My first love is the physics of information and computation, and
the informational modeling of physics. This was the subject of my PhD
version, searchable version), and has been
the focus of most of my subsequent research. I was privileged to work
with Edward Fredkin, Tom Toffoli and Charles Bennett at
the MIT Information
Mechanics Group between 1980 and 1995, first as a PhD student, and
then as a Research Scientist.
At MIT, in addition to (and often instead of) more theoretical work
on physics and
cellular automata, I worked with Tom Toffoli on the design and use
of Cellular Automata Machines (book), and
led the CAM-8 CA
machine project, working closely with Tom. CAM-8 was a
spatially-organized mesh-architecture multiprocessor that provided a
tool for investigating the possibilities of the kind of large-scale
fine-grained parallelism that is available in nature. It was
successful in this, but DARPA canceled all of
its parallel processing projects before CAM-8 machines had been built
that were large enough to let us see into the previously inaccessible
"band of the computational spectrum" that was our true target. My
later SPACERAM design generalized CAM-8's
architecture into an almost-ideally-efficient building-block for
spatial SIMD computations and bit-mapped virtual reality, but has not
yet been built.
My current research is again focused on theoretical questions at
the interface between physics and computation. A finite physical
system with finite energy has only a finite set of distinct (mutually
orthogonal) quantum states, and changes between distinct states at
only a finite rate. This
finite-state character makes all physical systems close kin to
digital computers, with fundamental physical quantities such as
energy, momentum and action being generalizations of fundamental
computing quantities. Classical spacetime is effectively discrete,
because finite energy and momentum play the role of finite bandwidth
in rate-limiting distinctness in the quantum wavefunction. Quantum
uncertainty reflects a continuous description of discrete quantities.
models can play the same
foundational role in dynamics that they do in statistical
Finite-state classical mechanics (2018, discusses how a reversible lattice gas evolution can be equivalent to discrete samples of a continuous classical mechanical evolution, with energy and momentum tied to state change in a realistic manner. Fixing classical mechanics to be more realistic informationally and energetically is foundational for mechanics).
Counting distinct states in physical dynamics (2021. Counting is as fundamental in dynamics as it is in statistical mechanics -- it defines basic quantities. Counting distinct states refines our understanding of uncertainty and measurement and defines a finite classical resolution for space and time. Classical mechanics should be treated as maximally distinct, not infinitely distinct, and the least action principle counts distinct motion).
A simulation of a six direction lattice gas fluid
flowing past a half cylinder, exhibiting vortex shedding. Visualized
by also simulating a "smoke" fluid within the CA. System is 2Kx1K.
Diffusion and sound waves in a reversible lattice gas
The four direction TM lattice gas is started with a 50% density of particles, except for an empty region (black) in the center. Half of the particles are colored blue and half yellow, so that both diffusion and waves are
visible at the same time. The lattice is 512x512.
Slow-time model of refraction and reflection
Block-partitioning version of invertible momentum-conserving lattice gas, with particles moving diagonally. Locations marked with blue are left unchanged in half of the updates. We show a soliton colliding with a circular slow-time region. The lattice is 512x512.