Ok matt. lots of questions.
cause factories make gears, right?
No. those are "manufacturing points" and each one can be turned into a hammer or shield.
how do those gears get divided up into hammers and shields? so shields can become hammers, right? is the reverse true?
Yes,I think you need to understand how the economy sliders work.
The production capacity slider lets you set what percentage of your TOTAL production you want to use.
Each slider under it is either for social production (hammers), military production (shields), or research (beakers).
These sliders allow you to set what percentage of your current production you want to use towards any of the different things (hammers, sheilds, and beakers).
So if you have a factory on a planet that can produce 8 mp (manufacturing points) a week and your production capacity slider is set to 100% while your military slider is set to 50%, the factory will only make 4 of those mp's a week.
If you move the prod. capacity slider to 50% and keep the military slider at 50%, that factory will only make 2 mp's a week. because you are making 50% of the 50% which is 25% of the total,

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when i hit the focus-on-shields, the planet makes a ship. where's that come from? is that money from hammers transfered over?
focus is so each planet can be individually somewhat managed. Your factory & Research facilities can be used to make sheilds if sacrifice some of what they are already making. And yes, the money is transfered over and spent on sheilds too.
so shields can become hammers, right? is the reverse true?
Sheilds and hammers don't actually exist they just display how much in each catagory you are producing. thought I'd point that out.
where can i see my civilization total hammers, shields, and beakers? (total potential and total actually used.)
Um..... There's a colony list in the civilization manager screen that shows you each planets production in each category, money spent/gained, morale level, what it's building, and everything, so maybe you could use that.
Hope this helps, because it took a long time to write...
-me