The SETI Game

When listening for signals from aliens, it isn’t enough to just point an antenna at the sky. One must also choose details like directions, angles, frequencies, bandwidths, pulse widths, and pulse intervals. Apparently most SETI searches assume that for a given signal power density, aliens would pick details to make it as easy as possible for us to detect their signals. So standard SETI searches are optimized for such easily-seen signals. Two excellent papers, published back in July, instead consider what sort of signals would be sent by “beacon” building aliens, who seek to create the maximum possible power density at any given distance away from them.  (One of the authors is SF author Greg Benford.) Such signals are quite different, and most of today’s SETI searches are not very good at seeing them:

Minimizing the cost of producing a desired power density at long range … determines the maximum range of detectability of a transmitted signal. We derive general relations for cost-optimal aperture and power. … Galactic-scale beacons can be built for a few billion dollars with our present technology. Such beacons have narrow “searchlight” beams and short “dwell times” when the beacon would be seen by an alien observer in their sky. … Cost scales only linearly with range R, not as R2. … They will likely transmit at higher microwave frequencies, 10 GHz. The natural corridor to broadcast is along the galactic radius or along the local spiral galactic arm we are in. …

Cost, spectral lines near 1 GHz, and interstellar scintillation favor radiating frequencies substantially above the classic “water hole.” Therefore, the transmission strategy for a distant, cost-conscious beacon would be a rapid scan of the galactic plane with the intent to cover the angular space. Such pulses would be infrequent events for the receiver. Such beacons built by distant, advanced, wealthy societies would have very different characteristics from what SETI researchers seek. … We will need to wait for recurring events that may arrive in intermittent bursts. …

A concept of frugality, economy. … directly contradicts the Altruistic Alien Argument that the beacon builders will be vastly wealthy and make everything easy for us. An omnidirectional beacon, radiating at the entire galactic plane, for example, would have to be enormously powerful and expensive, and so not be parsimonious. … For transmitting time t, receiver detectability scales as t1/2. But at constant power, transmitter cost increases as t, so short pulses are economically smart (cheaper) for the transmitting society. A 1-second pulse sent every 10 minutes to 600 targets would be 1/600 as expensive per target, yet only *1/25 times harder to detect. Interstellar scintillation limits the pulse time to >10-6 s, which is within the range of all existing high-power microwave devices. Such pings would have small information content, which would attract attention to weaker, high-content messages. …

Cost-optimized beacons … can be found by steady searches that watch the galactic plane for times on the scale of years. Of course, SETI literature abounds with consideration of the trade-offs of search strategy (range vs. EIRP vs. pulse vs. continuous (continuous wave, CW) vs. polarization vs. frequency vs. beamwidth vs. integration time vs. modulation types vs. targeted vs. all-sky vs. Milky Way). But, in practice, search dwell times are a few seconds in surveys and 100–200 seconds for targeted searches. Optical searches usually run to minutes. And integration times are long, of order 100 s, so short pulses will be integrated out. …

Behind conventional SETI methods lies the assumption that altruistic beaming societies will send persistent signals. In searches to date, confirmation attempts, when the observer looks back at a target, in practice usually occur days later. Such surveys have little chance of seeing cost-optimized beacons. … Distant, cost-optimized beacons will appear for much less time than as assumed in conventional SETI. Earlier searches have seen pulsed intermittent signals resembling what we (in this paper) think beacons may be like, and may provide useful clues. We should observe the spots in the sky seen in previous work for hints of such activity but over year-long periods. (more)

Of course both the usual assumption that aliens will pay any cost to make a given power density signal easy for us to see, and the new assumption that aliens ignore our costs and merely seek to maximize power density, are both somewhat unsatisfactory. It would be better to model this interaction as a game, where each side has a limited budget and seeks to maximize the probability of at least one successful communication, holding constant the behavior it expects from the other side. Each side would of course also have to integrate over possible locations and budgets for the other side.

I’m very interested in working with (sim, math, or physics) competent folks to more formally model this SETI communication game.

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  • Robert Koslover

    Robin, I’m not an astronomer or SETI participant, but I invent, design. and analyze antennas (especially high power microwave antennas) for a living. You know where to reach me. :)

  • Jason

    Looking at our own economically constrained system, I see a galaxy of civilizations all solving that game by adopting a strategy of listening, while rarely (potentially randomly) sending deliberate beacons. The primary emissions in that case would be from aliens communicating with themselves or their long range probes, potentially with analogs of the Deep Space Network (including repeater stations for longer distances, so highest directivity would be towards nearest/nearest habitable/nearest useful stars).

    In that case, they are likely sending large amounts of information at high bit rates, and economic constraints would lead you to actually minimize energy density at fixed range (i.e. just enough to meet requirements).

    The fundamental theoretical constraint for detection is the amount of energy required to erase one bit of randomness (I’m here!) = k T log 2 at a given range, which leads you to maximize energy density at fixed range in optimal directions. Although I think a more detailed analysis with the Shannon limit is called for. Optimal communication through a noisy channel should minimize false alarms. Since signals are presumably rare, you don’t want the one you find to turn out to be a fluctuation.

    It also looks like a coordination problem. If some alien species had found another one, then they might be more likely to “cooperate” and maximize the probability of communication with a new species.

  • Danny

    Not that different from a game where someone is trapped in rubble say, and others are searching for them. How loud should you yell and how frequently to maximize the probability you are found.

    • Jason

      Good analogy!

  • Chris T

    This is why I think SETI is a waste of time and resources at present. We’re a decade or two away from being able to directly search for life bearing planets. At that time any search for signals could be made vastly more efficient and precise.

    The range of possibilities is far too broad right now to have much hope of detecting anything.

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