Why Mathematical Computer Simulations Are the New Laboratory for Scientists

Abstract

In this paper, we introduce a new powerful scientific paradigm to understand natural and cultural processes. This new paradigm is based on two fundamental keywords: Data, as representative sample of the process we need to analyze, and Artificial Adaptive Systems, as a new mathematical technique able to make explicit the nonlinearity embedded in the process. We will try to make explicit these concepts analyzing how the distribution of events into the physical space may reveal the hidden logic connecting these events together.

Keywords:

• geographic profiling
• artificial adaptive systems
• neural networks

Notes

¹ Dengue fever is amosquito-borne tropical disease caused by the dengue virus. Symptoms include fever,headache, muscle and joint pains, and a characteristic skin rash that is similar to measles. In a small proportion of cases the disease develops into the life-threatening dengue hemorrhagic fever, resulting in bleeding, low levels of blood platelets and blood plasma leakage, or into dengue shock syndrome, where dangerously low blood pressure occurs. Dengue has become a global problem since the WW11 and is endemic in more than 110 countries. It ha increased dramatically since the 1960s, with between 50 and 528 million people infected yearly. http://en.wikipedia.org/wiki/Dengue_fever Downloaded 12/6 14

² Escherichia (commonly abbreviated E. coli) is a Gram-negative, rod-shaped bacterium of the genus Escherichia that is commonly found in the lower intestine of warm-blooded organisms (endotherms).

³ Listeriosis is a bacterial infection most commonly caused by Listeria monocytogenes. Listeriosis primarily causes infections of the central nervous system (meningitis, meningoencephalitis, brain abscess, cerebritis) and bacteremia in those who are immunocompromised, pregnant women, and those at the extremes of age (newborns and the elderly), as well as gastroenteritis in healthy persons who have ingested a large inoculum of the organism. Listeria is ubiquitous in the environment and is primarily transmitted via the oral route after ingestion of contaminated food products, after which the organism penetrates the intestinal tract to cause systemic infections. The diagnosis of listeriosis requires the isolation of the organism from the blood and/or the cerebrospinal fluid. Treatment includes prolonged administration of antibiotics, primarily ampicillin and gentamicin, to which the organism is usually susceptible.

⁴ The Italian Unabomber is a name given by the international media to an unknown terrorist tied to a series of booby-trap bombings in northern Italy, specifically in the Veneto and Friuli-Venezia Giula regions, which began in 1994. These bombs were hidden in innocent items such as Easter eggs, coloring markers, bubble blowing tubes. and umbrellas and the the perpertraortor was thought to be targetting children. Italian law enforcement officials and the American FBI believed that Unabomber was Elvo Zornitta, an Italian 49-year-old engineer who was been charged with planting 20 bombs after police raided his home in August 2006. The case was dropped in 2009 after the prosecutors asked for its dismissal, for lack of evidence. Elvo Zornitta received €2,500,000 as compensation for his arrest and trial which were based on false evidence.

⁵ Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. Compared to traditional binary sets (where variables may take on true or false values), fuzzy logic variables may have a truth value that ranges in degree between 0 and 1.

⁶ In mathematics, the convex hull or convex envelope of a set X of points in the Euclidean plane or Euclidean space is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape formed by a rubber band stretched around X.

⁷ The reader is referred to a stimulating thesis by Rittel and Webber who have suggested that problems can, and should, be usefully categorized into two types: “tame problems” and “wicked problems” The former are solved in a linear, traditional known and tried “water fall paradigm”; gather data, analyze data, formulate solution, implement solution. The latter “wicked problems” can only be responded to individually, each time anew, with no ultimate, repeatable solution. Rittel, Horst, and Melvin Webber, (1973) Dilemmas in a General Theory of Planning”. Policy Sciences, Vol. 4, pp 155-169. When considering this thesis it is necessary to also consider that with the advent of artificial science and its theoretical underpinnings (chaos, complexity, and uncertainty theories) it is now posited that much of human behavior is complex, dynamic, multi-dimensional, level/phase structured, non-linear, law-driven and bounded (culture, time, place, age, gender, ethnicity, etc.). “Substance use”, however it is delineated and defined, and which is the focus of SUM's publications for the last 50 years, would be such a behavior/process. There are two important issues to consider from this thesis and which are derived from this: (1) Using linear models/tools to study non-linear processes/phenomena can and does result in misleading conclusions and can therefore also result in inappropriate intervention; (2) the concepts prediction and control have different meanings and dimensions than they do in the more traditional linear ‘cause and effect’ paradigms. (Buscema, M. (1998), Artificial Neural Networks, Substance Use & Misuse, 33(1-3). An additional stimuating thesis to consider when researching human behaviors is the one posited by the cyberneticist Heinz Von Foerster. He posited that there are two types of questions; legitimate and illegitimate ones. The former are those for which the answer is not known and is, perhaps, even unknowable during a given state of knowledge and technology- the effective control of man's “appetite” for a range of psychoactive substances, whatever their legal status An illegitimate question is one for which the answer is known, or, at the very least consensualized.The asking of illegitimate questions has been, and remains, by and large, the acculturated norm. Heinz Von Foerster, Patricia M. Mora, and Lawrence W. Amiot, “Doomsday; Friday, 13 November, A.D, 2026,” Science, 132, 1960. pp. 1291-1295. The reader is referred to Pablo Neruda's The Book of Questions for a poetic exploration of legitimate questions. Editor's note.

Additional information

Notes on contributors

Massimo Buscema

Since 1986, Massimo Buscema has been Director of Semeion, Research Center of Sciences of Communication, Rome, Italy. From 2010: Adjunct Professor in the Department of Mathematics and Statistics of the University of Colorado, Denver. Member on the Editorial Board of various international journals. He has designed, constructed, developed new models and algorithms of Artificial Intelligence. Author of scientific publications on theoretical aspects of Natural Computation, with over 250 titles (scientific articles, essays, and books (23) on the same subject) and over 35 Software Systems used in many university and research Centers. Inventor of 22 international and USA patents.