John Ramsay McCullogh: The principles of political economy: with a sketch of the rise and progress of the science (1825)

(1789-1864)

John Ramsay McCullogh follows the tradition of classic British economists, such as Adam Smith, Ricardo and Malthus. He is definitely not a very original thinker, but his work is a representative example of this current of thought and takes its ideas to a certain extreme. Good example is McCullogh’s opinion on labour as a source of wealth. This thought goes back to at least Adam Smith, but McCullogh upholds it in a very one-sided manner, explicitly denying that anything else could ever produce any wealth. In a famous example, he tries to show that passage of time as such does not produce any additional wealth. McCullogh asks the reader to think of a barrel of wine that its owner locks in cellar. Seemingly, McCullogh notes, the barrel appears to become more expensive just by itself, but actually, McCullogh insists, it is the act of placing the barrel in the cellar and waiting that has produced the additional wealth.

McCullogh’s example is rather unconvincing in itself - certainly the act of putting the wine in the cellar has the least to do with the chemical and biological changes in the wine that make it more valuable. A clear counterexample is provided by the generation of oil and diamonds. The starting point of the process is something relatively cheap - dead life forms and coal. These have become valuable just because they have lied underground for several generations, under the pressure of Earth’s crust, and no person has definitely buried them there.

What engages McCullogh most is the question how to increase the effectiveness of labour. Answer he provides are familiar from previous economists: guaranteeing property rights makes it possible to amass capital to different endeavours, which enables different persons and even different nations to specialise on their own type of industry. McCullogh's three main classes - workers, landlords and entrepreneurs - and their respective sources of income - wage, rent and profit - follow the ideas of previous economists, but feel a bit outdated nowadays, when landlords rarely exist and individual entrepreneurs have been replaced by global corporations.

McCullogh, like other economists of his time, is thus more than a bit blind to the influence of his own cultural context - this is somewhat paradoxical, since McCullogh begins his work with an account of the history of economy. His special blindspots - which he shares with other economists - are the questions of population growth and gluts. On the first issue, McCullogh follows Malthusian idea that increased wages will eventually lead to an increase of population and thus to a return of wages to the old level, when the amount of potential workers has grown. As we know from the state of Western Europe, this “eventual” link is no law of nature, since there the development of effective contraceptives and liberation of general mores have suppressed the population growth.

When it comes to gluts - that is, excess of supply in relation to demand - McCullogh is far more radical than either Malthus and Ricardo, who agreed that gluts were a real problem. McCullogh, on the other hand, simply states that gluts appear only in cases where markets are unnaturally regulated e.g. by monopolised fields of commerce. In a completely free market, on the contrary, gluts would be only temporary and would - again, eventually - vanish when capital was transferred to more lucrative fields of business and workers would find new type of employment. One might agree that this happens eventually, but it could still be that this transfer would take an inordinate amount of time, especially from the viewpoint of an individual worker. This is especially important question in our time, when many jobs require extensive, specialised training. Indeed, there might be whole generations full of people who have basically educated themselves to an outdated and obsolete profession.

In addition to the reliance on eventual change of things, McCullogh’s work, like that of Ricardo before him, suffers from emphasis on mass market products, like corn or wool, where one item is just like any other and easily reproducible. Indeed, McCullogh himself admits that there are items, like rare artworks, which create natural monopolies, since e.g. there is only one artwork of certain sort in existence and their supply cannot be augmented. Just like with Ricardo, we may well ask whether the modern economy contains more and more examples of industries concentrating on such rare goods.

By far the most interesting part of McCullogh’s work is the last chapter on consumption. His definition of consumption is rather problematic. While labour, he says, changes matter into a form useful for us, in consuming we at the same time take advantage of this usefulness and turn matter into a form in which it is not anymore useful for that purpose. This definition works well in case of food items, where eating something both benefits us and destroys what we eat. Still, it seems clear that this combination of using and destroying things is not necessary. Firstly, we may well lose usefulness of a thing without using it, for instance, when we break a household item. Secondly, there are a lot of things we can use without destroying them, such as a book which can be read many times over.

Despite the flaw in the definition, we can at least agree upon the general sentiment behind it: we use things, and while we use them, they tend to lose their cohesion. McCullogh notes that this process of using things does incite us to produce new things and thus increases the amount of labour. Hence, McCullogh concludes, consumption is not as such a bad thing, but can increase the wealth of a nation. Indeed, McCullogh goes even further. While earlier economists had considered service sector to be of secondary importance in comparison with industries, McCullogh sees no essential difference between them. Thus, he says, there’s no clear economic difference between farmer’s work of producing corn and cook’s work of preparing corn for a dinner. In fact, McCullogh quite radically suggests that even seemingly useless tasks, like building a house of cards, can be economically useful, if they incite people to work harder for the rest of time - an important concession for the importance of spare time.

Although McCullogh is thus positive about the power of consumption, he admits that in some cases consumption should be restricted. The ground for such a restriction, McCullogh insists, is formed by the limits of consumable resources. The main target of McCullogh’s point is frivolous government spending, but nowadays, instead of this laissez faire -reading, one might as well choose its unintended ecological meaning - resources form a strict limit for consumption, and human race cannot continue its economic growth unless it will take care that this growth remains sustainable and does not overstep the boundaries.

Maine de Biran: New essays on anthropology (and other late writings)

While Maine de Biran’s works have thus far been exclusively psychological, his final, unpublished works show a new interest in religious experiences. Furthermore, while Maine de Biran began as a follower of ideological school of Destutt de Tracy and then moved away from this school through Kantian influence, in his last works Maine de Biran also wanted to distance himself from the conservative school of de Bonald and Lamennais. Although Maine de Biran did not have much to say about the politics of the French conservatives, he did ridicule their way of arguing with analogies - although body might be ruled by soul, one could not deduce from this that country should be ruled by a monarch.

In fact, Maine de Biran could not even accept de Bonald’s definition of human being as a soul or intelligence served by an organism. Firstly, he noted that one might equally well say that bodily organism is served by the guidance of intelligence. Furthermore, he added that both statements describe only a certain harmonious condition in which humans might exist, while often these two elements of human being are at odds with one another, and indeed, in the fallen state of humanity this discord is prevalent.

Maine de Biran did accept the basic dualistic account of human being, but unlike French conservatives, he expressly did not want to endorse it just because of religious authority. Instead, Maine de Biran held on to Platonistic notions, according to which human being can through introspection note that there’s something more stable than fleeting sensations. Means for rising to this stable, intellectual level were, for instance, love of not particular beauties, but beauty in general, and pure geometry.

In one of his last, unpublished works, Nouveaux essais d'anthropologie, de Biran tried to outline the basic structure of the whole human being - hence, the use of title anthropology, instead of the more usual psychology. Human being is not just soul or mental, de Biran wants to say, but also has its bodily aspect. On the other hand, against some physiologists of his time, de Biran wants to emphasise that mere organic processes cannot explain all of human behaviour. More precisely, de Biran wants to state that biology does not explain the mental side of human being. At most, it could tell us something about sensations, which we share with animals, but the consciousness of these sensations is still something beyond mere biology.

In addition to physiologists, de Biran also spoke against metaphysicians like Malebranche and Leibniz, who did accept the existence of body and soul, but then made their interaction into a divine mystery. Interestingly, de Biran notes, Malebranche and Leibniz faced this problem because of opposite reasons: Malebranche made human soul into something completely passive, which could not act on anything, without the help of God, while Leibniz thought that body was a complex of similar active monads as soul, but because of their activity, soul could not truly affect these other monads. The obvious solution to this conundrum is then, de Biran notes, that mental and physical sides of human being are, respectively, active and passive.

This basic notion of the difference of mental and physical de Biran connects with Kantian and Fichtean considerations. What de Biran is searching for is not soul as a substance, which at best is just an abstraction out of concrete experience of ourselves and at worst suggests that our mental side would be a substance in the same sense as all physical objects. Instead, de Biran says, when we begin from the very experience of ourselves as controlling our body, we perceive ourselves as activities or forces. De Biran appears to connect this activity that we are with will, which he distinguished from mere organic desires.

Just like Fichte before him, de Biran notes that this active I can break out from a solipsist outlook by noting that something hinders its own activity - we can justifiably belief in the existence of external world, because we cannot control everything. Furthermore, this hindrance extends even to our own bodies, which we at times must struggle to make obey our commands. This experience of willing to control an unwilling body, de Biran sometimes appears to suggest, contains a hint toward the final, unwritten part of his work, where he would have tried to argue for the existence of a personal God. De Biran’s particular target would have been pantheism of Spinoza and Schelling, where all things would have been modifications of one basic force. Instead, de Biran appears to suggest, the world is not swallowed by a single force, but we experience many contrary forces, although we have an inkling of a higher entity, which can use its force without any external hindrance.

Samuel Taylor Coleridge: Opus Maximum

Coleridge’s unpublished Logic was actually just a part of larger project, which he called at different times either Opus Maximum or Magnum Opus. Logic, together with an account of history of philosophy, was meant to be a preliminary study leading to the central problematic of the grand work - a proof of mainline Christanity and especially the notion of trinity. This central part exists only in several large fragments, but these are enough to indicate what Coleridge's train of thought was.

We miss the opening chapters of Opus Maximum and enter the stage in medias res, with Coleridge considering the question what differentiates morality from other sciences. He notes that statements of morality have quite a peculiar flair. If morality tells me that I ought to do something, it does not mean that this action would be absolutely necessary - morality is no mathematics. Yet, the moral “ought” is also something completely different from hypothetical necessity of physical sciences.

Coleridge is clearly following the lead of Kant’s Critique of Practical Reason and it is thus no wonder that he invokes as a primary assumption underlying morality the notion of will. Coleridge’s idea appears to be that this will is somehow responsible of its actions and moral statements then indicate, what actions fulfill this responsibility and what actions actively break it.

What is this will then? Coleridge notes as its primary characteristic a capacity to begin causal series. Yet, he remarks, this is no true explanation in the usual sense of the word. Ordinarily, things are explained, Coleridge says, when they have been connected to some previous item that has caused it. In case of will we can never really do that, since this very ability to begin things anew is something completely inexplicable. In other words, the notion of will is an idea, that is, something that definitely underlies our experiences and so must be in our reach, but as a final link of explanation admits no further explanation.

Coleridge is at once opposed to the idea that all morality could be reduced to mere prudential love of oneself. Firstly, he notes in a Kantian manner that this “self” is nothing more than mere formal binding of a bundle of experiences and thus incapable of being loved, or then it means our true self that is beyond all experience and thus beyond mundane love. Indeed, he continues, what is loved in this self-love is usually the earthly representative of our self or body. That is, self-love is just love of bodily pleasures or other benefits, which eventually can be used for a more pleasurable bodily life. But when we are told that we ought to do something, we are not told to do it because of future pleasure.

Coleridge avoids the Kantian disparagement of moral emotions by restricting the notion of pleasure to bodily pleasures. He states that already the satisfaction felt when we use our cognitive abilities is far different from bodily pleasures, and even further removed is the feeling of bliss generated by morality and religion. Thus, there is no demand that moral actions should be done grudgingly.

Maxims of morality, Coleridge notes, seem like commands from another, higher self - what Kant would call our noumenal self - and consciousness of these commands we call conscience. Now, Coleridge continues, even becoming conscious of these commands demands something - we must act in certain manner so that we would not be blind to demands of conscience. In other words, he concludes, conscience is possible only if we actively admit that we are answerable to a superior form of our self and so have faith in something beyond sensible reality.

Coleridge goes even further and says that not just morality or ethics, but every kind of consciousness is dependent on such faith and conscience. We may perhaps detect influence of Fichte here. Coleridge notes that what he has called conscience is in a primary sense self-consciousness - consciousness of our true self as a source of norms for action. Furthermore, whatever we are conscious of - that is, more than just aware of, in the way mere animals are - we have immediately related to our self. To conclude, for Coleridge, the whole human experience is underlined by a consciousness of what we must do in the world we experience.

Coleridge’s next move has also Fichtean tones. He notes that in order to relate any object of experience to ourselves as a moral subject, we need the notion of an object that is also a moral subject, although different from ourselves - every I needs You. When we look at a certain viewpoint, we can not differentiate between the two persons, Coleridge insists, and then we are speaking at the level of reason, that is, at the level of what is necessary according to all subjects. It is only when we move on to the level of will that we can differentiate between persons, and even then our conscience tells us that the other persons are equal to our own self and should be treated as such.

Morality, Coleridge argues, can then be regarded as a demand to subjugate the level of will - differentiation of persons - to the level of reason - equalisation of persons. Furthermore, he notes, our idea of God is just an idea of an entity, in which these two standpoints coincide absolutely - absolute will, which is unified with universal reason. In other words, Coleridge's suggestion is that morality demands that we gain conscience, which is just our communion with the divine level.

Coleridge’s next question is how we humans come to have a link to God. He at once notices that this cannot happen through any ordinary sort of proof. Much like Jacobi before him, Coleridge suggests that such proofs risk the confusion of divine and mundane levels, which leads to pantheistic explanations. Instead, he remarks, faith in God is something we learn even from our mother’s milk. During the first period of our life we humans do not have the capacity to separate ourselves completely from our mothers, and indeed, we are aware of our full dependence of her. When we then see our mother praying to a Superior Being, we gain an inkling of a universal parent taking care of all persons.

One might think that this genetic explanation of our notion of God is an argument against this notion - people from different cultures and people with no previous education would have no idea of God’s existence. Coleridge tries to show that even the Lockean notion of tabula rasa analysis of human experience points towards a notion of God. Coleridge’s argument begins by noting that Lockean philosophers analyse the experienced things by the characteristics these things are perceived to have. He then remarks that these characteristics differ from one perceiver to another - a plant poisonous to one observer might be harmless to another. Hence, he concludes, these characteristics are not so much passive properties, but active powers that can appear in different manners in different surroundings. The source of such activities, Coleridge insists, must ultimately be a self-causating activity or will.

Having thus based all consciousness and experience on the existence of responsible will and the existence of that will on absolute will, Coleridge next wants to show that this absolute will is no deistic impersonal God. Indeed, in order to be not just reason, but also will, God must be a person, that is, an I compared to You or to another person. From another viewpoint Coleridge notes that God is supposed to be a pure creating activity and therefore must have some result, if nothing else, then this second person.

This necessary result of divine activity, Coleridge says, is nothing more than the so-called second person of trinity - Word or Logos, which could be said to conceptualise the original power of self-creation by creating distinctions within it. In addition to being differentiated into two persons, Father and Son, these two persons also recognise their identity in an act of mutual love, which is represented by Spirit or the third person of trinity. In a sense, then, God must create to itself a community of persons just to exist as a person.

At this point Coleridge notes the peculiarity of religion as a sort of synthesis of philosophy or science dealing with necessities and of history dealing with contingencies. While the trinitarian nature of divinity belongs in Coleridge’s eyes to the necessary portion of religion - God must be a self-created community of persons - the existence of evil does not. Only the possibility of evil is necessary, but its actual existence is not.

In fact, evil offers a true conundrum for Coleridge, because its existence should be explained. It cannot be explained through any activity of God, who cannot be a source of imperfection. The only possibility that Coleridge can fathom is then that evil is similarly self-caused as God himself. The difference is that while God exists necessarily, evil does not. Evil, that is, a will not abiding with God’s absolute will, has just willed itself to existence. Of course, temporal notions are here only a metaphor. In a less figurative sense, evil just is something that need not be, but still is, and since it exists, it retains itself, as long as nothing is done about it.

What is particularly important for Coleridge is to show that evil is not a necessary outcome of the energy of divinity, unlike in Plotinian philosophy, where evil has a mere shadow of an existence, necessarily projected by the ultimate reality. Closely connected with this attempt is Coleridge’s project of showing that certain key tenets of the Bible can be justified philosophically, which would bolster the status of Christianity against Neoplatonism and its modern appearance in Schellingian philosophy.

At this particular stage, Coleridge’s work becomes even more fragmentary, but certain key moments can be discerned. Coleridge evidently tries to show that the biblical story of Genesis can be rationally reconstructed by incorporating what he considered to be the most developed account of natural world - the Schellingian philosophy of nature - but leaving out its seeming pantheism, which denigrates the idea of personal God.

The starting point of Coleridge’s account seems to be the fact of evil - that is, of a will which at the same time stubbornly upholds its own particularity against the truly absolute will of God and tries to place itself in the place of absolute will, remaking all of existence in its own shape. This muddle of contradictory tendencies of particularisation and universalisation in the original evil will Coleridge calls chaos - it is the primordial puddle of contradictory forces, which by itself cannot do anything.

Just like God recognised itself in the other personality and thus loved it, Coleridge continues, God’s love extends also to the primordial chaos, despite its imperfection. This divine love or “breath of God” gives chaos a more stable existence and makes it a potential material for further shapes of existence - chaos becomes aether. In the same act, the differentiating person in trinity or Logos shapes a portion of this aether into a carrier of active energy or light. Thus, Coleridge weds the Biblical tale of God saying “let there be light” with the Schellingian idea that physical world is built out of opposition of active light and passive matter.

Next in Coleridge’s account is the multiplication of these basic opposites into various forms of opposition: separation of unit from true unity in centrifugal force opposed to a search of true unity in centripetal force, mutual repulsion of material units opposed to their coherence as a unified material object and volatile expansion or diffusion of matter opposed to its contraction into a tighter unity. This is followed by construction of air as mediating between mere vacuum and visible matter, and move to concerns of chemistry. We need not go into details, but merely state the obvious parallel of Coleridge's account with Schellingian ideas.

Opus Maximum ends as abruptly as it began, with no indication how Coleridge would have finished the work. Still, we have seen enough to recognise which parts of the work would have been more fruitful. It is especially the idea of ethical underpinning of human consciousness and the notion of necessity of community for personality that hold most interest to a modern reader. On the other hand, his attempt to synthesise Genesis with German philosophy of nature seems like a peculiar and ultimately futile project.

Jean-Babtiste Joseph Fourier: Analytical theory of heat (1822)

(1768-1830)

The history of the interaction of mathematics and physics has not just been one of unidirectional influence. Certainly the development of mathematics has been of great importance to physics, by providing it new and improved tools for modeling natural phenomena. Yet, physics has also offered inspiration and spur for development of new mathematical tools. The tale of Fourier’s Théorie analytique de la chaleur is of the latter sort.

Fourier’s starting point was the revolutionary use of mathematics in understanding nature, instigated by the works of Descartes and completed, in a sense, in the works of Isaac Newton. What they did was to extend the use of mathematics from mere tool for studying of figures into a tool for studying the motions of bodies. The success of Descartes and Newton inspired others to investigate whether mathematics could be useful in studying other natural phenomena.

One obvious candidate was the propagation of heat through a substance. Whatever heat was thought to be - often it was considered a distinct caloric substance that permeated all objects - it certainly appeared to “flow” through these objects, touching at first only one spot of the object in question and gradually spreading through the object and finding a point of equilibrium. The physical model was simple enough, all that was needed was to express the movement of the heat mathematically.

Fourier noted, firstly, that the movement of heat in an object was dependent on three things specific to the object, its constitution and its relation to its environment: the capacity of the object to assimilate heat (heat capacity), the capacity of its parts or molecules to transmit heat to one another (thermal conductivity) and the capacity of the environment to transmit heat to the object in question. In practice, we can limit our attention to the first two, because they form the basis of his theory of heat flow and the question of one object transmitting heat to another merely complexifies the basic theory. For simplicity’s sake, Fourier regarded these two quantities as simple constants, although the heating of an object might in reality affect them.

While physical objects are, of course, three-dimensional, we can first concentrate on the simple case of one-dimensional transfer of heat, e.g. within a barlike object. Clearly, the more distant a point in the object is from the source of the heat, the colder the point is and the opposite end from the source remains coldest. Now, Fourier supposed that the temperature of a point, at a given time, is in a sense proportional to the distance from the heat source. To put it more precisely, if at some time the temperature at the heat source is a and temperature at the opposite end of the bar is b and e is a given unit of temperature, then at a given point of the bar, with a distance z from the heat source, the temperature at that point can be calculated by subtracting z(a-b)/e from a.

Now, the temperatures a and b do not remain same, since heat is continuously flowing from one end of the bar to another and a keeps decreasing while b increases. To make the situation easier to handle, Fourier supposes that temperatures a and b are artificially kept constant, e.g. through an external heat source warming a. This means, he continues, that all the temperatures between the extremes of the bar also remain constant, that is, the temperature v always decreases while we move away from the heat source, at a rate (dv/dz) opposite to (a-b)/e. At the same time, heat is constantly flowing through the bar, and this flow, Fourier argues, is at least partially expressed by the formula (a-b)/e, that is, the greater the difference between the ends of the bar, the more heat flows from the warmer to the colder end.

If we forget the assumption of a and b being constant, we might say that (a-b)/e or −(dv/dz) partially represents the flow of heat characteristic of a bar of certain substance at a certain point of time. This expression cannot be the whole truth of the notion of flow of heat, because different substances have different capacities for conducting heat through them. Then again, he concludes, this expression together with the constant K describing the thermal conductivity of the substance describes completely the flow F of heat through a bar: F = K(a-b)/e or in terms of an infinitesimal change of temperature dv through an infinitesimally long length of bar dz, F = −K(dv/dz).

Next step in Fourier's argument is generalization of this formula to three-dimensional flow of heat. He begins by considering a prism, with one corner having the highest temperature A and heat flowing from this corner to all the other directions. Just like with the case of the bar, the further one goes from the source of hear, the less is the temperature, although now we have to account for three dimensions, when counting temperature at a given point at a given time - that is, the formula for counting the temperature of point (x, y, z) of prism looks something like A − ax − by − cz. Again, just like with the bar, by keeping the temperature constant at the limiting surfaces of the prism the temperature remains constant at all the points within the prism. By restricting then the investigation to heat flows in one dimension, heat flows in lines crossing planes perpendicular to x-, y- and z-axes will then be respectively −K(dv/dx), −K(dv/dy) and −K(dv/dz).

The final ingredient to be added to a general theory of heat is time. We again remove the assumption that the limits of a solid would have constant temperatures. Then the temperature of points within solid change as time goes on and heat flows in some manner through the solid, that is, temperature becomes a function of spatial coordinates and time: v = f(x, y, z, t). Fourier’s next move is to restrict the attention to flow through an infinitesimally small circle o at an infinitesimal instant dt, where due to extreme smallness the condition of the precious paragraph then apply. If we suppose the circle to be situated perpendicularly to z-axis, the heat flow going through it should be, Fourier says, −K(dv/dz)odt.

The notion of infinitesimals is, undoubtedly, unclear gibberish according to more modern understanding of differential and integral calculus, but even greater gibberish is to follow. Supposing the ring o to have an infinitesimal thickness, dz, we can distinguish between the heat flow coming within o and heat flow leaving o. The former is, expectedly, −K(dv/dz)odzdt, while the latter is almost the same, differing from this already infinitesimal quantity by “an even smaller infinitesimal”. The difference of the two quantities - that is, the amount of heat left within the ring after the instantaneous flow of heat - is just this type of “second-grade” infinitesimal, namely, K(d2v/dz2)odzdt. Here the expression (d2v/dz2) and its relation to (dv/dz) - rate of change of temperature, when moving through z-axis at moment dt - can be understood through an analogy with the relation of acceleration and velocity. In effect, (d2v/dz2) describes how the value of (dv/dz) itself changes, when moving through z-axis at moment dt.

Now, Fourier notes that the shape of o is not important and that we might as well take instead an infinitely small rectangle dxdy, making the flow through that rectangle, at instant dt, −Kdxdy(dz/dv)dt. Consider then an infinitely small cube of size dxdydz. The heat flow forming within that cube, at instant dt, is the sum of heat flows left within the cube, when heat flows coming in and going out from and to all three directions have been accounted for, namely K(d2v/dx2 + d2v/dy2 + d2v/dz2)dxdydzdt.

Now that the quantity of heat accumulating within an infinitesimal point of a solid at an infinitesimal instant of time has been, in a sense, determined, we can answer the question how does the temperature of that point develop over a period of time. It is not just a matter of dropping dt out from the formula, since heat and temperature are not completely same thing. Instead, we finally need the notion of heat capacity C of substance, which Fourier defines as the relation how much heat is required for increasing temperature of an object of certain weight. In order to get the required quantity of weight, we also need to take into account density D, that is, the relation how much certain volume of this substance weighs. By putting all these ingredients together, we find out that the rate of change of temperature over time, dv/dt, equals (K/(CD))(d2v/dx2 + d2v/dy2 + d2v/dz2).

What Fourier’s complex argument has provided is a position, where we can continue with purely mathematical methods. It is still unclear what the function f(x, y, z, t) determining the temperature of a point within solid at a certain time should be. We do know that the equation Fourier has found could correspond to infinitely many functions, but that certain additional conditions might be enough for determining the function. What really interests us is the method Fourier uses in solving the function from given conditions. To put it shortly, Fourier starts with an assumption that the function in question can be expressed in terms of simpler functions. To be more precise, he assumes that the function can be expressed as a sum of a possibly infinite series of trigonometric functions. The assumption happens to make sense in the context of heat transmission, because this physical process is not too erratic. In other words, the changes in the transmission can be approximately described with sums of cosines and sines. All Fourier then needs is a systematic method for determining these constituent functions, which is a simple enough task.

The idea of using sums of trigonometric functions as a way to determine heat functions was not completely novel. Yet, Fourier was the first person to assume that this method could be used in so extensive manner. While trying to solve a physical problem - how to describe movement of heat - he launched a completely new area of mathematical studies, the so-called Fourier series.

Gustave Fechner: Panegyry of current medicine and natural history (1822)

(1801-1887)

At the fringes of philosophical schools there have always been solitary figures who do not neatly fit into any category. Gustave Fechner is one of those solitary figures, not the least because his works often lay somewhere between philosophy, psychology and physiology. One might broadly include him within the philosophical current of idealism, but Fechner was also highly critical of many of the more notable idealists. Furthermore, when reading Fechner’s books, one is never sure whether Fechner is serious in what he writes or is he just makig fun of things

Fechner’s Panegyrikus der jetzigen Medicin und Naturgeschichte is a good example. It seems like Fechner’s purpose was to raise the value of medicine. Yet, when one hears what he suggests as reasons for his panegyry, one gets the impression that perhaps we should take the whole text with a grain of salt. Firstly, he considers the advantage of the medicine of his time to lie in a specialisation - not just surgery demand a completely different education from pharmacy, but also each and every substance used for medication has its specialists, capable of using their favoured drug for every imaginable condition. Whether it is coincidental or not, Fechner appears to raise the irony by giving as exemplary drugs such substances as Prussic acid, which we know to be highly poisonous. He also comments on the practice of bloodletting by telling of his friend who continued using this treatment on a patient who had already died, just because it had already proven so effective against scrofula of the patient.

Fechner also has something to say about the so-called Brunonian medicine, which was highly appreciated in the Germany at the time, especially by natural philosophers of the Schellingian school. The main idea behind Brunonian medicine was to divide all diseases into two classes - sthenic and asthenic, which one might describe as over- and underexcited - and the cures for the diseases consisted of finding a healthy, balanced state between the two extremes. Fechner notes that the Brunonian terminology was just a ruse for using quite old methods under new names, in order to make people believe again cures, which they had already deemed to be worthless. Another fashionable school of medicine Fechner mention is that of Hahnemann, founder of homeopathy, just to note that pharmacists will definitely be able to make even teaching of this school profitable for themselves.

With current medicine suggesting such an extraordinary amount of medical treatments Fechner notes that he could simplify medical textbooks - he could just list what ailments are not cured by the treatments. Indeed, Fechner suggests an even more condensed text book, which would consist simply of two statements - all treatments work for all ailments and all ailments can be healed by all treatments.

Just to make the idea even more ridiculous, Fechner suggests that earlier medicine was undeveloped, because it relied on the idea that nature should provide all medical treatments. Fechner notes, on the other hand, that current medicine thinks quite oppositely that the quality of a drug is instigated by the amount of work used for creating medicine - instead of herbal treatments, one should prefer pills. Combining this suggestion with the principles mentioned in the previous paragraph, Fechner concludes with a wink in his eye that a simple drug combined out of all possible medical drugs would be the ultimate medical treatment. To prove his ironic point that this ultimate treatment should be preferred over all natural medical substances Fechner argues that no natural substance could ever be of such foul tasting nature as all proper medical substances are - indeed, a person suggesting that the purpose of medical substances is to make one feel better is, Fehchner jokingly states, a barbarian, since the proper aim of a drug is to taste bad, just like its Platonic opposite or cooking tries to make everything taste good.

As one cause of the state of current medicine Fechner mentions the connection to practice many medical writers of the day had - they had spent more time as barbers and had thus seen more veins than supposed professionals who had wasted their time on learning Latin names for members of body. Fechner goes even so far as to instruct students on how one is to act to become a proper physician - to awake an air of professionalism and profound learning one should ask about completely unrelated matters, when a patient tells of a condition, always sound certain on one’s diagnoses, and to assure that occurring deaths were inevitable and that treatment must have lengthened the remaining lifetime of the patient. Just to heighten the ridiculousness of the medical practice of the time, Fechner tells a story of a practitioner who accidentally amputated a wrong foot, then noticed the sick foot had started to heal by itself and declared the healing process as an effect of the amputation.

The main reason for the sorry state of medicine, according to Fechner, appears to be a tendency to make unnatural divisions and classifications that do not describe the richness of the living nature, but as it were, kill the living unity, just like anatomists have to kill an animal when they dissect it. As an example of a natural phenomenon that current theories of nature could not explain Fechner takes whales, which mostly resemble mammals, although they happen to live in water. In a parody of teleological explanations, Fechner tells a story of Jupiter designing all the animals and only at the last minute noticing that the limbs of whale were quite unsuitable walking and then just throwing it into an ocean. Fechner also notes that so many different classifications of animals had been suggested that a classification of all such classifications was soon required. His final word on the issue appears to be that nature is infinite in its variations and can therefore never be tied down by any classification.