Back in March I wrote:

Somewhere around 2035 or so … the (free) energy used per [computer] gate operation will fall to the level thermodynamics says is required to [logically] erase a bit of information. After this point, the energy cost per computation can only fall by switching to “reversible” computing designs, that only rarely [logically] erase bits. … Computer gates … today … in effect irreversibly erase many bits per gate operation. To erase fewer bits instead, gates must be run “adiabatically,” i.e., slow enough so key parameters can change smoothly. In this case, the rate of bit erasure per operation is proportional to speed; run a gate twice as slow, and it erases only half as many bits per operation. Once reversible computing is the norm, gains in making more smaller faster gates will have to be split, some going to let gates run more slowly, and the rest going to more operations. (more)

The future of computing, after about 2035, is adiabatic reservable hardware. When such hardware runs at a cost-minimizing speed, half of the total budget is spent on computer hardware, and the other half is spent on energy and cooling for that hardware. Thus after 2035 or so, about as much will be spent on computer hardware and a physical space to place it as will be spent on hardware and space for systems to generate and transport energy into the computers, and to absorb and transport heat away from those computers. So if you seek a career for a futuristic world dominated by computers, note that a career making or maintaining energy or cooling systems may be just as promising as a career making or maintaining computing hardware.

We can imagine lots of futuristic ways to cheaply and compactly make and transport energy. These include thorium reactors and superconducting power cables. It is harder to imagine futuristic ways to absorb and transport heat. So we are likely to stay stuck with existing approaches to cooling. And the best of these, at least on large scales, is to just push cool fluids past the hardware. And the main expense in this approach is for the pipes to transport those fluids, and the space to hold those pipes.

Thus in future cities crammed with computer hardware, roughly half of the volume is likely to be taken up by pipes that move cooling fluids in and out. And the tech for such pipes will probably be more stable than tech for energy or computers. So if you want a stable career managing something that will stay very valuable for a long time, consider plumbing.

Will this focus on cooling limit city sizes? After all, the surface area of a city, where cooling fluids can go in and out, goes as the square of city scale , while the volume to be cooled goes as the cube of city scale. The ratio of volume to surface area is thus linear in city scale. So does our ability to cool cities fall inversely with city scale?

Actually, no. We have good fractal pipe designs to efficiently import fluids like air or water from outside a city to near every point in that city, and to then export hot fluids from near every point to outside the city. These fractal designs require cost overheads that are only logarithmic in the total size of the city. That is, when you double the city size, such overheads increase by only a constant amount, instead of doubling.

For example, there is a fractal design for piping both smoothly flowing and turbulent cooling fluids where, holding constant the fluid temperature and pressure as well as the cooling required per unit volume, the fraction of city volume devoted to cooling pipes goes as the logarithm of the city’s volume. That is, every time the total city volume doubles, the same additional fraction of that volume must be devoted to a new kind of pipe to handle the larger scale. The pressure drop across such pipes also goes as the logarithm of city volume.

The economic value produced in a city is often modeled as a low power (greater than one) of the economic activity enclosed in that city. Since mathematically, for a large enough volume a power of volume will grow faster than the logarithm of volume, the greater value produced in larger cities can easily pay for their larger costs of cooling. Cooling does not seem to limit feasible city size. At least when there are big reservoirs of cool fluids like air or water around.

I don’t know if the future is still plastics. But I do know that a big chuck of it will be pipes.

**Added 10Nov 4p:** Proof of “When such hardware runs …” : V = value, C = cost, N = # processors, s = speed run them at, p,q = prices. V = N*s, C = p*N + q*N*s2. So C/V = p/s + q*s. Pick s to min C/V gives p = q*s2, so two parts of cost C are equal. Also, C/s = 2*sqrt(p*q).

**Added 6Nov2014**: According to 2012 data, pipes turn out to be the most “complex” product, i.e. the product that most indicates that a nation is able to produce many difficult things.

"The surface area of a city, where cooling fluids can go in and out, goes as the square of city scale , while the volume to be cooled goes as the cube of city scale."

Wouldn't the volume to be cooled be proportional to the surface (so ^2), and the "in and out" to perimeter (so linear)?

Unless you picture pipes coming in and out from the ground or top, and the height of cities growing with scale for some reason.

According to Terry Gilliam's movie "Brazil," the future is ducts, lots and lots of ducts.