ArticlePDF Available

Limits on the Communication of Knowledge in Human Organisations



Content may be subject to copyright.
Limits on the Communication of
Knowledge in Human Organisations
Jacky Mallett
Communication is ubiquitous. It is the invisible thread that binds all
attempts at human organization together. We use communication to give
orders, make suggestions, laboriously acquire and pass on knowledge; but rarely
stop to think about the mechanics of the process of communication itself. All
forms of co-operative human activity though, depend on communication
through their success, or failure.
Hayek was notable among economists in considering the economic
implications of the communication and possession of knowledge within
society. He recognised the dependency of economies on the actions of multiple
agents, none of which could possibly have complete knowledge of their mutual
endeavour. He recognized in particular the impossibility of the condition that
total knowledge of an economy could be known at a central point, the
requirement that is implicit in the idea of centrally planned economies.
Knowledge as such, although very real, is hard to quantify. Its
communication however is not. Constraints on communication in terms of
bandwidth, the amount of data that can be transmitted; latency, the time it
takes to transmit it; and message processing, the amount of effort or work
receipt of the contents of the message incurs, have become well understood
within the fields of real time data networks, and distributed computing. The
successful construction and operation of complex, world spanning
communication systems, the phone and data networks in particular, are the
results of this understanding.
Communication in data networks is handled as a problem of message
exchange between independent network nodes. Data networks are organised
collections of nodes, controlling communication links that can now route
traffic between hundreds of millions of end computers. The end computers in
their turn run individual instances of distributed applications that co-ordinate
their results over large numbers of computers by exchanging messages with
each other, via the underlying communication network.
Communication within human society, can also be viewed as a problem
of message exchange between independent agents, or people. Human society is
organised as collections of people, working co-operatively to achieve co-
ordinated results, using the exchange of messages between individuals to
facilitate their activities. In many respects, with appropriate adjustments made
for lower speeds and rather less reliability, the field of data communication
networks provides a wealth of theory and experience for understanding the
communication constraints that operate upon human organisations.
In this paper, we will discuss the effects of communication constraints
on human social and economic organization, from the perspective of some fifty
years of engineering and scientific endeavour in real time computer networks.
From this perspective it is straightforward to prove that Hayek was correct
about central planning, and that for large communicating systems, it is provably
impossible to perform this function with anything approaching complete
knowledge. Similar considerations of the arrangements of the communication
paths between nodes, their topology as it is referred to in computer
networking, play out in all forms of organized activity, with an opposing
tension between the topology most suitable for efficient distribution of control
or command information – the centralised, strictly hierarchical organisation -
and that which provides the largest capacity for the distribution and sharing of
information or knowledge, an organized partial mesh.
This allows us to add to Hayek’s explanations of spontaneous
or emergent order, an analytical explanation for some of their
features in terms of the restrictions they place on the
communications that can be performed by their constituent
members, and the source of some of their advantages and
Information Capacity
Claude Shannon’s paper, A Mathematical Theory of Communication[1],
published in 1948, is generally credited with providing the foundations of the
field of information theory and digital data communication. In it he formalized
several key concepts critical to the development of communications theory,
amongst them the idea of information as a single, unique message. This
definition of information was important, since it introduced the idea that there
is a quantitative difference between sending the same message to a number of
recipients, or sending each of them a different message. Shannon’s paper was a
discussion of the mathematics of data transmission and receipt, with respect to
how signals could be compressed in order to make communication more
efficient. (At that time, low bandwidth and error prone communication links
were the norm.) In this context the presence of repeated identical information
allows for considerably more compression of the signal, and hence faster
communication, than would otherwise be the case.
Shannon quantified the amount of communication that could be
achieved between a single sender and receiver in terms of the amount of
information that could be transmitted on that channel during a specified time
interval, i.e. the number of unique messages that could be sent. He showed that
given the latency characteristics of a channel, where latency is the time taken to
transmit the message, that there is a limit on the total amount of information
that could be transmitted between two nodes in a given time period. Nodes
may have more or less information than that available for transmission, but if
one node tries to send more than the channel can provide the capacity for, then
some messages must be dropped.
When larger numbers of nodes are connected together, other
communication constraints emerge that are created by connectivity constraints
between the nodes. Not all nodes may be directly connected to each other, and
messages may have to be relayed by intermediary nodes. This reduces the total
message carrying, or as we will term it, information capacity of the network.
However, in real time networks with very large numbers of nodes it is hard to
exactly characterise this impact. Recently however, an upper limit on the
amount of information that can be transmitted by meshed communication
networks has been derived as part of work in the sensor network field.
The idea that there are limits on the total amount of communication
that can be performed by a set of nodes, is also the crux of Hayek’s argument
against central planning. Hayek presented it as an argument that economies are
necessarily dependent on independent, imperfectly informed agents working on
local knowledge[2]. It was apparent to Hayek that the form of conscious
control represented by central planning was not capable of co-ordinating the
day to day activities of individuals in something as complex as an economy. By
recasting this as a problem of real time message transmission, receipt and
processing, we can show that this is indeed the case.
To demonstrate a simple example of these issues, consider a typical 1
hour project meeting for a large project co-ordinating many people’s efforts
towards a shared goal. Each “node” present in the meeting both increases the
amount of potential knowledge about the project that can be contributed to the
meeting, but also reduces the average amount of time available for that
contribution. Nor is this solely a property of the broadcast communication
method being used to communicate at the meeting, it is similarly a fundamental
property of the physical topology used to connect the nodes, in conjunction
with the real time constraint on communication imposed by the meeting’s
Consider the case for networks where all nodes are in direct
communication with each other, in network parlance connected by a single
hop, as shown in Figure 1. There are two distinctive topologies: the client-
server or strictly hierarchical, and the fully connected mesh topology where
each node has connections to every other node in the group. In a client-server
topology, all nodes in the network communicate directly with a central node, so
that any communication between clients also has to pass through the server,
even if the central node has no need for the information in the message. The
upper limit on the total amount of communication that can be performed by
the network is thus constrained by the communication capacity of the central
node. This is directly analogous to the topology of central planning, and the
bottleneck on economic organisation that it can create.
In a fully connected mesh topology however, the communication
capacity of the group of nodes is a function of N, the number of nodes in the
network, since each node is connected directly to every other node. The upper
limit on communications is the number of nodes that each node can connect
to. However, direct messages between pairs of nodes can occur in parallel,
unlike the client-server topology. This topological limit on one-hop
connectivity is something we will refer to as the group size limit.
The significance of the group size limit is most apparent when group
sizes are constrained to small numbers of nodes, such as in human
organisations, than for distributed computer applications. Specialised
equipment now allows some computer based client-server applications to scale
to millions of nodes, albeit only for applications, such as credit card
transactions, where client-server communication is well defined, extremely
simple and there is little or no client-to-client messaging. In activities that
require a continuous exchange of information in order to achieve co-operative
results, achievable human 1-hop group sizes generally seem to range up to
about 10. Scaling above that size requires that communications between
individuals that are not directly connected must be relayed by intermediaries
that are.
Both mesh and hierarchical topologies can be extended to scale beyond
single groups, in terms of providing connectivity. That is, they can both
provide message routes that provide a communication path between all nodes
in the network. What neither can do is allow all nodes to communicate with
each other simultaneously. The existence of a message route between nodes,
and the ability of that route to deliver messages in real time are two very
different things. So differences in information capacity that occur when the
same number of nodes are arranged in different topologies are of interest, since
this implies that they place a fundamental constraint on the amount of
messages, or communicated knowledge in some sense, that the topology can
Theoretical understanding of the behaviour of traffic within large packet
switched networks has lagged behind the ability to build them. In particular, the
limits on the amount of traffic that can be carried within the network have not
been well defined.
One result on capacity limits on information capacity of
large, partial mesh networks, has recently been provided as a result of work in
the field of sensor networks by Gupta and Kumar[2], and refined by Scaglione
and Servetto[3]. Since Scaglione’s proof is extremely elegant, and also
illustrative of the set of issues being discussed, we will reproduce it near
verbatim changing only the descriptive node, to people.
Figure 2: The Capacity of Mesh Networks
In Figure 2, N individuals are spread uniformly over a unit square, [0,1] x
[0,1] (N large). Take a differential area of size Δ (Δ small). With high probability
the approximate number of people in the strip, shown in the figure is NΔ.
Since the total number of people is N, we must have N = NΔ x NΔ (because
the total area of the unit square, is the product of the areas of two strips as
shown in the figure, one horizontal and one vertical), and hence the number of
people in a strip as shown is NΔ O(N) for sufficiently large N.
In the original sensor network problem discussed by Scaglione, all the
nodes in the network were required to receive information from all the other
nodes on a continuous basis, and the question posed by the paper, to which the
answer was clearly no, was is this in fact possible? In the example here, we will
impose a less demanding requirement, that there is a single planner node
somewhere in the network, that must receive all information from all the other
nodes in order to create a perfectly informed plan. In order to reach the
planner, the information must flow through the nodes in the strip. The
question is, can the network in fact transport this much information?
The identical argument used by Scaglione applies here. The people
present in this network have a limited number of other people they are each in
direct contact with, we will call this L – their link capacity. Consequently, the
maximum capacity of the strip cannot be greater than O(LN). From the max
flow/min cut theorem we know that the capacity of any network cut of this
form is an upper bound on the network capacity, and so the total transport
capacity of this network cannot be higher than O(LN). In order for the
central planner to have complete knowledge on which to base his plans,
information must be obtained from every person in the network, so O(N)
messages must be received by the planning node. But for large numbers of
people this considerably exceeds the O(LN) capacity of the network. So the
central planner cannot have complete information of the network state on a
continuous basis.
This is not to say that the network is incapable of obtaining information
from every person, and transmitting it to a single point. The problem is that in
real time, economic agents must be assumed to be continuously changing state
and consequently producing information updates which have to be collected on
a continuous basis. Once the size of the organisation has gone above the group
size limit of its topology, this is no longer possible.
Central planning though, might still be regarded as an optimal choice, if
it could be demonstrated that it allows more information about the system to
be processed and intelligently acted upon than any alternative arrangement.
Unfortunately, exactly the opposite is in fact the case.
To illustrate this, consider Figure 3 where we can see the approximate
network capacity obtained for two different topologies, the partial mesh
analysed by Scaglione and Servetto, where all nodes are maximally connected to
other nodes, and the strictly hierarchical topology where all nodes are
connected through one single node. In this case the limit on direct node-to-
node connectivity is 10. To give some idea of the rapid degeneration of the
problem as the number of communicating nodes increases, the number of
connections that would be required if every single node were connected to
every other node, N(N-1) is also provided.
On the left hand side of the graph, we can see that for communication
networks with small numbers of nodes, topology does not matter, the required
information capacity is less than the theoretical maximum O(LN). However,
as the number of nodes exceeds the group size, the partial mesh clearly
provides considerably greater capacity than the strictly hierarchical topology,
which is always constrained by the capacity of its central node. For very large N
though, even the partial mesh solution scales badly, as the extra information
capacity added by additional nodes is negligible.
It is however, possible to improve on O(LN) for large N, if the
communication network is divided into groups of directly (ie. 1-hop),
connected nodes, which are linked by overlapping membership between the
groups. If we assume that the total number of nodes is divided into groups of
size L-2, so allowing for inter-group connectivity with redundancy, we can
approximate the information capacity of the resultant network as the sum of
the individual information capacities of its’ constituent groups, thus:
O((N/(L-2) * L * (L-2))
shown in Figure 3, for a network of 1000 nodes, with a link limit of 10.
This is an interesting result, and bears examining. Why would
introducing structure improve network information capacity? Going back to
Scaglione’s proof, and consider the connectivity problem for the entire
network, if it is divided into slices of maximally linked nodes. In an
unorganised network, messages must flow through a set of nodes in order to
reach their destination. In the worst case, this is from one side to another, or
through a series of slices. However if the network can be divided into a set of
overlapping groups, where at least one member of each group is also a member
of the overlap group, then routing distance is reduced to at most two hops.
Since the primary loss of information capacity within networks arises from the
need of intermediate nodes to route messages for other nodes in the network,
minimising this loss increases the total available capacity to the network.
This communication capacity result for organised networks provides an
alternative explanation for the fairly widespread phenomena of emergent orders
in communicating organisations, to the topology growth explanation provided
by Barabási and Albert[8]. In dynamic systems both effects probably play an
important role, in that not only does organised distributed structure provide the
most capacity, but also that there is a straightforward growth path to obtain it.
Taken together, these results provide a set of observations on the limits
of information transfer within any communicating network, or organisation
that are dependent on its topology. They are not strictly quantitative,
significant details are being hidden behind big O notation, in particular more
detailed calculation of the applicable communication latencies, which
contribute to the value for L. Still the limits are relatively clear, in the presence
of similar bandwidth and message processing rates, an organised mesh will be
capable of more communication than a partial, unorganised mesh topology,
and both considerably outperform a strictly hierarchical topology. However, in
all cases, only for very small networks (or very limited data communication) can
any topology accommodate all the communication that the nodes are capable
of. Large networked systems will always be faced with the problem of adapting
to limited communication space.
Mesh based organisations can take advantage of what for a hierarchically
structured organisation is a large amount of wasted communication capacity
between the client nodes. It bears repeating that communication is by
definition real time. While a single central node is processing one set of
messages, it is not capable of simultaneously handling other messages – they
are queued waiting for attention, or discarded. Distributed topologies provide
choice, if one link is congested, traffic can be directed towards an alternate
route. If one node is overloaded, the information can potentially be processed
by another. This principle applies at all levels of abstraction.
Information capacity cannot however, be the sole determinant of
organisational topology, else it would be hard to see why any other topology
than a partial mesh, or group based mesh would be used. The differences in
information capacity shown above are very significant. Since historically,
centrally planned and hierarchical organisations have from many perspectives
dominated most of human development, there must be some other factor in
play. It is certainly true that centralised systems are in many respects simpler to
organise, and can work well with small numbers of nodes, which may and
indeed often does lead people to believe that central planning is a good solution
for large systems too. However the difference in information capacity between
the two forms is several orders of magnitude. A clear historical preference for
hierarchical organisation is hard to explain purely on the basis of simplicity.
The Influence of Latency on Communication Toplogy.
Latency is the time it takes to send a message within a communicating
organisation. Strictly it should be regarded as having two components, the time
taken to transmit the message, and the amount of computational effort it
induces on receipt. The latter depends greatly on the application receiving the
message, which might be required to perform complex, time-consuming
calculations with the received data before it can process the next message.
Outside of some specialised real time streaming applications, the time taken to
physically transmit the message is now so small in the majority of computer
networks, that transmission time itself is often disregarded.
Until relatively recently the situation for most human organisations was
exactly reversed. Throughout most of history, transmission of human
communications has been extremely time consuming. When messages have to
be physically moved between people, or alternatively arrangements have to be
made for individuals to meet, in order to exchange information,
communication latency dominates as a constraint on any form of co-operative
activity that requires the exchange of information.
Communication within distributed organisations is not solely dedicated
to the exchange of information. It is also used for decision-making and for
control. Centralised topologies are optimal for the quick distribution of a single
set of instructions to all nodes, but not for receiving and processing
information from those nodes. It may well seem highly desirable to maximise
the amount of information available to all levels of decision making, but this
again ignores the problems implicit in real time communication. If a decision
has to be made by tomorrow, and it will take at least a week to receive a
response to a query for information, then that decision must necessarily be
made without that additional information.
This is where centrally organised systems can have a considerable
advantage. In systems with long message communication times, and a need to
make comparatively rapid decisions on an appropriate set of actions for the
participating nodes; there may simply not be enough time for the distributed
exchange of messages that allow such systems to enjoy a larger information
capacity. As it is quicker with long transmission latencies both to issue orders
from a central point, and to concentrate information there, a centralised
topology is optimised for faster response, albeit a much less informed one. The
longer the latency of the messages, the worse the communication problem will
become though, until eventually, for large networks, central control also fails.
In this circumstance, especially when there are local nodes significantly closer
than the centre, centralised control is likely to break down in favour of local
communication, as message communication becomes faster with the adjacent
Since military activity depends for its success on solving real time
communication, information gathering, and control and co-ordination
problems, it provides many interesting examples of the communication
challenges these problems create. Hayek (1944: 152) commented that the
difference on commercial and military organisation was “a fundamental one
between two irreconcilable forms of social organisation” in the Road to
Serfdom, but did not particularly consider why military organisation should be
so different. Certainly the persistence through history of certain organisational
patterns within the military, such as the tiered, hierarchical group structure, is
unlikely to be an accident.
In the context of military organisations, the clearly defined ranks and
hierarchies of the military can be regarded as a solution to communication
routing under conditions of sudden node failure. Network systems that use
dynamic topologies, that is they can adjust the relationship of their
communication links with each other, suffer from a problem of broadcast
storms, where the instantaneous amount of communication required to inform
nodes of the new topology can exceed the capacity available for
communication. The ranks, and known reporting structures of the military
provide a self-healing network topology which requires minimal
communication overhead, in that nodes can recover their local part of the
topology from purely local knowledge in order to create a global organisation
with known information routeing paths, albeit extremely low capacity ones.
This is critical, since if network connectivity is sufficiently damaged, not only is
it impossible for nodes to co-ordinate their activities, but it may also be
impossible to recreate the communication linkages that provided network
connectivity in the first place. However, it can also create problems of overload
and command failure.
There are many examples from military history that can serve to
illustrate the real time nature of communication constraints, and the
unfortunate choices that consequently confront centralised organisations. In
1893 at the height of British Naval power, the battleship HMS Victoria was
rammed and sunk by the HMS Camperdown during a training exercise in calm
waters on the Mediterranean. The incident resulted in the death of 358 sailors,
including the Admiral in charge of the manoeuvre. At the time of the accident,
the fleet was approaching the Tripoli coast in two parallel columns, and was
ordered to execute a 180˚ degree turn, in order to reverse course. Rather than
achieving this by turning outwards as was customary, the fleet was ordered to
perform a manoeuvre whereby the ships turned inside of each other. Owing to
a misinterpretation of received orders, and it should be said, a strict rule of
obedience to those orders, the two lead ships turned onto collision courses
with each other. [5]
Naval communication at the time was still performed by flags used to
send messages between ships. This is a very low bandwidth medium, and over
time, a system of codes had evolved which increased the amount of
information that could be sent between ships. Groups of flags provided a code
that referenced a pre-computed message from a codebook, essentially an early
form of hash table. Although this allowed complex messages to be sent,
sending, receiving and decoding was still time consuming and typically took
several minutes.
In real time then, the fleet was already too close to the coast, when the order to
turn was given, for any exchange of messages clarifying the orders to occur. In
the time it would have taken to get a response, the fleet would have grounded
itself on the Tripoli coast. In this example, and many others the emphasis in
military training on blind obedience to orders can be seen as a reaction to
communication constraints when operating under conditions of high message
The dilemma then that communication constraints create for
communicating organisations, such as the Navy under conditions of slow
message transmission, or high latency, is as follows. A strictly hierarchical
topology can provide the optimal co-ordination of simultaneous orders that is
necessary for the independent nodes, or ships to act together, since it optimises
the transmission of information from a single point. However, if there is any
miscommunication, misunderstanding or simple mistakes in the orders
transmitted, then although local knowledge exists that this has occurred, there
is not enough time to communicate this knowledge to the central point. As the
subsequent inquiry revealed, the commander of the Camperdown was only too
aware of what was potentially about to happen, but had to assume that the
Admiral of the Fleet, on board of the Victoria knew what he was doing. Since
the ships were so close, once the turn began, the laws of physics took over, just
as the direct cause of the accident were the laws of information transfer.
Communication, Economics and Market based systems.
Can consideration of these various network effects that influence
organisations provide possible analytic answers for the relative success of
market based and democratic systems in human history? Hayek phrased his
answer to these questions in terms of the importance of local knowledge, and
the impossibility of central planning ever being able to provide this for large
economic systems involving millions of agents. As we have shown, we can now
support that answer by considering simply the constraints on the
communication of knowledge within large systems of agents operating in a
continuously changing real time environment. In such systems there will always
be more information produced than the network is capable of transmitting to a
single point for analysis, irrespective of the analytical tools available at that
From this perspective, following Hayek’s example, we can analyse
societies and economic organisation in terms of the ability of their underlying
network structures to transmit information.
From a purely network perspective, we can regard money as a form of
packetized information, and markets as hubs in a large scale distributed
network that uses it to provide a continuous determination of relative supply
and demand across society. Market based systems in this sense can be regarded
as a distributed way of computing in real time, a local supply/demand
equilibrium. It is not that the flow of information, in the form of money, (or
indeed of market information), can be perfectly efficient in a market based
system – it follows directly from the argument above on communication limits
within large networks that neither the market itself, nor the market participants
themselves can be – but simply that it is provably more efficient than any
centrally planned alternative, and by several orders of magnitude.
Proponents of central planning, such as Lange, have often pointed to
computer developments as the solution that will enable central planning to
ultimately succeed. Leaving aside the communication problems we have so far
discussed, there are more subtle issues with this proposal. Centrally organised
systems have some advantages, they are conceptually easy to understand, and
easy to create. Simplistically, only one piece of information needs to be
communicated to each node in the network in order to create it – the identity
of who they report to. In any situation where communication is limited, this is
an important advantage, since communication of topological information to
each node is an activity that can very easily exceed the information capacity of
the network itself.
It may well be possible to establish a rigidly hierarchical
control structure where it is not possible to create a more distributed one
because there is not enough communication capacity to create it.
It could also be argued that there is nothing stopping a centrally planned
organisation from deliberately creating a distributed communication structure.
This might look identical to the similar structure that would have been created
by an emergent process, but there would still be a significant difference, the
structure chosen by the central planner would have been necessarily based on
far less information, than that of the similar emergent structure.
Further once a communicating organisation has been established, it is
unlikely to remain static. A hierarchical, centrally planned organisation can be
regarded in some sense as the lowest achievable communication state for a set
of co-operating nodes. If it is successful, it will act to increase the economic
output and consequent complexity of its society, to the point where this
exceeds the capacity of the central planers to completely control it in real time.
Once this occurs the natural tendency for those at the periphery at the
organisation will be to create local links in order to avoid the bottleneck at the
centre. As much as latency considerations permit, the system will grow to a
more distributed state. Absent coercive measures, a successful centrally planned
economy is liable over long periods of time to sow the seeds of its own
destruction, simply by building the network communication infrastructure that
allows a more complex society to emerge.
The Age of Low Latency.
The phenomena of globalisation that has been widely noted in the last
20 years could be more accurately characterised as a world wide drop in
communication latency to near zero. Although strictly it began with the
introduction of the phone and cable communication systems in the 19
century, it is the widespread and extremely rapid deployment of the Internet,
and mobile phone networks that has triggered world wide side effects. As we
have seen, changes in latency can be peculiarly disruptive to communicating
organisations, since they directly affect the topologies of organisations that rely
on that transmission.
So it should perhaps not surprise us that we are living once again
through a period of economic and social turmoil, as these effects play out in
real time. Hayek’s question from the end of another period of rapid
communication changes in the 20
century remains to haunt us, “What is the
problem we wish to solve when we try to construct a rational economic
order?”[5] How can we control something that is provably uncontrollable?
Should we even try?
The conflict between the hierarchical and distributed approaches is not a
simple one to resolve, it is in some senses un-resolvable, since their advantages
and disadvantages are often mirror images of each other. Hierarchical
organisations have a single point of failure, distributed organisations can be
robust to the point of indestructibility. Distributed organisations can process
more information, and in theory at least, react more intelligently. However,
there is no single point of control if circumstances require the organisation to
react quickly; and they are often, and quite correctly, accused of being unable to
easily reach decisions.
For much of human history, there has been little or no choice for
societies operating above the group limit of organisation; communication
latency considerations have forced them to use some form of more or less
hierarchical control. With the introduction of the Internet and mobile
communications, this is however no longer the case.
Emergent orders and social organisations that have evolved over
centuries cannot be changed overnight, even if the communication conditions
they are adapted too are changed underneath them. There is an often un-
remarked persistence to the structure of human organisation, even through
violent attempts to change it, that reflects the impossibility – in terms of
communication overhead - of successfully transmitting wide spread topology
changes within large networks. Local knowledge can allow a communicating
organisation to be reconstructed, creating a new one requires that
communication links are already present.
So the economic and political challenges of this century will be at least
partially framed in the context of the adaptation of existing organisations, as
well as the emergence of new ones, to the changes in communication
conditions. We are already seeing this process with the emergence of Web
based organisations such as Wikipedia, which have conceptually reversed the
client-server topology to allow local knowledge from many sources to be
concentrated at a single point. There will doubtless be many others, and given
that low latency conditions in many respects favour distributed organisations
able to access and combine local knowledge, it can be expected that there will
be concerted attempts to leverage local knowledge rather than central control,
creating tension within existing hierarchically controlled organisations.
These effects also raise many questions. What new topologies can be
exploited, now that communication latency considerations no longer apply?
Given that even with the enhancements that come from ubiquitous laptops and
small addictive communication devices, the time taken to process messages has
decreased far less than the time to communicate them, how can processing
time be better distributed in organisations? How do we manage the resulting
information overload that has been created, bearing in mind that one
significant problem of partial mesh networks is that they lack the natural
throttles on network overload that the strictly hierarchical network provides? In
this context one advantage of a more distributed topology is that it can
distribute message processing more evenly too – but this still leaves the
problem of handling decision making better.
Hayek’s arguments then, are perhaps even more important today, than
when they were first published in the rubble of the 20
century. Central
planning will always be a temptation in times of crisis, perhaps at least partly
because our social instincts betray us. In the small co-operative groups that we
have the most direct experience with, central control is more efficient, and the
problems of low information flow that it creates are rarely experienced because
these groups are too small to experience them. In the large and complex
organisations and societies that we have constructed in the last century it has
proved to be disastrous. Perhaps, a better appreciation of the communication
issues within co-operating networks, their historical changes, and how they
affect all levels of organisation, will help us navigate the latency changes of this
century a little better than the previous one.
Acknowledgements: I would like to thank Dr. Mike Bove and the MIT Media Lab for
support for the co-operative robotics research on which this paper is based; Sean Wheeler
for first suggesting I should explore the works of F.A. Hayek; Dr Ari Benbasat for
discussions on network capacity constraints in communicating systems; and Dr Lorin Wilde
for patiently enduring and critiquing several discussions on network theory as applied to
human organisation.
For example, if it is known that the next part of a message consists of a repeating sequence, for
example, ‘ababababab’; then it can simply be suitably encoded as 5ab. Cfgyturerw on the other hand,
would have to be sent in its entirety. Broadcast communication technologies such as Television for
example, where the same message is sent to many participants, may be very efficient ways to
communicate, but are extremely inefficient ways to distribute information.
Wide area networks have been built more empirically than may be generally apparent, and could be
regarded as an emergent order in their own right. Network operators typically monitor real time
traffic behaviour, and add capacity when certain limits are reached; if the addition of new switches or
links cause problems they are swiftly removed until the cause of the problem is understood.
This has been noticed in the context of the decline of many empires by Turpin[7], who recorded an
historical pattern of new empires arising on the borders of previous ones, rather than from the old
Modern armies now experience a different set of problems that can be broadly characterised as
information overload. This is a direct result of a drop in communication latency allowing far more
battlefield information to be provided than was hitherto the case. The attempts by military
organisations which have evolved under conditions of long latency and limited communications
capabilities, to adapt to conditions of low latency and information overload will be interesting to
This explains incidentally why it is critical to prepare disaster response organisations well ahead of
time. Generally disasters dramatically reduce available network communications, whilst
simultaneously increasing the amount of communication that is needed to co-ordinate a response,
Consequently, it is important that disaster communication be pre-arranged and as much as possible
pre-computed, in order to be as efficient and robust as possible; and to not require any extended
communications to re-arrange the network’s topology once the disaster has occurred. Temporal
shifting of communication load, in the form of rules, procedures, and pre-arranged response plans,
are another frequently seen solution to communication issues in human organisations.
Shannon, C.E. 1948. “A Mathematical Theory of Communication,” Bell System Technical
Journal, 27: 379-423.
Barabási, Albert-László and Réka Albert. 1999. “Emergence of Scaling in Random
Networks,” Science, 286:509-512.
Gupta P. and P. R. Kumar. 2000. “The Capacity of Wireless Networks,” IEEE Trans. Inform.
Theory, 46(2): 388–404.
Hayek, F.A. 1944. The Road to Serfdom, University of Chicago Press.
Hayek, F.A. 1945. “The Use of Knowledge in Society,” American Economic Review, 35(4): 519-
Hough, Richard. 1959. Admirals in Collision, NY: The Viking Press
Scaglione, Anna and Sergio Servetto. 2002. “On the Interdependence of Routing and Data
Compression in Multi-Hop Sensor Networks,” The Annual International
Conference on Mobile Computing and Networking.
Turchin, Peter. 2002. Historical Dynamics, Why States Rise and Fall, Princeton: Princeton
University Press.
... That is related to the size of the blocks for underlying transactions to be validated and hence to speed. See Mallet (2009) and Townsend (Forthcoming). In a different context, Altinkiliç and Hansen (2000) and O'Hara and Ye (2011) document non-increasing returns to scale in equity underwriting and equity exchanges, respectively. ...
Full-text available
We present a tractable model of platform competition in a general equilibrium setting. We endogenize the size, number, and type of each platform, while allowing for different user types in utility and impact on platform costs. The model is applicable to the recent growth in digital currency platforms. The economy is Pareto efficient because platforms internalize the network effects of adding more or different types of users by offering type-specific contracts that state both the number and composition of platform users. Using the Walrasian equilibrium concept, the sum of type-specific fees paid cover platform costs. Given the Pareto efficiency of our environment, we argue against the presumption that platforms with externalities need be regulated.
We present a tractable model of platform competition in a general equilibrium setting. We endogenize the size, number, and type of each platform, while allowing for different user types in utility and impact on platform costs. The model is applicable to the recent growth in digital currency platforms. The economy is Pareto efficient because platforms internalize the network effects of adding more or different types of users by offering type-specific contracts that state both the number and composition of platform users. Using the Walrasian equilibrium concept, the sum of type-specific fees paid cover platform costs. Given the Pareto efficiency of our environment, we argue against the presumption that platforms with externalities need be regulated.
Conference Paper
Full-text available
We consider a problem of broadcast communication in sensor networks, in which samples of a random field are collected at each node, and the goal is for all nodes to obtain an estimate of the entire field within a prescribed distortion value. The main idea we explore in this paper is that of jointly compressing the data generated by different nodes as this information travels over multiple hops, to eliminate correlations in the representation of the sampled field. Our main contributions are: (a) we obtain, using simple network flow concepts, conditions on the rate/distortion function of the random field, so as to guarantee that any node can obtain the measurements collected at every other node in the network, quantized to within any prescribed distortion value; and (b) we construct a large class of physically-motivated stochastic models for sensor data, for which we are able to prove that the joint rate/distortion function of all the data generated by the whole network grows slower than the bounds found in (a). A truly novel aspect of our work is the tight coupling between routing and source coding, explicitly formulated in a simple and analytically tractable model – to the best of our knowledge, this connection had not been studied before.
Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mech-anisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
Conference Paper
How much traffic can wireless networks carry? Consider n nodes located in a disk of area A sq. meters, each capable of transmitting at a data rate of W bits/sec. Under a protocol based model for successful receptions, the total network can carry only Θ (W√An) bit-meters/sec, where 1 bit carried a distance of 1 meter is counted as 1 bit-meter. This is the best possible even assuming the nodes locations, traffic patterns, and the range/power of each transmission, are all optimally chosen. If the node locations and their destinations are randomly chosen, and all transmissions employ the same power/range, then each node only obtains a throughput of Θ (W√nlogn) bits/sec, if the network is optimally operated. Similar results hold for a physical SIR based model
What is the problem we wish to solve when we try to construct a rational economic order? On certain familiar assumptions the answer is simple enough. If we possess all the relevant information, if we can start out from a given system of preferences, and if we command complete knowledge of available means, the problem which remains is purely one of logic. That is, the answer to the question of what is the best use of the available means is implicit in our assumptions. The conditions which the solution of this optimum problem must satisfy have been fully worked out and can be stated best in mathematical form: put at their briefest, they are that the marginal rates of substitution between any two commodities or factors must be the same in all their different uses. This, however, is emphatically not the economic problem which society faces. And the economic calculus which we have developed to solve this logical problem, though an important step toward the solution of the economic problem of society, does not yet provide an answer to it. The reason for this is that the “data” from which the economic calculus starts are never for the whole society “given” to a single mind which could work out the implications, and can never be so given. The peculiar character of the problem of a rational economic order is determined precisely by the fact that the knowledge of the circumstances of which we must make use never exists in concentrated or integrated form but solely as the dispersed bits of incomplete and frequently contradictory knowledge which all the separate individuals possess.
When n identical randomly located nodes, each capable of transmitting at W bits per second and using a fixed range, form a wireless network, the throughput λ(n) obtainable by each node for a randomly chosen destination is Θ(W/√(nlogn)) bits per second under a noninterference protocol. If the nodes are optimally placed in a disk of unit area, traffic patterns are optimally assigned, and each transmission's range is optimally chosen, the bit-distance product that can be transported by the network per second is Θ(W√An) bit-meters per second. Thus even under optimal circumstances, the throughput is only Θ(W/√n) bits per second for each node for a destination nonvanishingly far away. Similar results also hold under an alternate physical model where a required signal-to-interference ratio is specified for successful receptions. Fundamentally, it is the need for every node all over the domain to share whatever portion of the channel it is utilizing with nodes in its local neighborhood that is the reason for the constriction in capacity. Splitting the channel into several subchannels does not change any of the results. Some implications may be worth considering by designers. Since the throughput furnished to each user diminishes to zero as the number of users is increased, perhaps networks connecting smaller numbers of users, or featuring connections mostly with nearby neighbors, may be more likely to be find acceptance
A Mathematical Theory of Communication Barabási, Albert-László and Réka AlbertEmergence of Scaling in Random NetworksThe Capacity of Wireless Networks
  • C E Shannon
Shannon, C.E. 1948. “A Mathematical Theory of Communication,” Bell System Technical Journal, 27: 379-423. Barabási, Albert-László and Réka Albert. 1999. “Emergence of Scaling in Random Networks,” Science, 286:509-512. Gupta P. and P. R. Kumar. 2000. “The Capacity of Wireless Networks,” IEEE Trans. Inform