Knowledge cannot be passed on via your DNA to our descendants (obviously), so any innate knowledge about the world found in our brains must have been found through natural evolution. But...
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That does not follow. Genome codes a complex developmental program composed of powerful interacting modules (proteins, microRNAs, ...) that in turn assembles the body including the brain.
However efficient the compression mechanism being used, and even taking into account the interaction with information that's external to our DNA, it remains that a pre-trained connectome would have a certain entropy, and that our DNA has limited entropic capacity.
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But not so limited that it doesn’t contain enough information to program the development of enormously complicated structures in the brain and other organs. Why would a “connectome” be different?
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The fact that DNA (with its limited capacity) can store generative programs for the body & brain is evidence that these systems are not very large in information terms, and that implies that the brain does not store much knowledge about the world, since that would be high-entropy
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1/ Great observations. The first caveat is everything though -- it can't be passed through DNA. With costly entity like a human, getting a single bit of information per death is not good enough. Complex animals transmit information by demonstration from parent to child.
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2/ Really complex animals transmit information through language from parent to child. More complex, through written language in mandatory schools. Exceptionally complex, through mass electronic communication.
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You cannot just talk about the information in the program, you have to also include the information in the called library functions. The functionality of a protein or microRNA is the result of billions of years of molecular evolution -- how many bits in those choices?
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You are talking about Shannon entropy measurably now and looks like you make same mistake assumptions like Maxwell daemon. DNA is an evolutionary sequence so it's entropy is always going up
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