I'd like to see a fresh explanation from the serious math heads on this one. I *think* it now depends on whether you're playing a version that has per-weapon firing as opposed to the old-school all-at-once blast.

As a rule of thumb for ship design purposes, it seems reasonable to me to think of an "off" defense as providing its square root in help against other forms of attack. But I'm pretty sure the math isn't that simple.

I think he was referring to a ship that had  defense of four in all three areas.   If the second is not true then its better to build a ship with x in one area and  nothing in the other area unless you can achieve greater than x^(1/2) i n that area.......maybe the game takes whichever is higher? however if I have 4 worth of armor and only one of shield,,,,if the armor provides limited protection from lasars why would it cease to do so just becuse there is a light shield tht provides less overall protection........?  on the other hand even though the armor provides slighlty more protection why would the shield have no effect..in this case the possible defense is reduced by a third if we ignore the shield so it is significant even though it is less.

(I'd like to note that its beyond me how the point defense as described in the game affects lasers at all......)

On more than one occasion, I've gifted weapon technology to AIs to encourage them down a certain path. Yes, they get better weapons than what they had, but they're weapons I already have the defenses for.

For the most part they do - but you have to give them weapons at least 2 or 3 steps ahead of what they already have. This works best as an early-game strategy - give someone Laser V when all they have is mass driver theory, and they will abondon mass drivers entirely.