The non-certificated pilot of the amateur-built amphibious SeaRey departed a hard-surfaced runway for a flight to, and landing on, a lake approximately 10 miles away. According to the pilot, about 10 minutes into the flight, he cycled the landing gear to the retracted position. He then observed that the wing flap position differed from that displayed on the cockpit indicator. While on the downwind leg of the traffic pattern for landing, he deployed the flaps to an estimated position of 10 degrees, and on the base leg, he attempted to position them to the landing setting of 20 degrees. When the airplane touched down on the lake, it stopped abruptly, and partially submerged. The impact resulted in a serious injury to the pilot, and substantial damage to the airplane. According to the pilot, he did not realize that the landing gear was extended for the water landing, and he did not select or command the extended position. Post accident information provided by a Federal Aviation Administration inspector revealed that the landing gear was in the extended and locked position, and the landing gear controls were in the corresponding position. According to the designer of the airplane, two separate controls must both be activated to extend or retract the landing gear, no single action can cause the landing gear to extend, and the gear cannot free-fall to the extended and locked position.