"I get my best ideas in the bath tub."
Recognized as the greatest mathematician of antiquity, Archimedes is perhaps best remembered today for the anecdote about his discovery of how to measure the volume of an irregularly shaped object. Challenged with determining whether a crown was made of solid gold or contained some silver, he knew he could not melt down the headpiece to measure its density, for that would destroy it.
Taking a break from this work challenge, Archimedes lowered himself into his bathtub, and in doing so he observed that the water level rose -- and he realized that this principle could provide a way to measure the volume of the crown. As it was submerged in a bath, an amount of water equal to the volume of the object was displaced. Dividing the weight of the crown by the weight of the water displaced, Archimedes arrived at the density of the crown; a lower density would mean other materials had been added to the gold.
Thrilled by his discovery, the scientist cried "Eureka" (I have found it!), leapt from his bath and, excited to immediately share the news, apparently ran through the streets naked. (It's unlikely, however, that people hearing Archimede's one-word exclamation thought he had just invented the first vacuum cleaner...)
Often the stimulating power of a bath or shower can allow us to make our own discoveries on topics other than the water itself.
The fact that many people discover great ideas while in the shower is partly biological: warm water on the scalp and through the pores increases blood flow, which gets the brain churning. The mere sound of the water, producing a constant repetitive white noise (or wet noise) has a hypnotic and relaxing effect, too.
Merely stepping away from a work environment to the privacy of a shower stall or tub can release anxieties and clear one's mind.
Perhaps most significantly, a morning shower is the culmination of a period when the brain has switched to subconcious activity during sleep. It's at night that our minds have a chance to mull over the challenges of the previous day. Turning off the conscious brain, freer thinking rises to the surface, and fully escapes during a reinvigorating shower.
To capture the "Eureka" moment, some thinkers, attuned to the moments when their best ideas come to them, might even have a wax pencil ready to immediately write down their brainstorms right there on the tiles of the shower wall.