So the best solution seems to be cable lighting. Low-voltage cable lighting is originally a halogen application where two wires are strung across a space, and bulbs are hung between the two wires. Because the voltage is low, bare metal can connect the bulb to the wires allowing for minimalist design. Here's a site from the UK, and here's one from the US that sell such systems. The US site has a couple of LED systems, and the UK site says that LED bulbs can be fitted instead of halogens, but from email correspondence with them, it sounds like they have had some problems installing these, and don't recommend using a dimmer.

There is a potential technical problem with low-voltage cables though, and another fundamental difference between LEDs and incandenscents that takes a bit of work to get the head around. The basic problem seems to be that LEDs are semiconductors. This puts them in the realm of electronics, and beyond Ohm's law and the traditional domain of electricians.

Wire and light bulbs conduct electricity, and conduct more current the higher the voltage is, following Ohm's law: V = IR, where V is voltage, I is current and R is the resistance. If we use the analogy of water as electricity, which sometimes works, we can visualise current and voltage by thinking about a waterfall. The height of the waterfall represents the voltage; the width the current. The power is a combination of the height and width, so you could have a very low, wide waterfall or a very high, very thin waterfall and both would have the same power. In mathematical terms, this is P = VI, where P is power, V is voltage and I is current. In an IV curve, which is a straight line when we're following Ohm's law, the power is the area underneath. Incandescent bulbs basically work as resistors, so the more voltage there is, the more current goes through. Usually, power supplies have fixed voltage, and incandescent lights will draw the appropriate current depending on the voltage. Give 240 volts to a 60 watt bulb and it will draw 0.25 Amps. Divide the voltage by the current and it must have a resistance of 960 ohms. Put 120 volts through this and you'll get half the current and a quarter of the power.

Semiconductors sometimes conduct and sometimes don't. Diodes will conduct one way but not the other, transistors will conduct from one place to another if you apply a voltage in the middle. If we use the analogy of water as electricity again semiconductors are like taps or valves.

The other thing we'd like in our system is a dimmer. For conventional lights, dimmers work by changing the voltage. Because the lights follow Ohm's law, more voltage means more current, and they will give out more power. Because LEDs don't follow Ohm's law, changing the voltage is going to result in no light at all for a long time, then variable light if you tune it very finely, and then the LED will start melting as there is too much voltage and too much power. Slight differences between bulbs could mean that the voltage at which one LED has not come on yet is the same as the voltage at which another LED is at full brightness. If LEDs are in parallel, the difference could mean that one LED comes on and draws all the current while the others are still off. Putting LEDs in parallel is widely held to be a bad idea. For conventional bulbs, any difference will just mean a slightly different angle of the Ohm's law line, and a slight difference in power. Putting conventional bulbs in series is a bad idea as one of them could blow at any moment, and will stop the whole lot from working. This is also true for LEDs in series, but with lifetimes of tens of thousands of hours, the problem is several years in the future, even if the lights are on the whole time.

Fundamentally, all LEDs are dimmable. If they get less power, they will put out less light. The difference is that they can only be dimmed by changing the current. Although fixed voltage power supplies have been standard for the past century and a half of electrical appliance design, power supplies that put out a constant current are also available, and in many of these the current can be varied. Here is a 2cm chip with a dimmer that will send fixed current between 70 and 350mA. In terms of parts there is a lot of stuff out there. Manufacturers are busily putting LEDs into light fittings designed for an electrical system that Edison would mostly recognise, and each fitting has an LED driver, which is basically regulating the current. The problem for us is finding the right products. To the left is a 2 x 2 cm circuit that will do the job. Here's an LED dimmer for 780 yen, . Here's a remote control dimmer for 1,980 yen.And here's someone else lamenting ignorance about how LEDs actually work: