touching on the carbon cycle and the long ago

Canto: Okay, before we go on about this, Jass you said that plants emit carbon dioxide in huge amounts by respiration, and then absorb huge amounts by photosynthesis. This idea of being big emitters and big absorbers at the same time is hard to make sense of. Could you explain that a bit more?
Jacinta: Let me briefly explain the carbon cycle. There are two main sources of carbon in our atmosphere, carbon dioxide and methane. Think of the atmosphere, above us, as at the top of this cycle. At the bottom of the cycle, far below us, the earth's crust and mantle contain carbon which is forced upwards and outwards by volcanic and geothermal activity. The other parts of the cycle are the terrestrial biosphere [our territory - though not owned by us, as we share it with other terrestrial animals and plants], the oceans, and underground sediments [in which are found the fossil fuel reservoirs we're so keen on]. Now the terrestrial biosphere and the oceans in particular can be sinks or sources of carbon dioxide, depending on the balance between absorption and emissions. Because it's a bit like profits and losses, climatologists call this the carbon budget [whether of the oceans, or a particular ocean or region, whatever]. And it's always changing...
Canto: Mmm, and some areas, like rainforests, are really big carbon sinks, right? So if all the land was covered in rainforest, would that mean that the amount of atmospheric carbon would be right down? It would all be somehow fixed in the plants and in the soil?
Jacinta: No, I'm not sure about this, but with lots of rainforest, and that means thick vegetation, lots of plants and lots of animal and insects species thriving on them, you'd have lots of respiration, and lots of rotting, because lots of life also means lots of death and decay. In fact, during the early Eocene epoch there was a burst of warming, probably initiated by releases of methane [a much more potent greenhouse gas] into the atmosphere. I won't go into the reasons for that release here, but there was certainly more carbon dioxide in the atmosphere then than there is now. The Eocene became so warm and wet [the ice caps had melted, inundating much of the land, and water was evaporating from the oceans - water vapour is also a greenhouse gas] that vegetation was springing up everywhere - tropical palms in Alaska and Siberia, for example.
Canto: My god! How did they save the planet?
Jacinta: Well, the planet was going along just fine, which doesn't mean we should be sanguine about the current situation. The Eocene saw an absolute burgeoning of life, as you might imagine, though the short sharp warming burst, which lasted only 100,000 years or so [that's only one two hundredth of the whole epoch] caused a mass of extinctions. And if it wasn't the period of the birth of primates, it was the period of their greatest development and success.
Canto: Wow, this long-term view really puts things in perspective. When exactly was the Eocene epoch?
Jacinta: I'll tell you next time. It's worth reflecting on global climate history and the evolution of species. It's a complex but compelling subject.