My favorite quote regarding simulations comes from Dr. George Rose, professor at the Johns Hopkins School of Medicine:
Running simulations is very much like masturbation. Do it often enough, and it starts to feel better than the real thing.
The advantages and disadvantages of computer simulations are somewhat obvious. On the plus side, simulations are cheap (generally - supercomputer time can be expensive) and just cost computer time. Simulations can be used to model population dynamics without going out in the field and counting populations of animals. Simulations can estimate which drugs will be good candidates for interactions with a certain protein, thereby narrowing the number of chemicals to synthesize in drug trials. For the researcher, simulations allow total control over every parameter in the system. In molecular dynamics, one can separate the energy from hydrogen bonds, from electrostatics, etc., something which is nearly impossible in experimental setups.

The down side is, as the aforementioned quote warns, that simulations only model what they are told to model, not necessarily reality. The simulation may even work in special cases, but changing any of the parameters might cause it to behave unpredictably. The cornerstone of good simulation science is constant communication with experimentalists. A healthy respect for the limitations of the simulation, and efforts to verify simulated models with real data, strengthen both the validy of the simulation, and the understanding of the experimental results.

More graph excitement, for your viewing pleasure.

Given two graphs G1 = (V1, E1) and G2 = (V2, E2), and a binary relation R, R is a simulation if for every vertex in V1 and V2 and every edge in E1, if there is a mapping between two vertices (x1 and x2) (that is, an entry in R), and an edge from the vertex in V1 - x1 - to another vertex in V1 - y1 - then there is a mapping from that second vertex - y1 - to a vertex in V2 - call it y2, and an edge between the vertices x2 and y2. You can make your simulation more strict by labelling the edges, and requiring that the edges in each graph that are 'equivalent' be of the same label.

Perhaps a picture would help. Let's say you've got three 'points'. You've got an edge from x1 to y1, and a mapping from x1 to x2:


If that's the case, then there must be some point y2 that makes the picture look like this:

 |         |
 |         |
\/         \/

One use of this sort of thing - relations, simulations, graphs - is typing semistructured data. The above writeup breathes its full force in this case - the tighter the typing you make, the more complex is the model you end up with. The less strict, the less closely your model resembles the original system, and potentially the less useful the model is.

A simulation is a concrete abstraction of the relevant features of some real world problem.

A simulation differs from a mathematical formula in that mathematical formula are represented in abstract symbols whereas simulations are represented in symbols with a direct correspondence in the real world problem space. A good example of this is gravity: gravity can be modelled as a well known set of formula first developed by Sir Isaac Newton or a set of spheres (each representing an object in the solar system) in a machine which moves them approximately as the real world celestial bodies moves. In pre-computer eras these models were often elaborately made from brass and oak, now they are typically made on a computer.

The ultimate simulation is Albert Einstein's class of "thought experiments" in which he encouraged researchers to simulate experimental setups in their mind. In this role the imagination is the ultimate simulator.

Simulations often suffer because one of more relevant features is not included in the simulation, thus the selection of features requires some skill. Including all features is not possible (since such a simulation would be as large and complex as the real world thus both impossible to build and not an abstraction). When simulations are performed using a computer rather than the imagination or physical models it is much harder to catch these problems because the operators have less contact with what is "really" happening.

Another problem with computer simulations is that you generally need a good mathematical formulation of the problem and a reasonable idea of the starting state.

Sim`u*la"tion (?), n. [F. simulation, L. simulatio.]

The act of simulating, or assuming an appearance which is feigned, or not true; -- distinguished from dissimulation, which disguises or conceals what is true.

Syn. -- Counterfeiting; feint; pretense.


© Webster 1913.

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