If we have done away -like postmodernism- with the notion of absolute truth, and we are living in a life-world where observers with limited knowledge try to 'make sense' of their envirnoment, then we we have certain freedom to define other forms of truth.
3: Patterns, Objectivity and Truth
In a pattern-orientation, there is at least one sort of truth that we could think of, and that is when two patterns make an exact match. In other words, two patterns have an identical structure, and thus make a form that is exactly the same as the pattern. When a pattern that is stored in the brain -the brain is a pattern-processor- makes an exact match with a conceptual pattern, we could say that there is a 'little truth of matching', or 'it is true that two patterns match'. Does this mean that there are no universal truths? No, it simply means that under the premise of limited knowing, no observer can conclusively prove that there is such a truth. So all that remains is the truth that two patterns match, or that an assemblage of patterns match with a more complex one. This is the way that we recognise forms (and it is also the way how forms are created in the 'philosophy of PAC').
Truth and Reminiscence
The result of this metaphysical DIY-ing is somewhat disturbing. For the 'truth' that we have defined is not very powerful, like the old truths that have driven science in philosophy in the past. Suppose for instance that we have an exponential growth function, like the annual increase of money on a bank account due to the interest rates (and which we know because we have a savings account). Now we look at the world population -a different medium than money- and see the same pattern (which is conceptual because we see it for the first time). The world population grows exponentially. So now we have discovered a truth, namely that two patterns match. However, both patterns are completely unrelated. The first exponential growth function exists by design -it is a construction-, while the other is an observable phenomenon in our life-world. The only reason why we know the the world population grows exponentially is because we have stored this pattern by a previous experience -when we opened a savings account in our example- and yet both are unrelated phenomena. This, in science would be called a spurious relationship, and the only reason why they match, is because both are the result of a process that generates new stuff (money,people) from an existing situation (of money or people). We know from mathematics that these processes always have an exponential form. The underlying pattern is therefore related to a process, and its manifestation (or expresiion) in certain media is comparable. Yet this truth is fragile because it may lead us to draw conclusions that are wrong! In complexity theory, this methodological problem has also been called the reminiscence syndrome, but with PAC we can give an explanation why this goes wrong. The 'truth' is that you have a match, but this does not mean that two phenomena (targets) are related. And this immediately is a criticism of much theoretical work, for theories, frameworks and also computer models may appear to display the same behavioiur as real-world phenomena, but this does not mean that they actually represent them! Suddenly we are in deep problems, because this extrapolation of scientific models to real-world phenomena is often doen implicitly! This is one of the reasons why a model needs confirmation from various conceptual angles (perspectives). This has already been elucidated in the article on Pattern-oriented modelling that I metioned in my previous post.
There's spurious and there's spurious
There may also be another reason why two patterns appear to be matching. Suppose you measure the increase of CD sales worldwide, and do the same for shoes. You see both growing exponentially, so you start looking for a relationship between CD sales and shoes, which seem to have very little in common. Then these measurements are cross-referenced with the growth of the world population and they match! So basically you have two measurements that point to the same underlying phenomenon: you have two measurements of the increase of the world population! The problem now is that you basically only measured one pattern (growth of the world population), and it could be that you bring up a multitude of these measurements that all point at a growing human population! All these measurments basically are one measurement and hardly bring new perspectives for the underlying model that you are trying to verify! I have used this in my criticism of transhumanist Ray Kurzweil in his assessment on the impending Singularity.
Of course, it can also be the case that a pattern that is stored in your brain is exactly the same as a pattern that you observe. Yesterday you saw the sun go up in the east and settle in the west, and today you see the same pattern yet again. This stronger equivalence between patterns is called an isomorphism (similarly shaped) and this holds a stronger truth than a spurious relationship. Construction work typically is based on isomorhpisms, as the models that are made (design plans, blueprints, etc) are meticuously extrapolated into the modeller's life-world by the constructive activities, so the relationship between model and (constructed) target have a strong equivalence. However, the opposite direction of making models by observing a target is much more difficult, and so the chance of capturing an isomorphism in your model is a difficult task when the target is complex. The double helix form of DNA is a good example of a model that proved to be a successful isomorhism of the 'actual' form.
The success of the use of isomorphisms in engineering and other applied areas, has been a strong driver to do the same in other areas. Especially the system theories hinge strongly on this idea. However, the discovery of isomorphisms remains much more difficult than constructing them, and the risk of spurious relationships is very large. This is a well-known problem in electronics. When you try to recreate electronic circuitry by looking solely at the behaviour at the outside (a 'black-box approach), then this task quickly becomes undoable with even slightly complex phenomena. Usually the introduction of memory (states) in the circuitry is enough to make a black-box approach undoable. Extrapolating this, this means that using solely empirical approaches to understand complex targets is way too limited!
The strongest form of equivalence between patterns is when they are scale-invariant. this is truly a contribution from complex systems research and non-linear mathematics. Scale invariance means that the pattern does not change within a certain range. For instance, the placement of our arms, legs, head, fingers, toes and so on, do not change after the foetus has reached a certain stage of development, and remains in tact well after we are dead. Many aspects of the form of our bodies remain scale-invariant with respect to our physical growth.
In physics, many forces are scale-invariant because they adhere to power laws. Gravity for instance works at tremendous minute scales, to cosmological scales. Scale invariant patterns are therefore amongst the most robust ones we have, although we must realise that they always are bounded within certain ranges, which depend on the media in which they manifest themselves. Usually their behaviour is influenced by these boundaries, and they may display different behaviour around them. The exponential growth curve of human populations will, for instance, display different behaviour if it is bounded by the scarcety of food (which is likely to cause a dampening effect around an equilibrium state) or by a sudden shortage of something that completely runs out (say, oil), which may result in much stronger fluctuating effects and sudden decline.
Note that scale-invariance also means that some patterns defy traditional disciplinary boundaries in science, philosophy and professional practices, so these patterns can be manifest in different areas. Because they can be recognised by specialists, this means thast these patterns allow a cross-disciplinary point of connection for themes that by their nature are much larger than the disciplinary scope. For instance, sustainability issues often are a combination of issues related to scarcity and issues related to justice, ethics and morality. Traditionally these would be taken up by science, philosophy and professionals in isolation, with the result that all contributions to sustainability issues are too limited in scope (In terms of PAC: naïve). Professionals and scientists will tend to be naïve on the ethical and moral implications, scientists and philosophers on the practical implications, and professionals and philosophers on the scientific aspects. The patterns of PAC are specifically selected for their ability to assist in cross-disciplinary research, because they form a sort of graphical pidgin language.
The Pattern Library of PAC
It may have become clear that the pattern library of PAC aims to be a collection of threse scale-invariant patterns, because they are the most robust. Implicitly this includes a lot of mathematical patterns, but now they can be assessed with a robustness criterion, which also is added to theories, frameworks and methodologies (including PAC itself). This very practical criterion therefore does not aim to replace current theories, frameworks, and so on, but rather allows an additional quality control. At the same time, the methodology tries to be very aware of its own boundaries and limitations, as I've tried to demonstrate above. This is due to the self-referential nature of the methodology: every boundary or constraint that is observed, may have implications on the methodology itself!
Patterns, Objectivity And Truth
By Kees Pieters | March 25th 2011 03:47 AM | Print | E-mail