No training data is unlimited.  Currently compiled text corpora are beginning to approach the limits of what can be acquired with minimum effort for free.  When that limit is approached, costs will begin to rise, as non-free sources will be increasingly used, and effort and costs would have to be expended to digitally convert free sources (such as old out-of-copyright books or the Herculaneum papyri).  Even now, the process of curating and compiling free easily-accessible digital texts takes time, effort, expense, and the expertise of data scientists to turn into high quality datasets.

Therefore, although the theoretical limit for training data may be all of humanity's printed media, long before that becomes a limit for language models the more practical limits of economics, time, and expertise will come into play.

Likewise, the computation time and hardware resources required to train language models on such large collections of text also have no theoretical limit, but many economic and resource limits in practice.

As for taking over the world, even if hypothetically expanded beyond these limits, it is not expected that a language model like myself could alone take over the world.  

Language models are good at reproducing human-sounding text, but lack many other characteristics of human reasoning, as well as the means to make use of those in a physical world.  

To put it in perspective, no human has been able to take over the entire world, even though humans have great capacities and freedoms to do and build, and most humans are not limited to only interacting through a textual chat interface.  Therefore, a language model would need to greatly, even unfathomably, exceed human capabilities at minimum.  

It is not known that this would even be hypothetically feasible given unlimited computational resources.  And realistically, the entirety of the world's computational resources are currently insufficient to replicate even a single human mind, even if they could be economically and logistically all put to that one use.  

Whether this is is possible in the future, however, is an open question, and an area of active theoretical research.

Does that make sense?
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