Was Titanic's captain's decision correct? I just saw a documentary on Titanic. Someone in that documentary told Captain Smith 

"Shall we close the water tight doors, sir?"

and the Captain replied

"No, let it be open. Let the water be distributed uniformly throughout
  ship, so that we could lower the life boats."

Note: The quotes are not exact but very near to exact.

My Question
If and if, the watertight doors were shut, was there a chance of Titanic to escape from its tragic fate? 
And what exactly is a water tight container?
I presume that this is related to physics :)
 A: You asked two questions; I am going to give a very long answer. But the TL;DR is:
As posed in the title: "Was Titanic's captain's decision correct?" - the answer is "probably yes"
As posed lower down: Was there a chance of Titanic to escape from its tragic fate?:- the answer is "once they had hit the iceberg the way they did, no". 
The Titanic was considered "unsinkable" because any four of the sixteen compartments could be flooded and she would still float. These compartments (see picture below) were basically vertical "walls" throughout the ship. If the region between any two walls flooded, the water could not flow to the other compartments (when the flood doors were closed). Think of it as 16 smaller boats welded together and you get the idea.
However, when you look at the diagram you will see that these "walls" didn't reach all the way to the top. The ship's designer was on board for the maiden voyage, and he told the captain that she would not survive - losing more than 1/4 of the buoyancy was just too much, and as the ship started to list water would start to flow over the watertight barriers, filling compartment 6, 7, ... So closing the doors would not have helped. They key was to get passengers off the boat - at which they did a terrible job (not only did they not have enough life boats, but the ones they had were not all filled because there had been really no proper training - after all, she was "unsinkable").
If they had not tried to avoid the iceberg, but had instead hit it head-on, then they would have destroyed the front compartment (maybe even two); but they could have closed the watertight doors, and the ship would have survived. The bottles on the shelf in the first class bar might not have because the impact would have thrown everything and everyone around quite badly.
For more details see this which is also source of this image:

The tragedy was that by attempting to avoid the collision they scraped the iceberg (most of which was underwater - there's the physics bit) and it cut open five consecutive compartments (actually - the force of the collision popped the rivets). This led to a lack of buoyancy which caused the ship to tilt - and the flooding water ended up above the level of the watertight compartments (which didn't go all the way to the top) so other compartments could flood.
It is probably true that leaving the watertight doors between compartments open slowed the process of tilting. Once the ship reached a certain angle, stresses became too large (bending force from the front trying to sink and the back trying to float). It is believed that the boilers (remember this was a huge steam ship) broke loose and "fell" through the length of the ship, punching a hole as they picked up speed. The hull may also have snapped in half as the bending stresses were far greater than she was designed to withstand. At this point, the electricity generators failed, the hole in the hull became massively bigger, and the whole thing was over in seconds.
Source: My recollection from reading "A Night to Remember"
I just realized I am writing this on the 102nd anniversary of the sinking... That may be why you just saw the documentary.
UPDATE
The question "what if they had not tried to steer away" was still lingering in the back of my mind. Here is what I know:


*

*During sea trials they did an "emergency stop": from full power ahead (21 knots) to full power astern, it took 195 seconds to come to a stop; in that time they covered 850 yards

*It took the officer in command of the bridge 37 seconds to react to the "iceberg ahead" warning: he shut off propulsion and put the helm hard to port. Because of the size of the rudder, Titanic had (steam powered) power steering.

*When he responded, the distance remaining was estimated at 900 feet, and the velocity was about 22 knots: close to the maximum velocity (which was 24 knots). Remember they were going for the Atlantic speed record...


So now we can do some math. 
First question: 
What kind of deceleration could they achieve with their engines hard astern?
Given $v=10.8m/s$ and $t=195s$, deceleration was $v/t=0.055 m/s^2$
Second question: 
If they had thrown the engines full astern with 900 feet to go, how fast would they have been going on impact?
With $d=274m$, $v_{init}=10.8m/s$ and $a=-0.055m/s^2$, $v_{impact}=9.3m/s$
Note - that is the speed you would go if you dropped approximately 4.4 m, or jumped from the second storey of a building. Ouch.
Third question: 
If they had reacted 37 seconds earlier, what would the answer be?
We subtract $at$ from the original answer and get $9.3 - 0.055*37 = 7.2m/s$. This corresponds to a drop from 2.6 m - a bit more than half the height from the previous answer.
Final question: 
How much would the ship have crumpled with that kind of impact?
That's a tough one. The hull was made of 1 to 1.5 inch thick steel plates that were riveted together (and in fact it's the rivets popping that created the fatal hole in the hull). With a mass of over 53,000 tons (depends who you ask - they were going through 600 tons of coal per day so that number changed very quickly; but we're doing physics here so $5.3x10^7 kg$ is close enough) it had a momentum of 
$$9.3 * 5.3 * 10^7 = 4.9*10^{10}Nm$$
<briefly switching to imperial units. I'll be right back>
Now the yield strength of steel is "around 40,000 psi", and let's assume that only the part of the ship below the waterline is involved in the collision. With a draft of 34 feet, and estimating the bow section to be 32 feet wide, we have approximately 100 linear feet of steel, or 1200 linear inches of steel. But these plates will have had considerable reinforcement, and bending that much steel would require a lot of force. But then Titanic had a lot of momentum...
<back to SI units>
Consulting http://dspace.mit.edu/bitstream/handle/1721.1/77770/47046428.pdf , it is clear that the full calculation is quite complex - but photos in that thesis give us the general idea that the distortion might be "of the order of" 1/3 the height of the ship. That would be around 10m. If she did in fact come to a complete stop in 10 m, this would have required an acceleration of about 0.7g . So yes, there would have been casualties, especially among the fine china. Losing the front 10 m would have destroyed one compartment - but only one.
I suspect that a lot of ice would have been broken too - after all, the yield strength of ice is quite low compared to steel (at least 15x, although the values vary tremendously). But then the hull was "hollow" so as soon as the bow penetrated more than a couple of feet, the ice would win.
Would the iceberg have moved? With 9/10 of its volume below the surface, and with the iceber height comparable to the height of the ship, I am going to venture "not really" without attempting to do the detailed calculation.
Finally the question of the third propeller:
The third propeller was mounted in line with the rudder. 

In such a configuration, when the propeller is thrusting forward, the water flow past the rudder and enhances the action of the rudder. When you "throw the engine in neutral" as was done just before the collision, the rudder is quite a bit less effective, and the ship will turn more slowly. In the extreme case, if you could reverse the thrust on the central propeller you would have to turn the wheel the other way to get the same turning effect.
Large modern vessels have a "bow thruster" - this is a turbine that is mounted transversely near the bow, and that allows lateral force to be applied regardless of the speed of the vessel. This allows for far greater maneuverability on these long ships - much more than "one forward one reverse" could ever do (just think about the difference in the arm of the force).
Another interesting reference:
physics world
I do have one lingering question in my own mind: when a sailing boat is slightly damaged in a collision, one will sometimes "keel haul" a sail - essentially pulling it underneath the hull so that it covers the hole and slows the rate at which water enters. I wonder whether Titanic had enough rope and cloth (and maybe steel plates) on board that a clear-thinking engineer might have carried out a similar emergency repair on the water. After all, it wasn't really necessary to stop the water from entering: it just needed to be slowed down enough to give the pumps a fighting chance; that said, the initial rate of flooding was 12x greater than the capacity of the pumps - so any "patch" would have had to be really quite good...
And one more excellent reference (contains discussions of much of the above in a lot more depth, and probably by more qualified people) is http://www.encyclopedia-titanica.org/ . I hesitate to post it because I only just found it, and it doesn't always agree with my analysis... I may have to write another update after I have digested some of its contents.
