Crossing the boundary - analogue universe, digital worlds

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6.4 Setting models in motion – the power of simulation

Our universe – everything about us – appears to obey laws, which govern how aspects of the world relate to one another. Scientists refer to these as natural laws, as they seem to be constants of nature, and to distinguish them from laws made by people.

Exercise 17

Write down any example of a natural law you can think of. What does the law tell us? Why do you think it is called a law?

Discussion

One of the most obvious is the law of gravity. This tells us that any two bodies will be attracted to one another by a force that depends on their masses and their distance from one another. Gravity is a law because it applies to every mass, always and everywhere.

The features included in both the classes of model I described above are also regulated by laws. For climate models, such laws include:

• the Navier-Stokes equations which relate the movement of air, up and down or east and west, to the earth's rotation, friction, turbulence and pressure;

• the thermodynamic equation which relates rises or falls in temperature to heat coming from the sun, from condensation and from other sources.

Matter, dark matter and the energy of the early universe are similarly governed by laws, such as gravity and the three laws of thermodynamics.

All these laws describe how things change in relation to one another over time – how air flows, how things warm up and cool, how matter clumps together. Now, if we write and run a program that applies the relevant laws to the model, we can show how things will change as time goes on. We can project the model forward into the future to predict what things will be like then. Of course, in our world time passes smoothly and continuously, in analogue fashion, so we will have to split it up into a series of intervals, rather as we did with the sampling of a waveform in . So, as we run the simulation forward in time, the picture looks like Figure 33.

Figure 34 Running a simulation forward in a series of discrete steps

Finally, we need some means of visualising the digital model as it evolves over time. This is a difficult issue, beyond the scope of this course. There are examples of such visualisations below.

Running climate simulations enables us to forecast the weather, in terms of future temperatures, winds, rainfall, and so on. Data gathered from weather stations and satellites is entered into the model and it is run forward in time to predict future weather patterns. Examples are shown in Figures 34a and b.

Figure 35 Simulated predictions of weather patterns

Even more significantly, atmospheric simulations help with predictions about the long-term future of the climate. We can range over a number of possible futures, looking for answers to the sorts of questions I raised earlier.

By contrast, cosmological models help our understanding of the past and the present. We know how things look now. If our simulation evolves from its beginning at a point early in time into a state resembling the present-day universe, then it means the model of the cosmos in those very early times is an adequate one. There are some visually stunning presentations of this in Figures 35a and b.

Figure 36 Simulations of the early universe (a) about 500 million years after the Big Bang (b) after about 1 billion years

There are also cosmological models to range into the future. For example, one simulation probes the results of the collision between the Milky Way and the mighty Andromeda galaxy, one of our near neighbours in the Local Group (it is only about 9 million, million, million miles away). It might be premature to take out extra insurance, though. The crash is due to happen in about 3 billion years’ time.

Unfortunately, your desktop PC will not be able to handle simulations like these. The application of very complex laws, over and over, requires immensely powerful computers called supercomputers. Supercomputers are specially designed to carry out billions of numerical calculations a second. Even at these speeds, simulations may take hours, or even days, to run.

Other simulations

The range of possible simulations is endless, and each one can tell us things about the past, present and future aspects of our world. Two that might interest you are:

1. economic models;

2. the Tierra model of artificial life.

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