Originally Posted by iacas
7-2 forbids it.
One could easily ask you to show us the rule that permits playing two balls at one time.
There isn't one. The Rules of Golf explicitly allow "one ball" to be "in play" at any given moment except that you may have two balls (kind of) "in play" when you're playing a provisional. But the "kind of" I put in parentheses is important, there, because even then technically only one ball is "in play" - it's just that you've not been able to determine which one it is just yet.
They get pretty specific on topics. for example:
1-1/1 Two Balls in Play Simultaneously at Different Holes
Q. Two players on the 8th hole play their approach shots to the 8th green. They agree to tee off at the 9th hole and then putt out on the 8th green. This is to avoid having to walk back up a hill to the 9th tee and to save time. What is the ruling?
A. In match play, the players are disqualified under Rule 1-3 for excluding the operation of Rule 2-1 by failing to play the stipulated round.
In stroke play, the competitors are disqualified under Rule 3-2 for failing to hole out on the 8th hole before making a stroke from the 9th tee.
I would have thought this type of question has come up many times before. The rules and decisions seem to be almost exclusively geared towards competition play. While I personally wouldn't want a rule that allows a player to play 2 independent rounds at one time, even just for pupose of recording a handicap, it would be nice if they addressed it explicitly. For competions I would see it as a complete no-no, for an individual recording rounds for handicap purposes might only be hurting themselves.
P.S. Rule 3-3. Doubt as to Procedure does deal with completing a hole with 2 balls but does not cover the OP's question
In stroke play, if a competitor is doubtful of his rights or the correct procedure during the play of a hole, he may, without penalty, complete the hole with two balls.