What is plotting? How does farming a plot work?
Edit: Why do people plot with SSDs? Is there a speed element to it?
Plotting: you fill your free space with bingo cards. You need 300-400GB of free temporary space and TBs of writes in that space. This uses a lot of compute and eats SSDs for breakfast.
Once you have filled your space (assuming you don't go out and buy more disks), you can stop plotting. This is where the claimed "greenness" of Chia comes into play: you eventually stop using compute resources. Of course, there are whales who are adding drives to their servers daily.
is this like pre-computing the values to a hash function against different inputs? Where is the write thrashing coming in? If you only need X hundred gigs, why do you write terabytes? Because you can't store intermediary values in RAM (since ram is expensive and small in comparison)?
I get how bitcoin style block-chains use hashing to secure the transaction chain, and the POW factors into hashing... how do responding to the challenges factor into a currency?
This happens during plotting (not farming). The plots are sorted, which is where the write thrashing happens. Once you've completely plotted a farm, it is never written to.
Everything else you said is basically spot-on.
Plotting is an compute- and IO-intensive process which eventually generates a ~100 GB block of data after a large number of read/write operations to that data. This is the part of the process that involves (and destroys) SSDs.
Farming is a slower process which is performed on those blocks of data, which involves occasional read operations on small sections of that data. The data blocks are typically transferred to slower bulk storage (like hard disks) for this.