Herschel's Mysterious Doodle

As discussed on Numberphile, here is John Herschel's doodle, sent to his friend Charles Babbage.

Herschel said: "Interpret this hieroglyphic, it contains a great discovery."

The figure at the centre is described as: "Dionysius the God of Functions, alias the genius of numerical magnitude."

Just silliness between two friends, or something more?

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