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Technology Marches On: Mike invents computer-generated imagery, to the shock and surprise of the humans around him, who never imagined such a thing could be possible (he even gives himself a digital screen appearance as a human, and takes quite a while adjusting the CGI to achieve full realism). Meanwhile, in the real world, it takes a bank of supercomputers and a none-too-small team of professionals to achieve the same result, and they take a somewhat longer time. Of course, it can be argued that Mike, having hookups across Luna, as well as having access to a large chunk of everything humanity has ever written down, is both a bank of supercomputers and a team of professionals. And it helps that he can think far faster than a human.
It's specifically mentioned in the text that in order to fake one single video image in real-time, Mike had to co-opt virtually all of the spare computing capacity on Luna.
Manny protests that what Mike was attempting was impossible: this would require thousands, maybe millions of calculations per second. This is called a megahertz; the Intel 8086 was released a mere decade after the book and in a single chip represented virtually the entire processing power on Luna more than a century hence as Heinlein imagined it. To be fair, Moore's Law only was articulated in popular press a year before the book and the full impact of the transistor revolution had yet to be felt or even named as such.
This trope affects pretty much all of Heinlein's relatively near-future fiction, particularly computers and calculating devices of all kinds.
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