Various topics in complex systems


A "broken" planet?
Simplicity and complexity
The impact of metrics on a complex system
Transparency and game-playing
Exceptions handling in complex systems
Complex systems, the tax regime, and the housing market.
Complex system design - or evolution?
Complex systems and the attraction of media studies
Reducing complexity to patterns
Reform, restructuring, and entropy production in organisations
Automatic decision-making in combined systems
System time-scales
Tasks better performed by humans
Targeted complex software
Complex acoustic instruments
Information, matter, and energy
(...Irreducible representation of information)
Wealth distribution and fundamentalism
How effective is quantum computation?
Interaction of science with media reporting.
Pictures - - "eye-candy"

A "broken" planet? or perhaps just "sick".

Under what conditions is a complex system (when under stress) still undergoing change and adaptation, and alternatively when can it be considered to be irrevocably "broken"? We have now become used to the idea of robustness in naturally-emerged complex systems, in the sense that they can accommodate quite extensive variations in imposed conditions and still adapt to them. To some extent, a "broken" state is one of definition or point-of-view.

In engineered systems it is sometimes easier to detect a state of "broken". The mechanic who listened to my Rover Metro in the 1980s after it had run a water pump bearing, when asked how long it might be drivable for, said sourly "well, it is no use like that, is it?".

With the recent impacts of human activity on the planet, these seem to be very apposite remarks. We might speculate on how long we can patch up the damage we have wrought, but then the little voice of the Gaia mechanic says " is no use like that is it?..."

An open question.

What is certain is that the planet is not "here to support or encourage humans", or indeed life of any form. It is a complex adaptive system that will adapt naturally to the stresses on it without regard to any human views on "utility". In a sense, if we want to take the anthropomorphic Gaia view of the planet, it is running a temperature and trying to shake off the viral infection represented by the humans.

Change, when it finally comes, may be very sudden, as can be seen in the trapping in a simple electronic chaotic oscillator.

Copyright © David Jefferies, 2005

14th September 2005. Revised 2nd December 2005.


Simplicity and complexity

Engineering SIMPLICITY is becoming topical. Even the BBC has a magazine piece about useability.

Here is a quotation from a "technology consumer" in New York, on 27th April 2005

The car (Audi) is lovely, rides beautifully but I still haven't sorted out the electronics. It rained this AM and it took me a while to figure out how to use the rear window wiper. The majority of the controls still haven't been deciphered. This is after a half hour of orientation. The only way to learn is when one has to use something. On the other hand, the Audi is a work of simplicity compared with the BMW and Mercedes. The expensive BMWs such as the 5 and 7 series are not selling because their software requires users to go through a series of menus in order to do something simple - such as change the station on the radio or change the temp on the A/C.

There is a Design Institute at Stanford University which has just been set up to tackle these problems.

And, the BBC has these following comments on 21st May 2005.


     A back-to-basics mobile is launched

     Vodafone is launching a back-to-basics mobile phone in response
to customer demand for simplicity.

     Vodafone Simply will be available in two handsets offering just
voice and text services.

     Both phones have a large screen with legible text and symbols,
and three dedicated buttons for direct access to the main screen,
contacts and messages.

     The pared down phones represents a backlash against the drive to
create more and more advanced services.

     "We also have customers who just want to make and receive call
and text messages on their mobile phone," he said.

     This sentiment was echoed by two celebrity backers, chat show
hosts Richard Madeley and Judy Finnigan.

     "I think there are a lot of people like me out there who feel
that we have been busy doing other things and steadily technology has
almost escaped us," said Ms Finnigan.

     "This is the perfect solution for people like me who simply want
to make calls and send the odd text message," she said.

     The desire for an uncomplicated phone was greater as the age of
users increased, its survey found.

     Eighty percent of the over-55s craved a simpler handset whereas
youngsters wanted all the bells and whistles on their phones.


Lists of mobile phone technology abbreviations and acronyms.

   * 1G first generation
   * 2G second generation
   * 3G third generation
   * 3G-MSC/VLR third generation mobile switching centre/visitor
location register
   * 3GPP third generation partnership project
   * 3G-SGSN third generation serving GPRS support node

   * AC access class
   * ACK acknowledgement
   * ACLR adjacent channel leakage ratio
   * ACS adjacent channel selectivity
   * ADC analogue to digital converter
   * ADF application dedicated files
   * AGC automatic gain control
   * AI acquisition indicator
   * AICH acquisition indication channel
   * AID application identifier
   * AK anonymity key
   * AM acknowledged mode
   * AMD acknowledged mode data
   * AMF authentication and key management field
   * AMR adaptive multirate
   * AP access preamble
   * APN access point name
   * ARQ automatic repeat request
   * AS access stratum
   * ASC access service class
   * ASIC application specific integrated circuit
   * ATM asynchronous transfer mode
   * ATT AICH transmission timing
   * ATT attach flag
....etc all throught the alphabet....

The concept of emergence relies on complexity arising "naturally" out of simplicity, as in the case of the MIT programming exercise at the Media Lab linked at the head of this piece. We might also postulate a contrasting concept which we might call "demergence", where the control of an intricate engineered system is achieved by the minimum number of interactions on the part of the user.

We might compare this "ideal scenario" with the report of an installed electronic system in the Sydney Hilton Hotel which seems to be causing disquiet amongst its users.

Copyright © David Jefferies, 2005

21st October 2005.


The impact of metrics on a complex system

Does a measurement affect the system being measured?

In a quantum-mechanical system we have grown used to the idea that a measurement necessarily perturbs the system being measured. More correctly, if the data that the measurement observes is "made available to the outside world" then the quantum properties of "being in many states at once", collapses. This condition (of being in many states at once) may be represented as "having incomplete knowledge" about the system. There does not actually need to be an observation for the collapse to happen; just the potential for an observation.

In most complex systems, people are usually working with incomplete knowledge about how the system is performing. For many complex systems, this is unimportant, as they can be left to get on with their business. Examples are the weather, the climate, the growth of ecosystems, the detailed behaviour of groups of people in the marketplace.....but wait a moment, there is pressure here to "find out" what is happening, the better to adjust or influence the system to develop in some kind of "desired" direction.

So, the first step is to acquire information about what "is happening now" in order to apply constraints.

Our thesis here is that for many complex systems, especially "aware human systems", the metrics themselves (that is, the act of observing the system and collecting data) provide a powerful controlling influence or constraint on the system being measured. In fact, the analogy with the quantum case considered above is even closer, for people behave differently if they know they are making data available "which might be observed", whether or not there is an actual observer.

Thus, the act of acquiring and publishing immigration data in a country can encourage immigration pressures and alter the dynamics of any immigration there may be on the behaviour and attitudes of the existing society. The act of publishing League Tables for educational establishments will nearly always greatly affect the quality of the educational experience on offer. The process of amassing publication data for "research assessment" both affects the quality and quantity of research done, and concentrates activity towards the past rather than the future.

Many astute politicians and public policy experts realise this fact, and design metrics with a view more to the "control" aspects than to the "measurement" aspects.

It is debatable as to whether this is a good idea, but the whole point of a metric, to some ways of thinking, is that it is disinterested, in the sense that it is neutral with respect to the behaviour of the system being measured.

Copyright © David Jefferies, 2005

5th September 2005.


Transparency and game playing.

There is a fashion recently for promoting "transparency" in the way organisations relate to their stakeholders. The idea is that it is universally good if everyone dependent on the organisation can be informed of the rules governing the organisation, and in particular informed of the way it distributes resources and makes decisions.

Here, we give a counter-example which may illuminate this practice. A certain University has the habit of "governance by spread-sheet" and distributes resources around the organisation according to a publicly communicated algorithm which is somewhat complex. The intelligent Heads of the various departments then take this algorithm and optimise it for their own particular subset of the University. This results in decisions made for the good of the department rather than the good of the organisation as a whole.

For example, it has been found that the central University charges departments for the space that they occupy which is directly related to their teaching and research activity, but not for connecting space such as hallways and corridors. This has led various departments to restructure their space, increasing the hallway and corridor space at the expense of lecture theatre and research office space. The resulting savings are felt by the department, and the net result is that the University as a whole shrinks.

It is clear that the effectiveness of an organisation can be seriously compromised if the reasons for taking decisions are communicated transparently. It is for this reason that countries have "secret services". We have recently been led into the situation where everyone expects to be able to manipulate organisations which affect them, and consequently this is regarded universally to be a Good Thing and "democratic".

7th November 2005

Copyright © David Jefferies, 2005


Exceptions handling in complex systems.

Why are "exceptions" important?

There is a commonplace observation that in organisations, "90% of the effort goes in dealing with the 10% of activity that causes a problem".

One can class problem situations as being "exceptions" to the general smooth running of the organisation. As far as the users of the system are concerned (and here, we mean both the customers and also the employees, for example) the "feel" of the organisation is largely determined by the ease with which it copes with exceptions.

There are various approaches to the handling of exceptions. The first, and very common approach, is to ignore them until they blow up out of all proportion, and then fire-fight them. The second is to have a dedicated subset of people who, by human intervention, try to put right things that have gone wrong. The third is to shunt the exceptional cases into a queue or siding, and hope that if they are ignored for long enough they will go away, or solve themselves.

By far the best way of dealing with exceptions is to have an automatic procedure specified by algorithm, either through the intermediary of humans or else automatic subroutines, that is entered when the exception is identified. This can be an adaptive algorithm, or it can be an alternative pre-specified way of handling the business of the organisation.

The best complex systems that are intermediated by computer have smooth exceptions-handling that rarely, if ever, requires decisions to be made by mutable and erratic humans. To get to this state requires conscious effort of refinement, from the experience of dealing with past exceptions that have arisen. In this way, the proportion of exceptional cases can be greatly reduced from the notional 10%, and the amount of effort expended in dealing with them lessened proportionately. It does not seem to be sufficient to have an "ad hoc" learning process to arrive at this state. Rather, the complex system designer must design in ways of learning from exceptions into his original scheme for the system.

If one applies the insights of this article to items of computer software, to the tax authorities, to the utility companies, to the educational establishment of one's choice, and to private sector companies, one can soon arrive at a sensible assessment of the culture of the organisation and of the amount of thought that it has put into the handling of its exceptions.

Copyright © David Jefferies, 2005

5th September 2005.


Complex systems, the tax regime and the housing market.

Why are house prices linked to the tax regime?

Executive summary

Expanded discursive argument

In most economically active regions of the planet, it seems that housing is in perpetual short supply. Our remarks here don't really apply to places where there is a surplus of housing.

It also appears to be the case that people expect their housing provision to be a hedge against inflation, or even an appreciating capital investment.

Under these circumstances, people will spend as much of their disposable wealth as they can on their housing. If the country elects a government which believes that "growth is stimulated by reducing the tax burden" the primary effect is to divert savings into the prices of housing. This uniformly increases the amount of wealth in the housing stock; the wealth comes from lower taxation and is not available for the government to spend on other goods and services.

In this scenario, people are actually worse off :- they have increased spending on bricks and mortar which are not actually any better in quality for absorbing more of their savings. At the same time they are suffering the privations of cuts in public services imposed by the government to fund the tax cuts.

Paradoxically therefore, if you tax people more highly then their quality of life is enhanced, and the price of housing is more affordable.

In a low tax regime, there is a group of punters who really benefit greatly. These are the people who have so much money that they don't need to spend as much as possible on their housing. Neither are they potential consumers of public services as they have sufficient surplus to buy in their needs. This seems to be the focus of right-wing politics in both the USA and the UK over the past 25 years.

Copyright D.Jefferies 2005
revised 28th September 2005


Complex system design - or evolution?

Recently, the design and evolution of third generation mobile telecommunications products has become a topical subject. Some of the nomenclature is summarised in another page by this author.

There is also the continual development and evolution of computer operating systems, whether they be Mac, Linux, or Microsoft.

From a complex systems theorist's point of view, one of the interesting facets of this kind of technological advance is whether the new versions of technology represent discontinuous change, or gradual evolutionary advance. Sudden advances, such as in the presentation of the Dyson vacuum cleaner technology, can cause upsets in the marketplace.

We see the same problems in evolutionary systems in nature; in speciation, where the emergence of a new life form happens necessarily over many generations, and is not suddenly released on an unsuspecting world.

If one is a complex systems designer or engineer, one has to develop a strategy on how to proceed. How long should one keep a product in development and unreleased, in order for it to have the desired impact? One has to be reasonably certain of the success of one's end product, in order to spend many years developing it.

One question which arises is concerned with the time-scale over which developments occur. A human lifespan would seem, historically, to be the longest "attention span" for systems development. Some European Cathedrals are known to have taken times of this order from conception to implementation. But there is the problem that the technology of the component subsystems is always advancing and developing, and there is a significant risk that the product development will be overtaken before it comes to completion.

Emergence is best

It would appear that gradual incremental advance is a more satisfactory way to proceed. This also entails forward and backward systems compatibility. Such systems gradually evolve over time until a kind of "phase transition" forces a readjustment of technology. An example might be quoted from the advances in mechanical recording, from the digital musical box to the analogue gramophone, and then a sudden readjustment to the digital compact disk and computer storage of music. In the case of compact disk technology, it is true that backward compatibility with existing audio technology was not maintained.

One might draw the analogy with tectonic plate movements; every now and then there is a sudden readjustment.

It is possible that the complex structure of man-made systems is inherited, and passed on to subsequent generations of technology, rather in the same way that so-called "junk DNA" is passed on in humans and other life forms. For, in our music recording example, the digital method remained in the knowledge base, and dormant, until the arrival of other forms of storage that made it successful again.

Copyright D.Jefferies 2005
17th April 2005


Complex systems and the attractions of the media

Why are media studies displacing the Hard Sciences and Mathematics?

Humans are predominantly social animals, who thrive on communication. They communicate in many different ways and with many differing technologies; they travel physically and virtually to visit each other and are constantly seeking new contacts, whether on or off the planet Earth. They are even in possession of the concept of "God" with which to communicate when all else fails.

It would seem that one of the principal driving forces behind human development on the planet, now at the start of the 21st Century, as for many centuries past, is the need to communicate and to share experiences and ideas. Indeed, self-referentially, that provides the motivation for this Web Page. Communication is enabled and enhanced by many modern technological developments, from transport improvements to electronic and computer communications systems, from enhanced literacy to enhanced education generally. There has been an explosion in the topics and subjects about which people communicate. New communication partners are constantly being sought; this provided the motivation for the early global explorers such as Marco Polo, Magellan, Cook, and Columbus. Nowadays it provides the motivation for programmes such as SETI ("Search for extra-terrestrial intelligence") and it doesn't look as if it will ever stop. Indeed, one of the primary motivations for having children would seem to be to provide a new generation with which to communicate.

The word "communication", in the academic context, has a number of differing flavours. It is used in technology ("communications systems", "satellite communications") and as a description of an academic publication or paper; it is used in a social context to describe the general field of "media studies", and it is used to describe what happens when two or more humans meet. It is also generalised to describe what happens in biological processes involving chemicals, and it provided much of the motivation for establishing archival libraries, mausoleums and monuments such as the pyramids, and museums.

Once one accepts the presence of communication as a powerful human motivation, much of the current thrust of technological development and of the popularity of educational courses in the media becomes more understandable. Those people seeking to promote their own disciplines therefore do well to enhance the communication aspects of their activities.

In the science and engineering fields, the rewards of communication in the past have been seen to lie in refereed publication in Journals and books, in international and in local conferences, and in attracting interested and competent students. Many engineers take their greatest satisfaction from creating products and artifacts that they then see taken into widespread use in the community. In this way they communicate by means of their creations.

In the arts and in literature, the painting, composition, or book represents an attempt at one-many communication. In University life generally, the lecture fulfils, in a small way, the same function, and the production of accompanying text books and course materials seeks to extend this. The process is often taken to excess; usually the most successful communications are those that serendipitously hit on a comfortable length for assimilation.

Once one releases an enhanced technology of communication into the population at large, developments can be somewhat unexpected. The prevalence of spam email is an example of over-eager communication ambitions; the take-up of text messaging on mobile phone handsets was not foreseen by most of the texting service designers. Much political argument is about the control and use of communication channels, of "freedom of expression", of "security on the internet", of "rules of engagement in the debating chambers", and about "truth and honesty in news reporting".

There is therefore little that is surprising about the attractions, in the developed nations, of media studies and of the information service industries generally. Many starting graduates, when asked about the satisfying aspects of their occupation, quote the human-to-human interactions that go with the work aspects. In previous centuries, when travel and communications were harder, the focus of communication was in the church, or equivalently in organisations such as the womens' institute and the working men's clubs.

Communication requires three things to be in place; a source or transmitter, a receiver that is usually assumed to be a willing recipient, and an appropriate channel that connects them. This channel may be two-way, or unilateral. In the case of one-many communications such as magazine publishing and broadcasting, the channel is heavily biased in one direction. If we eavesdrop on a political argument, we are likely to hear communication which is unilateral in both directions; neither party is paying attention to the message (or the underlying intention of the message) transmitted by the other.

Sometimes, an apparent communication involves discussions which start from different premises, and very frequently it would appear that true communication, as in the religious sense of communion, is totally absent from the exchanges.

The task, therefore, of educators who seek to promote "difficult" subjects such as mathematics and physical sciences, is to put back a larger opportunity for significant communication into the student experience. This involves establishing some bi-directionality into the activity. It may be for this reason that one-on-one tutorials, and student projects, provide such a good way of enthusing and educating.

People differentiate themselves after their education, into groups which have a common language of experience or of communication. In the 1950s in the UK there was a significant cohort of classically-educated people who understood Latin and Ancient Greek. There was also CP Snow's idea of the "two cultures", separating those who spoke "science" from "the rest". Even earlier on there was a huge division between those people who could read, and those who were illiterate.


Reducing complexity to patterns

Remembering an irregular sequence of binary digits (1s and 0s) is quite difficult unless you have some kind of method in mind. For example, the sequence 1001101111101101101 if deconstructed carefully translates into 9 11 2001 and once this is realised, then it is easy to reconstruct the sequence.

There is a mapping from the qwerty computer keyboard into musical representations described in, which is quite clever, and which makes use of this kind of equivalence. Music is mapped here onto easily-memorisable patterns on a qwerty keyboard.

Here is given a follow-up note on the topic of patterns on keyboards/pads, which isn't music-related, but rather is concerned with how to memorise phone numbers.

It may be found that this is well-done using pattern techniques. For example, a local phone number is in part 446593

and when mapped onto the keypad of a UK phone

     1 2 3
     4 5 6
     7 8 9
one can see a memorisable pattern which is a T on its side...... This gives one another (alternative) method of remembering the number, unrelated to a sequence of digits.

Two more examples:-

Charles has a number which is ***** 779651 which is a sort of similar pattern, but displaced, to Keith's number which is ***** 889653

and neither of these are easy to remember without the pattern aid.

Some people can remember sequences of numbers by the sounds, others by the visual appearance of the string, but a mapping onto a standard keypad seems to be a useful alternative.

Copyright © David Jefferies, 2005

15th September 2005.


Reform, restructuring, and entropy production in organisations

Natural thermodynamic systems, close to equilibrium, have the property that the entropy (a measure of disorder) of the system tends to increase over time as the system is left to equilbriate.

In the News there are frequent reports about the "need for change" or "reform of the system". "We are the changemakers" says Blair.

If, on the other hand, we are followers of the adage "if it ain't broke, don't fix it", then why is this constant restructuring necessary?

If we observe our own institutions or workplaces, or even the providers of goods and services with whom we interact, it is clear that after a reform or restructuring, gradual relaxation of standards sets in and the original efficacy of the reform is lessened over time. Therefore, if there was no urge to continually change the working systems we would expect them to decay naturally into a state of inefficiency.

It would be very helpful to have a scientific and quantitative method of measuring such disorder or "entropy" in a human system.

28th September 2005


Automatic decision-making in combined systems

Problems will arise in complex systems when decision-making is shared between humans and automatic algorithms. We have probably all had experience with government organisations or utilities or health service providers when the system breaks down because the human has not been aware of decisions made automatically by the machines within the organisation.

Here is a recent example. In the UK it is commonplace to flash one's headlights during the daytime, to indicate to other road users that one will give way and let them have priority. Some Japanese cars are equipped with "daylight detectors" and the headlights may be set on "automatic", to come on when the car enters a tunnel or other dark area. A BMW waiting to enter a traffic stream on the side road was prompted to do so by the automatic turning on of headlights caused by some shady trees, thereby very nearly causing a collision. The BMW driver automatically assumed that the human in the other car had deliberately flashed the headlights.

2nd October 2005


Time scales for planning in complex systems

The minimum time scale over which any efforts to combat global warming will produce observable effects is probably between 10 and 100 years.

It is said that the Chinese take a long term view of the measures needed to combat global warming, and think in terms of a century or more. It is commented that "this is because their government does not need to be re-elected".

In Western democracies, any planning beyond 10 years into the future is negated by the exigencies of the democratic process, or, in the case of business, the likely time scales over which investors expect sensible returns.

In evolutionary terms, the various kinds of political system have adaptations to differing time scales for change on the planet. Western democracy is adapted best to rapid ongoing change.

16th October 2005.


Division of labour

In a "combined complex system", where decision making is shared between computer algorithms and humans, it is important that the control of decision-agent is handled cleanly so that no conflicts arise. Here is an extract from Complexity Digest.

  Amazon Creates Artificial Artificial Intelligence, Seattle Post

  Excerpts: With Amazon Mechanical Turk, Amazon plans to supply 
  "artificial artificial intelligence" that connects programs needing 
  the human touch with humans, such as the simple task of identifying 
  objects in photographs (which humans can do better than computers). 
  Examples of what humans can do for computers? Evaluate beauty, 
  translate text and find specific objects in photos.

  "Today, we build complex software applications based on the things 
  computers do well, such as storing and retrieving large amounts of 
  information or rapidly performing calculations," the company said. 
  "However, humans still significantly outperform the most powerful 
  computers at completing such simple tasks as identifying objects 
  in photographs -- something children can do even before they learn 
  to speak."

    * Source: Amazon Creates Artificial Artificial Intelligence, 
    Kristen Millares Bolt, Seattle Post, (05/11/04) (yy/mm/dd)

14th November 2005.

Targeted complexity in software

Google now targets its search returns on the country in which the engine domain resides. You may see this if you search for, e.g.,



This experiment is confounded by the fact that if you enter in the UK the target is automatically redirected to

Clearly we are now in the state of not knowing how people in other parts of the world are viewing the web. Such domain-dependent targeting seems to be getting more prevalent, and makes rather a nonsense of the idea of "freedom of speech" or "freedom of expression"

Guildford, 28th November 2005


Complexity in real acoustic instruments

It is fashionable to replace real acoustic pianos by electronic keyboards. Other instruments have been similarly treated; electronic church organs are much more affordable than real pipe organs.

In many complex, non-linear, possibly chaotic, real experiments it is now accepted that simulations give results that can diverge widely from the observed real-life behaviour.

A simple experiment with an acoustic piano will rapidly reveal why the electronic keyboard is an inadequate replacement. Hold down the bottom C on the acoustic piano taking care not to sound it, and then firmly strike the G above it listening carefully to the sound made when the G is released.

One observes that the instrument produces sound from the undamped C string, which may be totally unrelated to the fundamental frequencies of either the C or the G. Typically, this sound changes in character and increases in volume if the G key is held down for longer before being released.

A simple extension to this experiment raises the dampers on a number of notes at once, then striking an unrelated note elsewhere in the keyboard, again for variable lengths of time, and listening to the result. (Alternatively, a note in the bass register can be sounded, then the tone colour listened to, as the dampers are raised and lowered with the sustaining pedal, while the sound is decaying.)

The rich variety of sounds produced gives the instrument its character and varies from one instrument to another, depending on the tuning, the history, and the maker. In contrast, repeating the experiment on a digital piano like a Yamaha Clavinova results in complete silence.

Electronically simulated or digitally-recorded instruments are in no way a substitute for real acoustic versions, although they may have a character all of their own, and become preferred by the majority of listeners after sufficient ear-training.

Another well-understood phenomenon explains why loudspeakers always sound like loudspeakers rather than like the instruments they are supposed to mimic. There is Doppler intermodulation between the frequency spectra emitted at differing pitches. A large-excursion bass note moves the cone back and forth, Doppler-modulating the higher frequencies by an amount that varies with the amplitude of the bass note as well as its frequency. In loud passages of complex music, the loudspeaker can always be distinguished from the real acoustic instruments.

Guildford 2nd December 2005


Information, matter, and energy.

Information has been quantified by Claude Shannon. In terms of the number of bits (binary digits) per symbol, it can be represented as log[2](the number of equiprobable symbols) which go to make up a message.

Information is an important commodity in the modern world. Here we wish to make the case that there is an equivalence between information, and mass m and energy E which we already know are related by Einstein's celebrated formula E = mc^2, with c the velocity of light 3E8 in SI units. Here, we are not suggesting that a certain amount of information HAS mass and energy, but just that it REQUIRES a mimimium of energy and mass to REPRESENT it in a way in which it can be "used" subsequently. It is easy to imagine a large amount of information - e.g. "the works of Shakespeare" - but this is quite different from enumerating or reciting "the works of Shakespeare".

Irreducible representation of information.

For information to be utilised, it has to be conveyed (that is, transmitted) or else it has to be recorded in some recoverable format (that is, it requires material memory). We can postulate an "irreducible minimum" of material to record the information, or an irreducible amount of energy to transmit it (which will require a certain time.)

Consider the recitation of a transcendental number such as pi or e, the base of natural logarithms. However fast we enumerate the digits or bits, it will take an indefinitely long time and even then we will have made negligible inroads into the enumeration. Such is the concept of the infinite. The same holds for any irrational number such as might be used to specify, completely, the initial state of a chaotic or complex system.

Thus, we have no practical possibility of describing even the simplest chaotic system's starting point in a way that gives us the chance of indefinite accurate prediction, except possibly a set of special initial points of measure zero.

For practical complex and chaotic systems therefore, information is necessarily incomplete. Here we attempt to asses how much work we have to do to provide this incomplete information.

Considering the transmission of such information first, the bandwidth required to transmit N bits per second is 2N Hz, which requires photons of energy up to at least 2Nh where h is Planck's constant (6.63E-34 SI units, Joules-seconds) and therefore for a total amount of information Ntot = NT bits transmitted over a time T seconds we require a total signal energy E of at least 2(Ntot)Nh = 2hT(N)^2 or an energy per transmitted bit of 2hTN = 2h(Ntot)^2/T Joules (SI units again).

Let's equate this energy, associated with information transmission, with a mass m using E=mc^2. We might then expect that it is not possible to write down or record this information on a physical amount of matter smaller than this mass, which is 2h(Ntot)^2/T(c^2).

Let's stop for a dimensional check. Planck's constant h has alternative dimensions metres^2 kilograms/sec so our formula has dimensions (units) of kilograms.

Now, let's imagine we have to specify the location of a Newtonian point particle of mass m in space (not considering quantum mechanics for the moment). Suppose we localise it to a position delta(x) where 1/delta(x) = Q in SI units (reciprocal metres) where there are Q choices per metre for the localisation position. The amount of information per metre we need to perform this localisation is log[2]Q, and if we give ourself a 1-dimensional space of L metres the total infomation in the localisation is log[2](QL) which we might speculatively equate to (Ntot) above.

We ask the question, what is the limit to which this argument allows us to determine the position of the mass m = 2h(Ntot)^2/T(c^2) ?

Well, we have log[2](QL) = (Ntot) for the total amount of information needed to localise within the distance L. Thus m = 2h{[log[2](QL)/c]^2}/T. This gives us a formula for delta(x) which certainly needs thinking about if any sensible interpetation is to be forthcoming.

However, this work has application to the chaotic dynamics of a Newtonian system of point masses where the initial conditions need an infinite amount of information for a description that allows us indefinite prediction of the trajectories subsequently.

Guildford, Surrey, UK; 14th January 2006.


Wealth distribution and fundamentalism

There is a suggestion, in keeping with complex systems thinking, that a great divide in wealth between the rich and poor in a community breeds fundamentalism, whether it be Marxism, Maoism, Fundamentalist Islam, or Fundamentalist Christianity. This destabilises the communities in which it is found, and exports terrorism and intolerance.

Guildford, Surrey, UK; 29th January 2006.


How effective is a quantum computation?

There was a recent temptation to sell Landau and Lifshitz's excellent 1950s book on "Quantum Mechanics". Rereading this book produces thoughts about the current fashion for claims made about quantum computation. The book predates discussions of "entanglement", but seems to be quite clear about the results of any "measurement" on a quantum system.

Considering a two-state quantum system (spin up or down, polarisation sense of a photon, etc.) even when the system consists of separated entities or "particles" which have been entangled, the result of any determination of the state will have one or two bits of information at most.

The question remains, how much information "processing" can happen in the superposition of states which is presumed to occur before the measurement event? How much information can this superposition of states contain, or represent? Recent articles in the popular scientific press seem to suggest that we can have "something for nothing" in a quantum computer, and that it can potentially solve problems way beyond the capacity of classical computers.

A question posed for the reader is therefore, in a two state quantum system described by classical continuous variables, to what precision can we assume that these classical variables can be described "quantum mechanically speaking"? How many distinguishable regions of phase space can there be? Is this information retained when to wave function collapses into the one or two bits of the "answer"? How does it come to affect the "answer" and what does the "answer" represent about the quantum computation?

The professional scientist is always wary of schemes that propose "something for nothing", two examples being the perpetual motion inventions, and the crossed field "antenna".

Guildford, Surrey, UK; 15th April 2006.


Interaction of science with press reporting

The BBC radio ran a programme about exaggeration (reputedly by scientists) of the significance of global warming. This interesting programme (20:00 BST on 060420) raises the "complex systems" interaction which may be summarised as follows :-

Here we have "selection away from the average". The majority of cases cluster around the mean, particularly in a statistically random sequence of results. Such cases are unremarkable, and are not deemed worthy of reporting.

Therefore, people who take their view of science from reports in the press are likely to have their information unreasonably slanted towards the less likely occurrences. This (probably) then brings the conduct of science into disrepute.

Guildford, Surrey, UK; 20th April 2006.


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see also Complexity International Journal, Australia.