This is another myth that falls into the "suspend the laws of physics" category. That hasn't happened yet in my kitchen, and if it has in yours then you can probably get on TV.
Seriously, to illustrate how ridiculous this idea is without getting into physics and formulas, think of it this way. If you put cold water on to boil, at some time before it boils the water will have become warm. Let's say it takes time "A" for the water to go from cold to warm. Then after some additional time it will boil - call the time it takes to go from warm to boiling "B". So, the time it takes the cold water to boil is "A + B" and the time it takes the warm water to boil is "B." If this myth were true then time "A + B" would be less than time "B" and there's just no way this could be no matter how many martinis you've had.
Apparently this myth has its origins in the fact that cold water heats faster than warm water. A pot of water at 40 degrees will reach 60 degrees faster than a pot of 70 degree water will reach 90 degrees, given the same heat source. This is because the rate of heat transfer is proportional to the temperature differential between the heat source and the item being heated. But the cooler water will always take longer to boil.
Note, however, that many people generally avoid using hot tap water for cooking because hot water may not be as clean from sitting in the water heater or from leaching substances from the pipes (a particular worry in houses with old plumbing)
