In Newcombs paradox you choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose, a prediction algorithm deduces your choice, and fills the two boxes based on that de
duction. Newcombs paradox is that game theory appears to provide two conflicting recommendations for what choice you should make in this scenario. We analyze Newcombs paradox using a recent extension of game theory in which the players set conditional probability distributions in a Bayes net. We show that the two game theory recommendations in Newcombs scenario have different presumptions for what Bayes net relates your choice and the algorithms prediction. We resolve the paradox by proving that these two Bayes nets are incompatible. We also show that the accuracy of the algorithms prediction, the focus of much previous work, is irrelevant. In addition we show that Newcombs scenario only provides a contradiction between game theorys expected utility and dominance principles if one is sloppy in specifying the underlying Bayes net. We also show that Newcombs paradox is time-reversal invariant; both the paradox and its resolution are unchanged if the algorithm makes its `prediction after you make your choice rather than before.
What would SETI Beacon transmitters be like if built by civilizations with a variety of motivations, but who cared about cost? We studied in a companion paper how, for fixed power density in the far field, we could build a cost-optimum interstellar B
eacon system. Here we consider, if someone like us were to produce a Beacon, how should we look for it? High-power transmitters might be built for wide variety of motives other than twoway communication; Beacons built to be seen over thousands of light years are such. Altruistic Beacon builders will have to contend with other altruistic causes, just as humans do, so may select for economy of effort. 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 will be a rapid scan of the galactic plane, to cover the angular space. Such pulses will be infrequent events for the receiver. Such Beacons built by distant advanced, wealthy societies will have very different characteristics from what SETI researchers seek. Future searches should pay special attention to areas along the galactic disk where SETI searches have seen coherent signals that have not recurred on the limited listening time intervals we have used. We will need to wait for recurring events that may arrive in intermittent bursts. Several new SETI search strategies emerge from these ideas. We propose a new test for SETI Beacons, based on the Life Plane hypotheses.
This paper considers galactic scale Beacons from the point of view of expense to a builder on Earth. For fixed power density in the far field, what is the cost-optimum interstellar Beacon system? Experience shows an optimum tradeoff, depending on tra
nsmission frequency and on antenna size and power. This emerges by minimizing the cost of producing a desired effective isotropic radiated power, which in turn determines the maximum range of detectability of a transmitted signal. We derive general relations for cost-optimal aperture and power. For linear dependence of capital cost on transmitter power and antenna area, minimum capital cost occurs when the cost is equally divided between antenna gain and radiated power. For non-linear power law dependence a similar simple division occurs. This is validated in cost data for many systems; industry uses this cost optimum as a rule-of-thumb. Costs of pulsed cost-efficient transmitters are estimated from these relations using current cost parameters ($/W, $/m2) as a basis. Galactic-scale Beacons demand effective isotropic radiated power >1017 W, emitted powers are >1 GW, with antenna areas > km2. We show the scaling and give examples of such Beacons. Thrifty beacon systems would be large and costly, have narrow searchlight beams and short dwell times when the Beacon would be seen by an alien oberver at target areas in the sky. They may revisit an area infrequently and will likely transmit at higher microwave frequencies, ~10 GHz. The natural corridor to broadcast is along the galactic spiral radius or along the spiral galactic arm we are in. Our second paper argues that nearly all SETI searches to date had little chance of seeing such Beacons.
In Newcombs paradox you choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose though, an antagonist uses a prediction algorithm to deduce your choice, and fills th
e two boxes based on that deduction. Newcombs paradox is that game theorys expected utility and dominance principles appear to provide conflicting recommendations for what you should choose. A recent extension of game theory provides a powerful tool for resolving paradoxes concerning human choice, which formulates such paradoxes in terms of Bayes nets. Here we apply this to ol to Newcombs scenario. We show that the conflicting recommendations in Newcombs scenario use different Bayes nets to relate your choice and the algorithms prediction. These two Bayes nets are incompatible. This resolves the paradox: the reason there appears to be two conflicting recommendations is that the specification of the underlying Bayes net is open to two, conflicting interpretations. We then show that the accuracy of the prediction algorithm in Newcombs paradox, the focus of much previous work, is irrelevant. We similarly show that the utility functions of you and the antagonist are irrelevant. We end by showing that Newcombs paradox is time-reversal invariant; both the paradox and its resolution are unchanged if the algorithm makes its `prediction emph{after} you make your choice rather than before.
Remnants of AGN jets and their surrounding cocoons leave colossal magnetohydrodynamic (MHD) fossil structures storing total energies ~10^{60} erg. The original active galacic nucleus (AGN) may be dead but the fossil will retain its stable configurati
on resembling the reversed-field pinch (RFP) encountered in laboratory MHD experiments. In an RFP the longitudinal magnetic field changes direction at a critical distance from the axis, leading to magnetic re-connection there, and to slow decay of the large-scale RFP field. We show that this field decay induces large-scale electric fields which can accelerate cosmic rays with an E^{-2} power-law up to ultra-high energies with a cut-off depending on the fossil parameters. The cut-off is expected to be rigidity dependent, implying the observed composition would change from light to heavy close to the cut-off if one or two nearby AGN fossils dominate. Given that several percent of the universes volume may house such slowly decaying structures, these fossils may even re-energize ultra-high energy cosmic rays from distant/old sources, offsetting the ``GZK-losses due to interactions with photons of the cosmic microwave background radiation and giving evidence of otherwise undetectable fossils. In this case the composition would remain light to the highest energies if distant sources or fossils dominated, but otherwise would be mixed. It is hoped the new generation of cosmic ray experiments such as the Pierre Auger Observatory and ultra-high energy neutrino telescopes such as ANITA and lunar Cherenkov experiments will clarify this.
