Norm Margolus
I am a Research Affiliate at the MIT Computer Science and Artificial
Intelligence Laboratory. I also consult for an Internet startup
(Permabit) that I helped start.
My first love is the physics of information and computation, and
the informational modeling of physics. This was the subject of my PhD thesis (MIT Physics 1987, 12MB PDF) 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 for a period instead of) more
theoretical work on physics and on reversible cellular automata, I led the design and
implementation of the CAM8 CA machine,
working closely with Tom Toffoli who led earlier
CAM projects. CAM8 was a spatiallyorganized mesharchitecture
multiprocessor that provided a tool for investigating the
possibilities of the kind of largescale finegrained parallelism that
is available in nature. It was successful in this, but the project
ended at the prototype stage, before CAM8 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 CAM8's
architecture into an almostideallyefficient buildingblock for
spatial SIMD computations and bitmapped 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 character makes all physical systems
close kin to digital computers, with fundamental physical quantities
such as energy and momentum being generalizations of
fundamental computing quantities. In fact, the mathematical
machinery of hilbert spaces and hamiltonian dynamics provides a natural way to describe
classical finite state systems using continuous time and space and
sampling theory: this correspondence lets us regard quantum mechanics
as a generalization of
finitestate classical mechanicsin the same way that quantum
computation is a generalization of classical computation.
 Some of my papers:
Physics and Lattice Gasses

PhysicsLike Models of Computation
(from 1984, in Physica D,
page 81).

Quantum Computation
(from 1986, in New Techniques and Ideas in Quantum Measurement
Theory, edited by Daniel Greenberger).

Parallel quantum
computation (from 1990, in Complexity, Entropy, and the Physics
of Information, edited by Wojciech Zurek).

A Bridge of
Bits (from 1993, in Proceedings of the Workshop on Physics and
Computation, edited by Doug Matzke).

The
maximum speed of dynamical evolution (from 1998, in Physica D,
page 188).

Crystalline Computation
(from 1999, in Feynman and Computation, edited by Anthony Hey).
 Universal cellular
automata based on the collisions of soft spheres (from a
conference in 1999, appears in Collision Based Computation,
edited by Andrew Adamatzky, page 107, (2002), and in New
Constructions in Cellular Automata, edited by David Griffeath and
Cristopher Moore. page 231, (2003)).

Looking at Nature as a Computer
(from a workshop in 2001, appears in International Journal of
Theoretical Physics 42:2, page 309, (2003)).
 Mechanical Systems that are
both Classical and Quantum (based on a talk given at the
Unconventional Computation Workshop, Santa Fe, March 22 2007). Roger
Critchlow turned one of the examples in this paper into a cute quantum/classical clock
demonstration in which the exact continuous motion of the clock's
hands is displayed
as a continuously evolving superposition of integertime states.

Quantum emulation of classical dynamics (2011, provides an isomorphism between classical finite state dynamics and quantum finiteenergy dynamics).

The maximum average rate of state change (2014, extends energy bound on maximum speed of dynamics to include average speed bound, relativistic bounds, and higher moments).
Lattice Architectures

Cellularautomata supercomputers for
fluid dynamics modeling (from 1986, in Physical Review Letters,
page 1694).

CAM8: a computer
architecture based on cellular automata
(from 1993, in Pattern Formation and LatticeGas Automata,
edited by A. Lawniczak and R. Kapral).
 An FPGA architecture
for DRAMbased systolic computations (from 1997, in Proceedings of
the IEEE Workshop on FPGAs for Custom Computing Machines, edited by
Arnold et. al., page 2).

An Embedded DRAM Architecture for
LargeScale SpatialLattice Computations (from 2000, in The 27th
Annual International Symposium on Computer Architecture, page 149).
 Mechanism for
efficient data access and communication in parallel computations on an
emulated spatial lattice (United States Patent 6,205,533
applied for in 1999, issued in 2001).
Lectures

Emulating
Physics: Cellular Automata that exhibit finitestate, locality,
invertibility and conservation laws
(a talk given at the Computing Beyond Silicon Summer
School, CalTech, June 24, 2002).

Physical
Worlds: Cellular Automata with computation universality at small and large scales
(a talk given at the Computing Beyond Silicon Summer
School, CalTech, June 25, 2002).

Spatial
Computers: Architectures and algorithms for largescale spatial computations
(a talk given at the Computing Beyond Silicon Summer
School, CalTech, June 26, 2002).

Nature as
Computer / Computer as Physics: Physical concepts enter Computer
Science and computer concepts enter Physics
(a talk given at the Computing Beyond Silicon Summer
School, CalTech, June 27, 2002).
Some Lattice Gas Movies
The models depicted in these movies are discussed above in the
paper "Crystalline Computation" and in the lecture "Emulating
Physics." All simulations were performed on CAM8.
 Diffusion and
sound waves in a reversible lattice gas (10MB): 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.
 Lattice gas fluid
flow (5MB): 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.
 "Slowtime"
model of refraction and reflection (5.7MB): blockpartitioning
version of invertible momentumconserving 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
slowtime region. The lattice is 512x512.
 Long range
forces in a lattice gas(3.5MB): a simulation of a six direction
lattice gas fluid with longrange forces. Force particles act at
three discrete distances to produce clumps that form an elastic
crystal. The model is discussed in A lattice
gas with long range interactions coupled to a heat bath (Yepez,
1993).
 A reversible model of
crystal growth (8MB): when a grey gas particle diffuses next to a
green crystal particle, it joins the crystal and emits a red heat
particle. The reverse also happens. The model is discussed in A thermodynamically
reversible generalization of diffusion limited aggregation (D'Souza and
Margolus, 1998).
 A cautionary tale...
email: nhm at mit.edu