Science as a symbolic description

I

In 1872, Ernst Mach defined theoretical physics as a science that aims to provide an abstract and generalised (economical) description of natural phenomena. If we were to consider this event through the lens of the history of philosophy, it would seem neither grand nor even particularly remarkable. It did not give philosophy any new methods or ideas. Yet for the broader philosophical circles, this year of 1872 could be considered a turning point. Something broke in the pompous, self-assured harmony of materialistic metaphysics, which was previously enjoying its absolute and uncontested dictatorship over everyone's hearts. A condescending smirk was spotted somewhere. Of course, even now, when traversing the outer fringes of contemporary thought, you could still meet a marauder who keeps stubbornly ranting about the good old times of the 'scientific' worldview. Yet it was then, precisely then, that this sham palace started to crumble.

Let us take it from a historian of science: 'The French Encyclopedists of the 18th century believed they were on the verge of explaining the entirety of nature via physical and mechanical methods. Laplace even envisioned an intellect capable of predicting the universe's future for all eternity provided it knew the mass, speed and initial position of every object. In the 18th century, those joyous exaggerations of what the newly devised physical and mechanical methods were capable of could be excused. We could even say it was a refreshing and noble sight, and we can sympathise with this intellectual rejoicing, for it is so rare to see in history. Yet now, a century later, when our judgement is much clearer, the Encyclopedists' worldview appears to us as a mechanical mythology, not so far away from the animalistic mythology of ancient religions. Both these views contain erroneous and fantastical exaggerations stemming from an incomplete understanding'. A fuller understanding could be achieved through sustained and extensive research. 'To try to predict the result, or to even attempt to introduce it to some kind of modern scientific research would be mythology, not science'. Such is the impartial view of Ernst Mach. In 1872, it was still only in its infancy.

Two years later another researcher, also known for his work and, most importantly, his sharp mind, declared that the primary task of mechanics was to 'give the fullest and simplest possible description of all movements occurring in nature'. That was one of the most celebrated physicists of the 19th century, the famous founder of spectral analysis Gustav Robert Kirchhoff. Yet if young Mach's ideas went largely unnoticed, how could a renowned scientist's definition be ignored? This definition 'greatly astonished everyone'. We can now only be astonished by this astonishment. Moreover, viewing the mathematical natural sciences as a mode of description was not a break with tradition but rather a continuation of it. This was established by Newton, reiterated by Rankine in 1855 and built upon in philosophy by Schuppe since 1870.

Less than thirty years later, astonishment gave way to recognition. Mach's subsequent works, Heinrich Hertz's Principles of Mechanics, Pierre Duhem's works on the history of the methodology of physics, Wilhelm Ostwald's natural philosophy, the highly authoritative reflections of Henri Poincaré, the bright star of French mathematics, the methodological discussions of Clifford, Stallo, Enriques; William Thomson's (Lord Kelvin's) modelling — perhaps even against the researcher's own intentions... Various philosophical movements followed, in particular the Empiriocriticism of Avenarius, Cornelius, Petzold, Holzapfel and others. This movement was formally proclaimed as proletarian philosophy, yet it was actually half-mystical; due to this erroneous proclamation, it ended up zealously propagated by the intellectual proletariat of all nations. The general consciousness of physics, represented by many scientists, joined forces with these schools of philosophy. In less than 30 years this joint effort managed to convince us all that theoretical physics was truly nothing more than a symbolic description, a 'simplified and orderly description'. However, what exactly physics is a description of remains unclear.

This view, expressed in different ways by different researchers, is now a common ground for epistemology and philosophical methodology, with both originating in the historical study of the methodology of physics and other natural sciences. To prove they are descriptive would be to try to barge through an open door. However, we should be careful to avoid the assumption that to accept this means to voice support for scepticism and phenomenalism. For we have yet to discuss what exactly physics describes, how metaphysically significant this description is and, finally, what it means for it to be economical.

II

However, in order to stay focused from here, let us take a closer look at the very basics explained by Heinrich Hertz. Hertz's scientific method is this: 'We form for ourselves images or symbols of external objects, and the form which we give them is such that the necessary consequents of the images in thought are always the images of the necessary consequents in nature of the things pictured'. This method has a necessary precondition that our spirit and nature are in harmonious agreement. Our experience tells us that this precondition can be fulfilled. 'When from our accumulated experiences we have succeeded in deducing images of the desired nature, we can then in a short time develop by means of them, as by means of models, the consequences in the external world which only arise in a comparatively long time, or as a result of our own interposition. We are thus enabled to be in advance of the facts, and to decide as to present affairs in accordance with the insight so obtained. The images which we here speak are of our conceptions of things. With the things themselves they are in conformity in one important respect, namely, in satisfying the above mentioned requirement. For our purpose it is not necessary that they should be in conformity with the things in any other respect whatever. As a matter of fact, we do not know, nor do we have any means of knowing, whether our conceptions of things are in conformity with them in any other than the one fundamental respect.

The images which we may form of things are not determined without ambiguity by the requirement that the consequents of the images must be the images of the consequents. Various images of the same objects are possible, and these images may differ in various respects.' These images must not contradict the laws of thought; relations between images must not contradict relations between things; and, finally, images must be most appropriate. 'Of two images of the same object that is the more appropriate which pictures more of the essential relations of the object, the one which we may call the more distinct. Of two images of equal distinctness the more appropriate is the one which contains, in addition to the essential characteristics, the smaller number of superfluous or empty relations, the simpler of the two. Empty relations cannot be altogether avoided: they enter into the images because they are simply images, images produced by our mind and necessarily affected by the characteristics of its mode of portrayal'. As such, images must be correct and appropriate. Yet these conditions can be met through a variety of methods. Even within mechanics Hertz saw three completely different systems of images, which he referred to as 'the three images of the world'.

There are three such systems, although that does not limit the number of distinct images (we are not considering here the newest approaches that make mechanics into a subfield of electrodynamics). 'Strong and narrow' minds, as Duhem describes the French and the Germans, aim to reduce the number of images, joining them together where possible to form a cohesive chain of deductions that does not say much. 'Broad and weak minds', as Duhem describes the English, aim for the complete opposite as they produce a great variety of bright and independent models. The gardens of Versailles and the parks of England: that is the difference between the continental and the English approaches. It is clear, however, that we can only be talking about aims, limits and absolutes here. If we were to take a close look at the works of the French, we would notice a lot of inconsistencies and contradictions; similarly, the English romanticists of science do not entirely eschew at least some sort of system. Yet it does not make much sense for us here to discuss the continental approach, for it is precisely what we were taught science was ever since we were little children. It would do us more good to consider the works of the English mind, for when it comes to science, it does not tolerate haughty self-importance. We shall consider the brave thought that presents itself the way it is, plain and unembellished, with all the contradictions and digressions that are a natural part of the work of a living mind.

When I say 'it would do us more good', I do not mean to exclude the continental approach from science. I only mean this would make it easier for us to understand what science is at its core.

III

We read in Duhem that to an English mind, 'Theory is for him neither an explanation nor a rational classification of physical laws, but a model of these laws, a model not built for the satisfying of reason but for the pleasure of the imagination. Hence, it escapes the domination of logic. It is the English physicist’s pleasure to construct one model to represent one group of laws, and another quite different model to represent another group of laws, notwithstanding the fact that certain laws might be common to the two groups. To a mathematician of the school of Laplace or Ampère, it would be absurd to give two distinct theoretical explanations for the same law, and to maintain that these two explanations are equally valid. To a physicist of the school of Thomson or Maxwell, there is no contradiction in the fact that the same law can be represented by two different models'.

For example, let us consider William Thomson’s lectures on molecular dynamics and the wave theory of light. He was ennobled and received the title Lord Kelvin for his scientific accomplishments.

[To be continued]

IV

These are all different representations of the same idea. Yet this contrast becomes even more pronounced in the algebraic sections of English works.

Open any classical physics text written by a French or German author. You will find a structured and coherent sequence of statements attired in the form of mathematical analysis. It will be preceded by an introduction that presents the hypotheses linking empirically derived values and justifies their mathematical treatment. Algebraic analysis serves merely as a tool to facilitate calculations; ultimately, its results can always be expressed in logical syllogisms. Such an approach is entirely absent in the works of English physicists, even the most brilliant among them. They not only fail to justify entirely new elements but also neglect to define them. They show complete indifference to what one might call deduction. The algebraic part of the theory is not a tool but a model of its own. 'It is an apparatus functioning by signs accessible to the imagination and subject to the rules of algebra; it imitates more or less faithfully the laws of the phenomena under study, as an apparatus of different bodies moving in accordance with the laws of mechanics would imitate the laws of the phenomena'. One would search in vain for anything resembling the continental approach in English scientific works. They focus on either machines (physical models) or the abstract mathematical symbols of their imagination, which they twist and transform in various ways instead of considering the actual processes they are analysing.

The brilliant Poincaré says this about the brilliant Maxwell: 'The first time a French reader opens Maxwell's book, his admiration is tempered with a feeling of uneasiness, and often of distrust. <...> The English scientist does not try to erect a unique, definitive, and well-arranged building; he seems to raise rather a large number of provisional and independent constructions, between which communication is difficult and sometimes impossible'.

In the development of algebraic theories, we observe the same lack of order and method as in the construction of mechanical models. Duhem, who carefully analysed the brilliant work of the English physicist, comments on it with thinly veiled indignation. He asserts that Maxwell lacks both logical rigour and mathematical precision: 'The reasoning and calculation by which Maxwell tried on several occasions to justify [his equations] abound in contradictions, obscurities, and plain mistakes'. And here is his final sentence:

Maxwell’s Treatise on Electricity and Magnetism was in vain attired in a mathematical form. It is no more of a logical system than Thomson’s Lectures on Molecular Dynamics. Like these Lectures it consists of a succession of models, each representing a group of laws without concern for the other models representing other laws and, at times representing these very same laws or some of them; except that these models, instead of being constructed out of gyrostats, spiral springs, and glycerine, are an apparatus of algebraic signs. These different partial theories, each developed in isolation, indifferent to the previous one but at times covering part of the field covered by this predecessor, are less properly addressed to our reason than to our imagination. They are paintings, and the artist, in composing each of them, has selected with complete freedom the objects he would represent and the order in which he would group them. It matters little whether one of his clients has already posed in a different attitude for another portrait. The logician would be out of place in being shocked by this; a gallery of paintings is not a chain of syllogisms.

V

Such is his sentence. Although this sentence is clearly necessary from the point of view of the French and German physicists, is it not a bit of a blunder that demonstrates how continental physics does not even understand itself? Yes, of course, Laplace, Ampere, Cauchy, Neumann, Helmholtz and others are all true scientists. Would it not be more accurate to say that one would sooner distance physics from Faraday, Thomson, and Maxwell than distance them from physics? And if, for example, the electromagnetic theory of light does not meet the methodological requirements of French physicists, does it not simply mean that these requirements are but an expression of the French approach, as opposed to the nature of the physical knowledge itself? Voltaire once called a great genius of English (or perhaps even world) poetry a barbarian for much the same reasons. Yet the 'barbaric' plays stood the test of time, while even historians of literature barely read Voltaire's tragedies that were suffocated by the pretentious limitations of the three classical unities. It would seem obvious that in physics, too, the scientific value of Maxwell or others is not defined by how logically they are organised. On the contrary, Maxwell's liberties demonstrate that science does not necessarily need an external system and self-imposed strict logical order.

In that case, what is Maxwell's theory that gave us modern physics – or perhaps even a new way to understand the world? Hertz, who deeply and carefully engaged with the Treatise on Electricity and Magnetism, says this: 'I would not be able to answer the question of what Maxwell's theory is any better than this: Maxwell's theory is Maxwell's system of equations'.

But if so, we have to ask ourselves: what is the meaning of those equations? The simplest answer would be something like this: first, to include light phenomena in the field of electromagnetism; second, to be able to mechanically explain the field of electromagnetism. This would give us the impression that Maxwell's theory celebrates the mechanical worldview; even though Maxwell did not provide the explanation itself, he at least proved its existence is possible. And yet that is only an impression. We will become convinced of this once we consider what it means to 'be able to mechanically explain' anything.

Before we explain a physical phenomenon, we must establish it. But establish means to empirically discover which values of q determine it, find them and establish a connection between them and also time. These defining figures are called parameters, and the connections are normally expressed through differential equations. Once we have the differential equations of these parameters, it means we have described the phenomenon. What, then, would it mean to explain it mechanically?

It would mean to imagining movements within a medium and replacing the phenomenon with them, in such a way that the differential relations thereby remain unchanged. To be more precise: the q parameters must be expressed as spatial coordinates of points or particles within a moving medium, and in being expressed as such they must satisfy the compatibility conditions of differential equations. Aside from that, since our medium is moving, it is in those movements subject to the fundamental laws of mechanics. In other words, the movements we imagined are not an arbitrary swapping of new variables, but mechanical movements that are subject to the law of conservation of energy and Maupertuis's least action principle. There is no need for us to explain these now, and we do not have the time. It is enough to remember that both those principles are mathematical expressions that tie together coordinates, mass and time.

Yet there is no need to actually find the movement we are analysing. Theoretical physics gives us an easier solution. We need to consider two functions, U and T, where U is a function of q and T is a function of q and their time derivatives. U is the potential and T is the kinetic energy of our mechanical system. If we can find a pair of U and T that meet the requirements above, then it is possible to give a mechanical explanation of the physical process we are analysing. This is the solution. But what is the final answer?

Here it is. It is either impossible to find the U and T, and therefore impossible to find a mechanical explanation in principle. Or, if it is possible to find one pair of such function, it is possible to form an infinite number of them. In other words: either a mechanical explanation is entirely impossible or it is arbitrary, as it allows for an infinite number of mechanisms that are all equally appropriate and equally valid for analysing the phenomenon. Therefore all explanations are relative, for you could counteract any given explanation with an equally valid explanation. You could then counteract that explanation with a different one, and this could continue ad infinitum.

Yet all those explanations are not 'it is so' phenomena. They are 'if it was so' phenomena. That is, they are models, symbols, fictional images of the world; we substitute but cannot explain actual phenomena with them. An explanation inherently claims to be the only one, whereas these models of reality offer an infinite number of choices. An explanation implies precise knowledge, while these models are a game of fantasy. An explanation is apodictic, while models are only hypothetical, forever hypothetical, bound to be hypothetical by their very nature. Once we have said all this, it is clear that the actual, philosophical meaning of the 'possibility of a mechanical explanation' is precisely its impossibility. The word 'possible' could only be used here in a very niche working sense.

Maxwell began his research precisely with an attempt to design a mechanism that would imitate electrostatic and electromechanical phenomena. According to Poincaré, ‘his system was strange and not particiularly appealing, for he assumed a very complex structure of the ether. You could have thought you were reading a description of factory with a whole system of gears, levers transmitting motion and bending from force, centrifugal regulators and transmission belts.'

Maxwell subsequently abandoned his mechanism. Other attempts at this also felt uncannily artificial. Therefore science had to turn from trying to provide an explanation to proving if such an explanation is possible in principle. Exploring this mechanically eventually led to the conclusion we mentioned above. This conclusion explains the psychology of the English mind to us. As we have already said, physics is a description, but this description can be attired both in abstract mathematical symbols and concrete mechanical images.

Yet mechanisms, no matter how concrete, never lay claim to providing an explanation. They are also mere descriptions, and their value depends on how well they can describe. Several constructively incompatible mechanisms may, however, be quite unanimous in their supposed purpose, which is description. In that case there is nothing stopping us from using those mutually exclusive images, just as we could be using different analytical symbols. You could compare this to how the same values are referred to differently in different books or even chapters of the same book.

Letters and their combinations are mere substitutions for phenomena and not their metaphysical cores. Similarly, mechanical models are mere symbols that could only ever substitute their respective phenomena only in certain specific contexts, and only partly. In other words, neither mathematical formulas nor mechanical models do not reduce the reality of the phenomenon. They exist in parallel to it, next to it and for it. The explanation seeks to erase the phenomenon itself, to subsume its reality in the forces and concepts that it tries to substitute the actual phenomenon with. Conversely, the description seeks to use the symbols of our spirit to make us pay attention and help us deepen our understanding of the reality that belongs to us.

These contradictions between English models and English formulas vividly testify to the English desire not to explain the world, but only to describe it. And not just describe it, but do so by those means which are the most appropriate and economical to the English mind. It would be quite insensitive to consider a single way of thinking, your own, to be the most economical. Or not to understand that to understand how economical a mental action is would depend not on the action as such, but on its place and purpose in the integral spirituality of a given psychological type or even thinker.

English physics, in its general ways and its being, in the silence of historical growth and not just the norms proclaimed by this or that thinker, lays a lesser claim to explanation than any other kind of physics. It cares for raw facts. It cares for nature. It cares for describing reality by means of symbols, chosen each time to be most appropriate to a particular researcher's way of thinking. Figuratively put, the English love wood with its natural fibres, unpainted with oil; they love everything that is natural and comes from the soil, the forest and the sea.

VI

We describe reality by means of symbols or images. But if this description of reality had only had this reality as its subject, then symbols would cease to be mere symbols and become, in our minds, their own independent reality. That is why the description also needs to account for the symbolic nature of the symbols themselves. It has to include both the symbol and what it symbolises. A description must be twofold. We can achieve this through the criticism of symbols.

We read in Hertz:

We require of this that it should lead us to a clear conception of what properties are to be ascribed to the images for the sake of permissibility, what for correctness, and what for appropriatenesss. Only thus can we attain the possibility of modifying and improving our images. What is ascribed to the images for the sake of appropriateness is contained in the notations, definitions, abbreviations, and, in short, all that we can arbitrarily add or take away. What enters into the images for the sake of correctness is contained in the results of experience, from which the images are built up. What enters into the images, in order that they may be permissible, is given by the nature of our mind. To the question whether an image is permissible or not, we can without ambiguity answer yes or no and; our decision will hold good for all time. And equally without ambiguity we can decide whether an image is correct or not; but only according to the state of our present [and personal; from Pavel Florensky] experience, and permitting an appeal to later and riper experience. But we cannot decide without ambiguity whether an image is appropriate or not; as to this differences of opinion may arise. One image maybe more suitable for one purpose, another for another; only by gradually testing many images can we finally succeed in obtaining the most appropriate.

These methods, and perhaps others, serve to define and constrain the symbolic image. It is defined as a particular phenomenon and constrained as an epistemic phenomenon. We find here the same duality as we find in art. Artistic images express the highest degree of true-to-life concreteness. Yet a wise artist would probably put the most effort into ensuring that as those images cease being mere symbols, they would not thereby also escape from the pedestal of aesthetic isolation and would not intrude into life, claiming to be part of it.

Images that break free from their frames, art so realistic it invites touch, music that mimics natural sound... Any attempt to replace art with an attempt to imitate life is criminal. It is a crime against both art and life; it is similar to how blurred the line is between scientific images and the reality that is being studied. But not only a portrait that came to life (Gogol) or a shadow that separated (Andersen) could leech off of life and suffocate it. A materialised outline of science, like Système du Monde, Kraft und Stoff or a diagram of social classes, could do this, too. Only the one who can tame images has the right to create them. True art does not lie in the mastery of execution; it lies in the ability to view those images with ascetic sobriety.

What does it mean to tame an image, whether in the arts or sciences? How can you prevent an image from becoming an object, entirely detached from description, and instead ensure it remains a tool of knowledge? What does this seemingly unbreakable connection between the image and the description tell us?

It tells us that image and description are uniform. In other words, the description itself is an image or a system of images, but considered critically, i.e. precisely as images. And, conversely, images that the description contains are nothing other than clots, consensations and crystalls of that very description. That is, they are the description itself, but a living description that verges on autonomy.

It is true: since description is speech, it consists of words. Yet words are, first and foremost, concrete images, miniature works of fiction. Every word and every combination of words is inherently illustrative. This illustrativeness, in essence, is not any different from that of physical models or mathematical symbols. We are used to seeing words, and as such we impatiently glance over them instead of focusing on every single one separately. Similarly, once we get used to images, we glance over their composition, stop noticing their colours and become blind to the details. Images, to us, become instruments.

Scientific description is like the ceaseless murmur of the sea. Waves travel across the surface, pushed by a passing ship. The surface of these waves is scarred by a giant fish's fins; and there, in turn, we see smaller and smaller ripples, up until the smallest. Description is very similar to this. The main images that outline this painting of words consist of secondary images; those images, in turn, consist of smaller images; and so on, and so forth. The main rhythm is complicated by secondary rhythms; they are in turn complicated by tertiary ones. All of them together weave a complex rhythmic fabric. Therefore, if we consider an image to be our starting point, then all description of reality turns out to be a colourful rug of interweaving images.

However, we could also consider the description itself. How, then, would images and symbols appear to us?

No matter how complex a symbol or name might be, we still give it a name, thereby making it a word; it is part of a description as a word, and could not be part of it otherwise. Next, we can elaborate on each of those words: we will describe an image or define and explain a mathematical symbol. Therefore those images and symbols could be replaced by their descriptions, which in turn contain images and symbols that could be replaced by their respective descriptions. And so on, and so forth. Every symbol and image of the highest order could be replaced by its description composed of images and symbols of the lowest order, up until we reach sentences, the most basic descriptions. No matter how complex or mysterious a scientific concept may seem, it can always be expressed with the same precision—though often at the cost of brevity and efficiency. Physics describes reality through differential equations and similar mathematical expressions. Yet there is no differential equation or any other mathematical formula that you could not explain with words. There is no and cannot be such a formula. Similarly, there is no mechanism, no matter how complex, that could not be described with words; there cannot be such a mechanism. The gift of the word is a universal gift. The domain of the word is at least as vast as that of consciousness—perhaps even greater. Everything touched by consciousness turns into words.

Speech consists of words. If we consider these words (Wörter, mots) separately, then physics is images and symbols, a system of images and symbols, a system of systems of systems, etc. That is, ultimately, it is words and combinations of words. If we instead consider words in their interconnectedness—as cohesive speech, as Worte or paroles—then physics becomes a description, a system of descriptions, a system of systems, and so on. In that case, physics ultimately is speech and combinations of speeches. Both viewpoints are antinomically connected; no matter where language analysis could lead you, it is always both a word (given by a sentence) and a sentence (consisting of words). Everything you would say about language in general you could also say about physics in particular. In both viewpoints, physics is nothing other than a language. And not just any language — it is our shared language, albeit adapted for precision and convenience.

VII

We have now arrived at the formula of 'physics is a description', and from there we got 'physics is a language'. Yet was it truly necessary to exert ourselves so much to determine the nature of a given science? Perhaps you are silently wondering about this — or at least, you should be. And your doubt would be justified—unless you recognise that our argument follows an a fortiori reasoning: if it holds for physics, it holds even more so for every other branch of science, and thus for science as a whole. Is physics not regarded as the archetype of precision, the perfect natural science? No one doubts that physics represents the cutting edge of the mathematical natural sciences, granting it the highest possible explanatory power. Physical chemistry, chemistry, astronomy, mineralogy, dynamic geology, meteorology, psychophysiology, psychology, and morphology: these sciences can be arranged from least to most descriptive. "No one would deny that these sciences are primarily descriptive. However, they also contain an explanatory dimension (in inverse order), which depends on the extent to which physics informs their methodology.

Nobody would question the role of physics in astronomy, chemistry, mineralogy, and even the biological sciences, particularly physiology. It also appears obvious that once you put aside this explanatory part that physics plays in those sciences, you are left with a pure description. A kind of general morphological description, if we define morphology as the study of structure in the broadest sense. Physics is not only the queen of sciences because of its place and development, but also the main substance of science. That is evident from its participation in all the natural sciences. It is universally relied upon by researchers in these fields. And yet physics itself, the last safe haven of explanatory claims, turns out to be a pure description that is not in any way better than all those other fields of science. They, too, are descriptory; but since their descriptory nature is obvious, they do not need the analysis we are providing for physics here.

You could consider how precise and insightful physics is in its descriptions compared to other sciences. You could compare their objects of study or, in other words, the lines and fields that separate different sciences' view of reality and tasks. It would then be necessary to compare the relative depths that define different sciences' fields. In this sense and many others you could then finally devise a variety of classifications of sciences.

Yet all sciences share the same fundamental basis, an intrinsic core. That is the fact that they are all modes of describing reality. This means all sciences are only a language. This brings us to Abbé de Condillac’s famous aphorism: 'Une science n'est qúune langue bien faite' — a science is only a well-constructed language. John Stuart Mill echoed this idea in a softer form: 'Language is a catalogue raisonne of the notions of all mankind'.