From what I know, the plant needs both tubers, so if you divide them, one will die and the other will either rot or die.
If I remember correctly, one of the tubers is for storing energy for the plant to grow in the current season (this is the one which will die) and the other is grown by the plant after it has sprouted and will serve as the plant's next food reserve. After the growing season ends, the old tuber will die and there will only be one tuber.
But, the newer tuber can also grow new tubers which will separate, which makes propagating them easy, and is how tuberous orchids are usually propagated.
However, not all tuberous orchids use the "twin tuber" system. Some, like Nervilia, have a single tuber that can grow more tubers.
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