2015 48th Hawaii International Conference on System Sciences
Toward a Theory of Knowledge Economics: an information systems approach
Martin Hilbert
University of California, Davis; [email protected]
engineering and computer science. This article applies
concepts from theories developed for the engineering
of technologies systems to social systems and
economic dynamics. The idea is to use our
understanding of how information systems work with
knowledge to describe aspects of how the knowledge
economy works. If we are able to formulate both
technological systems and economic processes within
the same analytical language, we will also be able to
create a theory that treats socio-economic and
technologic information processes as the mutually
dependent whole that they reassemble in the
knowledge economy.
The approach taken in this article shows that the
reformulation of general economic evolution in terms
of information theory sheds a new light on several
aspects of economic dynamics. It follows a long
tradition in taking an evolutionary and multilevel
approach to knowledge [32,33]. More than using these
concepts as analogies, it formalizes them in concrete
mathematical representations. For example, economic
natural selection (such as through market dynamics)
can be modelled as uncertainty reduction through
negative entropy. Concepts like ‘economic fitness’
obtain a new meaning as the literal information ‘fit’
(the quantifiable amount of mutual information)
between the evolving socio-economic system and its
environment. Such fit occurs over multiple levels. As a
natural result of this approach, it shows that absolute
knowledge of economic dynamics can maximize
economic payoff. The presented derivations work with
formal notions of information and knowledge (such as
entropy, mutual information, and Kolmogorov
complexity), which can be quantified (for example in
bits and bytes). This effectively converts the amount of
knowledge into a quantifiable ingredient of economic
growth.
Intuitively the argument of this article is as follows.
If you have information about a specific event, you
have the potential to act on it and to extract economic
benefit from it; if you don’t, you don’t. How you
obtain this information (be it through empirical
analysis, a humanly communicated cue, or any other
hint) is another question. Fact is that the amount of
information is quantifiable (for example in bits), and
that the equations of economic evolution can show a
Abstract
A comprehensive theory of knowledge societies and
knowledge economics is still missing. This article
shows that the analytical tools from computer science,
information systems and information theory provide an
adequate language to work toward such theory. The
presented formalization follows an evolutionary and
multilevel approach, and embraces both the concepts
of information and knowledge. It is shown that
economic evolution can be modeled as a process that
selects superior strategies from a set of possibilities
through natural (market driven) selection. This reduces
uncertainty by the production of negative entropy
(‘negentropy’). Furthermore, economic ‘fit-ness’ can
be modelled in terms of the informational ‘fit’ of the
economic system with its environment, which takes the
form of Shannon’s mutual information. In the case of a
deterministic dynamic, uncertainty reduction takes the
form of a predictable algorithm, which is quantified
through Kolmogorov complexity. The length of such
algorithm represents the knowledge about the
unfolding dynamic. This shows that we might be able
to eventually describe both, economics and
technological information systems within the same
analytical framework.
1. Introduction
“Many of the most general and powerful
discoveries have arisen, not through the study of
phenomena as they occur in nature, but, rather, through
the study of phenomena in man-made devices, in
products of technology… Our knowledge of
aerodynamics and hydrodynamics exists chiefly
because we created airplanes and ships, not because of
the existence of birds and fishes. Our knowledge of
electricity came mainly not from the study of lightning,
but from the study of man’s artefacts” [1]. In this
sense, our understanding of what information and
knowledge is benefits significantly from the study of
artificial devices that replicate intelligent processes.
This suggests that knowledge economics can best be
understood not by studying it as it occurs in the
complex business setting of companies, but by looking
at it from the perspective of theoretical communication
1530-1605/15 $31.00 © 2015 IEEE
DOI 10.1109/HICSS.2015.461
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On the other side, adopting a formal definition from
information theory, information is related to the
reduction of uncertainty and uncertainty implies
probabilities. One bit of code in a telecommunication
message provides the reduction of uncertainty of a
probability space by half [4-5].
The crux of the presented argument here consists in
the fact that both quantities (i.e. both bits) are
equivalent asymptotically. This asymptotic equivalence
of knowledge and information is due to the asymptotic
equivalence of deterministic and probabilistic
processes. The relevant proof is quite subtle and goes
back to Kolmogorov in 1968 [2], and was fleshed out
by Zvonkin and Levin two years later [6]. It has been
popularized in the information theory community by
Leung-Yan-Cheong and Cover [7] (see also the
standard textbook on information theory ([5], Ch. 14.3)
and among computer scientists and physicists by a
series of papers that eventually exorcised Maxwell’s
120 year old demon by the hands of Zurek [8-10] (for
an introduction see [11]). While we will not go into the
relevant math of this proof at this point, we review the
general intuition behind the argument.
Theoretically, the right measure to quantify the
notion of a deterministically unfolding process (an
algorithm) has been established by Andrey
Kolmogorov [2,12], and was independently developed
by Solomonoff [13] and Chaitin [14], and is known as
“Kolmogorov complexity” [2]. Kolmogorov defined
the amount of information in a deterministic algorithm
to be equal to the minimum number of symbols that we
need to efficiently describe an object to a specific level
of detail. Knowledge about the unfolding of a
dynamical system with two environmental states
requires a binary code (e.g. 1 and 0), resulting in an
algorithm that describes the occurrences of either the
one, or the other environmental state, like:
100100100100… . If this pattern is stable, we can
compress (e.g. by noticing that a 1 is always followed
by two 0s, resulting in a compressed algorithm that
looks something like: [repeat 100]). This algorithm
defines a stable endless series in a deterministic
manner. The length in bits of this optimally
compressed algorithm is its Kolmogorov complexity. If
the sequence would be totally random, we would need
to know bit by bit, and the algorithm would be just as
long as the sequence. The final length of the algorithm
quantifies the amount of knowledge the agent needs to
unequivocally describe such dynamical environmental
system.
Shannon [4], the founding father of information
theory, basically looked at the same issue the other
direct relation between this amount of information and
the economic potential to grow.
If you know about a series of unfolding events in
the future, you can even extract more economic
benefit. This converts (probabilistic) information, into
(deterministic) knowledge). Here we work with socalled algorithmic information theory (in the sense of
Kolmogorov complexity), not anymore with
probabilistic information theory (in the sense of
Shannon’s entropy). The more knowledge about a
process, the more potential to grow. The amount of
knowledge can also be quantified in bits (the number
of bits of the shortest program that describes the
algorithm). It turns out that the amount of information
about a possible event (such as measured in bits) is the
same as the amount of information needed to describe
the deterministic unfolding of a specific event (such as
measured in bits). In the first case, uncertainty is
reduced through communication (provision of
probabilistic informational bits). In the second case it is
provided by knowledge about the process (provision of
a deterministic algorithm encoded in bits).
2. How to formulize information and
knowledge
The natural branches of science to tackle the task of
formalizing knowledge and information are computer
science and information theory. It turns out that from
the point of view of these solid theoretical frameworks,
both knowledge and information are two sides of the
same coin. Just like two sides of a coin, they are not
identical, but they are two faces that show the same
quantity.
On the one side, adopting a strict computer science
definition, knowledge implies a step-by-step recipe of
doing something, a deterministic algorithm. If there is
knowledge, there is no doubt, there is a deterministic
procedure [2-3]. One bit of code in an informatics
program provides a deterministic instruction on a
binary choice on how to proceed in the algorithm. The
number of bits required to represent the shortest
expression of an algorithm is called Kolmogorov
complexity [12-14]. As such, knowledge (represented
in form of an algorithm) can be quantified in bits.1
1
It might be that the explicit form of the algorithm is
not revealed [20]. This does not change this logic, as
some kind of underlying process is surely executed
(even so it is not disclosed). The literature of
knowledge economics is full of examples where such
tacit knowledge algorithms are made explicit (such as
in the case of the famous home-baking machine in the
“knowledge creating company” of Nonaka and
Takeuchi [34]).
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way around. He asked: what is the likelihood that we
will pick one specific environmental state if we draw
randomly from the universe of all possible states? He
concluded that this likelihood is equivalent to the
amount of uncertainty that gets reduced when we are
‘informed’ about the correct state. Shannon’s
information is defined as the reduction of uncertainty
and uncertainty quantified with probabilities. He
defines that one bit reduces uncertainty exactly by half.
On the one hand, Shannon’s measure identifies the
object of interest based on the likelihood that this
object will appear amidst all possible objects
(probabilistic). On the other hand, Kolmogorov’s
measure involves a step-by-step description, an
executable procedure, or unambiguous recipe, in short,
an algorithm. When executed, such algorithms unfold
in time, because time is required to execute them.
Economic life is full of (more or less well defined and
approximate) algorithms. Economic routines [15] and
behavioral patterns [16] are often mentioned examples,
as are cultural norms [17] or institutionalized
mechanisms, procedures and habits [18-19]. The agent
might not be aware or might not be able to formulate
the details of the procedure (as with tacit knowledge,
[20]1), but it still has to be sorted and executed from
somewhere. Some procedures might also only be
approximate heuristics [16], which means that they are
not the optimal solution. However, in all of those
cases, the process is still deterministic (not
probabilistic). Kolmogorov’s measure quantifies the
amount of information in an algorithm and is therefore
often called “algorithmic randomness” [8] and
“algorithmic information” [9].
In short, Kolmogorov describes something by
contrasting it against all other possible things, and
Shannon evaluates the probability that something
appears among all other possible things. Since the
likelihood and the description are linked to the number
of alternative possible choices, both are approximated
on average by the information theoretic equivalent of
the law of large numbers (called the ‘asymptotic
equipartition property, see [5]). One consists of
‘knowledge’ (the ability to describe/recreate something
by following a deterministic procedural structure in
time) and the other one of ‘information’ (the reduction
of probabilistic uncertainty about a structure). In the
words of Cover and Thomas, who wrote the standard
text book on information theory: “It is an amazing fact
that the expected length of the shortest binary
computer description of a random variable is
approximately equal to its entropy” [5], and in the
words of Li and Vitanyi, who wrote the standard
textbook on Kolmogorov complexity: “It is a beautiful
fact that these two notions turn out to be much the
same” [3].
3. How economic evolution processes
information by reducing uncertainty
We will now apply both concepts to the general
notions of economic evolution (see also [21]). On the
one hand, if we have complete knowledge about any
economic dynamic, we can predict the deterministic
unfolding of the environment step-by-step. This means
that we have knowledge about the dynamic. If we
know the future, it is straightforward to maximize
economic growth within a given reality by reallocating
100% of the resources to the best available strategy.
On the other hand, if we have uncertainty about the
unfolding of the environment, economic evolution will
identify the superior strategy (or company) by means
of natural selection. The fittest strategy of all applied
strategies will survive. We can model this in terms of
conventional information theory as follows (see also
[22]).
We start with the traditional interpretation of fitness
as the factor of reproduction or economic growth,
and define the number of most fine-grained units at
time
as
, with:
, whereas the units of
the evolving population are freely selectable,
indivisible, positive integers (number of US$ of
gamble bets and payoff, number of US$ of GDP, or
number of economic agents, etc.). Without loss of
generality, we can represent growth factors on a
logarithmic scale. This is common practice in
economics and in our case normalizes fitness at 0 for
. For
an unchanging population,
in
example, a logarithm of base 2 represents fitness
terms of the number of population doublings at each
time step. This simple set up is sufficient to express
fitness in terms of Shannon entropies (in the sense of
[4-5]):
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Equation (1.1) shows that if we assume that each
individual of the evolving population has its own,
uniquely distinguishable type, fitness measures the
uncertainty inherent in the future population, minus the
uncertainty of the present population (both consisting
with different ‘alphabets’, or ‘number of types’ in this
case, which can be due to minuscular mutations, etc.).
In the case of many mutations that result in many more
, uncertainty increases,
unique types at step
(see equation (1.1)). In the
and
case that evolution leads to the survival of one single
member at the final equilibrium stage at time
(‘survival of the fittest’), there is no uncertainty
anymore about who of all population members is the
. In this
chosen one and
case:
fitness on a higher level more than the sum of its parts
on a lower level [22].
The population fitness during an environmental
state is its expected average fitness (over all types)
. The long
given the environmental state :
term logarithmic population fitness over periods can
then be partitioned in time into the product of the
growth factors in the distinct environmental states ,
each appearing in its proportion
. For example,
the overall growth rate of an industry over the entire
year is the product of the share of growth rates on days
with much growth, and days with little growth.
The negativity of entropy (sometimes also referred
to as “negentropy” [23-24]) shows that economic
evolution --just like any process of communication -reduces uncertainty. While a communication processes
reveals a desired symbol of an uncertain alphabet,
evolution can be understood as a process that reveals
the fittest member of a population. The amount of
uncertainty reduced by evolution is measured by the
.
amount of negative entropy
This logic can be generalized to evolutionary
processes that are out of equilibrium and still ongoing
(no determination of the ‘fittest’ (yet)) [22]. Relative
entropy (the so-called Kullback-Leibler distance [5])
turns out to be the correct information theoretic metric
in this case. Being a relative metric, it allows to
quantify the resolved uncertainty relative to the present
or relative to the future. From the perspective of the
future, uncertainty has already been resolved, resulting
in the subtraction of relative uncertainty, while from
the perspective of the present, the descriptive
complexity of the involved uncertainty (such as
expressed in informational bits) is a positive ingredient
of fitness, as it is still to be exploited.
In this notation the single-bar emphasizes the
(arithmetic) ‘space-average’ over the different
population members, while the double-bar emphasizes
the additional (geometric) ‘time-average’ over the
observed period. We can expand and reformulate this
in space and
average population fitness
time:
In this notation the single-bar emphasizes the
(arithmetic) ‘space-average’ over the different
population members, while the double-bar emphasizes
the additional (geometric) ‘time-average’ over the
observed period. We can expand and reformulate this
in space and
average population fitness
time:
4. How fitness is about the informational fit
We can expand this logic to include the dynamic
between the evolving system and the environment. By
doing his, ‘fit-ness’ attains an intuitive, but formal
interpretation as the amount of ‘fit’ between the
evolving population and its environment. ‘Fit-ness’ is
related to the amount of informational ‘fit’ on a certain
level. This amount of mutual information represents
the emergent quantity that makes the total population
If the environment and the future state of the
population are independent, Shannon’s much
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celebrated mutual information [4] between the
environment and the present population emerges
naturally from the equation [22]. This is always the
case at the final end state of an evolutionary process in
which only the fittest has survived:
population fitness (with
and
therefore
(for related work see also [26-28].
As such, equation (2.1) is a generalization of Kelly’s
special case result, since it also holds for the less
restrictive case with variety of growth factors among
types (for more recent results on Kelly’s criteria see.
The basic idea behind Kelly’s bet-hedging (also
called Kelly gambling, or the Kelly criterion) is to not
maximize short-term utility, but to consider the long
term return over time. To optimize the growth rate, we
have to adjust our shares of types (which refer to a
variety in “space”) to the shares of the environment
(which refer to a variety in “time”). Kelly’s result in
equation (2.3) shows that the best we can do is to
maintain the shares of types proportional to the
occurrence
of
their
respectively
favorable
environments. In other words, if we have two possible
environments that occur with a distribution of 70 %
and 30 % of the time, we should maintain a stable
share of 70% of the type that grows faster in the first
environmental state, and 30 % of the type that grows
faster in the other environmental state (this can be
shown with a straightforward Lagrange multiplier
maximization for the asymptotic case, see [5], or
simply consider the fact that in this case the term
in equation (2.3) becomes
0). This is called a proportional betting strategy. It is a
clear-cut one-to-one relationship between what is
likely to be expected (“in time”) and the allocation of
current preferences right now (“in space”).
The technical reason behind the superiority of
proportional betting is that a geometric expansion
always overtakes arithmetic expansion [5], which is a
well-known result in economic literature. The
superiority of geometric expansion has become second
nature to most economists.
We can also reduce uncertainty with additional
side information about the future state of the
environment. The two sources for possible side
information can be the observation of the past
(“memory”) and observations of third events from the
present that correlate with the future (“cues”). Let
suppose that we have a certain amount of memory that
allows us to extract information about the future. The
importance of data analysis to predict future patterns
becomes increasingly important in a big data world
[29]. We will ask how much such information from
memory can increase our maximal growth rate. Aiming
at maximal growth rates we stick to proportional
betting, and the DKL term of equation (2.3) falls out.
According to equation (2.3), the remaining focus is
therefore set on the reduction of the uncertainty of the
future (its entropy H(T)) due to memory. The memory
about the past represents a new conditioning variable
.
Equation (2.2) shows that mutual information
between the current population and its environment
adds to current population fitness on a certain level.
Fitness obtains an intuitive explanation as the amount
of mutual information ‘fit’ between the evolving
system and its environment [22]. The amount of
mutual information also quantifies the amount of levelspecific emergence involved in an evolutionary
is exactly
process: the total
more than the (weighted) sum of its parts.
We could now assume an extreme case of relative
fitness in which each environmental state has only one
surviving
type
with
superior
fitness,
,
while
in
this
environmental state all other types die out with
. Only one type fits the
particular environment. In this case the fittest type
represents the entire population after updating,
, and equation (8.2)
simplifies to:
Equation (2.3) is a well-known result derived by
Kelly in 1956 [25]. Since both
and
are always
positive, it says that the attainable average population
fitness is reduced by the level of uncertainty inherent in
, as well as by the distance
the environment,
of the distribution of the evolving population from its
. Among other things, this leads to
environment,
the celebrated result in portfolio theory that a
proportional bet hedging strategy maximizes
3845
on basis of which we need to condition the likelihood
of the occurrence of a certain environmental state and
the ensuing distribution among our types. For example,
the past could have been a prolonged bear or bull
market. Let us suppose that they occurred with a
likelihood q(t-1) and (1-q)(t-1), respectively. Given a
certain past (bull or bear) the probability of future bull
or bear will be different (conditioning). We therefore
end up with two separate distributions, which are
distinguished by the conditional variable q(t│t-1), the
likelihood of environmental state t, conditioned on the
past (t-1). Therefore, the long term optimal growth
rate, conditioned on this memory is:
This measure is again Shannon’s celebrated
mutual information [4]. In our case it is the mutual
information between the information extracted from
the past, and the current environment. It quantifies how
much the memory of the past can tell us about the
future (this relation is of course noisy and therefore
probabilistic). In words, it says that information about
the past can increase the optimal growth rate exactly by
as much as the past can tell us about the future. If the
past tells us a lot about the future, the mutual
information between past and future will be high, and
fitness can be increased decisively. If the future is
independent from the past, the mutual information is 0
[4], and no increase is possible. This one-to-one
relationship between the amount of information (as
quantified by Shannon) and the increase in growth rate
provides information with a value, a fitness value.
Much in the same sense, we can now extent the
analysis and ask about how much an outside cue from
a third, but related event might increase fitness [21].
For example, we might observe the behavior of other
economic agents, or obtain a tip from an expert. In the
simplest case, the logic basically stays the same and we
can replace the conditioning variable of the past (T-1)
with any other conditioning variable of a cue, and
obtain the mutual information between the cue and the
.
environment:
5. Empirical application of the knowledge
economy
The resulting term is the conditional entropy
H(T│T-1), that quantifies the amount of uncertainty
that is left after the conditional variable is known [5].
For the difference between the optimal long term
growth rate with, and without memory we get:
This section takes the ideas of the previous section
and applies it to the empirical case of the knowledge
economy. In specific we calculate the amount of bits
processed by the export trade of the U.S. economy over
a period of twenty years. Fig. 1 is based on the data of
international export of 512 product groups of the USA
between 1982 and 1987, measured in nominal value of
thousand US$. Fig. 1 aggregates the 9 groups (code 0
to 8) of the official Standard International Trade
Classification (SITC), revision 2 [35-37] into two
higher level groups: on the highest level we distinguish
between two groups (non-manufacturing and
manufacturing). The first consists of Edibles (code 0:
Food and live animals chiefly for food; code 1:
Beverages and tobacco) and Substances (code 2: Crude
materials, inedible, except fuels; code 3: Mineral fuels,
lubricants and related materials; code 4: Animal and
vegetable oils, fats and waxes); and the second consists
of manufactured goods (code 6: Manufactured goods
classified chiefly by materials), and Machinery (code
7: Machinery and transport equipment; code 8:
Miscellaneous manufactured articles) (see Fig. 1).
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In other words, following our binary population
structure on the first level of fine-graining, during the
period between 1979 and 2000 the U.S.’s export
economy reduced 0.0007 bits of relative uncertainty.
This illustrates that equation (2.1) (unusual as it may
seem at first) is not mere theory, but can readily be
applied to practical cases. We can quantify how many
bits and bytes are processed by the knowledge
economy.
Fig. 1. USA’s export from 1979-2000 in nominal value
of thousand US$ (based on the 512 most completely
recorded export items of the first digit classification of
SITC revision 2).
6. Conclusion
The previous sections have presented a formal
way to shows that information from past experience
and from present cues can allow us to predict the future
better and therefore allows us to increase the growth
rate of the population if we allocate resources
accordingly. This makes intuitively sense: if we have
more information about the environment, we can adjust
the evolving population to environmental conditions
(therefore optimize the informational ‘fit’ between the
environment and the evolving system) and optimize
population growth/fitness. Each bit of information
allows us to increase fitness accordingly.
The fact that Shannon’s probabilistic information
metric arises in these equation can be intuitively
understood as follows [30]: imagine complete
uncertainty among 8 equally likely choices (e.g.
investment options). Having US$ 8, the bet hedging
investor would distribute US$1 to each all of those 8
choices and surely walk out with one winning dollar.
Let us assume that we receive 1 bit of information,
which is defined by Shannon [4] as the reduction of
uncertainty by half). As a result, the investor would
know which half of the investment options fail, and
which of the remaining 4 options are still equally likely
to succeed. He would now equally distribute US$2 of
his US$8 to each of the remaining 4 choices and walk
out with two winning dollars. One bit of information
reduced uncertainty by half and multiplied the obtained
gain by two. The equation shows that the logic of
dividing uncertainty by 2 will increase gains by 2 is not
a numerical coincidence, but a solid relation between
uncertainty reduction and achievable growth.
Using a less stylized example, imagine that several
bakeries discovered hidden relationships between the
weather and the demand for specific baked goods: the
demand for cake grows with rain, the demand for salty
goods with sunshine. This insight can be obtained
through a big data driven information system, or
simply through human observation. Conditioned on a
cue for rain or sunshine, a bakery can calculate
likelihoods of how many salty and sweet products it
will sell and there optimize its economic growth. In
practice, productivity increments of up to 20 % have
The overall compound annual growth factor over the
involved 21 periods is 2.4284. The respective
evolutionary fitness matrix for the first level (nonmanufacturing vs. manufacturing) is presented in Table
1. It shows that one third of the time the environment is
characterized by superior fitness of the nonmanufacturing sector (7 out of 21 periods) and two
thirds vice versa. The respective compound annual
growth rates during these kind of periods are presented
in the matrix.
Table 1. USA’s export fitness and environmental
distributions Level 1.
1.055
0.989
1.022
1.085
Calculating the required values following the logic
outlined above in equation (2.1), gives:
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environment [8-11]. This article has shown an analogy
for economic evolution: the amount of information and
knowledge the social system has about the
environment is equal to its potential to grow. This is
intuitively pleasing: the more knowledge and
information we have, the more our economic system
can grow.
This leads to the final question of how much true
and solid information we can obtain about the shortand long term patterns. In essence, this question is at
the heart of what economic analysis does: identifying
compressible structure and patterns in market forces
and human behavior in order to extract laws and rules
of thumb that allow us describe and predict the
dynamics of the system and act accordingly. In this
sense, economics itself becomes an input ingredient of
economic growth. The more we know about the
economy and its dynamics, the more we can allocate
resources to enable growth.
This shows that concepts and analytical tools from
computer science, information systems
and
information theory provide an adequate language to
describe, model and quantify the general role of
knowledge in economic dynamics. The result is
promising, since it proposes the possibility that
eventually we will be able to describe both, socioeconomic-, and technological information systems with
the same analytical language. This will not only
provide theoretical coherence to describe sociotechnological systems and their interplay, but will
surely also deepen our understanding of the role of
information systems in the knowledge economy.
been reported for individual bakeries that fine-tune
their strategy with the help of the binary conditioning
random variable rain/sunshine [31]. Fitness depends on
what is known about the uncertain future environment.
That is the basic argument of this article, and equations
(1.1) – (2.4) provide a formal way of how to present
this logic in terms of information theory.
It is straightforward to close the argument by
reconnecting this logic back to Kolmogorov’s notion of
algorithmic information: if we have a deterministic
algorithm about the series of sunny and rainy days, we
can optimize long-term growth by simply allocating
economic resources to match the algorithmic sequence
of the identified environmental pattern. Deterministic
knowledge is the extreme form of probabilistic
information. In possession of deterministic knowledge,
there is no uncertainty. Going back to equation (1.2),
this implies that all uncertainty can be resolved
immediately. Instead of waiting for evolution to
produce negentropy through natural selection, planned
intervention can shift all required resources
accordingly
and
optimize
fitness
through
‘knowledgeable intervention’. In the presence of
knowledge, there is no uncertainty.
In other words, knowledge and information are a
quantifiable ingredient of economic growth. To
achieve this superior growth rates, we can use
deterministic knowledge, or at least probabilistic
information about the environment. By obtaining
additional information about the future state of the
environment (from past experience or from cues that
correlate with the future), the achievable growth rate
can even be increased on average. Shannon’s
probabilistic measure of information emerged naturally
from our equations, which provides a very concrete
quantification of the contributions of information to
economic growth. The amount of information about
the future is exactly equivalent to the achievable
increase in growth rate. Since Shannon’s measure of
information converges with Kolmogorov’s algorithmic
measure of information, this means that the
algorithmic/ deterministic “law” that describes the
unfolding of the environment. In this case we “know”
something about the dynamical system that governs the
environment and can predict it into the far future. This
algorithmic knowledge about the unfolding future
reduces uncertainty and allows for optimizing the
allocation of resources to extract work from the
environment and grow. Ergo, knowledge increases
fitness.
The same logic is at the heart of the argument that
finally exorcised Maxwell’s notorious demon by the
hands of Zurek [8]. Either informational observations
or deterministic knowledge about the dynamical
system allows the demon to extract work from the
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