Tuesday, December 02, 2008

Some notes on recursion, complexity & emergence


Recursive patters are structures that structure themselves. Examples of recursion are the ‘bases’ in mathematics, where integers (numbers) are organised into complex patterns based on some properties of the numbers themselves.

For example, each large set of numbers in base ten contains nested subsets of all the other base ten numbers – these are vastly complex patterns generated by just 10 numbers.


In recursive systems. Repeating a patterns like this creates a syntax (a grammar) which organises further iterations (repeats) of that pattern.

So far we have dealt with purely abstract numbers patterns. In the twelfth century, an Italian mathematician called Leonardo of Pisa (now better known as Fibonacci) came up with a famous example of recursion, which seemed to describe natural patterns. This sequence is known today as the Fibonacci sequence. It starts like this:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34

To make a Fibonacci sequence all you do is add to the sum of the two previous numbers together to get the next number in the sequence. So for example if you start with 0 & 1 then the next number would be 1, (0+1), and the next number would be 2, (1 + 1), then 3, (2 + 1), then 5, (3+ 2), then 8, (5 + 3) and so on……

Graphically represented, the Fibonacci numbers can be arranged as squares which results in a pattern like this.

Fibonacci numbers form a spiral pattern which occurs everywhere in nature:

They are in the branching structure of trees…

the fronds of ferns…

in the shells of crustaceans…

and in the structure of the human hand

Beyond noting their ubiquity, I am not making any claims for these spiral patters as some kind of key to existence. Fibonacci numbers only describes, they does not explain. Those who have searched through them for the answers to life, the universe and everything (and many have) discover rather that these numbers do not reveal truth, all they reveal is more iterations of the same structure - behind the patterns there are only more patterns, stretching into infinity.


The notion that behind a structure you get more structure is known as complexity. And this is also in essence the message of another concept called self similarity. Self similarity was examined in a famous 1967 paper by Benoît Mandelbrot “How Long Is the Coast of Britain? What Mandelbrot showed in that paper was that a measured length of a coastline behaves in a similar way over a range of measurement scales. He called this behaviour fractal.

Fractals are curves that are irregular all over. Moreover, they have exactly the same degree of irregularity at all scales of measurement. So it doesn't matter whether you look at a fractal from far away or up close with a microscope-in either case you'll see exactly the same picture. If you start looking from a distance (i.e., with a "long" ruler), then as you get closer and closer '(with shorter rulers) small pieces of the curve that looked like formless blobs earlier turn into recognizable objects, the shapes of which are the same as that of the overall object itself (Casti 1994, 232).
James Gleick in the book Chaos writes;

Although Mandelbrot made the most comprehensive geometric use of it… [s]caling also became part of a movement in physics that led, more directly than Mandelbrot's own work, to the discipline known as chaos. Even in distant fields, scientists were beginning to think in terms of theories that used hierarchies of scales, as in evolutionary biology, where it became clear that a full theory would have to recognize patterns of development in genes, in individual organisms, in species, and in families of species, all at once (Gleick 1988 , 115-116)

The principle of self similarity means that repeating patterns result in similar configurations nested over different scales

Here is the pattern the retreated tidal water makes in the sand...

Which is repeated in the configuration of a river delta...

Extraordinary complex phenomena can be broken down and modelled based on this concept:

The mathematician and brilliant computer scientist Alan Turing's last published papers, before his death in 1954, had studied the riddle of "morphogenesis"-the capacity of all life-forms to develop ever more baroque bodies out of impossibly simple beginnings. Turing's paper had focused on the recurring numerical patterns of flowers, but it demonstrated using mathematical tools how a complex organism could assemble itself without any master planner calling the shots (Johnson 2001, 14).

Turing's paper on morphogenesis found its application in Lindenmayer systems. These are sets of rules which can be used to generate self similar fractals that model the morphology of a variety of organisms.

The principles of fractal geometry are used in virtual reality modelling. The self similarity of fractals create extraordinarily life-like computer generated images....

These examples illustrate how recursion can generate extremely complex patterns by repeating simple configurations nested inside one another. The outer systems repeats the patterns are found in the inner systems, but those patterns act as structuring elements across the whole system.

Descartes’ legacy
in the 17th Century, the truth of Rene Descartes’ theory of being (ontology) was seemingly confirmed by the usefulness of his analytical geometry. Descartes argued that the true being of substance was contained in the simple fact that it could be extended in space along x, y and z axes. Today it can be argued that the truth of recursion, as a theory of being, is demonstrated in fractal geometry that creates stunningly simulations of the real world. (The fact that these are incompatible truths says more about the contingent and context bound nature of truth than it does about the weakness or either theory. The point being that a theory is true so long as it helps advance human understanding - as Descartes analytical geometry undoubtedly did in the fields of mathematics.)

In August of 2000, a Japanese scientist named Toshiyuki Nakagaki announced that he had trained an amoebalike organism called slime mold to find the shortest route through a maze. Nakagaki had placed the mold in a small maze comprising four possible routes and planted pieces of food at two of the exits. Despite its being an incredibly primitive organism (a close relative of ordinary fungi) with no centralized brain whatsoever, the slime mold managed to plot the most efficient route to the food, stretching its body through the maze so that it connected directly to the two food sources. Without any apparent cognitive resources, the slime mold had "solved" the maze puzzle.

How did such a lowly organism come to play such an important scientific role? Slime mold spends much of its life as thousands of distinct single-celled units, each moving separately from its other comrades. Under the right conditions, those myriad cells will coalesce again into a single, larger organism, which then begins its leisurely crawl across the garden floor, consuming rotting leaves and wood as it moves about. In the simplest terms, [systems like slime mold] solves problems by drawing on masses of relatively stupid elements, rather than a single, intelligent "executive branch." They are bottom-up systems, not top-down. …In a more technical language, they are complex adaptive systems that display emergent behavior. In these systems, agents residing on one scale start producing behavior that lies one scale above them… The movement from low-level rules to higher-level sophistication is what we call emergence. (Johnson 2001, 11-18)

Emergence is easier to spot in primitive systems like slime mold because paradoxically their complexity exist at the microscopic level and their individual elements are opaque to the naked eye. It is only when you move away from microscopic scales and view phenomena at a macro level that its emergent properties become apparent. The human species for instance when viewed at cosmic distances is easier to represent as an emergent system. While. at a human everyday scale of understanding, the individual entity is more salient and emergent properties are correspondingly much harder to demonstrate.

Experiencing the world ultimately comes down to the recognition of boundaries: self/non-self, before/after, inside/'Outside, subject/object and so forth (Casti 1994, 230).

From the individual’s point of view existence is diagrammed in its binary oppositions, black/white, good/bad wrong/right etc. As Mandelbrot showed mathematically, the complexity of life is always going to escape the confides of our diagrams. because "Mountains are not cones, clouds are not spheres, and rivers are not straight lines." Furthermore, as Nakagaki found out with slime mold - collectively, self-organizing systems are smarter than their individual components. If we accept that self similarity works across all scales we could presume that the human species is more intelligent at the species level than it is at the level of individual human beings. This is a notion intimated by Jung’s collective unconscious and by the idea of God.


Casti, J. L. (1994) Complexification. London: Abacus.

Gleick, J. (1988) Chaos. London: Sphere

Johnson, S. (2001). Emergence. Harmondsworth: Penguin.

Thursday, November 06, 2008

Change has come, but a little too late for the Daily Mail.

Bush…unforgivably, exploited Americans' fear and anger by launching an unfocused war in Afghanistan - which failed in its principal objectives of capturing 9/11 mastermind Osama Bin Laden and isolating Afghans from the Taliban. Then he started a pointless, bloody war in Iraq - which had never harboured Al-Qaeda - and achieved nothing other than establishing itself as a huge drain on America's human and financial resources.

This is not a quotation from the Stop the War Coalition, but Peter MacKay writing in today’s Daily Mail. That’s right, you did read that correctly, I said the Daily Mail. It would be naïve (not to mention a rather puerile attempt at satire) merely to point out the hypocrisy of Mr McKay or the Daily Mail for writing and publishing these words. What I wish to highlight is what I think must change if we are to take my Obama’s words as a pragmatic call to action - "Let's resist the temptation to fall back on the same partisanship and pettiness and immaturity that has poisoned our politics for so long." I take these words to mean an attack not just on the pettiness of US party politics but also on hypocrisy and and intellectual cowardice generally. The man or woman who has hidden behind patriotism in the past or fear, offereing up excuses for not speaking the truth about the US initiated wars in our recent history. This is a different kind of poison. This is the poision which permeats into our moral judgements as a nation (or group of like minded nations) this is a poison which allows us to look the other way when millions of young, innocent and for the most part silent people on both sides of conflicts have lost their lives or have suffered in ways in which we can only imagine.

The issues addressed in the Mail's quotation are no revelation of course. Some of us have been saying these things even before the war in Afghanistan in 2001 and certainly before the invasion of Iraq in 2003. Saying it loud, but for the most part in isolation, without the backing of the official media, or politicians (Clare Short your cowardice still cannot be forgiven) and least of all by the Daily Mail of course. The point is that in the early years of this decade, in those times of fear and paranoia, just uttering the truth meant being ignored, insulted, accused of being unpatriotic and above all being marginalized as some lunatic fringe. Unfortunately, that time was precisely the time when the truth needed to be heard. Needed to be spoken loudly and authoritatively by all who knew it to be so, but kept quite through expediency, or ambition, or cowardice or vanity. You silence, the silence of the whole system is stained by the blood of all the countless victims of this century's futile wars. So let me now commend the Daily Mail for its honesty and express my wish that we cease to live in a culture where the only way to effect the reorientation of our moral compass is to indulge in retrospective hand-wringing and scape goating. Instead let us live in a culture where the truth is spoken and acted upon at the time when it actually matters.

Wednesday, November 05, 2008

"[T]he true strength of our nation comes not from our the might of our arms or the scale of our wealth, but from the enduring power of our ideals: democracy, liberty, opportunity, and unyielding hope."

Close Guantanamo. End Torture.

Sunday, August 10, 2008

Weights and Measures
My lifelong incomprehension of imperial weights and measures can be told through two stories. The first concerns a memory of my father taking me and my twin brother for a walk in Savernake Forest when we were about twelve years old. In the forest my father got chatting to a local man. I have a memory of him being a blacksmith but I would not vouch for that (he seemed like a character out of a Thomas Hardy novel). The conversation turned to weights and measures. I remember this man pontificating to my father with passion about the short-sighted stupidity of the government for introducing the metric system and getting rid of the imperial system. Unfortunately, being only 12 years old at the time, I could not remember what was said in this argument, only the passionate way it was being expressed.

The second story concerns the teaching of weights and measures. I was born in the UK in 1965 and the metric system was introduced in 1971. Thus, the teachers at my primary school were grappling with the new system at the same time as my foundational knowledge of it was being taught. Suffice to say, I think my initial understanding of metric was grasped with a certain amount of politically-tinged mutterings. However, the metric system made sense to me: 100 centimetres to a metre; 100 metres to a kilometre—even though I had no real conception of what these lengths looked like, the system itself was easy to grasp. On the other hand the imperial system was just plain baffling—12 inches to a foot; three feet to a yard; god knows how many feet to a mile! And weights were different again: 16 ounces to the pound; 14 pounds to a stone—where was the logic in that? My problem was that I had assumed that imperial measurements belonged to a system but try as I might, I could not work out any rational principles underpinning it. So when it came to choosing between one and the other I really could not understand why people would prefer what to me was a wholly arcane, senseless system.

Very recently these two stories came together in an unexpected way. I was playing Trivial Pursuit with
my family. A question came up about imperial weights and measures and mentioned the story of the blacksmith and wondered again what he could have said. My mother-in-law (who lives with us) was obviously listening, because the next few day she showed me a newspaper cutting. 

In all the English-speaking countries, land is traditionally measured by the acre, a very old Saxon unit that meant "field" as a unit an acre was originally a field of a size that a farmer could plough in a single day. The acre was never visualized as a square, it is long and narrow: one furlong by 4 rods. A furlong was the length that could be ploughed before the horses needed to be rested which worked out at 40 rods (presumably a rod is something to do with the length of the wood of the plough). The distance the constitutes the 'width' of a field also measured out in chains - 1 chain is the distance a team of horses could go back and forth before their harnesses (the ‘chain’) were taken off and the animals rested for the day. This amounted to four furlongs: four furrows in the ground measuring 4 rods in width.

I realised this article contained the substance of what that blacksmith had said to my father all those years before. Imperial measurements were traditional measuring systems marked out distances that measures the earth using parts of the human body or the distance over time taken for human or animal labour. These were concrete things that came out of experience rather than abstractions that were imposed on it. In essence, the crucial distinction between imperial and metric was the level of abstraction contained in each. The units of the imperial system were a mini picture of what the culture was like at the time of their inception. By contrast the metric system was based on a metal bar in a vault in Paris: some arbitrary length whose function was merely to create a standard around which a system of scientific measurement could be built. However, the problems came when anyone tried to combine the concrete things that made up the imperial system. (
By the way, I assume it is called 'imperial' because of the various acts of the British parliament which heroically attempted to standardize all the ad hoc measuring systems in the 16th and 17th century). For when the ploughing regime of Anglo Saxon fields was matched with a mile--the distance that Roman soldiers marched over a thousand paces-- it is no wonder that imperial measurements did not fit neatly together .

The revelation in this story is I had simply failed to see the paradigm shift involved. As a 12 year old I was already thoroughly embedded in the abstract mathematical paradigm of metric. And it made perfect sense to me to see a measurement system as self contained and logically consistent. I had unquestioningly assumed that the imperial system derived from the same paradigmatic assumptions and had followed a similarly deducible logic; but merely substituting different scales: feet and inches for metres and centimetres. This ignorance of mine actually betrays a wider cultural ignorance about the land and the issues surrounding working and living on it. I am a 'townie,' I grew up in an urban environment and therefore have no conception of ploughing fields or horses, or any kind of agricultural labour.
Distance to me is the distance that grids a map. Distance wasn’t real like something you could touch. I thought my misunderstanding of imperial measure was simply a question of units when it was actually a question of how one saw the world. No wonder the blacksmith's speech seemed so mysteriously compelling.

On a more academic note, the theme of being disconnected from the concrete signs of material existence in a world of abstraction (and absurdity) plays into a very modernist narrative of alienation. I wonder, is this the real reason behind the general but poorly-argued hostility to metric? Maybe? But I don't want to use this post as a forum to rehash such arguments. I should already be apparent that I am not one of the traditionalists who want to preserve metric; and if its preservation is metonymically linked to the preservation of the past, then the past can can wither and decay as far as I am concerned. But while I don't care for imperial measures politically, I do care for them as one cares for archeology or etymology. Like old buildings or the origins or words, the stories behind weights and measures are fascinating, because they are embedded with whole cultural history of experiences, like tiny time capsules. But, that said, campaigning to bring them back now as viable alternatives to what we have today is as anachronistic as trying to revive Anglo Saxon English or the steam train.


Other Weights and measures

I have compiled a summary from Russ Rowlett’s excellent article, “How Many? A Dictionary of Units of Measurement

Short distance units are based on the dimensions of the human body.

The inch represents the width of a thumb; in fact, in many languages, the word for "inch" is also the word for "thumb."

The foot (12 inches) was originally the length of a human foot, although it has evolved to be longer

The yard (3 feet) seems to have gotten its start in England as the name of a 3-foot measuring stick, but it is also understood to be the distance from the tip of the nose to the end of the middle finger of the outstretched hand. Henry I appears to have ordered construction of 3-foot standards, which were called "yards," and William of Malmsebury wrote that the yard was "the measure of his [the king's] own arm.” In fact, both the foot and the yard were established on the basis of the Saxon ynce, the foot being 36 barleycorns and the yard 108.

The fathom - if you stretch your arms out to the sides as far as possible, your total "arm span," from one fingertip to the other, is a fathom (6 feet).

Longer distances have more idiosyncratic origins..

The mile is a Roman unit, originally defined to be the length of 1000 paces of a Roman legion. A "pace" here means two steps, right and left, or about 5 feet, so the mile is a unit of roughly 5000 feet (For a long time no one felt any need to be precise about this, because distances longer than a furlong did not need to be measured exactly).


In traditional English law the various pound weights are related by stating all of them as multiples of the grain, which was originally the weight of a single barleycorn. Thus barleycorns are at the origin of both weight and distance units in the English system.

Gallons are always divided into 4 quarts, which are further divided into 2 pints each. For larger volumes of dry commodities, there are 2 gallons in a peck and 4 pecks in a bushel. Larger volumes of liquids were carried in barrels, hogsheads, or other containers whose size in gallons tended to vary with the commodity.

On both sides of the Atlantic, smaller volumes of liquid are traditionally measured in fluid ounces, which are at least roughly equal to the volume of one ounce of water. To accomplish this in the different systems, the smaller U.S. pint is divided into 16 fluid ounces, and the larger British pint is divided into 20 fluid ounces.

Rowlet R (2001) "How Many? A Dictionary of Units of Measurement"

Tuesday, June 17, 2008

Paul Otlet - Grandfather of the World Wide Web

The New York Times published a fascinating article yesterday on the work of Paul Otlet (pronounced Otley), a Belgian bibliophile who in 1934 mapped out and started to produce a card index and telephone prototype of the World Wide Web. This was eleven years before Vannevar Bush published his seminal article "As We May Think" in the Atlantic monthly. An event which is often cited as the germ of the idea which spawned hypertext and then eventually the World Wide Web.

Wednesday, June 11, 2008

Quote of the day!

US president George Bush in an interview with The Times newspaper:
“I think that in retrospect I could have used a different tone, a different rhetoric.” Phrases such as “bring them on” or “dead or alive... indicated to people that I was, you know, not a man of peace”

Monday, June 02, 2008

I'd like to ask a favour to one of the millions of fans who read this blog who lives or is visiting London soon and is even slightly interested in issues of consciousness and how the brain works. Will you please go to Scoobs book shop, walk along the corridor (past the upright piano on your left) until you reach the end wall. There you will be faced with a shelf of popular science books. On the second or third shelf down from the top you will find a first edition hardback of Gerald Edelman's Bright Air Brilliant Fire. Will you buy it please. It is a brilliant book and it will not disappoint you, probably it will change the way you think about conscious and a whole lot of other things. It depresses the hell out of me that every time I go into scoobs I see the same edition still unsold on the same bloody shelf. Edelman deserves better than this people - as I'm sure you will all agree once you have read him - which I'm sure you will do now on the basis of this recommendation. If you are a bit of a bibliophile, Scoobs is well worth a visit anyway. Scoobs (or Scoob Books), is located at 66 The Brunswick London WC1N 1AE. The entrance to the shop is just off Marchmont Street, which is the street in London for bookshops. You will find it between Russel Square and the British library - nearest tube is Russel Square on the Piccadilly line. Please just go and buy this book now and put me out of my misery.

Thursday, May 01, 2008

Postmodern Phishing

Because I am the webmaster of a fairly popular site I get swathes and swathes of spam mail. Phishing mails are fairly common (along with Viagra Cialis and penis extension of course). The phishing mail quoted below was particularly audacious. It has I feel a self reflexivity awareness of its own status as a cultural (phishing) object, it has irony, it calls into question notions of authenticity and depth, quotes freely from discourses of security and commerce and calling into question Beckian notions of 'risk and trust', in short it has all the characteristics of a post modern artifact.

From:Abbey National Plc

Dear Customer
These days, fake emails are getting more sophisticated, so it can be tough to know whether an email is real or not,Test your knowledge with the Fight Phishing Challenge to learn what to look for and how to avoid a scam.This might be due to either one of the following reasons,so as a result we are making an extra security check on all of our Customers account in order to protect their information from theft and fraud.

Click on the link below and you will be taken straight to where you can activate your account.

Thursday, April 17, 2008

The Effect of Gamma Rays on Man-in-the-Moon Marigolds
I can't believe that no one has used the above headline in connection with this story so I thought I would.

Friday, March 28, 2008


The aim of post is threefold: first to clarify the concept abduction by showing how it is differentiated from induction and hypothesis. Second to show how abduction is related in Peirce’s philosophical system, especially to the understanding of ‘precepts’ and ‘perceptual judgments’. Thirdly to summarise Peirce’s ideas on abduction as an instinct for guessing. Finally I will critique Peirce’s notion of abduction from the perspective of embodied cognition.



The first point to consider when trying to clarify abduction, induction and hypothesis is the problems caused by Peirce’s habit at different stages of his life of assigning different neologisms to represent similar ideas. Abduction is no exception since it also went by the name of ‘retroduction’ and even ‘hypothesis’. It is important to make clear that differently named terms in Peirce’s system are not necessarily conceptually synonymous, see for example the forceful argument of Deledalle (2000) makes regarding how Peirce’s thought was subject to radical change in his lifetime. There really daunting implication of this is because of the fragmentary nature of Peirce’s writings, and because he published no canonical exposition of his philosophical system in his lifetime, the researcher who is primary interested applying Peirce’s thought has to become a Peircean scholar in order to navigate the minefield of misinterpretation and confusion.


The second problem, as already intimated, pertains especially to Peirce’s use of the term hypothesis. For hypothesis is often used, not just as a synonym for abduction, but also in the sense of its traditional meaning as defined in the Cambridge Dictionary of Philosophy for example as, “A hunch, speculation or conjecture proposed as a possible solution to a problem” (Honderich 1995, 385).

In this sense, an hypothesis is common to both modes of logical inference deduction and induction, the function of the hypothesis is to provide a claim that is tested in induction and, if found to be robust, applied in deduction. Peirce’s innovation was that he added a third mode of logical inference – abduction. Like induction and deduction, abduction involves a hypothesis, however, unlike them, the abductive inference does not begin with a hypothesis as its starting point, but rather it produces one as its end result.

I want to examine this last claim in more detail since it clarifies the confusion between hypothesis and abduction. The following quotation from Peirce explains the relationship between deduction, induction and abuction:

Deduction is the only necessary reasoning... It starts from a hypothesis, the truth or falsity of which has nothing to do with the reasoning; and of course its conclusions are equally ideal….Induction is the experimental testing of a theory. The justification of it is that, although the conclusion at any stage of the investigation may be more or less erroneous, yet the further application of the same method must correct the error….. Abduction consists in studying facts and devising a theory to explain them. Its only justification is that if we are ever to understand things at all, it must be in that way" (Peirce 1998, 205).

One of the unfortunate consequences of the concept of Abduction successfully entering the academic mainstream is that seemingly canonical definitions proliferate, but when they are examined they all differ in some important respects . Vagueness emerges especially in regards to an inappropriate emphasis on the principles rather than the process of forming an abductive inference. An example of this is the definition in The Oxford Companion to Philosophy which is quoted here in its entirety:

Abductive reasoning accepts a conclusion on the grounds that it explains the available evidence. The term was introduced by Charles Peirce to describe an inference pattern sometimes called 'hypothesis' or inference to the best explanation'. He used the example of arriving at a Turkish seaport and observing a man on horseback--surrounded by horsemen holding a canopy over his head. He inferred that this was the governor of the province since he could think of no other figure who would be so greatly honoured. In his later work, Peirce used the word more widely: the logic of abduction examines all of the norms which guide us in formulating new hypotheses and deciding which of them to take seriously. It addresses a wide range of issues concerning the 'logic of discovery' and the economics of research" (Honderich 1995).

The problem with this definition is that it does not demarcate with sufficient clarity the difference between ‘an inductive hypothesis’ and ‘an abductive hypothesis’. With the result that it becomes easy to conceive of abduction merely a species of induction. One of the reasons the confusion surrounding the terms is so prevalent is that even Peirce himself was guilty of convoluted abduction with hypothesis, he wrote, “in almost everything I printed before the beginning of [the twentieth] century I more or less mixed up [abduction] and induction . . .” (CP 8.227).

Thomas Sebeok (1981) highlights this problem of hypothesis being common to both induction and abduction. He claims that hypothesis is conceived of by logicians as “an overly “narrow and formalistic conception of inference as necessarily having formulated judgments from its premises" (33). However, with abduction no judgement can be formulated in this way because no premises exist in an abduction: all the inquirer has to work with is a set of seemingly unrelated facts.


In order to differentiate between the two kinds of hypothesis, Sebeok says that the analysis needs to be processes led rather than definition led. Process led means that it should focus especially on the chronology of the various hypothetical and perceptual steps which lead to either an induction or an abduction. The simple rule to apply here is, induction seeks some facts to prove its hypothesis, whist abduction seeks an hypothesis to explain its facts (Sebeok 1981 34).

In induction a person approaches the facts already armed with a theory to explain them. This inductive hypothesis may be ephemeral. Indeed ephemerally is arguably a characteristic common to all hypotheses. But in induction the hypothesis nevertheless should be strong enough to determine which facts are relevant and which are irrelevant - and consequently also suggest to the inquirer how the process of induction should then proceed. In abduction, however, the confidence is lower because the ordering of theory and facts is reversed. A person begins with a number of seemingly unrelated facts. But armed with the feeling that they may be related somehow (CP 7.218). Peirce notes that the abductive inference often comes in a flash of inspiration, which he calls an act of insight, but of an extremely fallible kind. While it may be true that all the different elements of the hypothesis are already present in a person’s mind before making the abduction, the idea of putting them together is what flashes the new suggestion before the person's contemplation (CP 5.181).

In summary, the way to differentiate adduction from induction is to realise that there must first be an abduction for an induction to take place. Simply stated, the difference between abduction and induction is that abduction produces the hypothesis while induction tests the hypothesis.

It is impossible to see this is one does not take a process-led approach, for when induction and abduction are presented as principles, the two stages of inference formation are easily collapsed into one overarching concept – the hypothesis. This is why in the scientific method pioneered by Galileo and Bacon, the abductive stage of hypothesis formation is simply collapsed into induction. In the twentieth century this collapse was ironically reinforced by Karl Popper's explication of the hypotheco-deductive method. Popper considers the hypothesis is considered to be just “a guess” (Popper 2002, 536), however, in terms of the chronology of the process, this guess is already the starting point for the testing of the facts in an induction, rather than an awareness of a possible connection between them that will produce a flash of insight characteristic of an abduction.


Another way abduction and induction can be distinguished is the strength of inferences which lead from them. An example of this is found in Sebeok (1981, 34). Imagine a crime has been committed. Detectives working on the case discover a vital clue when a torn piece of paper comes to light, containing a specimen of handwriting from an anonymous source. The identity of the author is suspected and his desk, to which only he has access, is thoroughly searched. In the desk a notebook is found, in which one of the pages has been torn out and whose torn edges exactly match that of the paper in question. Sebeok argues that it is a fair hypothesis to infer the owner of the desk is the author of the writing. But, if the hypothesis were taken an induction, then he argues inference could never be justified with this degree of certainty. For the only permitted conclusion that induction allows a person to make is that the two matching torn pieces of paper might suggest a rule by which other torn pieces of paper can be compared in future. Whereas in abduction it is the nature of the inference presumes the two edges are same because they seem to exactly match. (Sebeok 1981, 34). This seems contradictory until it is realised that the purpose of logic is to formulate general principles from particular insights. In this example, although the insight is dramatic and strong, it could only apply to the particular circumstances in which it occurred, thus it is a poor hypothesis for induction. Peirce warns that this apparent certainty is not the basis for ontological security but rather it is precisely what makes abduction a bolder and more perilous step (CP 2.632).

This once more underscores the point that the notion of 'hypothetic inference' found in both abduction and induction (and indeed in deduction as well) it is not the same inference in every case.


The second part of this post outlines theoretically how an abduction is arrived at by examining the relationship between abduction and two other Peircean concepts: percepts, and perceptual judgements. The concepts of Percept and perceptual judgements will be explained in the paragraphs to follow, but it is useful at this stage to familiarise the reader with the structure of the steps that will combine to produce an abductive inference, even though the steps themselves are undefined at this stage. These steps are three: the percept acts as the ground for the perceptual judgement which acts as the ground the abductive inference.


The percept can be defined as the direct object of all thought. In this sense it exists in a state Peirce calls Firstness, which is notoriously difficult to explain, because firstness does not refer to anything else, nor does it lie behind anything. The first is that which simply is of itself (CP 1. 356). If the analogy is helpful, a percept can be likened to a “thought-image”, but with the caveat that this image is only taken to mean product of a person’s direct perception, rather than being a representation (CP 4.539). Percepts are not representations as such, because they are produced by mental processes we are not directly aware of, that happen below the threshold of conscious awareness (7.624 ). This means that the percept is not capable of describing itself; for such a description would involve analysis. However this does not mean that once a person has a percept, they may not then contemplate it, and say to themselves, “That appears to be a yellow chair” for example. In which case in ordinary language it might be presumed that the chair of the previous example is perceived to be yellow. However this conclusion is erroneous, because the sentence, “the chair is yellow” contains a judgment about the chair, which because it is a judgement involves processes of conscious thought (7.626 ).


It is this judgement that Peirce calls ‘the perceptual judgment.’ A Perceptual judgment can be defined as, a proposition of existence determined by the percept, which it interprets. (4.539 fn) Such a judgment takes place in an act of forming a mental proposition and then assenting to that proposition, in the sense of professing to one’s future self what the character of the present percept shall be (5.115; 7.631).

Perceptual judgments are the first building block of knowledge. They appear to exist in what Peirce calls Secondness. Secondness consists in one thing acting upon another, -- [a] brute action (CP 8.330). Perceptual judgements impress themselves on the mind in this way. They have the characteristic of being “necessarily veracious in greater or less degree according to the effort made” (5.141). But just because they are veracious it does also mean that they are true. The reason for this is found when the relationship between percepts and perceptual judgements is explored more fully.

As I have mentioned, percepts cannot be subject to conscious discriminations because they are apprehended below the threshold of consciousness. They are for that reason neither true, nor false, they just are. Similarly, there is not enough information in a perceptual judgement to confirm of deny the percept. For instance one may be mistaken about one’s perceptual judgement that the chair is yellow, but all this means is that further contemplation of the chair yields a different percept which in turn yields a different perceptual judgement the particular veracity of which is no different to the first, but is felt to be contradicted only by linking the two judgements together in an action of mediation. That kind of judgement in which one could say which perceptual judgements is true and which is false can only be reached when a number of perceptual judgements are compared and evaluated. To clarify this point Peirce provides the following example:

I may judge that I see a clean white surface. But a moment later I may question whether the surface really was clean, and may look again more sharply. If this second more veracious judgment still asserts that I see a clean surface, the theory of the facts will be simpler than if, at my second look, I discern that the surface is soiled. Still, even in this last case, I have no right to say that my first percept was that of a soiled surface. I absolutely have no testimony concerning it, except my perceptual judgment, and although that was careless and had no high degree of veracity, still I have to accept the only evidence in my possession (5.141).
Another important characteristic of perceptual judgements is that, although they are of themselves strikingly singular in nature, the fact that they are judgements means that they also involve generality to some degree. Although at first glance this seems surprising: it seems counter intuitive that anything so immediate as a perceptual judgement could contain any generality at all. However if the term ‘general’ is defined in the Aristotelian sense of “being that which is fitted by nature to be predicated of many things”, then it must be recognized that every judgments contains an element of generality, because it identifies a percept with a quality, and a quality is a general, thus perceptual judgements involve generality in their predicate (5.151).


The human mind’s further consideration of percepts and perceptual judgments is the basis upon which abductions are reached. Armed with this information we can make a more precise definition of abduction. It is the evaluation a person makes to assess different perceptual judgements of seemingly equal veracity. This is where the element of mediation enters into the analysis, "to subject these processes to logical analysis is simply to arrive at the logic of an abductive inference" (CP 5.181).

To exemplify the process behind this idea consider the following quotation from Peirce:

Looking out my window this lovely spring morning I see an azalea in full bloom. No, no! I do not see that; though that is the only way I can describe what I see. That is a proposition, a sentence, a fact; but what I perceive is not proposition, sentence, fact, but only an image, which I make intelligible in part by means of a statement of fact. This statement is abstract; but what I see is concrete. I perform an abduction when I so much as express in a sentence anything I see. The truth is that the whole fabric of our knowledge is one matted felt of pure hypothesis confirmed and refined by induction. Not the smallest advance can be made in knowledge beyond the stage of vacant staring, without making an abduction at every step (Sebeok 1981, 20) [Ms. 692].


The above quotation pushes to the fore the most perilous aspect of abduction, for it is merely guessing. But Peirce was struck by the frequency that people guess right about things, which was far greater than would be presupposed by mere chance (CP 8.238). For example in the sciences:

Think of what trillions of trillions of hypotheses might be made of which one only is true; and yet after two or three or at the very most a dozen guesses, the physicist hits pretty nearly on the correct hypothesis…. Even now he cannot give any exact reason for his best guesses. It appears to me that the cleanest statement we can make of the logical situation…is to say that man has a certain Insight, not strong enough to be oftener right than wrong, but strong enough not to be overwhelmingly more often wrong than right. An insight, I call it, because it is to be referred to the same general class of operations to which perceptive judgments belong." This faculty is at the same time of the general nature of Instinct, resembling (Peirce 1998, 217).
Peirce maintained elsewhere that the ability of a newly hatched chick to pick up food, [is] like abductive inference," and can be further traced back to the “animal instincts for, respectively, getting food and reproduction” (Ms. 692, quoted in Sebeok 1981, 20).

Peirce considers abduction as resting upon the hope that there is sufficient affinity between the reasoner's mind and nature to render guessing not altogether hopeless, provided, he adds that, each guess is checked by comparison with observation" (CP 1.121).

That no new truth can come from induction or from deduction, we have seen. It can only come from abduction; and abduction is, after all, nothing but guessing. We are therefore bound to hope that, although the possible explanations of our facts may be strictly innumerable, yet our mind will be able in some finite number of guesses, to guess the sole true explanation of them. That we are bound to assume, independently of any evidence that it is true (Peirce 1998, 107).


The way that abduction relates to percepts and perceptual judgements can be criticised because of its complexity and unwieldiness. This I argue is due to Peirce trying to explain these concepts using a representational framework to describe something that is in essence not representational. The processes of judging percepts happens below a level of conscious understanding. This may be explained in the way Peirce has explained it, but the explanation implies too forcefully a process of conscious analysis, whereas it is in fact only an interpretation of what presumably goes on in the mind. Another way to articulate these preconscious processes is from the perspective of embodied cognition theory; what may be called the logic of simulation. This logic ironically owes a dept to Peirce, because it is based heavily of pragmatism. Here is a sketched account of this position taken from the work of Adenzato & Garbarini (2006).


A pragmatic dimension of the theory of knowledge has emerged from the present interdisciplinary analysis of the as if concept—an analysis involving the neurosciences, cognitive sciences, anthropology and ethnology. This pragmatic dimension underscores the role of action, and especially simulation and interaction, in the knowing process.

The embodied cognition perspective views the mind no longer as a set of logical/abstract functions, but as a biological system, which is rooted in body experience and interwoven with action and interaction with other individuals. Specifically acting in the world, interacting with the objects and individuals in it, representing the world, perceiving it, categorizing it and understanding its meaning are merely different levels of the same relationship that exists between an organism and its environment. For example, we might ask, ‘how do children manage to become expert walkers?’ An embodied cognition answer contends it is not due to the mere application of previous (genetically codified) instructions, but, rather, due to behaviour emerging out of the continuous interaction among neural, bodily and environmental factors.

Embodied cognition allows not only for the planning and execution of actions, but for their representation as well. Based on a principle of cognitive economy, the same mechanism that leads to the explicit execution of an action also allows for its representation (and for the representation of its underlying objects) when the action is only virtually activated. Hence, representing objects and actions implies a simulative process, an implicit as if action.

Recent discoveries in the neurophysiological domain have experimentally confirmed the existence of a mechanism by which an object’s shape and function are coupled and perceived directly by an observer. In a series of studies Rizzolatti and colleagues (Rizzolatti & Craighero, 2004) have discovered the existence of groups of neurons in the premotor cortex of monkeys and humans, which fire when specific actions are executed. Some are triggered by the mere observation of an object, while other called mirror neurons are triggered by observing another person executing that action with the object. The activity of these neurons can be conceptually captured by referring to a simulation mechanism in the sense that when an object is under observation, a motor schema appropriate to the characteristics of that object is activated as if the observer were interacting with it.

Similarly, when observing another individual executing an action with an object, the observer’s neural system is activated as if he himself were executing the same action. In both instances, motor activation is only virtual - the action is not actually carried out, but it is neurally simulated.

This perspective makes it possible to maintain a representational conception of the mind, without adopting the model of abstract representations of formal logic and the linguistic/propositional format in which they are expressed. People construct representations of their world based not on theoretical categories, as traditionally assumed, but on pragmatic categories, derived from the dynamic interaction of living organisms with their adaptive environments.

I believe that if a strict representational framework should be abandoned when the discussion turns to percepts and perceptual judgements and especially in respect of his semi-mystical formulation of an instinct for guessing. Instead an as if schemata/simulation frame work should be adopted, because this leads to a clearer picture of the function of abduction, which can be conceived of as a bridge between preconscious activity and the conscious reporting of that activity. By viewing abduction from the perspective of as if schema, it is possible to delineate the concept with more precision that Peirce could achieve. The feeling which is the basis of an abduction is in fact the result of cognition taking place below a threshold of conscious reporting. Not as Peirce asserted due to direct perception of representations. Abduction is therefore the flash of insight where a hitherto non conscious thought announces itself to consciousness.

Peirce is made an important if overlooked contribution to the understanding and development of the logic of representation, but his work was also an important precursor of the logic of simulation as well. Not only did he perceive the limits of analytical thought in respect of his critique of novelty, but his understanding of logic was so sophisticated that all the major tenants of simulation are recognisable in his descriptions, even though they are framed in terms which fight to mislead the inquirer at every step. It is as if a medieval alchemist works were found to contain all the laws governing modern chemistry, but written in a language best suited to discussion of the transmutation of base metals into gold.


Adenzato, Mauro and Francesca Garbarini (2006) “The As If in Cognitive Science, Neuroscience and Anthropology: A Journey Among Robots, Blacksmiths And Neurons” http://tap.sagepub.com/cgi/content/abstract/16/6/747

Deledalle, Gérard (2000) Charles S. Peirce's Philosophy of Signs - Essays in Comparative Semiotics, Bloomington USA: Indiana University Press

Flach, Peter & Antonis Kakas (editors), (2000) Abduction and Induction: essays on their relation and integration, Norwell, Mass, US: Kluwer Academic Publishers.

Honderich, Ted (editor), (1995): The Oxford Companion to Philosophy, Oxford, UK: Oxford University Press.

Peirce, Charles Sanders (1998): The Essential Peirce: Selected Philosophical Writings, Vol. 2 (1893-1913), edited by the Peirce Education Project, Bloomington, US: Indiana University Press
___________________ (1931-1935): The Collected Papers of Charles Sanders Peirce, Vols. I-VI, edited by Charles Hartshorne and Paul Weiss, Cambridge, US: Harvard University Press.
___________________(1958): The Collected Papers of Charles Sanders Peirce, Vols. VII-VIII, Edited by AW Burks, Cambridge, US: Harvard University Press

Popper, Karl (2002) Conjectures and Refutations: The Growth of Scientific Knowledge, London, UK: Routledge.

Rizzolatti, G., & Craighero, L. (2004). The mirror-neuron system. Annual Review of
Neuroscience, 27, 169–192.

Sebeok, Thomas with Jean Umiker Sebeok (1981): "You Know My Method" in The Play of Musement, Bloomington, Indiana USA: Indiana University Press

Friday, February 15, 2008

What is wrong with this picture?
In an interview with the BBC [President Bush] said information obtained from alleged terrorists helped save lives, and the families of the July 7 victims would understand that. Bush said waterboarding, which simulates drowning, was not torture and is threatening to veto a congressional bill that would ban it. [He also] insisted the US still occupied the moral high ground worldwide. (Guardian)

Friday, February 08, 2008

BBC iPlayer to hit Macs in 2008

The BBC will launch a download version of its iPlayer online video service for Apple Mac users by the end of 2008. Well its about bloody time, the question is why has it taken this long?

Explaining the decision to launch for just Windows users, Mr Thompson said it had been about "making the service available in the shortest time frame to the greatest amount of users".

Hmm, hasn’t he heard of flash players? Why the hell did the BBC have to use a proprietary windows player anyway??
Please take my survey.

If you have come across this blog I would be very grateful if you could click on the following link and take the survey.


You do not have to be a serious gamer to take part. all you need to have done is played a videogame. The survey is very short and should not take more than a few minutes of you time.

I am interested in why playing games is such a different experience from watching them, and from watching other kinds of media like TV and films. I have a theory that the feeling of greater involvement players experience with videogames is to do with the way people model the layout of their environment in their heads, which then gets applied to videogames as if they are real environments. This faculty is not so engaged when watching a film or TV because from a very early age we learn that we cannot interact with these kinds of media, so we tend to sit back and scrutinise them instead. I don't want to say more than that because I don't want those taking the survey to have their expectations micro managed.

Thursday, January 17, 2008

Two classic books on digital culture
are free to download

Julian Dibbell's account of life in a MOO, which
includes the infamous "rape in cyberspace" chapter
about the activities of Mr Bungle is now available
to download free at...


Also Steven Pool's great early book on videogames
"Trigger Happy"is free to download at


As far as I can tell both downloads are legal and
approved by the authors. They are must reads for
anyone interested in digital culture.

Monday, January 14, 2008

Check out this amusing video of Wii bowling tournaments in senior citizen homes in the US.

For the past nine months, residents in Erickson’s old people’s homes in the US, most of whom have never picked up a video game controller in their life, have been playing Wii bowling, tennis, golf, and baseball.
With professional graphics and their own team uniforms, it seems
that Erickson are taking the tournaments pretty seriously

"I've never been into video games," said 72-year-old Flora Dierbach last week as her husband took a twirl with the Nintendo Wii's bowling game. "But this is addictive."

Nintendo has been bolstering its senior-friendly image, partnering with retirement communities, including Erickson, which has received 15 free Wiis. Nintendo has more than doubled annual profits partly thanks to the popularity of its Wii consoles. In the UK, the Wii is the fastest-selling games console in UK history, Nintendo sellin 245,653 units in four weeks.