Road cycling and fly fishing have many things in common, other than a preponderance of carbon fiber. For one, both are viewed as "elitist" in some quarters, with lots of unwritten rules and specialized knowledge needed, and both are thought to require thousands of dollars worth of specialized equipment to enjoy properly (I know these things are not necessarily true of either fly fishing or road biking, but I'm dealing in broad generalizations here).
On the other hand, if you want a light, fast road bike, have a tight budget, and are willing to accept some limitations and extra effort, especially uphill, you can build yourself a fixed-gear bicycle, with a radically simplified drivetrain. With a single gear choice and no coasting allowed, fixed gear riding can be a lot of fun, and make for a super-efficient bike under ideal conditions, but when the conditions are less ideal (ie, hills) it can be a lot more work than a geared road bike.
It turns out fly fishing has a roughly analogous discipline in the Japanse style of fishing known as Tenkara. Tenkara uses a super-light, collapsible rod with no reel and no line guides. The fly line is tied directly to the tip of the rod and the length of line you tie on is the length of line you get. Like fixed-gear bikes, your equipment options are limited, but like the bike, you can still get where you're going and have a surprising amount of fun doing it.
I came across Tenkara while looking for an inexpense, lightweight fishing setup to bring with me on bicycle rides, and the stripped-down approach turned out to be just the thing I was looking for. The rods themselves are long, usually between 11 and 13 feet, but collapse down to about 20 inches long. The line is about the same length as the rod, to which is added a few feet of tippet (thinner line, which is all-but-invisible in the water) and a simple fly pattern of string and feather tied to a hook, which doesn't usually resemble any specific prey animal, but has a generally "buggy" look and motion underwater. It's cast just like a western fly line, with the long, flexible rod and heavier line being used to propel the tiny fly towards the target area. The fly is designed to sink under the water's surface, and is twitched up and down to attract the fish's attention.
See, the funny thing about me is, in spite of the fact that I fix bicycles for a living, and build my own musical instruments, and generally like to tinker, I'm not really a "Gear Guy." When I'm off on a ride, or on stage, or at the riverside, I really have no interest in fiddling around with my equipment. I don't want to adjust things, or swap out parts, or retune or whatever. If the choice is between "bring more complicated gear" and "work a bit harder," I'll generally opt for the slightly more challenging work. So the Tenkara approach, with its simple rod, short reach and traditional choice of only one or two fly patterns seemed to suit me well.
Does it catch fish? Yes it does. I've had more luck in my local water with the Tenkara rod and some hand-tied flies than I've had in several years fishing with a spinning rod and store-bought lures. I can't cast as far as I could with a more conventional setup, but I find myself being able to fish with more precision than with other gear. Most importantly, it's fun. I can grab my rod and a tiny bagful of gear (some flies, a line, extra tipped, a tool to cut line and forceps for unhooking fish) and go with no fuss and no preparation. Because the rod itself collapses so small, it can travel in a backpack or messenger bag just in case I happen to have time to kill while I'm out and about, making me more likely to explore new fishing spots.
So far, however, there is one major difference between Tenkara and fixed-gear cycling: you don't see urban fishermen trying to do it in skinny jeans.