Abstract
O
SETI is a controversial matter. For many, the subject is at the interphase between science and fiction. But this has not stopped scientists who are interested in SETI from devising new technological means with which to search the sky. Certainly, it has not prevented Claudio Maccone from exploring the subject from a theoretical point of view and conceptualizing new methodologies for SETI. For Maccone, a member of the International Academy of Aeronautics and retired professor of Italy's National Institute of Astrophysics, the division between science and fiction is blurred. He has an easiness about formalizing ideas that seem to be borrowed from science fiction rather than scientific papers with the intent to improve SETI in atypical, thought-provoking ways.
Among the many problems inherent to SETI, there are two fundamental issues. The first is that the estimate of N from Drake's equation is inaccurate. This is critical for a scientific appraisal of the SETI project, since it provides a justification for the allocation of scientific and economic resources. Unsurprisingly, the estimates of N are currently checked by considering the latest astrophysical data. Here, Maccone makes a difference, taking advantage of the fact that the factors of Drake's equation are known with little certainty. He had the simple but brilliant idea to give a statistical interpretation to Drake's equation. This allows the estimates for N to be refined and provides error bounds for it. With his new approach, Maccone goes beyond Drake's equation by building up a comprehensive theoretical framework with which to study the number of and distribution of distances between civilizations, civilizations' lifespans, and other related questions.
The second problem in SETI is an empirical one: after more than 60 years of radio searches, no positive beacons have been registered. For this, Maccone also brings improvements by introducing a new way of analyzing the signals that are received from the radio telescopes. Dishes capture a lot of noise, and buried within the radio uproar, meaningful patterns are often hidden. These patterns might be of any nature: gamma-ray bursts, supernovae, extragalactic pulses, beacons from intelligent sources, and many other radio transient signals. Although noise is the critical confounding factor, another factor to be considered is that the sky must be scanned in all directions and within a significant frequency range (currently, millions to billions of channels are surveyed), and the signals have to be recorded during a meaningful time window. Therefore, the nearly continuous data stream requires meticulous inspection that is computationally challenging. The classic way to analyze signals is by applying the fast Fourier transform (FFT), a “quick and dirty” numerical algorithm. However, this method is not powerful enough to detect many of the transient radio sources characterized by high noise-to-signal ratio. Among the signals, intelligent beacons might be present; if so, we are missing them. Maccone introduces a different toolbox for the analysis of radio signals, known in mathematics as the Karhunen-Loève transform (KLT). This is much more powerful than the FFT and equally convenient from an analytical and computational standpoint. Just like the FFT, the KLT assumes an orthonormal basis of functions and decomposes the signal in terms of different modes. It also bears some similarities to the singular value decomposition (or principal component analysis), in the sense that it finds the modes that explain and filter most of the variation of the data. The KLT is then employed to analyze several case studies, such as signals coming from objects in different trajectories of astrophysical relevance and distinct types of stochastic processes. Although in some cases the motivation behind solving some specific examples is unclear, it shows that the KLT is a pioneering method.
Toward the end, Maccone builds an interesting case: he discusses that a region on the far side of the Moon should be protected from radio frequency interference (RFI). An RFI-free zone is desirable in order “to detect radio waves which are impossible to detect on earth because of the ever growing RFI” (p 659). With detailed physical arguments, he delimits a region between two meridians at 150°E and W and proposes a point near the center, at the Daedalus crater, as a future location for a radio astronomical base. He actually took this interesting proposition to the United Nations; it is currently under consideration.
No doubt Mathematical SETI is full of original ideas and is probably one of the major theoretical advances in the last few years. In fact, Maccone has been awarded the Giordano Bruno award, given by the SETI League to scientists who have substantially contributed to SETI.
For the reader, Maccone's breakthroughs do not come for free. There is a high price to pay (apart from the economic one). The ideas, no matter how wonderful they may be, are hidden in the pervasive disorganization of the book (this is not unimportant considering that it has more than 700 pages). The text is an unlimited stream of step-by-step derivations that could have gone into appendixes. However, the appendixes are filled with verbatim, full-color, copy-pasted computer code, which would have been helpful only if provided digitally as supplementary information. These appendixes compose about half the book and would be unnerving to transcribe if in need. Mathematical SETI is full of curious facts all around (many are repetitive), intertwined with irrelevant personal anecdotes, stories, photos of the author, PowerPoint slides, and—literally—bits of science fiction. It is a truly postmodern mixture.
The disorganization of the book is a serious drawback, but Mathematical SETI suffers from other problems that are more fundamental. First of all, Maccone relies too much on his own perspective and intuition and sometimes relies only on Wikipedia articles (especially in the first part of the book) rather than scientific papers. Consequently, he has overlooked relevant literature, and the book contains major conceptual flaws. For example, Maccone develops a “new” mathematical theory for the number of species, which is overly simplistic and modeled as an exponential growth, and he wrongly argues that this is a theory of evolution (the study of the number and distribution of species is called “biodiversity,” and none of its theories predict exponential increase of species). In the epilogue, which contains an ill-informed syncresis of these notions, he claims that the “#1 message put forward” is that his theory unifies Darwinian evolution, human historical progress, and SETI. That is a big claim based on a naïve model and offered with no reference to the vast literature of the mathematical theories of evolution, ecology, or demography.
Second, throughout the book, Maccone performs many approximations, such as the application of the central limit theorem, but never bothers to show or demonstrate when (or if ) these approximations are valid. Despite the fact that the author claims too often that his theories are scientific, solely because they are based on mathematics, he violates a fundamental source of scientific trust. That is, he fails (too often) to show whether his theories work at all, either by comparison by way of simulations, other methods, or data. Maccone also misuses statistics frequently. For example, he argues that he “improves” estimates by stating that N is given by the mean plus a standard deviation of the distribution. But at the same time he is defensive against the converse possibility (the mean minus standard deviation): “please don't tell me that the lower limit…is ‘negative’. It is actually zero…so negative values…are ruled out from the start” (p 16, his emphasis). This is clearly a straw man and is an example showing that sometimes Maccone can use arguments or present conclusions that are more wishful thinking than science.
Despite the fact that many of the ideas here are great, they often are incomplete or not fully developed. In this sense, the book is scientifically unfinished. Altogether, Mathematical SETI seems more like a draft for a book than a finished effort.
Reading this work felt like looking into a cabinet of wonder: it is full of exotic items, ranging from the sensational and beautiful to the ludicrous and clumsy, with very loose relationship among them. Mathematical SETI presents many ideas that are stimulating and innovative and definitely worth exploring. The problem is that among them there are many others that are misleading and sometimes plainly wrong. For readers with little knowledge of biology, there is the chance that they build an incorrect notion of ecology and evolution. Read at your own risk.