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Register a new userA probabilistic analysis of the Fermi paradox in terms of the Drake formula: the role of the L factor
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Nikos Prantzos
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In evaluating the number of technological civilizations N in the Galaxy through the Drake formula, emphasis is mostly put on the astrophysical and biotechnological factors describing the emergence of a civilization and much less on its the lifetime, which is intimately related to its demise. It is argued here that this factor is in fact the most important regarding the practical implications of the Drake formula, because it determines the maximal extent of the sphere of influence of any technological civilization. The Fermi paradox is studied in the terms of a simplified version of the Drake formula, through Monte Carlo simulations of N civilizations expanding in the Galaxy during their space faring lifetime L. In the framework of that scheme, the probability of direct contact is determined as the fraction of the Galactic volume occupied collectively by the spheres of influence of N civilizations. The results of the analysis are used to determine regions in the parameter space where the Fermi paradox holds. It is argued that in a large region of the diagram the corresponding parameters suggest rather a weak Fermi paradox. Future research may reveal whether a strong paradox holds in some part of the parameter space. Finally, it is argued that the value of N is not bound by N=1 from below, contrary to what is usually assumed, but it may have a statistical interpretation.
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I propose a unified framework for a joint analysis of the Drake equation and the Fermi paradox, which enables a simultaneous, quantitative study of both of them. The analysis is based on a simplified form of the Drake equation and on a fairly simple scheme for the colonization of the Milky Way. It appears that for sufficiently long-lived civilizations, colonization of the Galaxy is the only reasonable option to gain knowledge about other life forms. This argument allows one to define a region in the parameter space of the Drake equation where the Fermi paradox definitely holds (Strong Fermi paradox).
Our proposed experiment aimed to test the validity of the Lorentz factor with two methods: The time of flight (TOF) of various particles at different momenta and the decay rate of pions at different momenta. Due to the high sensitivity required for the second method the results were inconclusive, therefore we report only on the results of the first method.
We discuss the hot hand paradox within the framework of the backward Kolmogorov equation. We use this approach to understand the apparently paradoxical features of the statistics of fixed-length sequences of heads and tails upon repeated fair coin flips. In particular, we compute the average waiting time for the appearance of specific sequences. For sequences of length 2, the average time until the appearance of the sequence HH (heads-heads) equals 6, while the waiting time for the sequence HT (heads-tails) equals 4. These results require a few simple calculational steps by the Kolmogorov approach. We also give complete results for sequences of lengths 3, 4, and 5; the extension to longer sequences is straightforward (albeit more tedious). Finally, we compute the waiting times $T_{nrm H}$ for an arbitrary length sequences of all heads and $T_{nrm(HT)}$ for the sequence of alternating heads and tails. For large $n$, $T_{2nrm H}sim 3 T_{nrm(HT)}$.
The twin paradox, which evokes from the the idea that two twins may age differently because of their relative motion, has been studied and explained ever since it was first described in 1906, the year after special relativity was invented. The question can be asked: Is there anything more to say? It seems evident that acceleration has a role to play, however this role has largely been brushed aside since it is not required in calculating, in a preferred reference frame, the relative age difference of the twins. Indeed, if one tries to calculate the age difference from the point of the view of the twin that undergoes the acceleration, then the role of the acceleration is crucial and cannot be dismissed. In the resolution of the twin paradox, the role of the acceleration has been denigrated to the extent that it has been treated as a red-herring. This is a mistake and shows a clear misunderstanding of the twin paradox.
The unplaced Fragment D of the Antikythera Mechanism with an unknown operation was a mystery since the beginning of its discovery. The gear r1, which was detected on the Fragment radiographies by C. Karakalos, is preserved in excellent contdition, but this was not enough to correlate it to the existing gear trainings of the Mechanism. After the analysis of AMRP tomographies of Fragment D and its mechanical characteritics revealed that it could be a part of the Draconic gearing. Although the Draconic cycle wa well known during the Mechanisms era as represents the fourth Lunar cycle, it seems that it is missing from the Antikythera Mechanism. The study of Fragment D was supported by the bronze reconstruction of the Draconic gearing by the authors. The adaptation of the Draconic gearing on the Antikythera Mechanism improves its functionality and gives answers on several questions.
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