S. Zambelli, Computable, Constructive and Behavioural Economic Dynamics, Routledge, 2010, pp. 73-78
The Information Economy
In honor of Kumaraswamy Velupillai's 60th birthday
One can imagine a future society in which natural resources are
irrelevant and all that counts is information. I shall discuss this possibility,
plus the role that algorithmic information theory might then play as a
metatheory for the amount of information required to construct something.
I am not an economist; I work on algorithmic information theory (AIT).
This essay, in which I present a vision of a possible future information
economy, should not be taken too seriously.
I am merely playing with ideas and trying to provide some
light entertainment of a kind suitable for
this festschrift volume, given Vela's deep appreciation of
the relevance of foundational issues in mathematics for economic theory.
In algorithmic information theory, you measure the complexity
of something by counting the number of bits in the smallest program for
program → Universal Computer → output.
If the output of a program could be a physical or a biological system,
then this complexity measure would give us a way to measure of the difficulty of
explaining how to construct or grow something, in other words, measure
either traditional smokestack or newer green technological complexity:
software → Universal Constructor → physical system,
DNA → Development → biological system.
And it is possible to conceive of a future scenario in which technology
is not natural-resource limited, because energy and raw materials are
freely available, but is only know-how limited.
In this essay, I will outline four different versions of this dream,
in order to explain why I take it seriously:
Magic, in which knowing someone's secret name
gives you power over them,
Astrophysicist Fred Hoyle's vision of a future society in his science-fiction
novel Ossian's Ride,
Mathematician John von Neumann's cellular automata world
with its self-reproducing automata and a universal constructor,
Physicist Freeman Dyson's vision of a future green technology in
which you can, for example, grow houses from seeds.
As these four examples show, if
an idea is important, it's reinvented, it keeps being rediscovered.
In fact, I think this is an idea whose time has come.
Secret/True Names and the Esoteric Tradition
"In the beginning was the Word,
and the Word was with God, and the Word was God."
— John 1:1
— knowing someone's secret/true name —
is very important in the esoteric tradition [1, 2]:
Recall the German fairy tale in which the punch line is
"Rumpelstiltskin is my name!" (the Brothers Grimm).
You have power over someone if you know their secret name.
You can summon a demon if you know its secret name.
In the Garden of Eden,
Adam acquired power over the animals by naming them.
God's name is never mentioned by Orthodox Jews.
The golem in Prague was animated by a piece of paper with God's secret name on it.
Presumably God can summon a person or thing into existence
by calling its true name.
Leibniz was interested in the original sacred Adamic language of creation,
the perfect language in which the essence/true nature of each substance
or being is directly expressed, as a way of obtaining ultimate knowledge.
His project for a characteristica universalis evolved from this, and
the calculus evolved from that.
Huygens, who had taught Leibniz mathematics in Paris, hated the calculus ,
because it eliminated mathematical creativity and arrived at answers
mechanically and inelegantly.
Fred Hoyle's Ossian's Ride
The main features in the future economy that Hoyle imagines are:
Perhaps it's best to let Hoyle explain this in his own words :
Cheap and unlimited hydrogen to helium fusion power,
raw materials readily available from sea-water, soil and air
(for example, using
extremely large-scale and energy intensive
mass spectrometer-like devices
[Gordon Lasher, private communication]).
And with essentially free energy and raw materials, all that counts
is technological know-how, which is just information.
[T]he older established industries of Europe and America...
grew up around specialized mineral deposits—coal, oil,
metallic ores. Without these deposits the older style of
industrialization was completely impossible. On the political
and economic fronts, the world became divided into ``haves''
and ``have-nots,'' depending whereabouts on the earth's surface
these specialized deposits happened to be situated...
In Hoyle's fantasy, this crucial information
— including the design of thermonuclear reactors —
that suddenly propels the
world into a second phase of industrialization comes from another
world. It is a legacy bequeathed to humanity by a nonhuman civilization
desperately trying to preserve anything it can when being destroyed
by the brightening of its star.
In the second phase of industrialism... no specialized deposits
are needed at all.
The key to this second phase lies in the possession of an effectively
unlimited source of energy.
Everything here depends on the thermonuclear reactor...
With a thermonuclear reactor, a single ton of ordinary water can be
made to yield as much energy as several hundred tons of coal—and
there is no shortage of water in the sea. Indeed, the use of coal
and oil as a prime mover in industry becomes utterly inefficient
With unlimited energy the need for high-grade metallic
ores disappears. Low-grade ones can be smelted—and there
is an ample supply of such ores to be found everywhere.
Carbon can be taken from inorganic compounds, nitrogen
from the air, a whole vast range of chemical from sea water.
So I arrived at the rich concept of this second phase of
industrialization, a phase in which nothing is needed but the
commonest materials—water, air and fairly common rocks.
This was a phase that can be practiced by anybody, by any
nation, provided one condition is met: provided one knows
exactly what to do. This second phase was clearly enormously
more effective and powerful than the first.
Of course this concept wasn't original. It must have been
at least thirty years old. It was the second concept that I was
more interested in. The concept of information as an entity
in itself, the concept of information as a violently explosive
John von Neumann's Cellular Automata World
This cellular automata world first appeared in
lectures and private working notes by von Neumann.
These ideas were advertised in article in Scientific
American in 1955 that was written by John Kemeny .
Left unfinished because of von Neumann's death in 1957,
his notes were edited by Arthur Burks and finally published in 1966 .
Burks then presented an overview in .
The crucial point is that in von Neumann's toy world, physical systems
are merely discrete information, that is all there is.
And there is no difference between computing a string of bits (as in AIT)
and "computing" (constructing) an arbitrary physical system.
World is a discrete crystalline medium.
Two-dimensional world, graph paper, divided into square cells.
Each square has 29 states.
Time is quantized as well as space.
State of each square the same universal function of
its previous state and the previous state of its 4 immediate neighbors
(square itself plus up, down, left, right immediate neighbors).
Universal constructor can assemble any quiescent array of states.
Then you have to start the device running.
The universal constructor is part of von Neumann's self-reproducing
I should also mention that
starting from scratch, Edgar Codd came up with a simpler version
of von Neumann's cellular automata world in 1968 .
In Codd's model cells have 8 states instead of 29.
Freeman Dyson's Green Technology
Instead of Hoyle's vision of a second stage of traditional smokestack
heavy industry, Dyson [9, 10] optimistically envisions a green-technology
small-is-beautiful do-it-yourself grass-roots future.
The emerging technology that may someday lead to Dyson's utopia
is becoming known as
"synthetic biology" and deals with deliberately engineered organisms.
also referred to as "artificial life,"
the development of "designer genomes."
To produce something, you just create the DNA for it.
Here are some key points in Dyson's vision:
Solar electrical power obtained from modified trees.
(Not from thermonuclear reactors!)
Other useful devices/machines grown from seeds.
Even houses grown from seeds?!
School children able to design and grow new plants, animals.
Mop up excessive carbon dioxide or produce fuels from sugar
(actual Craig Venter projects ).
On a much darker note,
to show how important information is, there presumably exists a
sequence of a few-thousand DNA bases (A, C, G, T) for the genome of
a virus that would destroy the human race, indeed, most life on this planet.
With current or soon-to-be-available molecular biology technology,
genetic engineering tools,
anyone who knew this sequence could easily synthesize the corresponding pathogen.
Dyson's utopia can easily turn into a nightmare.
AIT as an Economic Metatheory
So one can imagine scenarios in which natural resources are irrelevant
and all that counts is technological know-how, that is, information.
We have just seen four such scenarios.
In such a world, I believe, AIT becomes, not an economic theory, but perhaps
an economic metatheory, since it is a theory of information,
a theory about the properties of technological know-how,
as I will now explain.
The main concept in AIT is the amount of information
required to compute (or construct)
something, X. This is measured in bits of software, the number of
bits in the smallest program that calculates X.
Briefly, one refers to H(X) as the complexity of X.
For an introduction to AIT, please see [12, 13].
In economic terms, H(X) is a measure of the amount of technological know-how
needed to produce X.
If X is a hammer, H(X) will be small.
If X is a sophisticated military aircraft,
H(X) will be quite large.
Two other concepts in AIT are the joint complexity
H(X, Y) of
producing X and Y together, and the
H(X | Y)
of producing X if we are given Y for free.
Consider now two objects, X and Y.
− H(X, Y)
is referred to as the mutual information
in X and Y.
This is the extent to which it is cheaper
to produce X and Y together
than to produce X and Y separately,
in other words,
the extent to which the technological know-how needed to produce
X and Y can be shared, or overlaps.
And there is a basic theorem in AIT that states that this is also
H(X) − H(X | Y),
the extent to which being given the know-how
for Y helps us to construct X,
and it's also
H(Y) − H(Y | X),
the extent to which being given the know-how
for X helps us to construct Y.
This is not earth-shaking, but it's nice to know.
(For a proof of this theorem about mutual information, please see .)
One of the reasons that we get these pleasing properties is that
AIT is like classical thermodynamics in that time is ignored.
In thermodynamics, heat engines operate very slowly, for example, reversibly.
In AIT, the time or effort required to construct something
is ignored, only the information required is measured.
This enables both thermodynamics and AIT to have clean, simple results.
They are toy models, as they must be if we wish to prove nice theorems.
Clearly, we are not yet living in an information economy.
Oil, uranium, gold and other scarce, precious
limited natural resources still matter.
But someday we may live in an information economy,
or at least approach it asymptotically.
In such an economy, everything is, in effect, software;
hardware is comparatively unimportant.
This is a possible world, though perhaps not yet our
1 July 2008
A. Coudert, Leibniz and the Kabbalah, Kluwer, Dordrecht, 1995.
U. Eco, The Search for the Perfect Language, Blackwell, Oxford, 1995.
J. Hofmann, Leibniz in Paris 1672-1676, Cambridge University Press,
1974, p. 299.
F. Hoyle, Ossian's Ride,
Harper & Brothers, New York, 1959, pp. 157-158.
J. Kemeny, ``Man viewed as a machine,'' Scientific American,
April 1955, pp. 58-67.
J. von Neumann, Theory of Self-Reproducing Automata,
University of Illinois Press, Urbana, 1966.
(Edited and completed by Arthur W. Burks.)
A. Burks (ed.), Essays on Cellular Automata,
University of Illinois Press, Urbana, 1970.
E. Codd, Cellular Automata, Academic Press, New York, 1968.
The Sun, the Genome, & the Internet, Oxford University Press,
New York, 1999.
A Many-Colored Glass, University of Virginia Press,
C. Venter, A Life Decoded, Viking, New York, 2007.
G. Chaitin, Meta Maths, Atlantic Books, London, 2006.
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