[#15] Computer Simulations as Dynamical Metaphors
By Piet Hut
When we want to communicate really new ideas, we face a problem: we can't easily use existing terms to do so. So how to point out something new? A quick way is to use a metaphor; a more round-about but richer way is to employ a narrative. A computer simulation can embrace both: starting with a metaphor or analogy, we can let that condensed picture run, turning it into a movie. In that way, we can dynamically produce a story unfolding in time.
The distinction between analogies and metaphors is a bit fuzzy. When there is a clear one-to-one correspondence between reality and a computer simulation, we can speak of an analogy. A simulation of the orbits of bodies in the solar system, whether planets or asteroids or comets, typically has a single point particle representing each heavenly body. However, in a simulation of two colliding galaxies, the correspondence is much more indirect.
A nice example is the simulation of the future orbits of our own galaxy and our neighbor, the Andromeda galaxy. These two galaxies are on a collision course. In about four billion years, they will collide. The Earth, and our whole solar system, will be okay, since the stars of the two galaxies will not be affected. It will be as if two very dilute swarms of fire flies would meet and just pass through each other. But the overall shapes of the galaxies will change dramatically, as shown in the successive panels of the picture shown here.
Even though it looks as if each point of light corresponds to a star, in fact, the correspondence is much more indirect. Each galaxy contains many hundreds of billions of stars, far too many to simulate one-on-one in even the largest supercomputers. So what we astronomers do is to use a fluid approximation, conceptually smearing out all the stars into continuous streams (for the aficionados: in 6-dimensional phase space), as a first step. As a second step, we then add tracer particles to those streams, like smoke particles in a wind tunnel, to visualize those streaming motions. Finally, we color those particles as if they were stars, each shining a little light. And voila, the beautiful pictures of shining smoke in our cosmic wind tunnel.
Clearly, the specks of light in the pictures here are not a direct analogy of the stars in the galaxies. I think these simulations are more akin to a metaphor, but not a static metaphor: rather a metaphor that acquires meaning in the time domain, by dynamically showing how the "fluid" of stars evolves under the forces of gravity.
If we look at biology, where the phenomena are vastly more complex than in (astro)physics, we have a choice. Either we can try to set up computer simulations that are relatively close to the phenomena, in an attempt to set up a dynamic analogy, or we try to take a more bird's eye view of only the most essential characteristics. An example of the former is to map out a detailed metabolic network within a living cell, and to then simulate its behavior. An example of the latter is the game of life, a cellular automata simulation, shown in the banner at the top of this blog post. The game of life has only the barest minimum of some of the characteristics of life, and therefore I would call that a dynamic metaphor, rather than a dynamic analogy.
And if we look at philosophy, traditionally this has been fertile ground for the use of metaphors, or in longer forms allegories or parables, to illustrate key ideas. Plato's cave is one example. He posits a reality that is more real, his realm of ideas, of which our everyday world is only a distorted image, like shadows on the wall of a cave. Only by turning around and leaving the cave will we be able to see the full sunlight, according to him.
Modern philosophers have also posited a reality that is more fundamental than what meets the eye. Kant introduced the notion of a transcendental subject, something that carries a priori knowledge of space and time, for example, but that is not part of the world. It has no place in this world, neither the world of everyday life, nor that of natural science.
Another German philosopher, Husserl, in turn introduced his version of a transcendental subject, much more dynamic and accessible than Kant's version. His transcendental subject is in fact the very core of our conscious experience, which we can experience as such by learning to bracket the world of appearances, for which he gave a detailed recipe.
Einstein in his general relativity theory made Newton's absolute space and time dynamic, by allowing matter and energy to curve spacetime. In a similar way, Husserl allowed the transcendental subject to interact in a two-way street with the world around us, rather than only be given in the a priori way of Kant. This is a big topic in itself, which I would like to come back to in a future blog post. To give just one example: it would be very interesting to see whether we could find sensible ways to simulate the interaction between Husserl's transcendental subjects and the world in which we find ourselves.
I can't help think that some of the greatest philosophers of the past, who have given us a legacy of influential metaphors, would have also left us equally interesting simulations, if only they had access to the power of computers.
Piet Hut is President of YHouse (where this blog is hosted), Professor of Astrophysics and Head of the Program in Interdisciplinary Studies at the Institute for Advanced Study in Princeton, and a Principal Investigator and Councilor of the Earth-Life Science Institute in the Tokyo Institute of Technology.