>> Enter mechanical computing. :)

There's nothing wrong with that. Some of the iconic first computers were 
mechanical. ;-) (And I don't just mean Babbage's Analytical Engine; go 
look up the Zuse Z1 computer.)

> Imagine how hard you'd have to push if you connected together a handful 
> of these blocks!

Well, that's just it. The entire assembly is passive, whereas normally 
logic gates have their output power derived from a source independent to 
the input. (Especially buffers - that's essentially their entire point!)

It's not particularly easy to see how you'd do this with reciprocating 
mechanical signals; if you were using continuous rotational motion, it 
would be clearer that amplification is possible. (Although it's still 
not obvious what the best way to achieve it is...)

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