

For a scientific experiment, I walk upto a random person in a mall. I ask, "Do you have exactly two children, and one of them is a boy who was born in Tuesday?" The person answers "Yes". Assuming that he is telling the truth, what is the chance that he has two boys?

Assume all necessary clauses, eg. I don’t know the person, I can’t see his children, etc. Also note that exactly two "one of them" here means "atleast one of them", just as in normal English.

In so many ways the solution conflicts with intuition, that I can’t help feeling that this question has been designed to show that our intuitive ability fails when it comes to conditional probabilities.

If there was nothing mentioned about Tuesday

The first thought that comes to mind is that if one is a boy, surely we must find the probability of the remaining one being a boy - so the answer must be half. Well that’s simply not true, even forgetting the ‘Tuesday’ condition, the chance of both being boys is 1/3. It’s because we have 3 equally likely cases given there is atleast 1 boy –


Hence P(2 boys | atleast 1 boy) = 1/3, simply by counting cases.
Note however, this would change, and intuition would be right, and the probability will be half, if the question was framed in slightly different manner – “Do you have exactly two children? If so, if you choose any one of them at random, is he a boy?”

The original problem with one boy on Tuesday

We have to find P(both boys | atleast one boy on Tuesday).

Again intuition says, being born on Tuesday doesn’t change the question – atleast one is still a boy, and given that, the chance of both being boys is still 1/3. Wrong again – Tuesday is very relevant to the problem in an interesting way. It makes the boy being asked about special, and almost identifies him. Solution is given below .

By enumerating all equally likely cases

There are in total 196 cases, which are all equally likely. The table below lists them all.

The answer can be simply counted off the table, it’s 13/27.

Using conditional probability

The solution above is fine, but the approach breaks down if the problem was complicated – by increasing the number of children to 3 or 4. We then wouldn’t have the luxury to visualize the sample space (i.e. all possible outcomes) easily. Fortunately, another way of solving it which does not depend on a table exists, which is in nature and so will still carry forward in more complicated cases with ease. For the mathematically inclined, the solution using laws of conditional probability is given below.

We will use some abbreviations to remove the clutter -

BT = Boy born on Tuesday
BnT = Boy not born on Tuesday
G = Girl

So for example, (BT,BnT) means first child is a boy born on Tuesday, second is a boy not born on Tuesday.

P(both are boys, and atleast one boy on Tuesday) = P(BnT,BT) + P(BT,BnT) + P(BT,BT) = 1/2*6/7*1/2*1/7 + 1/2*1/7*1/2*6/7 + 1/2*1/7*1/2*1/7 = 13/196

P(atleast one boy on Tuesday) = P(BnT,BT) + P(BT,BnT) + P(BT,BT) + P(BT,G) + P(G,BT) = 1/2*6/7*1/2*1/7 + 1/2*1/7*1/2*6/7 + 1/2*1/7*1/2*1/7 + 1/2*1/7*1/2 + 1/2*1/2*1/7 = 27/196

So P(both are boys | atleast one boy on Tuesday) = P(both are boys and atleast one boy on Tuesday) / P(atleast one boy on Tuesday) = 13/27.

General case

Here the added condition was of being born in Tuesday. It can be seen that if we replace this with any other random condition (e.g. “Is his name Jacob?”), having probability p, the answer will turn out to be (2-p)/(4-p). This can be worked out easily if you replace all 1/7 with p, and all 6/7 with (1-p) in the solution given above.

Wikipedia has some more on this: