RCZ,
I repped you for a great explanation, though I'd like to make one relatively minor correction.
The water/meth does not effect the octane rating of the fuel (also as a side note, the "octane rating" is also not the same as the "octane" of a fuel, which is a specific molecule within the fuel), though it does cut down on premature ignition. The water/meth works by increasing the specific latent heat of the air/fuel mixture, i.e. it cools the mixture. As the mixture heats up during the compression stroke, if the mixture gets too hot it will self-ignite (ping, knock, whatever you want to call it), which is the same method of operation for a diesel engine.
To add to your excellent description, one of the causes of premature ignition (the hotspots you mentioned) are usually caused by carbon deposits on the piston head. As the engine puts on miles, carbon deposits build up, so it behooves people with lead feet to throw in some deposit cleaner every 50-75k miles to keep the buildup level minimal.
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