(Published previously on kragen-tol.)
Long-distance telecommunication is really important, and currently crucially dependent not only on the state of the global economy, but also on operationally centralized telecommunications companies, large telecommunications structures that are easy to bomb, and undersea cables. What's the minimal digital telecommunications infrastructure that would usefully enable intercontinental communication?
Shortwave radio (1.5MHz-30MHz) reflects off the ionosphere and can be received intercontinentally. This includes a couple of ISM bands in which unlicensed operation is permitted internationally: 13553–13567 kHz (22 meters) and 26957–27283 kHz (11 meters). Wikipedia's "High frequency" article says, "The maximum usable frequency regularly drops below 10MHz in darkness during the winter months, while in summer during daylight it can easily surpass 30MHz." Wikipedia's "Skywave" article says, "Signals of only a few watts can sometimes be received many thousands of miles away as a result." One hop off the ionosphere gets your signal up to 3500km.
This means that, in theory, you could set up a single unlicensed radio station providing communications services to you in most of a 7000-kilometer-wide circle. Something over a dozen such receivers could provide you with global coverage. Of course, you'd have to deal with interference: both decoding the received signals in the face of interference, and not generating so much interference to other users of the spectrum that they start to interfere with you in ways other than radio communication.
(Transmitting in the 22-meter band, especially using time-domain radio with low-power code division multiplexing and a low duty cycle, would also make it practically difficult to locate the radio transmitter; and of course the receiver would produce even less evidence of its presence.)
Shannon's Theorem, aka the noisy-channel coding theorem, has no minimum signal strength below which communication bandwidth is zero; the Shannon-Hartley limit is B log (1 + S/N), where B is bandwidth in hertz, and S and N are the power of the signal and noise. In the "power-limited regime", when S/N is very small, this is linear in S/N. A somewhat counterintuitive result here is that, practically speaking, your bit rate doesn't depend on frequency selectivity much at all --- if you use twice as much of the spectrum, you double B, but you also probably double N. This means you can choose your bandwidth to satisfy other considerations, such as minimizing interference with other users of the band, who are mostly still using frequency-division multiplexing, or minimizing device cost.
So, supposing you can send one bit per second in the HF band using one watt over a few thousand kilometers, you can probably send about one bit per 1000 seconds using one milliwatt, or one bit per day using 12 microwatts, and this regardless of whether your signal is 0.1kHz wide, 14 kHz wide, or 28.5 MHz wide.
Is one bit per second about right? Digital Radio Mondiale in the shortwave bands uses at least 6 kilobits per second, but that doesn't tell us much, since this could be slammed through by using hundreds of kilowatts. What we really need to know is how much background noise there is in these frequency bands, in an absolute sense, or how many words per minute people can send and receive with CW Morse code over what distance and what power. One bit per second would be about 1.2 "words per minute".
It seems like the keyword for this kind of thing in current amateur radio operation is "QRP operation", which means around 5 or 10 watts or less. QRPers consider anything below 1 watt as "extremely low power", or QRPp, and they consider a thousand miles per watt as a difficult benchmark to meet. PSK31 is the digital code most commonly used at present for this kind of thing, and it operates at 31 baud and a bandwidth of 31.25Hz; it does a 180-degree phase shift during an amplitude null to represent a zero bit after encoding the digital signal into Varicode, a huffman code for ASCII. There are 10-baud and 5-baud variants in use. PSK31 is commonly used down to the 160-meter band.
If we figure that talking a thousand miles (1609 km) on a watt already puts you into the power-limited regime, and guess that you can get some 10 bits per second out of it, then using skywave bounce, you should be able to talk N thousand miles at 10/N bits per second. For example, you should be able to talk 16000 km, about a third of the way around the world at one bit per second.
You could illuminate the moon with a rapidly modulated laser at night. The moon's albedo is about 12%, it covers about half a degree of arc, and you can get cheap 5mW semiconductor laser pointers with divergence of less than that, indeed closer to a tenth of a degree, so that all of their power falls on the moon. Similarly, an inexpensive lens focusing the moon's image onto a photodiode (which is faster than a phototransistor) can easily give you better than an arcminute of selectivity. A square arcminute is about 85 nanosteradians, so this corresponds to about 80 dBi of "antenna gain" on the receiving end, but focusing more tightly than the original laser pointer spot isn't useful, so you only get about 60 dBi in practice.
Against this you must weigh the fact that most of the light falling on the moon is reflected off into space. You can probably reasonably use a one-meter-diameter plastic Fresnel lens, but you're about 380 megameters from the moon. This means that the light signal you get is about 176 dB weaker than the light signal sent from the moon, which is presumably most of the 500μW or so of light emitted from a 5mW laser pointer, minus about 9dB for the low albedo. This means you're trying to detect a signal of some -188dBm, which is difficult but feasible. It's actually considerably more feasible than doing the same trick with radio waves, due to the higher "antenna gain".
I think common laser diodes have a Q factor around 1000 --- their light is mostly contained in a range of wavelengths of less than a nanometer --- which means you could improve your SNR by up to about 30dB by filtering the moon's image through a dichroic filter.
This leaves the question of how much noise you're dealing with in the first place, particularly important if you might have significant "crosstalk" from brightly-illuminated parts of the moon, say because your camera is imperfect. Sadly, I have very little idea how bright earthshine is, which is kind of the question.
Ultra-low frequency radio --- 300 Hz to 3000 Hz --- can propagate through the earth itself; there are apparently lots of NATO papers from the 1960s about using this for military purposes. As far as I can tell, though, this involves running antenna cables a distance comparable to half the wavelength (100 km or more) or to the distance you want to communicate. So I think this may be impractical.
Getting a balloon to 90km altitude is straightforward, at which point it has a line-of-sight radio path to anything within 9.57 degrees of arc (acos(r/(r + 90 km)), where r is 6371 km, the radius of the Earth) on the Earth's surface, about 1000 km; at this point it could quite reasonably communicate at gigabits per second using laser or highly-directional ultrawideband microwave to any of those points, if it can figure out how to align its transmitter and receiver. Furthermore, two such balloons will have a line-of-sight if they're less than twice the angle apart, or 2000 km. Twenty such balloons could ring the earth along a great circle, so a frequency-four geodesic sphere would suffice to provide global coverage with a bit under 200 balloons.
On the other hand, getting balloons to stay up there would be quite a challenging project. In fact, just getting them to work at all while they're up there is no walk in the park.
In 1998, Laima, an Aerosonde, flew successfully across the Atlantic on 5.7 liters of fuel in 27 hours. Aerosondes weigh about 13 kg, about the same as a large swan. One micro-SD card weighs about 500mg and can currently hold 64 GB of data, so a 2-kg payload would hold 256 TB. This would amount to a 21 Gbps transatlantic data connection.
In 2003, the 5kg Spirit of Butts Farm made more or less the same 3000km flight on under a liter of fuel, in just under 39 hours.
On one hand, these bandwidths are orders of magnitude higher than the bandwidths reasonably achievable by the other technologies mentioned above. On the other hand, the latency is also some five orders of magnitude higher, and also, this is a very unreliable way of transmitting data --- it is likely to result in the loss of the aircraft and its payload on a regular basis.
A lower-tech approach for north-south communication would be to attach high-capacity store-and-forward radio-communication nodes to long-lived migratory birds. When they came into communication range of other nodes, they would exchange messages via short-range, high-bandwidth radio.
Particle accelerators can generate large quantities of neutrinos in a beam, by accelerating large quantities of pions or kaons to relativistic speeds and letting them decay; if the neutrino beam is directed at the earth, most of them will penetrate to the other side. Unfortunately, detecting a change in neutrino flux is very difficult, because they can easily penetrate things like the earth. It's feasible using thousands of photomultiplier tubes and tens of thousands of tonnes of water or other transparent liquid deep underground, like the Super-KamiokaNDE and the Sudbury Neutron Observatory; such observatories see on the order of one natural neutrino decay per few days per thousand tons of matter included.
This is clearly a feasible technique for communication, but it costs tens to hundreds of millions of dollars (which is to say, hundreds to thousands of person-years of work) and the result should be communication with bandwidth measured in fractional bits per day. If it were possible to increase the number of neutrinos by several orders of magnitude, you could increase the bit rate substantially, and in the limit, you could have lower latencies for long-distance communication than communication methods for which the earth is an obstacle.
Low-frequency sound can propagate for hundreds of kilometers in air, which is the principle behind the West African talking drums, which were used for long-distance digital communication for several centuries, up to the mid-20th century. I think you can get up to tens of bits per second this way. The talking drums could transmit several kilometers (8 km, says Wikipedia), but not tens or hundreds of kilometers. Whistled speech can cover one to two km, and has in theory a higher bit rate.
High-frequency sound is unusably attenuated by air in a few kilometers, but can cover thousands of kilometers in water, where whales use it; it also travels above 1km/sec. There's the additional advantage that sound in the ocean tends to remain a few hundred meters from the surface, in a zone called the SOFAR zone or Deep Sound Channel, so its intensity falls off as 1/d instead of 1/d² over long distances.
A 1.6-km-tall mountain, such as Sandia Peak in Albuquerque, has a line of sight to some 140 km distance on a smooth-spheroid earth, and perhaps 100 km in real life. Even a 100-meter-tall tower can see for 36 km. This principle was used in semaphore telegraphs throughout Europe in the decades before the development of the electric telegraph: a line of fortified stone towers at 30-km intervals provided about one bit per second. If you put a cheap laser pointer on the tower, you can transmit over this line of sight at megabit speeds or better.
Of course, you can also use a reflecting mirror to reflect sunlight instead of a laser; such a "heliograph" can transmit up to 300km under ideal conditions or 50km under normal conditions, using small, hand-sized mirrors. Bit rates depend on how fast you can open and close some kind of "shutter", but at least hundreds if not thousands of bits per second should be attainable with inexpensive LCDs.
As suggested in the Lasermoon section, you can do this same kind of long-distance communication even without going up on the mountain yourself; it's sufficient to illuminate it from afar. Naval communication with Aldis lamps uses this trick to communicate by illuminating the bases of cloud formations, which enables communication at much greater distances; in theory, you could use cirrocumulus or cirrostratus clouds at their altitude of some 5–12 km to communicate to a station 500–800 km away, or perhaps even the 23-km-high tip of a cumulonimbus cloud to communicate with a station 1000 km away. This is more practical than using the moon, since you only have to detect light diffusing from the cloud 500 km from you instead of 380 000 km from you, giving you 60 dB less path loss in the cloud-to-you path than in the moon-to-you path. (As before, I think you can focus light onto the cloud well enough that effectively all the light you transmit reaches the cloud, so you effectively don't have any path loss.)
Why would it matter if you could transmit a millibit per second? Well, one bit can still be a crucially useful thing to be able to transmit. "I'm alive," for example, or "The killers weren't al Qaeda." But even a Tweet is only 1120 bits, so a bit per 1000 seconds would let you you transmit a Tweet every two weeks. The Annals of Spring and Autumn, 春秋, covers 541 years in 16000 characters; if each were 16 bits, that would be just over one bit per day on average. The Chappe semaphore line system transmitted about one "symbol" per minute out of 92 possible symbols, giving a bandwidth of about 0.11 bits per second; it was credited with giving Napoleon a decisive military advantage.
Consider the higher bandwidth of one bit per second, which I've hypothesized above requires about a watt of power over transcontinental shortwave. Two bits is roughly one letter of compressed ASCII text [0], so this is about 7000 words of text per day; one to ten Wikipedia articles per day, for example, or a fairly in-depth summary of daily international news, or a couple of hours of writing email per day, or a book per month. Furthermore, it's fast enough to permit someone to write a line of text in a chat system, transmit it, and get back a response from someone else within a couple of minutes.
[0] bible-pg10.txt is 824 146 words and 4 452 069 bytes; its .bz2 is 999 906 bytes, 1.80 bits per uncompressed byte; compressors other than bzip2 may be more efficient; but extremely high compression ratios may only be achievable with the transmission of large amounts of data. For example, if I split the same document into 64KiB chunks and bzip2 each one independently, the result is 1 214 055 bytes, 2.18 bits per uncompressed byte.
One bit per second, then, is a sufficiently rapid connection to permit real participation in the intellectual life of an invisible college; but it's less information than a person can read. Furthermore, with a broadcast medium such as radio, it's reasonable to transmit the same information to many recipients at a time, Usenet-style.
Commercially speaking, even one bit per second, or for that matter a thousandth of a bit per second, at low latency is enough to make you a hell of a lot of money in commodity arbitrage, if your competitors don't have access to equally fast communication. A price to three significant figures is only ten bits, and it's straightforward to encode names for widely-traded commodities in 30 bits or less. (This is why the stock ticker was such big business in the late 19th and early 20th century.)
Ten bits per second would give you some 70 000 words of text per day, which is almost as much as you could read in real time; and it would be fast enough to permit real-time hypertext navigation with a stateful two-way protocol. (If you're transmitting document contents containing the IDs of other documents in one direction, while transmitting the IDs of requested documents or document parts in the other direction, each ID will typically be within the last thousand IDs transmitted, so it can be encoded in ten or twenty bits.) Ten bits per second at 2.5 bits per character works out to 240 characters per minute, or 48 words per minute, so it's at least theoretically possible for one person to type faster than ten bits per second on a sustained basis; but it's fast enough that one-to-one text chat would be more or less real time.
A hundred bits per second would give you some 700 000 words per day, an entire book. This is enough that one person can no longer read all of it, if it's text, and eliminates the need for a stateful protocol for real-time hypertext --- although full HTTP might still be excessive. It's about 480 words per minute.
Acquiring one new book per day was an unachievable dream for nearly all individual scholars and the majority of libraries in most of the age of print. If the books were new cheap paperbacks, it cost about US$1800 per year toward the end of the 20th century, within the means of most of the population of the developed world, but new hardbacks pushed the cost up by an order of magnitude, to US$18000 per year. So a hundred-bit-per-second connection to a large data store could beat access to printing presses for all but the wealthiest.
If one person were trying to consume a hundred bits per second, they would probably want to do much of it in the form of still images. A high-quality color JPEG file typically uses about four bits per pixel, and black-and-white needs about half that. So a hundred bits per second is on the order of 100 low-quality pixels or 25 high-quality pixels per second. A low-quality 320×200 color image might download in 21 minutes.
As of early 2012, the English Wikipedia articles without pictures total 10 399 030 471 bytes in a compressed Zim file. At a hundred bits per second, this file would take 26 years to transmit.
For much of the twentieth century, most Telex systems ran at 45.45 bits per second.
A thousand bits per second is 7 000 000 words per day, some ten books. At this speed it's possible to receive text you don't intend to read yourself, just in case you want to read it later; but it's also fast enough that you don't need to if the connection is reliable. You could download the Wikipedia archive I mentioned above in 2.6 years.
It's also at the minimal lower limit where you can do real-time voice transmission. Many voice codecs (from early LPC work in the 1970s to HVXC and Speex today) have modes between 2 and 3 kilobits per second. I think transmitting intelligible speech at 1kbps is feasible, but only barely, and I don't know if it's been done.
At a thousand bits per second, you can completely kick the ass of printing-press-based communication systems, both providing instant hypertext access to faraway data stores and accumulating the equivalent of thousands of locally-stored books per year, plus, of course, email.
This is the speed at which much of Fidonet operated.
The very low power levels involved suggest that it might be possible to do these ultraslow transmissions with extremely steampunk equipment, or not even that. For example, for radio communication, perhaps you could trigger a static-electrical spark from a Wimshurst Influence Machine at intervals driven by holes in a rotating glass sphere, firing an electrical impulse into a dipole antenna. But a Wimshurst machine can produce more than a watt of power; a simpler generator, such as your hair and a balloon, might be sufficient. You just have to time your sparks correctly to make them interpretable by your (presumably much more capable) receiver, and successfully couple them into your antenna, maybe with a low-Q resonator containing a coil and a Leyden jar.
(In theory, maybe you could decode such a low-bandwidth signal by hand, too, but it's not obvious to me how you'd do it.)
(The earliest non-spark-gap radio, the Poulsen arc, used a carbon arc as a negative-resistance device to produce a dynatron oscillator; I think you could also use just about any gas discharge tube, such as a fluorescent lamp tube or even a fluorescent lamp starter.)
Of course, multiple ultraslow radios could form a very slow packet-switching network.
Moving further into the steampunk and cargo-cult direction, you could imagine a shorter-range purely passive radio transmitter, like a sort of switchable analog RFID tag. The "receiver" would wait for the transmitter to be energized by electromagnetic pulses produced by nearby lightning strikes; then it would measure a variable set of RF resonances in the device. A Leyden jar might have a nanofarad of capacitance, and a variable inductor with up to about a henry of inductance can be fairly easily constructed by hand, the two forming a tank circuit with a resonant frequency of as little as 5kHz and a Q of perhaps 100; a large number of such resonant circuits connected to an antenna will "ring" for tens or hundreds of oscillations when subjected to a radio impulse. If their frequencies are chosen in accordance with some kind of error-correcting code, a distant detector will eventually be able to determine what those frequencies are, after detecting enough impulse responses. Multiple receiving antennas could provide enough phase diversity to do beamforming.
Such a device is fairly inefficient, since most of the energizing pulse energy will not coincide with a resonant frequency of the transmitter and will thus simply reflect from the antenna. If you could store the pulse in some kind of device that allowed you to use it to continuously energize the resonators until it dissipated, you could use more of it. For example, with a semiconductor diode, you could store much of the pulse in a capacitor, and use that to power active oscillator circuits; or if you could circulate it through some kind of delay line, such as a piezoelectric acoustic delay line, you could use any nonlinear but nondissipative circuit element to shift some of the remaining pulse energy into resonable harmonics or subharmonics on each circulation through the system.
Pulse radio would allow for relatively reasonable decoding electronics and algorithms: while your average power might be, say, 100 milliwatts, if you're only transmitting for 100 microseconds out of every minute, that transmission would be at 60 kilowatts. (If it's a single 100-microsecond pulse, it would be a six-joule pulse; into a 63-ohm antenna impedance, it would be a momentary current of 31 amps, driven by 2000 volts, which could be stored in 3 microfarads, so this wouldn't require any particularly exotic circuit design.) Detecting the pulse at even a very substantial distance should not require particularly sensitive or highly linear analog electronics; the remaining task, then, is to figure out which subset of the detected pulses represent a decodable message.