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I've not heard of Tegmark before. It sounds like if it's true, then it's a great answer to the fine-tuning question. Is it all speculation, or is this a hypothesis with some evidence to it?
See Mathematical universe hypothesis on Wikipedia.
The multiple universes proposed by Tegmark are causally disconnected; nothing that happens in one of them can in principle influence what happens in the others. So we cannot do experiments with other universes. (This is different from quantum physics, where the parallel branches start connected, and for a short time we can interact with them.)
We could try to provide an indirect evidence. If we can make the theory more specific -- what exactly counts as a possible universe, and what measure do the universes ... (read more)