Abstract
The universe of computer simulations is vast, flourishing in almost every scientific discipline, and still resisting a general conceptualization. From the early computations of the Moon’s orbit carried out by punched card machines, to the most recent attempts to simulate quantum states, computer simulations have a uniquely short but very rich history.
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Notes
- 1.
It is worth noting that our neuronal network activity is, in some specific cases, faster than any supercomputer. According to relatively recent publication, Japan’s Fujitsu K computer, consisting of 82,944 processors, takes about 40 min to simulate one second of neuronal network activity in real, biological time. In order to partially simulate the human neural activity, researchers create about 1.73 billion virtual nerve cells that were connected to 10.4 trillion virtual synapses (Himeno 2013).
- 2.
Many philosophers have tried to understand the nature of computer simulations. What I have offered above is just one possible characterization. For more, the reader could refer to the following authors: Winsberg (2010, 2015), Vallverdú (2014), Morrison (2015), and Saam (2016).
- 3.
For the full code, see Woolfson and Pert (1999b).
- 4.
Strictly speaking, a simulation model is a more complex structure consisting, among other things, of a specification coded in a programming language as an algorithm and finally implemented as a computer process. Although the same specification can be written in different programing languages and implemented by different computer architectures, they are all considered the same simulation model. Thus understood, the programming language by itself does not determine the notion of ‘simulation model.’ I shall discuss these issues in more extent in Chap. 2.
- 5.
An interesting introduction to the history of computer science can be found in the work of Ceruzzi (1998), De Mol et al. (2014, 2015), and particularly on computer simulations Ören (2011a, b).
- 6.
Regarding this last point, Prof. Ören has organized in 1982 a NATO Advanced Study Institute in Ottawa focused on addressing the context for the uses of computer simulations (personal communication). See for instance, the articles published in (Ören et al. 1982; Ören 1984).
- 7.
The authors identify ‘numerical methods’ with ‘computer simulations’ (Ardourel and Jebeile 2017, 202). As I show next, these two concepts must remain separate. However, this does not represent an objection to their main claim.
- 8.
A clarification is due here. A computer is not technologically impaired to simulate an enriched uranium sphere with a mass greater than 100,000 kg. Rather, the kind of constraints we find in computers are related to their own physical limitations and those indicated by theories of computation. Now, given that researchers want to simulate a real target system, they must describe it as accurately as possible. If that target system is a natural system, such as a uranium sphere, then accuracy dictates that the simulation is limited on the mass of the sphere.
- 9.
There are many other contemporary authors that deserves our attention. Most prominently is the work of Claus Beisbart, who takes computer simulations as arguments (Beisbart 2012). That is, an inferential structure encompassing a premise and a conclusion. Another interesting case is Rawad Swaf and Cyrille Imbert (2013), who conceptualize computer simulations as ‘unfolding scenarios.’ Unfortunately, space does not allow me to discuss these authors in more extent.
- 10.
For details, see Humphreys (2004, 102–103).
- 11.
I should also mention that there are several other contrivances also involved in the design and programming of computer simulations. In this respect, Sect. 4.2 presents and discusses some of them, such as calibration procedures, and verification and validation methods.
- 12.
The problem can be best described as finding a way to cross each of the seven bridges of the city of Königsberg only once. The problem, solved by Euler in 1735, laid the foundations of graph theory.
- 13.
The Travelling Salesman Problem describes a salesman who must travel between N number of cities and keep the travel costs as low as possible. The problem consists in finding the best optimization of the the salesman’s route.
- 14.
Running a second computer simulation that could confirm these results is becoming standard practice (Ajelli et al. 2010).
- 15.
Although nowadays Schelling’s model is carried out by computers, Schelling himself warned against its use for understanding the model. Instead, he used coins or other elements to show how segregation occurred. In this respect, Schelling says: “I cannot too strongly urge you to get the nickels and pennies and do it yourself. I can show you an outcome or two. A computer can do it for you a hundred times, testing variations in neighborhood demands, overall ratios, sizes of neighborhoods, and so forth. But there is nothing like tracing it through for yourself and seeing the process work itself out. It takes about five minutes no more time than it takes me to describe the result you would get” (Schelling 1971, 85). Schelling’s warning against the use of computers is an amusing anecdote that illustrates how scientists could sometimes fail in predicting the role of computers in their own respective fields.
- 16.
Schelling also introduced a 1-D version, with a population of 70 agents, with the four nearest neighbors on either side, the preference consists of not being minority, and the migration rule is that whoever is discontent moves to the nearest point that meets her demands (Schelling 1971, 149).
- 17.
In truth, depending on how the Schelling model is design and programmed, it could also qualify as an Cellular Automata. Thank you Andrés Ilčić for pointing this out to me.
- 18.
This is especially true for the traditional sense of ‘evidence’ (i.e., empirically based) that Kröpelin refers to. Other forms of evidence also include results of well-established simulations, verification and validation, convergence of solutions, etc.
- 19.
A ‘word’ represents the minimum unit of data used by a particular computer architecture. It is a fixed sized group of bits that are handled as a unit by the processor.
- 20.
The prefix ‘pseudo’ reflects the fact that these methods are based on an algorithm that produces numbers on a recursive basis, eventually repeating the series of numbers produced. Pure randomness in computers can never be achieved.
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Durán, J.M. (2018). The Universe of Computer Simulations. In: Computer Simulations in Science and Engineering. The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-319-90882-3_1
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