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> If it can autonomously write software and author CAD files then it can autonomously design robots.

It can't because the LLM can't test its own design. Unlike with code, the LLM can't incrementally crawl its way to a solution guided by unit tests and error messages. In the real world, there are material costs for trial and error, and there is no CLI that allows every aspect of the universe to be directly manipulated with perfect precision.

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You don't need perfect precision, just a sufficiently high fidelity simulation. For example hypersonic weapon design being carried out computationally was the historical reason (pre AI) to restrict export of certain electronics to China.

OpenAI demoed training a model for a robotic hand using this approach years ago.