That's not what Tegmark says. Tegmark says the universe is embedded in mathematics. That I believe is another thing entirely, and one that's as false as it is provocative. Tegmark says the universe literally is a mathematical structure. But that cannot be the case, and for the exact reasons you give. Yes. Physical. But mathematical structures are not physical. They are abstract. Things like sets, groups, rings, fields, topological spaces, measure spaces and so forth, are highly abstract ideas that you have to learn from specialized teachers and textooks. There's nothing obvious about them and nothing physical. They do have applications to physical science, but their nature is that of abstract entities. Mathematical structures are not physical. And therefore the universe, being physical, can not possibly be a mathematical structure. Tegmark is thus refuted. Yet millions of serious-minded and educated people believe him. It's one thing to read his MUH because he's "interesting even if he's wrong." That's how I'm planning to approach the project. I know I'm going to hate every word. But reading his paper will make me smarter. But to actually believe that the world literally is a mathematical structure. I don't see how anyone can take that position. Math is part of the world. But the world itself is NOT a part of math. For being such a smart guy, Tegmark is mixing up the abstract with the physical. Perhaps that's his intention. Right. We're in complete agreement that Tegmark's MUH is wrong. Interesting, but wrong.