Man & Reality III

Pragmatism 

Let us attempt to define the philosophical position that currently dominates the widespread everyday attitude to Science and its role in society, not only in the technology dealt with above but in Science itself.

Elsewhere, I have established that “Technology rules OK”, and is often mis-named “Science”! Its productions abound! From space rockets to television, mobile phones to digital cameras, and washing machines to computers – everywhere these products seem to define the main thrust of society. But, what exactly is Technology? How does it relate to Science, and how have its worship, and its effect on the general world view developed to its present state? The essence to these questions must be at least started with the explanation of the relationship between Science & Technology.

It is clear that Science is about “Why?”, while Technology is about “How?”

Early in their development these two things had a different relationship to that they hold today. Long ago as soon as some “useful” thing or process was discovered, it was immediately “put to use” without any real explanation. But there was a danger in this lack of a meaningful explanation. The process was therefore all the more difficult to remember and pass on to the next generation, because it couldn’t be easily explained. So there developed a sort of “apology” for an explanation which often took the form of a quasi-religious or magical ritual, with associated mumbo-jumbo. There is little doubt that such closed shop procedures were in fact quite effective. Without understanding, practitioners were still able to maintain and pass on their powerful techniques. So, it seems that Technology preceded Science but was maintained by the mystical garb of myth. So, obviously, someone, somewhere actually, by chance or design, actually discovered the useful kernel that was later entrenched in the above performances, and indeed, this has to be seen as a kind of “embryo Science”, but any clear essential explanation was at this point absent. The process had mostly involved intelligent observation and realisation rather than any structured scientific activity.

So, from early in the history of modern man, the “practical” use of discoveries was established.

Now this paper is not meant as a history, especially as I am in no position to give chapter and verse on the detailed processes and development of this nascent Science. That is a task for someone better qualified than I in objectively interpreting and delivering History. But, if we are to understand the position as it stands today, we must at least give some time to seeing how that grew from its ground in man’s past. By the time of the Greeks, the situation had become noticeably more rich and complex. The beginnings of detailed observation, Mathematics, Logic and Philosophy were by then established as study-able categories, and the earliest “explanations” (in the modern scientific sense) were attempted. This was the start of true Science, but we would be very hard put to recognise it as such. With basic “elements” such as Earth, Fire, Water and Air, we find it hard to give any credence to it as what we would call explanation, but in an important sense we would be mistaken. It was an intelligent attempt. Its explanations were not stupid AND contained morsels of the truth. Our modern way of putting this would be to say that these concoctions STILL contained some objective content, even though they were wrapped up in mistaken definitions and understandings. None-the-less, for the first time it did put explanation “on the agenda” as a worthwhile undertaking.

By the time of the Industrial Revolution, all sides of the study and use of aspects of Nature had exploded into myriads of lines of development, and new forms of Abstraction had led to the birth of true Mathematics, as well as a range of separate sciences, and sophisticated technological methods of producing things for use. Though the Giants of Culture at this time were often “renaissance men” in that they participated in everything, the various subjects were becoming separately defined, and while Engineers built roads and locomotives, ships and bridges, Scientists attempted to get to the heart of things and explain WHY things performed as they did. By the time of Edison, the inventor/technologist was becoming separated from the pure investigating scientist in that his overriding question was not WHY? But HOW? And his purpose was the employment of discovery in commerce. That is the conversion of knowledge into saleable devices. The public more and more associated “science” with its use in readily acquirable devices and facilities. Those investigative workers, asking the question WHY? were relegated in public consciousness to the ivory towers of Universities where they could ponder the explanation of the world, while the real “useful” people were conceived of as the engineers and technologists.

Thomas Edison

A peculiar form of “research” began to develop that was not carried out by scientists, but by inventors and technologists, who KNEW the available science, but required outcomes that were immediately reproducible and acquirable by the population at large. This form can best be called “suck-it-and-see”. It involved using what science had discovered but with very different purposes. Every conceivable trick was used to find cheap and effective ways of delivery of what had been shown to be possible. Such DIRECTED experiments had reversed the priority relation with scientists. Most discoveries were now made by “disinterested” scientists, while the employment of these in everyday devices was carried out by technologists, involved NO new understanding, no new explanations, but it could reveal effective answers to practical employment and use. Thus occasionally things were made which led to catastrophic consequences, such as all the passengers on a train being suffocated as it passed through a tunnel. There had been nothing wrong with the underlying science. The engine chugged on through the tunnels and emerged unscathed, but no science had been done on how passengers would be expected to react within a tunnel and they all perished. But, though the human cost was very high, the methods of the technologists, after multiple tries, did usually, in the end, provide working solutions. This method has often been termed Pragmatism – “If it works – it is right! The “god” of pragmatism was undoubtedly Thomas Elvar Edison who, in the USA in the 19th century invented functioning electric light, phonographs and many others with the sole purpose of delivering them as saleable products on the market. His objective was to turn scientific discoveries into saleable commodities to millions of customers and thus amass a fortune. Yet Edison was no scientist, he was certainly a technologist. My favourite example of this approach was the saga of the Douglas DC3 airliner/cargo carrier of the 1940s.

Douglas DC3

This aircraft was thrown together and catapulted into its first test flight resulting in an immediate crash. But if you believe in “suck-it-and-see” it is clear what you do next. The fragments were gathered together and studied with a view to correcting the fault, and a new version was quickly completed and again immediately test flown. It crashed again! The process was then repeated many times at great expense and some considerable loss of life. BUT,thefinal product turned out to be a masterpiece! It became the backbone of military transport during the Second World War from packets to paratroopers, and continued after the war to serve airlines throughout the world for many decades. The DC3 was therefore produced by pragmatic methods and proved that they do deliver.

Now this experience, particularly in the USA, led to a philosophical position also, which embodied exactly the same approach – “If it works – it is right!” or “Suck- it-and-see!” “Let’s try it for Christ’s sake!” –“Don’t constantly think about it. DO IT!” And this rather lightweight philosophy was justified by success in commercial and economic terms. The total dominance across the world of American capitalism validated their home-bred, macho philosophy and was overlaid with high sounding conceptions such as “Democracy”, “Liberty” and “Economic Success!”

Now a particular effect of this has been a deification of technology as a panacea for all problems. Technology has been turned into “science”, and is repeatedly called Science. Its practitioners are always called “scientists”, and its achievements are credited with scientific qualities and merits, such as “explaining” the origins of the Universe, or revealing the mechanisms of Nature. An example of this is how the technology of video photography, radio communications and image post-processing (all pure technology) are said to SOLVE problems of the true nature of Jupiter’s moons and many other similar cases. But, of course, what is happening is that uninformed speculation is simply being demolished by new evidence, made available by technology. Technology doesn’t present alternative explanations. It is incapable of such tasks. It merely delivers the data for scientists to interpret and explain. The prevailing attitude to Technology is, of course, so much twaddle. Technology is not Science and as such makes NO contributions to understanding the world.

Such claims are like commending the piano for the creation of a Beethoven Piano Concerto.

Piano

What utter nonsense!

Now the establishment of technology as “the most important activity in the world today” has been entrenched also by the role of Mathematics as a quantitative tool in technological achievements and problem solving. Unlike scientific qualitative explanations and theories, technology’s ever-present bed-fellow is Mathematics. The relationship between the two is also the epitome of pragmatism. The limited, yet quantitative aspect of maths formulae fits like a glove with pragmatic technology. Formulae are used until they fail at some domain boundary, thereafter being replaced pragmatically by other more appropriate ones without compunction. No technologist feels any guilt at such suck-it-and-see procedures. They are, after all, his philosophical ground. “If it works – It is right! If it fails, dump it and instead use one that works!” Thus the quantitative and pragmatic aspects of functional mathematics, is the perfect partner to “problem-solving” technology. As long as Science provides the working theories, and maths maps these onto working formulae, technology can march ahead and deliver the goods.

The social basis for Pragmatism is also of significance. Both the current dominance of the USA and the preceding dominance of the British Empire underwrote a pragmatic view of the world. The standard of living at the centre of the dominant culture was always predicated on the extraction of profits from the rest of the world, and these were rapidly taken as being natural consequences of the superiority of the prevailing pragmatic ethos of the empire builders and corporate giants. So, if such a system could provide such elevated levels for most of its general population, its methods must be correct. At the same time the demise of the Eastern Block – simultaneously with this dominance - undercut the currency of socialism, and its place as the future of the world was replaced by a “property-owning democracy” or some other euphemism for the privileges of dominance.
Now, so far we have been concentrating solely on Applied Mathematics, and it is obviously vital in all industry throughout the world. But it doesn’t exactly “thrill you to bits” does it? It is the “toolbox” conception of mathematics. Perhaps that alternative ivory tower area of the subject needs a more detailed look. After all, it seems to be the source of all maths techniques, even those used in the above pragmatic ways. What is its remit and purpose?

This is the third in a new series exploring philosophy and mathematics: Man & Reality. Part IV will be published here next Monday. 

Man & Reality II

Applied Mathematics - The Toolbox!

Though it is rarely evident in the teaching of the subject, there are very different roles for maths in the modern world. Perhaps the first historically, and the most prosaic, is its use in production – in manufacture of all types. When relationships were detected in nature, the requirement was to find-and-fit a mathematical form to the revealed relation to allow quantitative questions to be asked and answered easily. Such “fitting” did not require any theory to be elaborated. No philosophy was involved. A mathematical artisan could rummage around in his toolbox of forms and find a rough fit, then use a few modifications and adjustments to effect a pretty useful final result. The maths would then be indispensable in the effective use of the revealed relation in diverse ways. Over what amounts to millennia, mankind developed a wide range of techniques which facilitated such undertakings, using every conceivable mathematical invention to purely practical ends.

This cycle of discovery, fitting of maths forms and USE has developed into a clearly delineated area, which keeps clear of theory (except as a source of yet more tools) and engages in practical tasks.

We call it Technology, or even Engineering, and its “fitting” activities are often very pragmatic, while being at variance with the concerns of pure scientists, who demand answers to the question “Why?” The pragmatists of concrete world problems are much more interested in the question “How?”

And the incessant clamour for the maths to facilitate their labours has led to a rich set of techniques which could only rarely be said to help in understanding. These techniques basically are superlative “fitting” methods. A few examples will give the clearest idea of what they are like. The most famous is the method of “Equating Coefficients” in generalised polynomial equations. Such generalised polynomials can have no theoretical basis, but can be put forward as the first pragmatic step in covering a well researched relationship (liberally supplied with data) in Nature.

So general, in fact, is this form that every single term is given an unknown constant – not much good so far! But with sufficient sets of related data from the real world, these can be substituted into the polynomial for a number of different cases, and the result can be a coherent set of simultaneous equations in the unknown “constants”. With these, there are algebraic methods (and later on determinants) that enable the solution of these equations involving the exact values of these unknowns. And when these are substituted back into the general polynomial, we end up with a mathematical formula that fits the facts.

Notice the total absence of explanation in these processes. They established a solid cycle between experimental data and mathematical expressions that can, and do, produce powerful, useable formulae.

Another similar process is the so-called “Fourier Analysis”, where almost any time based repeated pattern in nature can be “fitted up” by the addition of multiple “sine waves” suitably weighted. The method does work, but it would be incorrect to say that it throws any real light at all on the actual causality of the situation being modelled – quite the reverse. If anything such a method hides the causality. It is interesting to see that a modern example of such an approach is actually used to produce a so-called “theory”. This is the renowned String Theory which turns out to be of exactly the same ilk. There, oscillations of strings (?) are added together to produce Everything (?) in the Universe. And, if we are trotting out famous examples we must not omit the enduring Ptolemaic Theory of the heavens, which matched the recorded data with the ever more complex addition of epicycles to model the movements of planets, sun and moon as observed.

These are a few examples of the power (and weaknesses) of “fitting”. Mankind was not able to refine the Ptolemaic Theory until it arrived at the Copernican System, was it? For over a thousand years the former had held sway, AND was a barrier to a better theory. A revolution in thinking (and, I believe, in society) was necessary before this edifice was pulled down and something nearer the truth erected.

Perhaps I should include one final example. I am sure that I have made the point I wish to make, but I feel that this last inclusion is nonetheless unavoidable. It involves that icon of technology – the computer. Many calculations and manipulations in mathematics proved to be long-winded and tedious, and it soon became cleat that such tasks would perhaps best be carried out by some mechanistic aid – such as computers. These tireless mechanisms, given an effective algorithm (computer program or set of instructions) could trawl through the data until an acceptably accurate result was achieved. The very inclusion of the computer, though, caused an interesting regression in techniques. Over the centuries many, almost mindless, iterative techniques had been developed for finding the quantitative information required without understanding the causal features involved. These had not been attractive to human employment because of the mind-numbing boredom of repeated application, but also because they added nothing to our understanding. Computers, as you may guess, changed all that. Pragmatists wanting numbers to a certain accuracy were quite happy to consign the job to a computer program, which could churn away at lightning speed, and produce exactly what was required. The era of “the computer says” was born.

Computers paper over the cracks

Computers had another significant effect on the modelling of reality. The inevitable breakdown of individual formulae at domain boundaries was obviously a major problem in constructing effective computer-based models, and restricted such models to very limited context. But there was a way round this difficulty! Computer scientists had been including tests in programs since the beginning, and re-routing the path to different sets of instructions. But, normal procedural languages involved detailed programming of all the tests and switches, and because instructions were only obeyed sequentially, there were often delays until the requisite tests had been made. The solution was a new breed of computer languages called Object Orientated Programming Systems (OOPS!) These languages were effectively “interrupt driven”. They could be given rules that were of general significance, and could be kept separately from sequences of instructions. These rules encapsulated the precise conditions when one domain had become defunct and another had to be set up with its own, and different, instruction sequences. These were handled so that they were ever-available. This meant that the language implemented a runtime version in which the “house-keeping” roles CAME FIRST. That is, the rules were tested out at every single time-slot cycle. A positive result would mean that the current sequences of instructions would be interrupted and the switch in mode effected.

These features effectively papered over the cracks between different domains. As soon as the conditions for a change were encountered the switch was implemented. No understanding of why the switch was necessary - was involved. Some threshold or set of thresholds were designated as sufficient to implement the change. Significantly, the transition seemed “seamless” and “natural”. How lovely!

The dynamic content that always accompanies such changes was, of course, totally absent from these transitions. It was thresholds – Switch! I feel impelled at this point to bring in my evergreen anecdote about reaction fronts in liquids.

From time immemorial, budding scientists had been told to “stir well” and wait for equilibrium conditions before any meaningful data could be taken from an experiment. Breaking this rule led to all sorts of inexplicable data, and no conclusions could be drawn. In the 1980s I was lucky enough to work with some researchers who consciously disobeyed this rule. They wanted to study the reaction fronts when two different liquids reacted chemically. They never stirred! They almost forgot to breathe, as the slightest disturbance would ruin their experiments. They also chose a situation where a reversible reaction could be quite easily be caused to oscillate to and fro between the products at each end of the reversible reaction. They also carefully chose a situation where the products were of significantly different colours. The test tubes unfolded beautiful, striped structures as the oscillation proceeded, and the reaction fronts were clearly shown to be TOROIDAL SCROLLS. So much for stirring and equilibrium then!

Innumerable further examples could be put forward here, but I am sure that the point has been established. But, “Is that all there is?”, as they say. No, it isn’t! The methods described above use mathematics that was disinterestedly developed by pure mathematicians, but to purely pragmatic ends. Indeed this approach has been consolidated into, what may be called a philosophy. The philosophy of Pragmatism.

This is the second in a new series exploring philosophy and mathematics: Man & Reality. Part III will be published here next Monday. Part 1 can be found here.

Pure and Applied?

Philosophically, Mathematics has shown itself to be a very unusual discipline, in that it seems to be investigating Forms found in Reality, but is, in fact, more to do with how we humans conceive of, extract and handle such Forms in our thinking.

Historically, the recognition of such Forms in Reality-as-is was never a straightforward discovery - directly extractable as such from that source. For, to even recognise what we were seeing in that complex and varying context, Man just had to both simplify and idealise what he glimpsed, into something both fixed and intelligible. For such Forms as we arrived at, were not what we saw, for they were invariably imperfect and often somewhat transitory, so observers felt they were seeking an underlying perfection below the really existing complexity, and they, with experience and over time, became very adept at the necessary processes involved to reveal perfected and unchanging patterns.

As already mentioned, though seen as unearthing these Forms, they were always both simplifying and idealising them, into “ideal versions”, and, thereafter, studying them instead.

The believed excuse for such processing, was that these Pure Forms did seem to exist “out there”, and the processes of extraction were considered to be mere “tidying up”, and, thereby, releasing the crucial Forms from a natural context of confusing and inessential “noise”, caused by a complexity of other diverse causes, which could be removed to reveal the “real determining heart” of a situation. And, having extracted these causal essences, they could be investigated and their important intrinsic properties revealed.

It was, historically, the initial beginning of Science, even if the actual causality had been inverted, and effects labelled as the actual causes!

Yet surprisingly, many of these initial conceptions have been, at least partially, retained ever since!

And, again surprisingly, this discipline was the very first that Mankind was able to construct into what seemed to be a self-consistent set of relations and rules underlying Reality. And this was so universally taken on by those involved in such things, that, from the outset, these Forms were given Causal Attributes - real things were seen as behaving as they did, because they were obeying the eternal Laws of these Forms.

Hence, these first steps were clearly idealist, and not materialist, in the march of the human intellect.

NOTE: It ought to be mentioned at this stage, that the almighty retreat, in 20th century Sub Atomic Physics, embodied in the infamous Copenhagen Interpretation of Quantum Theory, was merely a retrenchment back to this ancient idealist stance.

Henceforth, in that area, Form was deemed to be the cause of ALL phenomena, and Equations replaced physical explanations almost completely.

So, in Ancient Greece, truly remarkable strides were made, particularly in Geometry, which was immediately available for investigation via drawing, and this amazing development ended up with what we now call Euclidian Geometry – which is still taught as a cornerstone of Mathematics worldwide.

But, it did have major drawbacks! And, these are not only in its idealist stance, but also in its major simplification by imposing eternality upon all its contributing Forms. They were fixed! And, the implications of this, along with their endowment of being also the cause of phenomena, had deleterious implications for the real study of Reality.

Clearly, the extrapolation of this assumption onto many other non-mathematical ideas was inevitable as well as being profoundly mistaken. For though Forms could be “found” in real situations, they were never the determining causes for those situations, and as the real determinators changed, so did the evident Forms.

Forms, as such, were permanent (that is as Formal abstractions), but their real existence was always temporary and never causal!

The consequences were extremely damaging: most things were dealt with as unchanging, and the basic tenet of Formal Logic, which was an intellectual product of this development – that is A = A – the Identity Relation, cast in stone the un-changeability of the ideas and elements involved in this major extension of what had been learned in Mathematics.

NOTE: That this is still around and propagated, was revealed in a book entitled A Certain Ambiguity by Guarav Suri and Hartosh Singh Bal, published only a few years ago (2010 - Ed).

But after, maybe, 2,000 years of Greek Science, based upon such a position, a breech was made in the then towering edifice of that “science-based-upon-Logic”, into one based upon careful observation of concrete Reality. Finally, a new approach was developed, which was, in fact, materialist Science.

Perhaps surprisingly, the new approach prospered in tandem with a rejuvenated Mathematics, because Science was now based upon quantitative measurements, and hence was regularly delivering dependable data sets, clearly also revealing Forms to be extracted and formulated into useable Laws. And, of course, the “ideal experts” for doing this, were the mathematicians, who by this juncture had amassed a truly remarkable number of Forms “to fit all possible patterns”.

An extremely fruitful cooperation developed between idealist mathematicians and materialist scientists, and sometime, and somewhere, something was bound to give! A unifying concept arose that was that of Natural Law. When experimental data was turned into an Equation, by the mathematicians, it was agreed by both parties to be a causing and eternal Law – the scientists had in fact succumbed to the idealist position of the mathematicians.

But, this purely pragmatic compromise was never a solution. Indeed, it was yet another example of a Dichotomous Pair of contradictory conceptions, which couldn’t both be true!

Yet, without a transcendence of the ever-evident theoretical impasse, the two groups pragmatically “agreed to differ” (at least partially), and both stances were kept – using one rather than the other, when it was clearly productive to do so.

And, though the idealism of Mathematics affected Science, the materialism of Science also affected Mathematics, and the result of this was the wholly different discipline of Technology – the application of scientific discoveries in advantageous inventions and devices.

These technologists were not interested in Theory, and they were also not enamoured of Pure Mathematics either.

They required a kind of Mathematics that enabled their purposes – they claimed Applied Mathematics as their own vital Toolkit, and indeed, regularly invented new tricks to facilitate their objectives, whether or not they conformed to either theoretical stance. They were completely pragmatic and nothing more.

Interestingly, the three, closely-related disciplines, not only went their own ways, but on quite different philosophical bases.

Science was primarily materialist.

Mathematics was entirely idealist (termed Pure Mathematics).

Technology stuck to Applied Mathematics, but was entirely pragmatic – “if it works, it is right!”