domain: shs scco math info

text:
Helmuth Blaseio

Economies of Symmetries (EoS) An Economic Approach to Scientific and Cultural Development

Keywords: rationality, symmetry, repetition, economies of scale, economies of symmetries, philosophy of science, cultural evolution, knowledge acquisition

This paper posits that the development of new knowledge is largely motivated by information-economic advantages. Focussing on examining the roles and sources of novelty in the form of new insights, cultural evolution, and innovation, the paper addresses a central aspect that lies at the intersection of the economics of development, information, and evolution.

The analysis shows that symmetries (repetitions, regularities) occur at the core of generalising insights and that they play a decisive role in realising efficiency gains by allowing shorter descriptions and superior orientation. This paper calls these benefits 'economies of symmetries' (EoS), traces their origins and outlines their vast implications for the discipline of economics, as well as for scientific and cultural development more generally. Ubiquitous examples of such concentrates are rules, behavioural patterns, explanatory models, natural laws and other forms of order, and they may be expressed as formulas, algorithms, models, or other expressions of abstract language.

Exploiting EoS potential reduces the costs of collecting, processing, documenting and exchanging information of all kinds. Such potential accrues across all disciplines and applications in all cognitive and communicative tasks, and it arguably underlies all scientific endeavour and economic progress. Besides reducing complexity, the recognition and/or implementation of symmetries often also triggers innovationa phenomenon which is at the core of most economic development but for which economists have yet to provide a satisfactory explanation. Yet despite their economic and rational nature, EoS cannot be the result of rational decisions, for otherwise their underlying insights would have to be known as decision alternatives in advance, in which case they would not be new insights. The systematic consideration of EoS could therefore herald a paradigmatic transformation of economics beyond the decision paradigm.

Introduction

This paper calls for a new kind of economics that offers itself for application in at least three of the discipline's key fields: development economics, information economics, and evolutionary economics. These branches of economics, among several others, share a common and central blind spot when it comes to the emergence of novelty in the form of new information triggering new inventions and is characteristic of economic evolution. Ever since [START_REF] Hayek | The Use of Knowledge in Society[END_REF] foundational article on "The Use of Knowledge in Society", economists have mostly been concerned with how agents use information, i.e., information that may still need to be found but, in principle, is already existing. This invariably applies to many of the field's classic and most widely cited works, including, among many others, Stigler (1961: 213, 224) focussing on the search for [existing] information or knowledge, and [START_REF] Akerlof | The Market for "Lemons": Quality Uncertainty and the Market Mechanism[END_REF] or [START_REF] Spence | Job Market Signaling[END_REF] with regard to uncertainty. In the field of development economics, the importance of information that is newly created by insights as the essence of new knowledge, in the guise of human capital, has been widely acknowledged at least since the advent of endogenous growth models (e.g., [START_REF] Romer | Increasing Returns and Long-Run Growth[END_REF]. Asking where that growth-boosting information is supposed to come from would likely yield but some vague reference to 'education' or 'research and development'.

The question that has much greater bearing on economic growth and human developmentand that has been all but neglected to faris this: How and why is valuable new information created, which gives rise to a new understanding and better orientation, thus triggering an innovative impact on organizational and technological development or on cultural evolution? 1 In each of the three branches mentioned above, economists keep running into problems whenever they try to transcend the well-known decision logic, i.e. whenever an economic phenomenon cannot be modelled on the basis of existing information that serves as the basis for decisions, or in other words: when new informational ground must be broken. While Schumpeter was well aware of the economic impact of innovation, for example when he wrote "innovation is the outstanding fact in the economic history of capitalist society" (Schumpeter, 2008(Schumpeter, [1939]]: 82), in line with today's mainstream, he unfortunately tried to reduce the problem of innovation to mere decision logic, believing that novelty arises as a new combination of already known information: "innovation [...] consists in carrying out New Combinations" (Schumpeter, 2008(Schumpeter, [1939]]: 84). On the unresolved question of the emergence of novelty, Hodgson and Knudsen (2010: 28f) wrote in their survey on evolutional economics, "While separate chapters [of our book] are devoted to selection and replication, no single chapter has variation as its primary theme. This is not because we regard the existence and sources of variation as unimportant. On the contrary, understanding the roles and sources of novelty and innovation in social evolution is one of the most important tasks ahead. [...] especially in the social sciences, innovation and novelty are among the most difficult phenomena to explain."

This paper introduces a novel economic approach that transcends and complements the decision or combinatorial logic, illuminating the blind spot that economists have been working around for decades.

Is there a common and perhaps even economic logic that underlies (virtually) all quest for new knowledge and therefore also all scientific endeavour? While economists build models to succinctly describe the complex behaviour of markets and economic agents, natural scientists look for natural laws that provide orientation in a bewildering universe, and engineers develop formulas and standard procedures to help them cope efficiently with recurring tasks. What may ostensibly seem like an array of disconnected efforts actually follows a common information-based economic logic: the exploitation of potential for complexity reduction. The subsequent analysis will show that such potential can be mined via a certain type of insightthe recognition of repetition or, more technically, of generalised symmetries. Compressing those symmetries by omitting redundant information yields benefits in description and orientation of the kind that have changed the course of history many times. This logic is at the root of all rules, formulas, norms, natural laws, regularities, schemes, structures of order, etc. The economic principle that determines these benefits shall be referred to as economies of symmetries (EoS). These benefits are generally attributable not to decision behaviour, i.e., the selection of the best available alternative, but to the human quest for insight or order, i.e., the search for superior and efficient orientation in a complex world. Therefore, postulating an economic cost-benefit logic behind all human quest for understanding the ordering principles behind observed phaenomena, economics becomes intrinsic to most sciences and consequently to the philosophy of science. The following will furthermore show that analogous behaviour underlies all cultural evolution and is even characteristic of everyday life.

Some initial examples of economies of symmetries

The law of diminishing marginal utility (hereinafter: 'LDMU'), arguably one of the most central propositions in economics, shall serve as the first example to illustrate the principles set out above. The LDMU says that additional units of a good will increase the utility of its owner by declining amounts. It is called a law because it has been found to apply with great regularity (recurrence, repetition) in many contexts. At closer inspection, there are two dimensions to that reference to repetition or symmetry. The first dimension refers to the repetition found in any given situation where the law applies. The observed regularity allows drastic savings in descriptive effort. To appreciate this, consider for a moment that the law did not hold: If the marginal utility of consecutive units of the good varied erratically in magnitude and in sign, finding and describing a utility function even just for a single good consumed by a single user would be a prohibitively cumbersome exercise. In reality, however, utility tends to develop with great regularity from one unit of the good to the next, and this regularity permits the approximation of the relationship between utility and the quantity of the good by various mathematical functions such as the square root. That recurrence of diminishing marginal utility as consecutively more units of the good are added is an example of what this paper shall refer to as an interior symmetry that has been discerned from the context of observation.

In all likelihood, however, there would be no law of diminishing marginal utility if that recurrence from one unit of the good to the next were all the symmetry content there was to be found. What makes the law so efficient as a descriptive tool and so powerful as a predictive tool is the second kind of repetition: the fact that the regularity holds across a vast number of goods and virtually all humans (as well as, to some extent, probably also most other conscious organisms). This scope of applicabilityacross different goods, different agents, at different points in timerepresents a further dimension of symmetry captured by the law. But applicability (the potential for application) is not yet the same as application itself, which reflects the actual demand. Besides the interior symmetry content that arises immediately within the question at hand and its transferability to similar questions, there is therefore also an exterior symmetry content, which refers to the actual frequency (demand) with which this question arises in the context of concrete tasks. This third symmetry dimension, which refers to the exterior demand for solutions, is independent of the underlying question, i.e., its scope is a result of the respective application context.

It is now time to proceed to several additional illustrative examples from beyond the typical object area of economics. However, this does not prejudice the economic nature of the analysis: In each instance, it will be shown how EoS serve to economise on descriptive effort.

For the second example, consider the series {7+8+10+13+17+22+28+35+43+52+62+73+85+98}. It clearly exhibits a regularity or symmetry: The difference between any two consecutive numbers exceeds the preceding difference by one. This is the law according to which the series was formed and could be extended indefinitely. Transforming the series into the familiar notation∑ (6 + 𝑖 𝑛=14 𝑖=1

) makes the information-economic potential for more efficient description relative to the original representation evident. Using the summation symbol ∑ and the index of summation i, the symmetric content of the series is folded into a compact expression. If the elements of the series were chosen arbitrarily, as in the case of the hypothetical utility function above, then, for lack of symmetry or repetition, a more efficient representation of the series would not be possible; every element would have to be stated individually.

As above, the regularity that is at the root of the opportunity for efficiency-enhancing folding (shorter description) is not something that could be subject to a decision. Recognising the symmetry requires an insight instead of decisions. While the interior symmetry content of this example is immediately obvious and can also be extended to similar series through further parametrization, as in ∑ (𝑘 + 𝑖 𝑛 𝑖

), exterior symmetries will be harder to find as not many worthwhile fields of applicability in other contexts come to mind that lead a significant demand. By contrast, exterior symmetries abound in the case of another (infinite) series whose elements can likewise be folded into a concise descriptive concentrate by virtue of the underlying regularity (formation rule): the famous Fibonacci sequence, which crops up in a vast range of contexts from mathematics, physics, computer science, biology, design, music, and, indeed, economics (von Brasch et al., 2012). Generally speaking, the extent of interior and exterior symmetries determines the ratio by which the description of a phenomenon or class of phenomena can be compressed. In other words, they determine the extent of the potential for informational efficiency gains, i.e., the economies of symmetries.

As a third example, consider the familiar formula for calculating the area A of a triangle, A = b * h / 2, where b is the base and h is the height of the triangle. Here, too, the interior symmetry references are immediately discernible as (1) only two pieces of information are required to calculate the area (first information concentration) and ( 2) the formula can be applied to any arbitrarily shaped triangle (second information concentration thanks to parameterization of base and height). As a result, thanks to the twofold concentration, a compact formula very efficiently covers an enormous range of potential applications. The exterior symmetry content is likewise very high as the demand for application is strong, comprising with a wide range of tasks in architecture, engineering, surveying, etc. Interestingly, in formal contexts such as this one, which apply to a large number of objects, another symmetry reference is often found: The formula can be proven, and in such a proof lies a fourth symmetry dimension, for if no proof were possible, the validity of the formula would have to be ascertained anew for each individual object. To provide just a brief glimpse of such a symmetry-based proof: The triangle can be expanded into a rectangle whose area, A = b * h, is exactly twice (symmetry reference) the size of the triangle. As this symmetrically holds for every triangle, it proves that the area of every triangle amounts to half of that of the rectangle formed by the triangle's base and height.

Figure 1: Symmetry relations point the way to a formula for the area of triangles

As the fourth example, consider a simple algorithm that controls traffic lights. The interior symmetry content is simple and quite evident: the algorithm has to switch the lights repeatedly following a cyclic sequence of three colours. The exterior symmetry content is vast. The algorithm meets a huge demand, serving around the clock, seven days a week, in millions of locations around the world. Given that a suitably parametrised version of the algorithm can analogously also control traffic in shipping, in mail or in chunks of information within computers or on the Internet (time-sharing), a huge potential demand becomes visible, and thereby a huge potential for economising on information. Efficiency dictates that such an algorithm is programmed only once and then copies (repetitions) of it are put to use around the world. Any association with economies of scale at this point is well warranted: As will be discussed in greater detail below, economies of symmetries can in fact be interpreted as a transdisciplinary, information-economic generalisation of economies of scale, all of which have the finding of generalized symmetries as their causal root and operating principle.

These four examples can be arranged graphically in terms of their interior and exterior symmetry content, as in the figure below. In each case, the distance from the origin provides some indication as to the size of the economic potential for descriptive contraction. In place of any number of other symmetryexhibiting examples, the figure additionally features the area of the circle as a highly symmetric twodimensional geometric shape which is also associated with vast exterior symmetry content.

Figure 2: Symmetry content of the examples

These examples show that, in any number of scientific and real-life contexts, manyindeed arguably allmajor advances in informational efficiency are attributable to the same cognitive phenomenon: the recognition of symmetries, i.e., systematic repetitions, that permits savings in terms of descriptive effort.

Occurring on the meta level, this efficiency gain can arise independently of whether the lowest level concerns economic behaviour, physics, number sequences, or any other object area to be described or modelled.

Three levels of observation can be distinguished. The lowest level is represented by the object area contemplated by a scientific discipline, e.g., cosmological aspects in physics or game-theoretic constellations in economics. The second level or meta level corresponds to the perspective of the observers (scientists), whose progress in knowledge is mainly reflected in the transformation or rather economical concentration of datasets of observations into laws, model notions or schemes. The third level, finally, is the perspective of this paper, which analyses the economic content of the scientific efforts on the second level. Since these scientific efforts again exhibit similarities (symmetries) across various disciplines, an information-economic concentrate can be formed on this third level, too. This concentrate characterises the dynamics on the second level; it is the general principle of EoS. The result, which finds that scientific effort is of a fundamentally (information-)economic nature, should be of relevance for the philosophy of science. And, as will be shown, it also applies beyond the realm of science.

Repetitions, symmetries, and their generalised form

How close is the connection between symmetry and repetition? In the strictly mathematical sense, Weyl was the first, in the 1950s, to render a precisealbeit very narrowdefinition of symmetry: "Given a spatial configuration F, those automorphisms of space [e.g., rotations and reflections in Euclidean space] which leave F unchanged [invariant] form a group G, and this group describes exactly the symmetry possessed by F." (Weyl, 1952: 45). For the purposes of this paper, the symmetry concept shall be generalised to "an observed invariance in a change of attention". The mathematical transformation is thus replaced with the general transformation of a "change of attention" (to another object, another situation, etc.). This means that two objects (situations, structures, etc.) are (partly) symmetric if an observer's perception of them remains (partly) invariant as the attention shifts from one object to the other. This generalised notion of symmetry, which is built upon the concepts of perception on the one hand and invariance or repetition on the other hand, is quite similar to the idea of symmetry used in everyday language, e.g., when talking about a "symmetric" face, and it indeed also encompasses similarity. This generalised interpretation is aligned with the formal one if the change of attention concerns a transition from an original geometric form to an isometrically transformed image of it.

Besides invariance, which refers to something remaining unchanged, this symmetry concept also encompasses repetition, which likewise addresses a sort of invariability. While the subjective perception of repetition (invariance) suffices for this generalised form of symmetry, the mathematical perspective demands an objective (intersubjectively indisputable) transformation of one object into another. Such objectivization means nothing other than a meta symmetry, namely that one observer's perception regarding a phenomenon recurs in the perceptions of all other observersit is intersubjectively invariant. In sum, the generalised concept of symmetry used in this paper rests on the concepts of perception on the one hand and invariance or repetition/recurrence on the other hand and arguably accords quite well with the common notion of symmetry in everyday language. 2 This generalisation permits wider application, for a repetition may refer to all sorts of phenomena that were so far associated with symmetry only colloquially, if at all. Examples include patterns of movement in stock prices, the similarity of situations in two different contexts, or the periodicity of character strings, e.g., in sheet music.

The nature and origin of EoS

As the next section will show using a wide range of examples, the expression 'generalised symmetry' was designed in such a way that the recognition of such generalised symmetries regularly opens up EoS potentials. Such potential marks the opportunity for the more compact description of some structure thanks to the recognised invariances or repetitive characteristics, which permits avoiding the explicit repetition of the individual recurring incidents (elements, steps, actions, etc.) in the description. For the same reason that a set of trees that are located sufficiently close together can be efficiently addressed as a 'grove' or a 'forest', a recurring stock market pattern need not be explained anew each time once its pattern has been described and assigned a name. Avoiding a reproduction of the individual recurrences can be achieved, for example, by identifying or establishing the pattern-generating rule (the formation law, the organisational scheme that underlies the repetitive pattern, etc.), by stating the characterising properties, or by stating an exemplary individual case as a prototype. The compaction of the description that is achieved by avoiding repetitions can also be interpreted as a summary, a consolidation, as the compression or concentration of information, etc. As the examples will show, the benefits of exploiting EoS-potential manifest themselves primarily in a more compact description, which is the consequence of complexity reduction due to recognised symmetries, and secondarily in advantages in orientation, speed, and/or effort, which follow from the primary effects. These benefits arise in any dealing with information (search, storage, processing, communication, analysis, etc.) as soon as some sort of order can be discerned. This gives rise to the following postulate for the philosophy of science, called the EoS hypothesis:

The striving for EoS benefits provides the governing motivation for the scientific quest for order.

Generalised symmetries can be recognised or created. In the former case, they arise through the finding of a rule or regularity by means of a discovery or insight (e.g., a law in physics, some order in chemistry, or a behavioural pattern). In the latter case, they exist because a rule is established, such as through technical standardisation (computer connections, charging plugs, traffic lights systems, etc.), through legislation (uniform traffic rules, common currency areas, etc.), or through contractual agreement (about concerted action, etc.). Whether it is recognised or created, a generalised symmetry is always associated with more repetition, which indirectly manifests itself as a greater degree of order.

The interdisciplinary scope and effect of EoS

Although the EoS effect is of an economic nature, it can be applied transdisciplinarily and indeed throughout human cultural life. However, the importance of EoS varies across disciplines, depending on the degree to which their research results can be systemised and generalised in the form of laws, theories, models, rules, structural schemata, patterns, etc. In natural sciences such as physics, where the scientific observations can be generalised to formal natural laws, EoS play a more prominent role than in more descriptive disciplines such as historyafter all, as Mark Twain said, history does not repeat itself (without repetition or symmetry, there is no scope for generalisation).

To prevent any misunderstanding, a distinction must be made between merely simplifying models, e.g., a scale model of some particular object, and generalising models, which refer to a multitude of objects or situations and connect them by generalization or rule formation. The concept of a 'theory' likewise permits two similar interpretations, since one theory may generalise from many individual cases while another one serves only to clarify a single historical incident, e.g., a criminal case, with no particular role for EoS. In the text, the predicates 'standardising' or 'generalising' are occasionally added to emphasize that this paper only deals with generalising or standardising models or theories, i.e., EoSexploiting representations of a multitude of objects, events, observations etc.

The first illustrative examples are from formal contexts, where the role of EoS is easily appreciated. When some familiarisation with the concept has been achieved, in Section 5.3, the exposition then moves on to examples from economics.

EoS in formal contexts

-Consider a set of numbers, such as {12; 12; 12; 12; 7; 7; 7}. Thanks to the repetitions in the set, exploiting the corresponding EoS, its representation can be abbreviated to {4r12; 3r7}, where the number that precedes each r indicates the factor of repetition regarding the number that follows r. This representation or coding using r saves having to reproduce every instance of the numbers. In this example, the benefit in terms of abbreviation is rather modest because the alternative representation requires additional symbols and greater effort to learn, apply, and read. Thus, there is some sort of minimum compaction ratio beyond which the transformation costs associated with coding and training only begin to pay off. In sets with greater repetition factors, such as {1117w12; 408w7; 978w11}, the effort of coding the repetitions is clearly justified.

-If in the initial set of numbers, the 12 is replaced with, say, with 'banana' and the 7 with 'apple', this example intuitively illustrates the EoS-driven invention of counting and, thus, of natural numbers.

-In the introductory example, ∑ (6 + 𝑖 𝑛=14 𝑖=1

), the summation operator ∑ served as a coding symbol that signals the folding the repetitions on top of each other, building a metaphorical stack. Each level of the stack or each repetition is addressed in abstract terms by the variable i. Instead of avoiding repetitions in a description, what is happening here can somewhat more figuratively also be described as folding the symmetry content at the mental symmetry axes between the repetitions.

Having folded the repetitions of a string of symbols, like in a stack of identical coins, it suffices to display a representative member. Because of the increase in value associated with the upward movement along the stack in the formal example, the proxy must be parameterized, e.g. (6+i). Furthermore, the height of the folded stack is typically indicated by the runtime variable n (14 in the example). In a similar and yet more general manner, the integral operator ∫ signals the limit value of the summation of infinitesimally many (and infinitesimally small) recurring components of the stack (integrand * dx), which need not be listed individually thanks to the generalised symmetry. From this it is easy to appreciate to what extent for example the short forms of a polynomial function such as 𝑦 = 3𝑥 4 + 1𝑥 -1 or its integral ∫ (3x 4 + 2x -1)dx 2 0

serve to exploit the repetitions and hence the folding potential in the series of numbers they represent. If the coefficients are additionally replaced with parameters, as in ∫ (ax 4 + bx -c)dx 𝑙 𝑘 , the expression serves to compress the description of an even wider field of observation.

-As a next example, take the decimal number 0,740740740740…, where the repetend, 740, constitutes the generalised symmetry. Recognising the periodicity yields the cognitive gain of an informationeconomic potential for contraction, which in this case allows the translation of the decimal number into the information concentrate 20/27. At times, the symmetry is more difficult to spot, such as in the infinite decimal number 0,7853981633974483096156608458198… Here, the symmetry or repetition lies not in the decimal number itself but rather in the series which Leibniz showed to be equivalent to that number: 1 -

1 3 + 1 5 - 1 7 + 1 9 -… This pattern can be compressed into ∑ [(-1) k * 1 1-2𝑘 ∞ 𝑘=1
], with (-1) k * 1 1-2k being the parametrised recurring element. The sum, finally, is a quarter of the mathematical constant π. Most readers will readily agree that Leibniz' discovery of a simple formation rule for π indeed constituted a cognitive gain.

-Anyone who seeks to generalise, i.e. prove, the contractibility of periodic decimal numbers will again encounter generalised symmetries, of the type which referred to as forth-level symmetries in Section 2 above. Generalised symmetries often provide the key to finding a mathematical proof when a multiplicity of objects is being addressed, as above in the case of proving the formula for the area of a triangle. 3 For example, contemplating the symmetry relationships involved reveals that a natural number is divisible by 3 and 9 if its digit sum is divisible by 3 and 9, respectively. Symmetry relationships similarly underlie the proof for the Pythagorean theorem etc.

The list of examples can be extended ad libitum both in algebra and in geometry. The only precondition in the metaphorical parlance introduced aboveis the stackability or foldability of generalised symmetries at mental symmetry axes. This stackability or foldability arises naturally from the repetitive nature of the matter at hand as soon as the pattern-forming lawthe cognitive gainhas been identified.

EoS in the natural sciences

The EoS-benefits in terms of thought and information, i.e., of the economic foldability of repetitions or generalised symmetries, are easy to appreciate in the context of mathematical expressions, and they are immediately transferable to the natural sciences. There, the research results already carry the symmetry reference in their conceptual structure as laws of natural science. Any knowledge about physical laws is the result of cognitive effort; simultaneously, it is an expression of recognised generalised symmetries, and it facilitates orientation and application by reducing the informational cost. The efficiency of noting the results of natural sciences in the form of laws was probably first noted concretely by the leading physicist Ernst Mach. In his 1882 lecture On the Economical Nature of Physical Enquiry, he expressly spoke of the economics of thoughtand yet his remarks appear to have had no impact on the discipline of economics. The symmetry reference of natural laws was addressed time and again in physics, for example by [START_REF] Rosen | Symmetry Rules: How Science and Nature Are Founded on Symmetry[END_REF] and Nobel laureates Wigner (1967) and [START_REF] Feynman | [END_REF]. The latter already used a very general concept of symmetry. The motive of repetition in natural laws is quite evident, for example, in Newton's famous law of universal gravitation. For the first time, it permitted a) the information-saving concentration of the mutual effect of masses in a formula (interior symmetries), and b) the uniform description of many different and yet physically similar phenomena (exterior symmetries). The scope of application extends to a falling apple, the speed of a cylinder rolling down a slope, the trajectory of a projectile, planetary orbits, etc. The efficiency of a single application of the formula, e.g., in terms of faster orientation and calculation, as well as more accurate predictions, is attributable to the interior symmetries, whereas the exterior symmetries, driving the frequency of application, increase the overall efficiency in informational terms. Contentually, the law of gravity at its core summarises phenomenologically observable regularities (e.g. planetary orbits), according to which different masses and distances always (inner symmetry) produce certain forces, which can be treated symmetrically, i.e. always in the same way. On closer examination, such a law is itself a result of even deeper symmetries, including:

the independence of the force from the system's position in space (inner symmetry of the homogeneity of space: the spatial position does not appear as a variable in the law), which is why the result of the calculation does not change when the system is rotated or translated, regardless of whether the masses are located in Europe, in Australia, on the moon or in another solar system, -the independence from the temporal position (inner symmetry of the homogeneity of time: time is not required as a variable), which is why the law holds at any point in time,

-the fact that material objects can be treated symmetrically with respect to their mutual attraction, even though they may be different in any number of aspects other than their mass.

The efficiency-enhancing foldability or summarizability of an effect in an abstract formula analogously applies to most other natural laws, be it in electrodynamics, thermodynamics, chemistry, etc. At closer inspection, it even extends to quantum mechanics, where although the measurements are statistically dispersed, this dispersion occurs within an established and recurring framework, which materialises in each measurement as one of the possible eigenvalues of a physical state under the influence of the experimental observation.

Thus, the EoS logic applies to the laws of natural science in just the same way (repetition!) as to the laws of mathematics.

EoS in formally oriented social sciences: the example of economics

Assuming that the EoS-hypothesis permits cross-disciplinary, economic interpretation of scientific theories and, based on this, of the pursuit of ever new theories, it should exert its explanatory power also regarding itself, i.e. regarding the results of economics, in a sense as a meta-economic statement about the discipline itself. On this subject, the economist Rubinstein (2000: 4) writes "Economics is an attempt to look for similarities in human interaction." According to Stigler (1982, 61), "If the problems of economic life changed frequently and radically, and lacked a large measure of continuity in their essential nature, there could not be a science of economics." While Rubinstein documents the symmetry motive in the economic science and Stigler recognizes that without invariances (symmetries) there can be no economic science, both do not yet address the ur-economic content of this motive. The EoS hypothesis, which interprets the primary scientific motive of economics in terms of the same information-economic benefits as in the case of physics or of mathematical formulas, assumes this task by identifying characteristic repetition (symmetries) in the object area for converting it to a compressed, theoretical representation that obviates all recurrences but one and thereby enhances efficiency in orientation and communication.

While this information concentrate typically assumes the form of a law or a formula in the natural sciences, in economics and other social sciences, the 'similarities' are generally condensed in the form of generalising models. These are often decision models because, unlike the object area of physics, the object area of the social sciences is human interaction between agents that do not simply follow the trajectories permitted by the natural laws but instead leave behind nested trails of decisions andin accordance with the focus of this paperalso trails of insights. Yet the scientific goal is the same across different subjects: to identify characteristic repetition and to represent it in an abstract form that is free of redundancy (free of repetition), such as a generalising model. Such a model reflects what is common or symmetric about an observed manifold, for example the pattern according to which a representative individual decides on her best course of action in a typical situation. Here the words 'common', 'pattern', 'representative' and 'typical' indicate the multiple symmetry or repetition signature. As already noted in Section 4, in order to model the regularities in an abstract, repetition-free fashion, several alternatives can serve as the nucleus of compression for folding, e.g., the pattern-forming ordering principle, the (decision) rule, the derivation procedure, an exemplarily highlighted item or typical attributes. Examples of such economic information concentrates in the economic discipline itself include the law of diminishing marginal utility, models of consumption decisions, Hicks' IS/LM model, the prisoners' dilemma, the Nash equilibrium, etc. 4

Economies of Symmetries vs. Economies of Scale

At closer inspection, it turns out that not only do the results of economics provide a good example of the working of EoS; indeed, the discipline has already been able to work out its own theoretical approaches to some special aspects of EoS. One such aspect consists in the familiar economies of scale, which can be traced back to Adam Smith's (1993[START_REF]An Inquiry into the Nature and Causes of the Wealth of Nations[END_REF]) reflections on the division of labour in the Wealth of Nations. Economies of scalephenomenologically: average cost savings in response to increasing outputare related to the information-economic EoS benefits that arise with generalised symmetries: 'Increasing output' implies larger numbers of identical products or processes, i.e. more repetition or greater frequency, and can therefore be subsumed under generalised symmetries. Economies of scale thus constitute a special case of EoS in the real economy.

From a more abstract perspective, however, the designation "… of scale" is a somewhat unfortunate choice of term because, although with its reference to a frequency (of repetition) it addresses a phenomenological correlation, it fails to address the causal trace to the most general root of the benefits: the folding potential from symmetries. In the real economy, the frequency of repetition, which manifests itself for instance in recurring events or processes, typically arises only secondarily as a consequence of deeper informational symmetries, such as organisational or constructional standardisation, natural laws, mathematical relations, etc. A producer, for example, can see already from the informational perspective of production planning that, for a given amount of output, it will be simpler and therefore cheaper to produce the same product, say a certain car model, over and over again. That way, the ever-same processes can be repeated with no additional set-up time required, which facilitates the organisation of production, saves research and development effort, and furthermore enables the procurement of fewer different parts, reducing the cost of materials thanks to bulk purchasing. Sales-side measures like reducing product variety or increasing sales mean that the task of producing a given product is executed more frequently (exterior symmetries). In parallel, potential savings can also be achieved through measures to increase interior symmetries, e.g., by using the ever-same screws, identical pipe diameters and material strengths, the same plastics, metals and glass grades, etc. That way, the variable cost of production can be reduced too. These cost savings, which are commonly referred to as economies of scale, are thus enabled by increasing the exterior and interior symmetries. They provide the basis for the condensation of the description of the production process and subsequently also the basis for its efficient realisation: by folding the recognized symmetries in the manifolds of products, parts, and processes at their mental axes.

EoS in the context of less theoretical sciences

As already mentioned above, in sciences where abstract-theoretical descriptions with a claim to universal validity are not so much the objective, EoS play a lesser role. In the extreme case of a science devoid of theory and standardising models, all that is left is the realistic documentation of events without the deduction of any theoretical structure, such as in historical descriptions, comparative juxtapositions, or the recounting of individual cases, e.g., a criminal case. In such a scenario, EoS are still encountered, but solely in the possibility of repeated access to historical uniqueness that documentation typically enables or in the repeatedly possible access to the differences established in a juxtaposition.

EoS in the context of norms

As already mentioned above, generalised symmetries can also arise from norms, e.g., in the form of harmonised driving behaviour in line with speed limits. Norms in turn arise, for example, from legislation, private agreements, orders given by holders of property rights, or technical regulation. Technical norms for example are typically based on voluntary agreements among the members of standards bodies. Norms and laws regularly lead to standardisation, for example in a technical sense, in an organisational sense, but also regarding the behaviour of people, companies, etc. The harmonisation of behaviour under a norm is not as strict as in the case of natural laws since human beings are free to violate the norm, perhaps because they are not even aware of it. Nevertheless, from the perspective of information, norms achieve a significant reduction of complexity in the sense of EoS. Here are just a few of the various sources of standardisation:

-Abstract legal norms, which are the rule for example in Germany, specify a context of similar circumstances, e.g., in the form of tax principles. That way, the legislator need not enumerate every possible individual case (complexity reduction) or prescribe the possible legal consequences for every such case (again, complexity reduction). Of course, this leaves the courts to decide whether the abstract norm applies to a given case. 5

-Technical standards may be established at the international (e.g., ISO 10001ff on quality management), European (EN), or national level (DIN in Germany). CE marking or the standardisation of plugs for example enable joint markets across all participating countries. Such standardisation clearly results in a reduction of complexity (EoS) due to less product diversity, fewer product descriptions, less need for product testing, etc.

-Standardised contractual relationships: In addition to the economies of scale discussed above, a second source of repetition-based efficiency can be found in the analysis of the rationality of organisational forms. Already in 1937, Ronald Coase established that frequent transactions of the same type (symmetry!) can be conducted more efficiently (EoS) within a stable contractual framework that reduces the costs of re-orientation and re-negotiation. Amongst other effects, these savings in transaction costs promote the rise of firms with standardised contractual relationships (cf. [START_REF] Coase | The Nature of the Firm[END_REF] both with internal (employees) and external parties (suppliers and customers).

EoS as a scientific leitmotiv

An inductive extension of the examples listed in Section 5 yields, as the EoS hypothesis, the result that scientific curiosity mostly follows the scent of generalised symmetries, hoping to reap informationeconomic benefits. This means that the EoS hypothesis not only deals with symmetries; it moreover manifests itself, on the third level of observation discussed in Section 2, as a meta-symmetry by bringing the logic of much of scientific endeavour down to a common denominator. Thus, the hypothesis itself follows an information-economic motive, which consists in structuring science along its recurring aspects and translating it into a descriptive concentrate in the shape of a hypothesis.

In somewhat more detailed terms: The EoS hypothesis maintains that the recognition of any repetitive pattern holds a cross-disciplinary potential for information-economic benefits. The potential consists in the ability, acquired via insight of symmetry, to summarise that which recurs in (or what is typical of) an object area in a non-repetitive (non-redundant) form. That summary can for example be expressed as a scientific rule, a theory, or a model, while the corresponding subject area can originate from any science. The potential for benefits consists, primarily, in the scope for descriptive compaction and complexity reduction resulting in the form of rules, schemes, formulas, models, etc., and secondarily, in the opportunity for faster information uptake and orientation, greater precision in information processing and rendering, and improved suitability for dialogue or further use, such as for recording, documentation, or information transfer. 6 What is the usual sequence of scientific cognition? EoS expectations correspond to a personal conjecture about some sort of order that has not yet been recognized. The perception of a repetition signals a potential connection between some phenomena, which may induce the statement of a contentual hypothesis about a rule. This hypothesis, formulated in the form of a (standardising) model, rule, etc., is then the descriptive concentrate into which the assumed or maintained generalised symmetries of the hypothesis have been folded in a non-redundant (repetition-free) manner. The stating of a symmetry hypothesis does not yet say anything about whether the observation is only a delusion, whether it proves to be incidental, whether it can subsequently be confirmed, or whether it even has predictive power. The empirical confirmation of a hypothesis should rather be considered a second-level symmetry (S2), i.e., the hypothesis proves to hold across a multitude of observations, and the achievement of intersubjective agreement about the hypothesis constitutes a third-level symmetry (S3), i.e., a multitude of parties agree that the hypothesis holds. A generally accepted law or a scientific result presupposes that all three levels are achieved.

In terms of the philosophy of science, the EoS hypothesis can be interpreted in two ways:

Cognitively: The logic of scientific discovery is directed towards the recognition of generalised symmetries and primarily strives for EoS potential. 7

Normatively: The logic of creating order follows the establishment of symmetry via norms (rules, laws, standards, institutions, etc.) and expectable EoS potential from symmetry conceptions (standard containers, ID formats, technical standardisation, etc.).

On the applicability of economic methods to the philosophy of science

Economic foundations of central concepts in the philosophy of science

The standard procedure in the philosophy of science is to check whether individual scientific disciplines such as economics represent true reality, whether they are able to find regularities regarding relevant issues within an object area, whether those regularities permit reliable predictions, and whether causal relationships are being described and perhaps even explained. The book "Philosophy of Economics" by [START_REF] Reiss | Philospphy of Economics[END_REF] explains this procedure in detail with respect to economics. Note, however, that those central concepts in the philosophy of scienceregularity, causality, predictability, reality and truthare themselves specific formulations of an economic logic, in that these cornerstones of scientific thought spring from the information-economic EoS logic. If that were indeed so, then the philosophy of science would at its core be of an economic nature, and given suitable realignment, economic thinking could become a leitmotiv for all sciences. To mention just one of countless other implications, today's relationship between economics and physics would be reversed. The reason is easy to see: To understand science from the bottom up requires a model of model-building (or a theory of theory-building), and that is just what the EoS logic provides. Such a model cannot come from physics or other natural sciences because their object areas are themselves not capable of building modelsthis kind of dynamics cannot be observed there (e.g., in cosmological systems).

As far as the concepts of regularity and causality are concerned, Hume already identified the reference to repetition (to symmetry) in their character. However, he was not yet able to point out the thoughteconomic benefits. According to Hume, it is experiences of invariance or repetition that induce an observer to hypothesise about a regularity: "after the discovery of the constant conjunction of any objects, we always draw an inference from one object to another" (Hume, 2002(Hume, : pos. 1506)). What this paper subsumes under symmetry, Hume ascribes to 'custom', i.e., a mental consolidation of observational data by the observer based on recall, which gives the impression of a routine: "For wherever the repetition of any particular act or operation produces a propensity to renew the same act or operation, without being impelled by any reasoning or process of the understanding, we always say, that this propensity is the effect of Custom." (Hume, 1993(Hume, [1751]]: 464) and "Custom, then, is the great guide of human life." (Hume, 1993(Hume, [1751]]: 465) Introducing a symmetry bracket between cause and effect that spans time and space, Hume reveals the distinction between mere regularities and causal laws: "There must be a constant union betwixt the cause and effect. It is chiefly this quality, that constitutes the relation. The same cause always produces the same effect, and the same effect never arises but [always] from the same cause.

[…] For when by any clear experiment we have discovered the causes or effects of any phaenomenon, we immediately extend our observation to every phenomenon of the same kind, without waiting for that constant repetition, from which the first idea of this relation is derived." (Hume, 2002) In this quote, Hume makes reference to repetition or symmetry through his use of the terms constant, repetition, same, and every. Per induction to future repetitions (expansion of the symmetry area), he furthermore manages to build a bridge from causal laws to the predictive function. This paper now adds the EoS logic, according to which the symmetries contained in these concepts enable thought-economic benefits per descriptive concentrationand this is the very core motive of abstract scientific thought.

The same logic applies to the concept of theory, which can be understood as the common explanatory content behind a set of related observed phenomena that conveys their recurring order (their symmetry structure) in a concentrated manner that is itself free of repetition.

Next up is the central demand of the historical ideal of science, namely that scientific results must generally be true and reflect reality. In contrast to this, this paper maintains that the ascertainable EoS benefits enable the same or even better evaluations of theories, without having to rely on idealised concepts such as truth and reality. For in empirical contexts, the truth or the true reality is an unprovable fiction because the degree to which a descriptive model depicts reality can only be speculated about in light of the repeated confirmation (symmetry!) of its orientational value and can be proven only when assuming axioms that are themselves unprovable. Any reference to the ideals of truth and reality implicitly means that these models provide satisfactory or repeatedly confirmed orientation. Yet this indicates nothing other than the observation of exterior symmetry relationships like the repeated confirmation of an investigation or finding (S2: reliability), the persistent forecast performance of experimental results, relevance in the sense of wide applicability (scope of validity), intersubjective agreement regarding the evaluation of the benefits obtained (S3), etc. These exterior symmetries reproduce the very same symmetry aspects whose apperception yielded the EoS benefits in the first place, as shown above. In the borderline case of no doubt, such exterior symmetry experiences tend to be subsumed under true reality, which, however, is an inductive conclusion regarding something that is ultimately unobservable.

The truth is generally taken to be unshakeable, whereas the EoS criteria might be criticised for entailing the risk of arbitrary interpretation. In fact, however, those idealised positions are less objectifiable than the information-economic criteria, which can be objectified for example as descriptive compaction, i.e., the ability of a model or theory to simultaneously describe or explain multiple phenomena (breadth of explanation or scope of validity), the ability to build upon few and simple assumptions (depth of explanation), calculability (e.g. using a formula), ease of understanding and memorising, suitability for dialogue, etc. Furthermore, like objectifiability generally, these criteria facilitate the achievement of the uniform intersubjective evaluation of a research result as a generalised S3-symmetry. Consequently, rather than overtaxing idealized concepts like truth or reality, which lie beyond the horizon of objectifiability, models and theories can be more scientifically evaluated using the criteria of the EoS benefits. An approach to the philosophy of science that rests on economic logic is therefore arguably inherently more scientific than idealistic notions.

In sum: An approach to questions of the philosophy of science that is oriented towards an economic logic promises to be inherently more scientific than any reliance on idealised notions.

Scientific results as competing goods

The information-economic character of the EoS-benefit of generalising models and theories, which includes the EoS hypothesis as a meta-theory, offers the philosophy of science an immediate basis of comparison and evaluation for competing standardising theories regarding some research question. This evaluability is the key to applying the decision logic which dominates the economic discipline today. Illustration shall be provided by means of interpreting a set of alternative scientific models, formulas, rules, schemata, theories, etc. regarding a certain phenomenon as competing goods within an abstract space of alternatives. In such a space, the choice of the most suitable theory can be interpreted as a decision task. The economic tradition holds that the best alternative is that which provides the greatest benefits. The interpretation of those benefits can now rely on EoS benefit criteria such as the degree of concentration (e.g., the factor of compaction or the number of phenomena captured by a model etc.), efficiency in orientation, suitability for dialogue, reproducibility of the result (confirmation), forecasting power, etc. Economic thinking thus offers itself as a central module to supplement the methodological toolkit of the philosophy of science.

In a systemic interpretation, applying economic thinking to the philosophy of science can elevate that thinking to a new level of abstraction. Thus, from the abstract perspective of the philosophy of science, economic models and theories can now themselves become objects of economic analysisin the form of self-referential attention. While economic models have so far mostly been applied to economic aspects, such as investment decisions under inflation, they can now furthermore be used to evaluate the usefulness (the EoS) of an individual model in relation to competing models, which thus become decision alternatives.

This yields the following generalising proposition: Economic models that discriminate in informationeconomic terms can provide a generally applicable toolkit to decide among competing goods that are weaved from the fabric of 'contentually describing information of scientific results'.

The condition of self-consistency in the philosophy of science and the EoS hypothesis

The possibility to contemplate itself is part of what makes the philosophy of science special: Its theoretical results regarding scientific theories aspire to be theories themselves. Thus, being a theory, the philosophy of science must itself satisfy the statements it makes regarding the theories it discusses.

In somewhat more abstract terms: The object area of the philosophy of science consists of theories, and since the discipline is itself a theory, its statements about theories must also apply to the discipline itself it therefore describes itself with regard to what makes it a theory. Consequently, both the theoretical edifice and the methodological approach of the philosophy of science must be consistent with themselves; they must exhibit self-consistency. As a candidate for the methodology of the philosophy of science, the EoS hypothesis satisfies precisely this criterion: It maintains that a recurring potential arises from all insights that are themselves based on recognised recurring patterns. As a cognitive hypothesis regarding generalised symmetries, the EoS hypothesis itself constitutes a generalised symmetry on the meta level. This makes it an insight that likewise rests on a recurring pattern; therefore, it is of the same nature as the objects of insight which it refers to. In other words, it describes its own theoretical nature in a self-consistent fashion. 8 And it is this self-consistency that makes the EoS hypothesis especially suited as the core of the philosophy of science.

The advantage of economics

The scientific results of economics build upon the assumption of actors who have rational expectations and seek to maximise their utility or benefit. Therefore, actors such as researchers are naturally an integral part of the object area of economics. By contrast, benefit-seeking subjects with intelligence and planning competence are not within the object area of the natural sciences or mathematics. Therefore, the development of scientific knowledge can be of no concern within the domain of these disciplines; scientific insights, ideas, theories and models only arise with the researchers themselves, yet these researchers are outside of the object area of their research. Comments by researchers from such disciplines are therefore of limited scientific value for illuminating what Popper (2014: 15) called the "growth of knowledge" and what he considered to be the "central problem of epistemology" (ibid.), which "can be studied best by studying the growth of scientific knowledge." (ibid.) Any such remarks can be neither an integral nor a methodologically sound part of their authors' disciplinestherefore they are merely individual offstage observations. Perhaps apart from AI, this generally applies to all sciences whose object area lacks autonomous research dynamics. Economics, by contrast, provides a natural methodological access to the behavioural patterns of rational actors, who constitute the primary area of the discipline. Such rationality may in particular be expected of scientists. Note, however, that in science, cognitive rationality has and deserves primacy over decision rationalitya change of perspective that this paper aims to promote. Other than that, quite in line with economic methodology, scientific endeavour follows the expectation of benefits from the aspired research results. Based on typical examples, the analysis has shown that such results regularly yield clearly specifiable benefits, that lend themselves to economic analysis and that comprise both the direct orientational advantage of new insights (the information-economic EoS benefits of generalising models or theories) and indirect subsequent benefits of, e.g., application (what new opportunities does the result open up?) or reputation. Consequently, economic behavioural patterns like rational behaviour, utility maximisation and benefit orientation, which are inherent to any research dynamics, suggest that economics is in a natural way methodologically close to the philosophy of science and promises to be of great value to it. This is even more true with the disclosure of the information-based benefit structurethe cognitive rationalityof scientific results by means of the new EoS approach.

Economics beyond decision theory

Our above emphasis on cognitive rationality as opposed to decision rationality already suggests that it will not suffice to simply transpose the methodology of current mainstream economics to the philosophy of science. This is because economics as it stands today cannot fully satisfy the methodological demands of the philosophy of science, as it still cannot theoretically describe the development and knowledge dynamics of its own object area, the economy. Yet such a description is crucial for modelling the knowledge-based development of science. The reason for the shortcoming lies in the limits of the decision approach that dominates economics: Like a planning economy, the decision logic suffers from an ex-post bias. To decide is to choose from alternatives. But, speaking from the perspective of the philosophy of science, how to choose the best explanatory model for some phenomenon if either no model has been devised yet (lack of alternatives) or if superior alternatives to the existing models can at best be surmised or hoped for (suspected incompleteness of the alternatives)? How relevant is this? The scientific spaces of alternatives that consist of competing theories indeed ought to be incomplete, for if there were no more room for new theories, science would be nothing but a static archive. As Schumpeter already remarked in his Theory of Economic Development over 100 years ago, the decision paradigm, which to this day dominates economics and which necessarily neglects future alternatives, in a sense constitutes the discipline's blind spot with regard to ideas, innovation and creative development.

Future alternatives, be they innovations (in the realm of economics) or new scientific theories or models, are not accessible by means of decisions; decisions can only be taken among known alternatives. The decision interpretation of economic behaviour therefore necessarily ignores new ideas, innovations and insights, although the superior solutions they provide almost certainly do more to promote science and the economy than optimal decisions among known alternatives. Schumpeter (2006Schumpeter ( [1912]]: 182) famously criticised this fixation with decisions: If decisions were all there is, he asked, "how come we no longer live in caves?" Without insights and innovations, the debate would still be about the choice of the best cave or, when it comes to travel, picking the fastest horse, rather than to use the train or, eventually, the Hyperloop.

Thus, economic behaviour in general and inquisitive science in particular go far beyond mere decisions.

In real life, they also include cognitive effort to achieve superior solutions, instead of contenting oneself with optimal decisions. To expend that effort is an investment in working time whose payoff must be estimated in relation to the best available alternative. Superior value, in science and in the economy alike, comes not from deciding between existing alternatives, but from 'creating knowledge', i.e., from creating new and superior alternatives. Therefore, for the philosophy of science, the decision logic that characterises the current economic discipline can never be more than an ex-post approach that refers to known alternatives, such as the choice of optimal theories or descriptive models, but it will never contribute to new models itself. The adoption of the EoS approach, which substantiates the rationality of the quest for new insights, therefore promises to free the economic discipline from its self-imposed methodological cage of the decision logic and points the way to a development logic.

EoS as the driver of cultural development

The following reflections about information transfer on the basis of natural language as well as about the theory of information and algorithms aim to show that the examples given so far, which related to science, are but special cases of the universal information-economic significance of EoS in the wider cultural environment. In particular, long before the emergence of modern sciences, the habitual exploitation of EoS in natural language was a standard cultural practice. Accordingly, the EoS in theories, laws of nature and models only represent the natural evolution of the EoS in language elements such as proper nouns, abstract concepts, universals or analogies. Similarly, information-theoretic deliberations reveal an EoS-based evolution of formal languages, from character strings via formulas to the architectural principles of algorithms. The question consequently arises whether EoS may be one of the drivers, if not the essential engine, of all cultural development.

EoS in the context of natural language

Language and proper nouns

Using language essentially amounts to denoting objects by sounds or symbols that represent these objects. Without representatives like symbols, communication would be limited to objects that are within pointing range (within sight) or, in spatial-temporal terms, within the here and now. The symbols extend the communicative capabilities, allowing the parties to refer to objects that neither the sender nor the recipient of the message can see. Areas that are more distant in time and space thus become equivalent in terms of communication to the parties' immediate environment. Establishing that equivalence reflects an act of symmetrisation, just as the various forms of standardisation discussed above. Like a reflex of standardisation, language presupposes an agreement on the meaning of the representatives: the more potential communication partners speak the same language, the greater the symmetry range of the standardisation and thus the greater the potential EoS.

The standardising (symmetrising) character of language is already evident in such simple elements as proper nouns. Proper nouns allow the repeated communication about an object without having to describe it in detail (without having to reiterate its bundle of properties), and communication about objects that are beyond pointing range (exploitation of equivalence). Reduced descriptive effort, extended range of communication, intertemporal validitythese are clearly EoS benefits that arise from the standardisation of communication enabled by language. 9 Consider the example, 'The news spread like wildfire'the EoS of language and of proper nouns in particular make this possible.

Abstract concepts

The introductory chapters already discussed abstract concepts or abstracta (as distinct from proper nouns) like triangle, working with their characterising properties from their definitions. From the EoS perspective, these properties are characterising symmetries that recur in every real manifestation of the abstract concept. A chair, for example, is distinguished by exhibiting the properties of having legs, a seating surface, and a backrest. These are the characteristic properties that in this specific combination recur only in chairs. All abstractatable, tree, or houseare defined via the properties that specifically recur in the designated objects, and these recurring properties are instances of generalised symmetries.

The fact that abstracta can be defined via properties has been generally known at least since Aristotle. 10 What this paper adds, however, is the insight that the formation of abstracta unleashes EoS potential: Abstracta designate a set of properties that symmetrically recur in every individual element subsumed under the conceptsuch an abstract term thus obviates renewed descriptions of the individual objects that can be assigned to the concept. 11 This was already used above in deconstructing key concepts of the philosophy of science. Like proper nouns, abstracta exploit the spatial-temporal equivalence; however, unlike proper nouns, abstracta can express a plural; indeed, they are a downright manifestation of the 'plural' principle. This enables them to efficiently address entire classes of similar objectseach of which would otherwise require its own descriptionwith only a single concept. That way, they introduce a further quality in the exploitation of EoS by language. Choosing the specific set of commonalities (symmetries) to be encoded in a concept furthermore allows the targeting of connotations and of a level of abstraction that is suitably concise for the context at hand. For example, an object's function may be all that matters for the purpose at hand, while the other properties are irrelevant.

To sum up, abstracta exploit information-economic EoS benefits along three dimensions: 1) the spatiotemporal equivalence achieved by using symbols, 2) the repeated access at no additional cost of description as already enabled by proper names and, beyond that, 3) the ability to address entire classes of similar objects with just a single word. According to this approach, the EoS potentials constitute the causal motivation for the formation of terms (proper nouns, abstracta or universals).

Unlike chair, abstracta for intangible objects like supply, demand, taxes or negotiation cannot be explained simply by pointing at the object; instead, their meaning must be explained or circumscribed. Thus, although the basic function is always the same, a further differentiation can be made within the class of abstracta. As discussed above, the triangle for example, unlike the tree, additionally features interior symmetries in the form of invariant relations that pave the way for formulas for further properties such as the area, the circumference, etc. Interior symmetry relations with EoS potential also play a role the in the abstract concept price, which is of great importance in economics. A price indicates an exchange rate between a certain good and an intermediary good which is exchangeable with every other good: money. That symmetry of money being exchangeable for every other good permits the information-economic reduction of the number of exchange rates between n goods from 𝑛 * (𝑛 -1)/2 to n.

The abstract concept 'theory' shall serve for the discussion of a final particularity. As in the example of Newton's law of universal gravitation, a certain theory addresses the explanatory common ground behind the observed phenomena regarding an issue, i.e., the perceived order as represented in a concentrated form that is free of repetition. If, on a higher level of abstraction, the members of a group of theories are compared to each other, then as with abstract terms, in this set of objects, too, common

properties become discernible that are encoded in a concentrating fashion by the concept theory. Thus, theory is a special abstract concept in that it encodes symmetry on a dual level. The properties that characterise the concept theory are what is common about a multitude of individual (generalising) theories, each of which in turn make a statement about what is common about some aspect of realitythe theory properties thus represent a meta symmetry. While simple abstract concepts such as triangle or chair only embody the exploitation of EoS in themselves, the concept of a theory even requires such EoS exploitation of its objects, i.e., of the individual theories whose common ground it encodesthe EoS potential on this object level represents the theoretical content of the individual theories. Also part of this requirement is that the postulated common ground and the ensuing EoS potential can be confirmed empirically (S2: symmetry of confirmation), that their EoS can be ascertained by the scientific community (S3: symmetry of intersubjectivity) and that they have satisfactory explanatory power (beyond phenomenology). In a certain sense, abstract terms are subject to a similar review as theories, but only implicitly, in that they may simply go out of fashion in the course of the natural selection of language usage if their benefits cease to be compelling: The disappearance of the benefits of the coded bundle of properties reduces the exterior symmetry (the frequency of recurrence) in its usage, as for example with concepts such as telephone box or LP. Notwithstanding some differences, generalising theories and abstract concepts like theory both follow the EoS logic, i.e., they exploit the same set of benefits from recognised symmetries: more efficient description and documentation, faster orientation, easier communication and understanding, etc. From the philosophy of science perspective, the EoS logic provides an original theoretical approach on both levels of theory: regarding the quest for theories (cf. Section 6) and, regarding the emergence of the abstract concept of 'theory' itself. That way, in performative congruence, the EoS logic is applied to capture the frequent exploitation of the EoS logic itself: EoS (EoS).

In the philosophical discussion, abstracta (ideas in Plato's words) played an important role in the socalled problem of universals. Focusing on the question of their relation to reality, realists concede to abstracta an existence in their own right in the sense of Plato's theory of ideas, whereas nominalists (cf.

Latin nomen = name) consider abstract concepts to be merely names or designations for a set of objects.

In contrast to this discussion, this question seems like a fruitless endeavour because, on the one hand, the concept of reality is itself an abstract term that requires clarification and, on the other hand, this discussion obscures the motive for the development and use of abstracta, namely: the exploitation of EoS benefits to improve efficiency in thought and communication. This exploitation of EoS benefits is postulated to be the true engine of the semantic development of language. Just imagine the learning and communication effort that would be required if every item and every mental object had to be described individually and in detail. Incidentally, although he did not yet work out the economic driving force, the 17 th century nominalist Thomas Hobbes magnum opus Leviathan already identified both the symmetry motive ('similitude' in the quote) and the way to summarily address entire sets of items ('any one of those many'): "One Universall name is imposed on many things, for their similitude in some quality, or other accident: And whereas a Proper Name bringeth to mind one thing onely; Universals recall any one of those many." [START_REF] Hobbes | Delphi Collected Works of Thomas Hobbes (Illustrated). Delphi Classics, Kindle version[END_REF][START_REF] Hobbes | Delphi Collected Works of Thomas Hobbes (Illustrated). Delphi Classics, Kindle version[END_REF]: 653) 12 Arguably, only an in-depth understanding of the benefits in terms of thought and information can reveal the motive for the development of abstract concepts: EoSefficiency in language thanks to the foldability or summarisability of recognised similarities or symmetries.

Complex figures of speech

The scope of EoS in the sphere of language even extends far beyond the use of abstract concepts. In modern linguistics, it was arguably George Lakoff who first got to the heart of the effective principle of metaphors, which he called the invariance principle: "Metaphorical mappings preserve the cognitive topology (that is, the image-schema structure) of the source domain, in a way consistent with the inherent structure of the target domain." (Lakoff, 1992: 215) The cognitive structural invariance in the transition from a source domain to a target domain that Lakoff describes is nothing other than a generalised symmetry between two spheres of attention (the persistence of structure in a change of attention). More than 2,000 years ago, Aristotle in his Poetics circumscribed this as similarity, a proxy for symmetry: "a good metaphor implies an intuitive perception of the similarity in dissimilars." [START_REF]Rhetoric, On Poetics, in: The Works of Aristotle[END_REF](Aristotle, : 1459a) Both Lakoff's separation into a source domain and a target domain and Aristotle's designation as dissimilars express trans-contextual symmetries (invariances, similarities). For the present purpose, the crucial point is the thought-economic aspect that arises from the symmetry structure. In this regard, too, Lakoff provides the groundwork: "Metaphor allows us to understand a relatively abstract or inherently unstructured subject matter in terms of a more concrete, or at least a more highly structured subject matter." (Lakoff, 1992: 244 f) A fine example is the metaphorical use of the planetary system (source domain) with its familiar structure to efficiently explain the inner structure of atoms (target domain). Metaphorsand analogies, which are structurally equivalentoccur in literature just as in everyday language, for example when a weather phenomenon is used to refer to a looming conflict: "a storm was gathering". Such use of metaphors saves descriptive effort: Mentioning the storm effectively and concisely (i.e., efficiently) conveys the idea that the conflict is already visible on the (likewise metaphorical) horizon, may bring devastation, can have a clearing effect, etc. Drawing on symmetries, metaphors are a way of reducing descriptive effort, i.e. of exploiting EoS! Lakoff (1992), Pinker (2008) and Hofstadter/Sander (2014), for example, provide plenty of examples of this effect of metaphors. This special type of the trans-contextual exploitation of symmetries can furthermore be extended to even more complex figures of speech such as similes, allegories and proverbs.

Modern forms of communication

Articles in scientific journals and newspapers typically feature contextual clues that serve to narrow down the contents of the article. Such aids include headings, abstracts, tables of contents, and key words. These frameworks constitute contentual invariances (symmetries) or a sort of guiding principle for what follows in the article, thus facilitating the reader's orientation.

As these examples show, the logic of EoS underlies all languages that use proper nouns, abstract concepts, complex figures of speech and the framing of longer textsthe EoS logic seems to provide the basis of semantics. Since the emergence of language marks a major cornerstone of cultural development, arguably the recognition of EoS potential constitutes a major driver not only of science but indeed of most cultural development.

EoS in information theory and data processing

Having shown that the EoS logic has a significant influence on the development of language, which is itself based on information and information transfer, it would be surprising if the EoS logic were not similarly importance in IT. The scope of that logic will be shown first with respect to information theory and then in the context of data processing.

Information Theory

In the 1960s, reflections on the compressibility of character strings yielded a little-known branch of information theory, for whom considerations about the shortenability of strings are central. This algorithmic information theory (AIT) was founded independently and almost simultaneously by [START_REF] Solomonoff | A Preliminary Report on a General Theory of Inductive Inference[END_REF], [START_REF] Kolmogorov | On Tables of Random Numbers[END_REF][START_REF] Chaitin | On the Length of Programs for Computing Finite Binary Sequences[END_REF]. The earlier example of the character string {1117w12; 408w7; 978w11} shall serve to introduce the core aims of the AIT. This entire string, consisting of repetitions of more than a thousand 12s and several hundred 7s and 11s (or almost two thousand 1s), could also be written as {12; 7; 1; P}, where P represents the program that contains the coded sequence of instructions as to how many times and in which order the three numbers are to be reproduced. While classical information theory measures the amount of information based on the length of the character string in binary notation, proponents of AIT would argue that in the above example, the amount of information consists in the three numbers plus the program (likewise in binary notation), presuming that this sum is lower than the amount of information of the original character string. 13 This AIT approach implicitly considers the EoS of the character string, just as was explicitly done above with respect to norms, language, natural laws, scientific models, etc. While the AIT tended to focus on non-compressible character strings and their random character, the present paper is more interested in the basis of compressibility and its implementation. In formulas, models, or abstract concepts, it was the EoS (e.g., in the form of common properties) that enabled a more compact description of a multitude of objects. Analogously, programs can only compress a character string if it contains some scope for EoS.

A program compresses or folds the detected symmetries by means of generalised multipliers such as loops, recursions, iterations, subroutines etc. The execution of such a program then amounts to the EoSbased reversal of the folding, i.e., the unfolding of the symmetries folded into the programa process that returns the original character string. The AIT algorithms can be interpreted as descriptions of the theoretical content of the strings because the symmetries encoded by the algorithms (the iterations, etc.) explain the achieved descriptive condensation. Furthermore, the symmetries represent newly recognized patterns that reveal new information. That information is generated by insights, rather than by decisions in the form of Bits & Bytes. This perspective of new insight-information leads to a new information category, which goes beyond economic concerns and is therefore discussed elsewhere (cf. Blaseio, 2021, Parts II and IV)

Data processing

Computer programs hold many more symmetry aspects than the above discussion on the AIT approach suggests. For the analysis, recall the earlier distinction between external and internal symmetries. External symmetries refer to the frequency of repetition of the task. There are at least three types: First, an obvious EoS benefit of programming is that a recurring task (symmetry!) can be performed time and again using the same programit is the symmetry of repeated processability over time without additional development effort. Second, an existing program can be copied at virtually no marginal cost this concerns the symmetry of spatially dispersed and possibly simultaneous (parallel) application. And third, through abstraction, e.g., by indexing, the program's scope of application can be extended. A sorting algorithm, for example, can proceed not only according to the alphabet, but equally based on size, date, etc. This multiplies the use of the program by opening up analogous fields of application (trans-contextual exterior symmetries).

In addition to these exterior symmetries, the implementation of algorithms in programs also holds great EoS potential in terms of interior symmetries. In many algorithms, certain instructions within the program must be executed many times (symmetry!). The documentation of a program with thousands or even millions of recurring processing steps would be prohibitively cumbersome if programmers had not devised shortcut ways by folding the repetitions. The execution can be programmed for example recursively or iteratively in loops, it can be repeatedly called in the form of subroutines or incorporated as a programming object. That way the program need not contain a dedicated instruction for every instance of a recurring action; instead, it can be folded at the mental symmetry axes between the repetitions. Incidentally, such interior symmetries are analogous to those that permitted the compaction of the character strings in the previous section. In sum, strategies such as these that capitalise on interior symmetries can achieve a dramatic reduction of program length and programming effort. Arguably, the entire development of programming paradigms can be interpreted as a sequence of strategies to manage repetitions of instructions in accordance with the EoS logic: from the initial goto statements to structured programming, which aims to avoid so-called spaghetti code, up to modern extensions such as objectoriented programming.

The examples of the working of EoS provided in this section could be extended to various other spheres of culture (with EoS in music for example offering particularly interesting aspects); however, this small selection should suffice to draw a conclusion regarding the potential future role of the EoS logic in economics and in the philosophy of science. According to the previous section, the exploitation of EoS is not only a scientific phenomenon with an economic logic but indeed one that spans much of human culture, being equally associated with the semantics of natural language and with the interpretation, analysis and processing of technical information. This pervasiveness suggests an inductive inference to a universal law that can make a significant contribution to understanding the nature of information 14 and the development of information-bearing systems of language, symbols and signals. It appears that, from the very beginning, EoS have been the decisive driver behind the evolution of competences regarding the use of language, symbols, and writing; perhaps they even constitute the causal motivation for all informational cultural development. If the theories and models that embody the EoS of today's insights are but the natural further development of the EoS contained in expressions of language such as abstracta and analogies, then languages offer a first, pre-scientific archive for such insights, even before the explicit passing on of new knowledge.

Conclusion

From the author's point of view, the empirical testing of the transdisciplinary EoS hypothesis is a joint task for economics and the philosophy of science. The task concerns economics because the explanatory model has an economic core, and it concerns the philosophy of science because the explanatory model explains the logic of explanatory models with generalising character, i.e., the type of models that constitute much of science. Besides the philosophy of science, similarly important with respect to cognitive results are related disciplines such as epistemology, AI, linguistics, etc.in other words, the cognitive sciences. Generally, economics is not considered to be part of this sector of science, and, from the EoS perspective, this is not just a major shortcoming but indeed counterproductive. So long as economics remains offside the cognitive sciences, the latter have difficulty accessing the economic techniques to model rational behaviour. On the other hand, economics will likely only devote more thought to the rationality of the quest for insights, i.e. to cognitive rationality, if it shares responsibility for the subject with the cognitive sciences. The same should apply to research into the rationality of the quest for innovation, for which insights are a prerequisite.

Extending the principle of rationality in economics

Some economists may hesitate to assign the quest for insights to the concept of rationality because the latter is historically associated with rational decision behaviour on the basis of the assumed relative utility of a set of known alternatives. Since a re-interpretation of the concept may be hard to accept, the rationality of the quest for insights in the sense of the creation and harnessing of EoS benefits shall be referred to not as cognitive rationality but rather as creationality. This coinage of a new concept shall serve to clearly distinguish the gain of new information in cognitive processes from the decision process that relies on already known information regarding available alternatives. If economics accepts this challenge of expanding its perspective and if it can simultaneously appreciate the creationality-driven emergence of new information as the engine of the economic dynamics, the discipline arguably deserves to become part of the cognitive sciences. While there is no cognitive economics as yet, this is precisely the challenge for the disciplineto embark on something entirely new, such as for economics to embrace rational cognitive behaviour (creationality) with the same vigour that it has been dedicating to rational decision behaviour. Such a reorientation would also create a stronger incentive for the philosophy of science to take into account economic thinking on rationality, or rather creationality.

Our demand for economics to transcend its accustomed methodological terrain is paradigmatic because, while both purposeful decision optimisation and cognitive effort represent rational (or creational) behaviour, the two spheres are of a fundamentally different nature. The standard economic principle of rationality addresses the rational behaviour of agents facing a choice of possibilities to reach their goals.

Agents are considered to behave rationally if they select the alternative that best serves their goals, i.e., that allows them to either minimise their effort to achieve a given output or to maximise output with a given amount of effort. Rational decisions yield the greatest benefitsbut only regarding the known alternatives. Such a notion of rationality is incomplete because it leaves no room for insights and innovation. the decision world offers for selection only known alternatives, which together constitute a decision space, creationality transcends the existing decision spaces by developing new alternatives. Thus, while decision theory can only operate within a given decision space, EoS-based creationality aims at an evolution of the decision spaces themselves. New insights and ideas are often superior to all existing alternatives because they were developed knowing those alternatives. To reiterate: Superior solutions or new insights trump optimal decisionsthis is the root of a superior market economy. It is the insights and ideas associated with new notions of symmetry, manifested in natural laws, formulas, norms, scientific models, abstract concepts, etc., as well as the resulting EoS benefits that together decisively determine cultural achievements and social welfare and whose consequences have led the way out of Schumpeter's caves. In the face of such impacts, cognitive effort should be considered at least as rational as rational decision behaviour based on a comparison of alternatives.

In addition to decision rationality, an extended economic logic or an extended model of homo economicus must also consider the creationality of creating knowledge, be it realised in the form of insights, intuition, ideas for proof, etc. For this purpose, the principle of rationality in the decision context should thus be supplemented with a second principle in the cognitive context, as outlined in the figure below. • Achievement of the maximum benefit with a given level of input (maximisation principle)

Decision Context

Rationality

• Achievement of a given benefit with the lowest level of input (budget principle)

• Documentation of a larger data volume at a given level of descriptive effort

• Documentation of a given data volume at lower descriptive effort The juxtaposition of the two principles of rationality shows them to be largely symmetric in structural terms. In the cognitive context, inputs are represented by descriptive cost, a major component of information cost. For example, a formula delivers the same output data as a stepwise calculation, but at much lower costs of information processing. Furthermore, instead of striving for an optimum, the aim in the cognitive context can only be to improve the ratio of output to input (data volume to descriptive effort) because of the inherent uncertainty as to whether further insights or ideas can yet be foundit is unknown where the optimum might be, or whether it even exists. All that can be expected is merely the symmetry characteristic associated with the EoS potential from (generalising) insights. As a further crucial difference between the two contexts, the improvement in the ratio of output to input is achieved not by decisions but by insights. Such an improvement materialises as informational benefits in the form of a gain in orientation or knowledge, faster communication, reduced complexity, more compact documentation, etc. While such benefits are initially purely of an information-economic nature, new information is a precondition for innovation and often triggers it. Thus, the information advantage can develop into an innovation with market potential, whose benefits, as in the case of an improved algorithm, may arise from reduced effort, or from improved margins, e.g. of a patented product or a predictable stock market pattern. The quest for insights is an expression of creationality, it builds upon empirical observations and mental projections alike, and it particularly also comprises norms, rules (of the game), the statement of axioms, etc. It is typically geared towards information-economic EoS benefits, which can usually be operationalised ex post. Since the resulting insights constitute an important and quite likely even the decisive precondition for innovations, taking them into account is a first step on a new and viable path towards a Schumpeterian development economics.

Integrating the EoS approach into economics

Instead of founding a new field called cognitive economics, the EoS approach might be integrated in two existing fields of economics: information economics and evolutionary economics. Information economics analyses the decision behaviour of actors under incomplete information, be it due to bounded rationality, the unavailability, or the asymmetric distribution of information. In particular, the field deals with the cost of procuring and offering information that is assumed to already exist somewhere, as opposed to information that has not yet been recognized or invented. Information economics for example discusses the influence that the limited access to information and the resulting costs have on the actors' decision behaviour. In this framework, information economics can accommodate neither innovations in the sense of the Schumpeterian demand for development economics nor new information from insights.

In contrast to information regarding known possibilities or alternatives, information that must yet be recognized cannot be bought on the market; it must be worked out. Accordingly, creationality refers to the (ex-ante) rationality of potential knowledge gains and their EoS using cognitive effort. These knowledge gains lay the ground for subsequent decisions, e.g., regarding the distribution or use of the new information. Thus, EoS potential from insights is not a result of rational decisionssomething that is not a known alternative cannot be the subject of a decision. From the reverse perspective, once the cognitive gain has been achieved and has opened up the access to superior solutions, as mentioned above, the decision whether to exploit that gain is often trivial: superior solutions trump optimal decisions.

Studies on the rationality of cognitive behaviour and on the EoS potential from insights could also form part of an extended evolutionary economics. The need for an extension is evident for example from a survey of the field by Hodson/Knudson (2010), which shows that evolutionary economics still follows the mechanistic-stochastic concept of evolution that it adopted from the natural sciences and that consists of the principles of random variation, selection, and information transfer (as an abstraction of inheritance). The first of these, random variation, is the reason why any attempt to transfer the evolution concept of the natural sciences to cultural evolution must fail: Progress based on insights cannot be explained by random variation because this presupposes a variation of known combinatorial alternatives. Although there is some awareness of the inadequacy of this notion of variation borrowed from the natural sciences (cf. Hodson/Knudson, 2010: 28f), economics has so far failed to develop a concept of novelty of its own that addresses the developing of new alternatives in the context of cultural evolution, rather than merely varying known alternatives. The natural science interpretation is admittedly tempting because it suggests that the principles of evolution can be mathematically modelled in the accustomed fashion as decision behaviour, i.e., in accordance with the predominant methodological paradigm of economics. Yet no mathematical procedure can produce new insights and ideas, otherwise everyone would try to get rich from it. This entanglement in formalism is what in Section 7 was referred to as self-imposed methodological cage. Crucially, a new insight or hypothesis marks the step from the known to the hitherto unknown, beyond the decision horizonthis also applies to ideas for mathematical proofs.

To appreciate the demand for a transcendence of mathematical modelling and natural science methodology in economics, which some may find outrageous, it helps to recall that the natural sciences on the one hand need not cope with an object area that is itself innovative and capable of insight, and that mathematics on the other hand is itself a result of, rather than the precondition for, scientific insights; in other words, mathematics itself is the result of the quest for abstract EoS potential. 15 Economics faces a much greater challenge than the natural sciences because the latter do not have to deal with the cognitive dynamics that constitute a core characteristic of the subject area of economics. This particular challenge is at the root of this paper's call for the economic discipline to go beyond the methodological principles it has borrowed from the natural sciences. The EoS approach introduced in this paper offers itself for such a paradigmatic step into new methodological territory.

:

  Consequences for economics and the philosophy of science 9.1 The role of economics in the philosophy of science and cognitive science

  decisions by means of insights (symmetry recognition)

Figure 4 :

 4 Figure 4: The extension of the economic principle in the context of knowledge

Notes

1 This shortcoming was also noted by preeminent information economist George J. Stigler in his Nobel lecture, observing that even Hayek "had not addressed the principles of acquisition of knowledge" (Stigler, 1982, 66). 2 For a more in-depth derivation of the concept of generalised symmetry, see the appendix in Blaseio (2021). 3 This was similarly observed for example by the mathematician George Polya (2010Polya ( [1949]]) with regard to analogical conclusions. For a more in-depth discussion, see Blaseio (2021: Part V). 4 Analogous examples also abound in the science of management: the Ansoff Matrix, the BCG Matrix, technical analysis of asset prices, etc. 5 The efficiency trade-off involved in the decision between abstract legal rules versus detailed guidelines has been discussed at length in the law and economics literature; see for example Schäfer (2006). 6 Note that these cognitive processes are closely associated with innovation. The primary and secondary benefits of a recognised or perceived regularity often prepare the ground for innovation as a tertiary consequence, e.g., the symmetrisation of freight handling through standard containers or the symmetrisation of the tracks as a prerequisite for the railway. 7 This interpretation, which is in stark contrast to Popper, who strongly rejected the "primacy of repetition" (Popper, 2014: 420) in his major work The Logic of Scientific Discovery, is discussed in depth in Blaseio (2021, Part III). 8 This is not a paradox because it lacks a negation. 9 The underlying symmetries are symbolised by the use of the terms equivalence, standardisation and repeatedly. 10 Regarding the derivation of definitions from similarities (a proxy for repetition or symmetry), cf. Aristotle (2014: Pos. 4975ff, [97b, 6ff], Pos. 5514-5517 [108b, 6ff]). 11 Initial but still ambiguous references to this are contained in the work of Locke (1993: 359). 12 Similarly Kant (1993: 197) "Every conception may be regarded as a point, which, as the standpoint of a spectator, has a certain horizon, which may be said to enclose a number of things that may be viewed, so to speak, from that centre." 13 Note that the amount of information of the program is as yet indeterminate because its length depends on the programming language used and any unknown symmetries in it that have not yet been exploited. 14 For a deeper information-theoretic analysis, cf. Blaseio (2021, Parts II and IV). 15 For more detail, cf. Blaseio (2021, Part V).