Why are Moths attracted to Light?

Most of my research as lead me to this conclusion:  They are not.  Not strictly speaking anyway. 

There are several different thoughts on why they seem to be though.

The first theory (T1) is they get confused by lights.  It seems that nocturnal moths use light for navigation.  Before we lit up the night with light polls, porch lights, and all the other lights we felt compelled to use at night; moths are said to have used the moon for navigation.  Our lights are brighter if they approach it, therefore they use it to navigate by rather than the moon.

Another theory (T2) is the moths are confused by the light because they are trying to get to the darkest spot next to the light.  This is due to "Mach Bands" (in the image below) where a color difference looks strongest at the point of highest contrast.  Meaning that the world looks darkest next to the light.  They are seeking the darkness and the bright light throws them off.  One scientist, Henry Hsiao, observed moths veering away from the light once they got close to it as they rarely actually bump into the light.

For some species of moth we have a third theory (T3) is moths just respond to different wavelengths (or color) of light differently.  This is why you are more likely to see moths around a white light than a yellow light.  One possible explanation of this is their food source.  They often eat the nectar from flowers, similar to butterflies.  Some flowers reflect ultraviolet light.  Ultraviolet light (UV) is a light that we cannot see as it is boarding the visible range.  Some insects like moths and bees can see in the UV range.  This means it is possible that they are approaching the light seeking out food rather than the light itself.

It seems that whatever the cause once they get to the light they are confused.  The reason they are seen sleeping near the light has two theories.
One: They often sleep as a reflex to the brightness mimicking the sun.
Two:  They merely tire themselves out flying around the light so they go to sleep on a near by surface.

A final note on moths: Not all moths are nocturnal.

References
T1 Links:
Penn State Research
Wikipedia
T2 Links:
io9
T3 Links:
How Stuff Works
Penn State Research