Is Life Analog or Digital?
Question for Edge discussion group
from Freeman Dyson
One of my favorite books is Great Mambo Chicken
and the Transhuman Condition" by Ed Regis.
The book is a collection of stories about weird ideas
and weird people. The transhuman condition is an idea
suggested by Hans Moravec. It is the way you live
when your memories and mental processes are down-loaded
from your brain into a computer. The wiring system
of the computer is a substitute for the axons and
synapses of the brain. You can then use the computer
as a back-up, to keep your personality going in case
your brain gets smashed in a car accident, or in case
your brain develops Alzheimer's. After your old brain
is gone, you might decide to upload yourself into
a new brain, or you might decide to cut your losses
and live happily as a transhuman in the computer.
The transhumans won't have to worry about keeping
warm. They can adjust their temperature to fit their
surroundings. If the computer is made of silicon,
the transhuman condition is silicon-based life. Silicon-based
life is a possible form for life in a cold universe
to adopt, whether or not it happens to begin with
water-based creatures like us made of flesh and blood.
Another possible form of life is the Black Cloud described
by Fred Hoyle in his famous science fiction novel.
The Black Cloud lives in the vacuum of space and is
composed of dust-grains instead of cells. It derives
its energy from gravitation or starlight, and acquires
chemical nutrients from the naturally occurring interstellar
dust. It is held together by electric and magnetic
interactions between neighboring grains. Instead of
having a nervous system or a wiring system, it has
a network of long-range electromagnetic signals that
transmit information and coordinate its activities.
Like silicon-based life and unlike water-based life,
the Black Cloud can adapt to arbitrarily low temperatures.
Its demand for energy will diminish as the temperature
Silicon-based life and dust-based life are fiction
and not fact. I use them as examples to illustrate
an abstract argument. The examples are taken from
science-fiction but the abstract argument is rigorous
science. The abstract concepts are valid, whether
or not the examples are real. The concepts are digital-life
and analog-life. The concepts are based on a broad
definition of life. For the purposes of this discussion,
life is defined as a material system that can acquire,
store, process, and use information to organize its
activities. In this broad view, the essence of life
is information, but information is not synonymous
with life. To be alive, a system must not only hold
information but process and use it. It is the active
use of information, and not the passive storage, that
The two ways of processing information are analog
and digital. An LP record gives us music in analog
form, a CD gives us music in digital form. A slide-rule
does multiplication and division in analog form, an
electronic calculator or computer does them in digital
form. We define analog-life as life that processes
information in analog form, digital-life as life that
processes information in digital form. To visualize
digital-life, think of a transhuman inhabiting a computer.
To visualize analog-life, think of a Black Cloud.
The next question that arises is, are we humans analog
or digital? We don't yet know the answer to this question.
The information in a human is mostly to be found in
two places, in our genes and in our brains. The information
in our genes is certainly digital, coded in the four-level
alphabet of DNA. The information in our brains is
still a great mystery. Nobody yet knows how the human
memory works. It seems likely that memories are recorded
in variations of the strengths of synapses connecting
the billions of neurons in the brain with one another,
but we do not know how the strengths of synapses are
varied. It could well turn out that the processing
of information in our brains is partly digital and
partly analog. If we are partly analog, the down-loading
of a human consciousness into a digital computer may
involve a certain loss of our finer feelings and qualities.
That would not be surprising. I certainly have no
desire to try the experiment myself.
There is a third possibility, that the processing
of information in our brains is done with quantum
processes, so that the brain is a quantum computer.
We know that quantum computers are possible in principle,
and that they are in principle more powerful than
digital computers. But we don't know how to build
a quantum computer, and we have no evidence that anything
resembling a quantum computer exists in our brains.
Since we know so little about quantum computing, I
do not consider it in this discussion.
I started thinking about the abstract definition of
life twenty years ago, when I published a paper in
Reviews of Modern Physics about the possibility that
life could survive for ever in a cold expanding universe.
I proved to my own satisfaction that survival is possible
for a community of living creatures using only a finite
store of matter and energy. Then, two years ago, Lawrence
Krauss and Glenn Starkman, friends of mine at Case
Western Reserve University in Cleveland, sent me a
paper with the title "Life, the Universe, and
Nothing". They say flatly that survival of life
for ever is impossible. They say that everything I
claimed to prove in my Reviews of Modern Physics paper
is wrong. I was happy when I read the Krauss-Starkman
paper. It is much more fun to be contradicted than
to be ignored.
In the two years since I read their paper, Krauss
and Starkman and I have been engaged in vigorous arguments,
writing back and forth by E-mail, trying to pokes
holes in each others' calculations. The battle is
not over, but we have stayed friends. We have not
found any holes that cannot be repaired. It begins
to look as if their arguments are right, and my arguments
are right too. We can both be right because we are
making different assumptions about the nature of life.
It turns out that they are right, and life cannot
survive for ever, if life is digital, but I am right,
and life may survive for ever, if life is analog.
This conclusion was unexpected. In the development
of our human technology during the last fifty years,
analog devices such as LP records and slide-rules
appear to be primitive and feeble, while digital devices
are overwhelmingly more convenient and powerful. In
the modern information-based economy, digital wins
every time. So it was unexpected to find that under
very general conditions, analog life has a better
chance of surviving than digital life. Perhaps this
implies that when the time comes for us to adapt ourselves
to a cold universe and abandon our extravagant flesh-and-blood
habits, we should upload ourselves to black clouds
in space rather than download ourselves to silicon
chips in a computer center. If I had to choose, I
would go for the black cloud every time.
The superiority of analog-life is not so surprising
if you are familiar with the mathematical theory of
computable numbers and computable functions. Marian
Pour-El and Ian Richards, two mathematicians at the
University of Minnesota, proved a theorem twenty years
ago that says, in a mathematically precise way, that
analog computers are more powerful than digital computers.
They give examples of numbers that are proved to be
non-computable with digital computers but are computable
with a simple kind of analog computer. The essential
difference between analog and digital computers is
that an analog computer deals directly with continuous
variables while a digital computer deals only with
discrete variables. Our modern digital computers deal
only with zeroes and ones. Their analog computer is
a classical field propagating though space and time
and obeying a linear wave equation. The classical
electromagnetic field obeying the Maxwell equations
would do the job. Pour-El and Richards show that the
field can be focussed on a point in such a way that
the strength of the field at that point is not computable
by any digital computer, but it can be measured by
a simple analog device. The imaginary situation that
they consider has nothing to do with biological information.
The Pour-El-Richards theorem does not prove that analog-life
will survive better in a cold universe. It only makes
this conclusion less surprising.
The argument of Krauss and Starkman is based on quantum
mechanics. If any material system, living or dead,
is finite, it will have only a finite set of accessible
quantum states. A finite subset of these states will
be ground-states with precisely equal energy, and
all other states will have energies separated from
the ground-states by a finite energy-gap. If the system
could live for ever, the temperature would ultimately
become much lower than the energy-gap, and the states
above the gap would become inaccessible. From that
time on, the system could no longer emit or absorb
energy. It could store a certain amount of information
in its permanently frozen ground states, but it could
not process the information. It would be, according
to our definition, dead. Krauss and Starkman thought
they had dealt a fatal blow to my survival strategy
with their argument. But I am still on my feet, and
here is my rebuttal. Their argument is valid for any
system that stores information in devices confined
within a volume of fixed size as time goes on. It
is valid for any system that processes information
digitally, using discrete states as carriers of information.
In a digital system, the energy gap between discrete
states remains fixed as the temperature goes to zero,
and the system ceases to operate when the temperature
is much lower than the energy gap. But this argument
does not apply to a system based on analog rather
than digital devices. For example, consider a living
system like Hoyle's Black Cloud, composed of dust-grains
interacting by means of electric and magnetic forces.
After the universe has cooled down, each dust-grain
will be in its ground-state, so that the internal
temperature of each grain is zero. But the effective
temperature of the system is the kinetic temperature
of random motions of the grains. Since electric and
gravitational energies vary inversely with distance,
the cloud must expand as its temperature cools. A
simple calculation shows that, in spite of the falling
temperature, the number of quantum-states accessible
to each grain increases with the three halves power
of the size of the cloud. The number of quantum-states
grows larger and larger as the cloud expands. In an
analog system of this kind, there is no ground state
and no energy gap.
An analog form of life, such as Hoyle's black cloud,
adapts better to low temperatures, because a cloud
with a fixed number of grains can expand its memory
without limit by increasing its linear scale. The
quantized-energy argument does not apply to an analog
system, because the number of quantum-states is unbounded.
At late times quantum mechanics becomes irrelevant,
and the behavior of the system becomes essentially
classical. The number of quantum states becomes so
large that classical mechanics becomes exact. When
analog systems work classically, the quantized-energy
argument fails. That is why survival is possible in
the domain of classical mechanics although it is impossible
in the domain of quantum mechanics. Fortunately, classical
mechanics becomes dominant as the universe expands
and cools. But Krauss and Starkman have not yet conceded.
I am still expecting them to come back with new arguments
which I will then do my best to refute.
It seems to me now that the question, whether life
is analog or digital, is more interesting and perhaps
more important, than the question of ultimate survival
out of which it arose.