I love the example here because of the flashlight :P
If we start at 3 lumens and multiply times 4 ..to get a percieved doubling of light.
We start at ..3 ...12...48...200...800.../ next doubling doesn't happen until 3200 lumens ..after 1000 lumens we have real heat and battery issues .
So when someone says either 800 or 1000 lumens I just shrug because it's almost impossible to see the difference between the two ..If output gains aren't relating to runtime it's pretty meaningless ...One reason I assume high end manufacturers don't normally overdrive their lights .Although I think even they realize that people love to be lied to and that Big numbers sell .
Unless I'm missing something the inverse square law does not apply here. It applies to calculating the "throw" of a flashlight, which is related to the light measured at different distances; but I don't think it can be used in regards to how the eye perceives light.
The cd is for .25 lumens shining on an object at a distance. Just a little more throw and you might put. .5 lumens on the object, so it looks like it throws twice as well. I’m not explaining it well but maybe you get the idea.