How to speed up the game

There are three main ways to get coal. The first two you'll get are the Coal Furnace and Deep Mining upgrades at the workshop. These will let you get small amounts of coal for each mine (0.003 per tick, 0.015 per second) and running smelter (base .005 per tick, .025 per second).

But, by far the best source of coal, is unlocking the Geology technology, and assigning Kittens to the Geologist job. Geologists are worth .015 coal per tick , equivalent to three smelters, or five mines. And kittens can improve at their jobs; a Master Geologist is earning about 0.026 coal per tick, which is over 0.1 coal per second each.

There are also quarries, which each give a +35% boost to mineral production, as well as another 0.015 coal per tick. They won't improve on their own the way Kittens improve their skills, but they still help a lot.

There are also several upgrades at the workshop related to coal which can help. Pyrolysis will increase coal gains by 20% from all sources. The Geodesy will increase Geologists' base coal per tick to 0.0225, making even a Dabbling Geologist worth four and a half Deep Mining mines. It also allows Geologists to produce a small amount of gold while they work.

I don't believe there is any other change, the text for the upgrade is slightly misleading but the code is clear. I certainly observed no change from that upgrade myself, besides a significant increase in maximum Science. Most notably, my science/second output did not change.

There is a very late game upgrade that gives a 100% auto-observe chance, though - although more Observatories still help cause the events, they're now background events, they just happen with no log entry and are always observed.