Has anyone ever seen a bicycle with a crank that did not go completely from right to left - instead each pedal was connected by a gear to a crank behind the seatpost?

Kind of hard to tell exactly what you are asking. Do you mean the bottom bracket spindle does not go through from one crank-arm to the other, and both cranks are connected to gears on a shaft to keep them rotating together? I have never seen anything like that.

There are cranks where each arm is independant, if you stop moving your left leg, the right can still pedal. Its a training tool for better spin.
There are cranks with a built-in step-down transmission to engage a lower gear. The cranks can spin faster than the chainwheel.
There are gearboxes that lie between the cranks and the chainwheel (G-BOXX), these are usually based on Rohloff style gear mechanisms.
Adding cogs and other bits adds weight, complexity and reduces efficiency so these are strictly niche products.

That makes no sense. If you decouple the crank arms, you screw up the mechanical action needed to actuate the drive train. Training wheels are often just a bit off the ground to train balance: experienced cyclists can ride in a straight line without the wheels ever hitting the ground; but they prevent you from learning to lean in a turn or curve, or really to steer properly at all. Training cranks? I can't imagine the usefulness, since (unless you're clipped in) your resting foot follows anyway, and breaking this link removes mechanical synchronization that is critical to learn.

You can't ride a bike by flailing your legs all over the place.

And since when has people let that get in the way of dreams and ideas?

pedalling with only one leg at a time is a fairly common training tip to improve technique as it absolutely forces you to deal with the upstroke as well.

Exactly. W/o the mechanical link you have to coordinate your movements instead.

Sure you can, look at the Alenax crank. And they're not the first. I believe similar setups have been invenvted and reinvented at least 3-4 times.

I like clipless pedals for upstroke dealing. It trains other muscles, and makes me more efficient. If my technique is wrong, I feel resistance around TDC and BDC, which is fatiguing; eliminating this automatically adds twice as much power (the resistance is caused directly by my own power input, so that power both ceases to be resistance AND becomes extra input power), which is all kinds of awesome.

Of course, for that, you have to be trying. I guess this is why bicycle rollers exist; though I also do this to get up semi-challenging hills. Maybe I should get rollers for testing the shifting systems and other stuff.

Or maybe you mean a lever-drive crank? This was a really old idea:



Here's another "de-coupled" crank - some videos on the site too:
https://www.powercranks.com/index.html

How do PowerCranks work?

PowerCranks are a patented training device that integrates a one-way clutch in each crank-arm. Each crank-arm will drive the chain but not each other. Imagine doing one-legged drills all the time, with each leg working independently from the other.

You do understand that you don't get any pulling force on the cranks. What you are doing on the up stroke is unloading that pedal.
That was proven years ago when "Bicycling" was a decent magazine and tested the idea with strain guages in the pedals.

Yeah, I do realize that. That's why I've developed telekinesis by occasionally toying around and lifting with my legs, but intentionally supplying no down force, climbing up hills entirely with my mind while not-really-pulling on my pedals. (what? I was bored.)

I think this was what the OP was talking about.

Wow! Thanks for the input. I am looking at the crank on my ebike. It is in the way of a place that would be an ideal candidate for a battery - low cog, protected from the elements, and not useful for any other thing. It is a bit of an extreme action but...sometimes the best ideas come out of looking into extreme situations and thinking outside of the box.

Ja think?