Charité: Johannes-Müller-Institut für Physiologie; Christoph Knoch
Charité: Johannes-Müller-Institut für Physiologie; Christoph Knoch
Charité: Johannes-Müller-Institut für Physiologie; Christoph Knoch

About us

Image Script Number. Founding Project for the Helmholtz Centre for Cultural Techniques

Theory and history of cultural techniques

The Helmholtz Centre focuses on the establishment of the concept of the cultural technique in history and theory. This concept draws on the interrelationship of image, script and number, a relationship investigated in an exemplary project by the »Image–Script–Number« research group (BSZ). 

The BSZ research group was funded by the German Research Foundation (DFG) from 2001 to 2007. The individual subprojects in the »Image–Script–Number« research group were led by university lecturers at the Humboldt-Universität, the Technische Universität Berlin and the Freie Universität Berlin.  It studied the theme of techné and culture in the shadow of the digital revolution – a revolution characterised by the extensive use of computers and open computer networks far beyond the domain of science.

The spectrum of research conducted by BSZ covers image, script and number as the essential media of modern communication – from their historical genesis to their current potency in digital coding, storage and processing. The individual topics examined range from counting and calendar techniques in Mesopotamian cultures, the origins of Greek geometry and the Greek alphabet, medieval forms of writing, symbols and counting, and early letterpress printing all the way through to hypertexts, the technical image, visual forms of argumentation and programmed modelling.

Inevitably, the field of image, script and number could not be covered in its entirety. Indeed the field per se is, in some respects, a definition of all cultural techniques. The group therefore drew on the extensive detailed accounts in various individual disciplines and concentrated on fractures and differences that lead – or led – to media transformations and transfers. Its work centred on a media-historical analysis on the one hand and the current process of digitalisation on the other. Put in general terms, it dealt with mathematically oriented symbol techniques and the turning points in their developments.

The term »cultural technique«, which describes the focus of work for the Helmholtz Centre, could therefore be defined more precisely – and its scope narrowed. It is not a question of producing an organically evolved picture of »culture«, let alone a comprehensive one, but rather of defining the essential elements at the points where they emerged and transformed. The objective is not to achieve a complete synopsis, but rather to precisely determine transfers of ideas, culture and technique – which includes intervening in current discussions within the sciences and humanities.



  • Representation as a Cultural Technique (Bredekamp, Schneider)
  • The Alphabetisation of Mathematics (Brüning, Meynen)
  • Showing and Referring (Brüning, Meynen)
  • Cultural Techniques: Instruments of Order (Cancik-Kirschbaum)
  • Image, Script, Number in the Turing Galaxy (Coy, Grassmuck)
  • Music and Mathematics (Kittler, v. Hilgers, Ofak)
  • From Script to Trace (Krämer, Grube, Kogge)
  • Cultural Techniques of Synchronisation (Macho, Hörl, Dennhardt)
  • Defining the Concept of the Model (Mahr, Wendler, Gulden)
  • Reading and Grasping the World (Wenzel, Münkner, Wedell)


  • »Stoicheia« (Brüning)
  • On the Interdependence of Image, Script and Number in the Calendar (Macho)
  • Reading and Grasping the World (Wenzel)
  • Representational Problems under Louis XIV (Bredekamp)
  • The Trigonometry of Image and Sound (Kittler)
  • »Notational Iconicity« (Krämer)
  • Arguing Visually (Coy)
  • The Digitalisation of Image, Script, Number and Sound (Mahr) 

Representation as a Cultural Technique. An Analysis of the Historical Formation of Representation Premised on the Image

Horst Bredekamp, Pablo Schneider

Despite all the historical changes in its forms and the theoretical explanations proposed for it, representation has remained a salient feature of the fabric of communication and its hierarchisation. Whilst the Enlightenment may have critically examined the concept, it also never fundamentally questioned it, and the same applies to 20th-century attempts to circumvent or discredit it through theories grounded in linguistics or discourse theory. The debate is still premised on a fundamental understanding that is essentially negative, one that interprets representation as a strategy for persuasion, and this has not furthered the analysis of the concept. The project seeks to take a different approach by focusing on representation in its function as a cultural technique defined by image theory in which the constructive possibilities are foregrounded so as to be able to understand the image in its productive dualism. For it was the combination of the support medium and the guiding of thought that enabled the structuring of representation and the formation of a cultural technique.

The early modern period provides an unexploited reservoir of potential given the interaction it witnessed between highly variable representational forms and correspondingly controversial debates, conducted on a fundamental level. In particular, the discrepancy between the »mysteries« of a system of sovereign rule and the findings in the natural sciences was expressed and stabilised in the image. A description was attempted in the productive dilemma but was never to be completed, primarily due to the image’s iconic characteristics. These characteristics include a fundamental aspect of representation per se that has yet to be understood in art history.

The Alphabetisation of Mathematics. Elements of the Cultural History of the Diagram

Jochen Brüning, Gloria Meynen

Deductive mathematics essentially owes its emergence to an innovation in the form of a cultural technique that combined letters and lines – the labelled diagram. Since the mid-fifth century BC, the labelled diagram has made it possible to translate numbers, letters and images into each other. This enables a technique of showing and referring that achieves an exemplary formalisation in Euclid’s »Elements«. Taking Euclid’s »Elements« as its case study, the project explores the media conditions of deductive mathematics. Its focus is the technique of referring in Euclidean diagrams and the implied relationships between image, script and number. Our central focus is the techniques of providing proof. Two aspects are therefore of interest:

1. Firstly, the surfaces used for writing and images in geometry. This is an aspect that Euclid’s »Elements« mask completely, just as they obscure the question of the materiality of mathematical proofs.

2. We assume that the materiality of image surfaces fundamentally determines the operations performed by the diagram. Therefore, the second focus of our investigations shifts from the media of the diagram to its tools: lines and letters.

The diagram combines elements of arithmetics and geometry. It is the product of manifold translation processes between Egyptian astronomy, the processes of geometrically sketching and setting out in Ionian temple construction and the Pythagoreans’ theory of music. The project is concerned with transfers between geometry and arithmetics. We believe that the emergence of the new cultural technique of the labelled diagram coincides with cultural and technological fractures.

Showing and Referring. The Diagram as a Cultural Technique

Jochen Brüning, Gloria Meynen

Project funded by the Fritz Thyssen Foundation

Deductive mathematics essentially owes its emergence to an innovation in the form of a cultural technique that combined letters and lines – the labelled diagram. Labelled diagrams first appear around 440 BC in the lunes used by Hippocrates of Chios to square the circle. Since the mid-fifth century BC, the labelled diagram has enabled numbers, letters and lines to be translated into each other, and visuality to be produced without images by recourse to letters. This new form of visuality is no longer purely based on vision and arithmetical knowledge, and it enables a technique of showing and referring that is closely linked to the earliest books in mathematical instruction, the format of Euclid’s »Elements« (Stoicheia).

This project studies the visual production of abstraction and ideality. Taking the cultural history of the process of providing mathematical proofs as our starting point, we will examine how deductive truth is produced on the image surfaces of geometry. The project therefore focuses on the relationship between visuality and imagelessness and on the question of how evidence and truth were able to become so evidently one of the functions of the image in deductive proofs.

Cultural Techniques: Instruments of Order. Investigations of the Written Records of the Ancient Near East

Eva Cancik-Kirschbaum

The records of the ancient Near East document in immensely diverse forms, developments and functions and over several millennia the cultural techniques from which phenomena such as »the image«, »script« and »number« are constituted. The success of these »media« in cultural history is based in no small part on their great capacity for ordering and their almost limitless compatibility. Taking three case studies of the cuneiform records from the ancient Near East, we will examine in depth the productive interdependence of these cultural techniques in different historical contexts. The three thematic groupings give an impression of the breadth of material from the ancient Near East. At the same time, they do justice to the diverse opportunities for access made possible by the project’s integration in the »Image-Script-Number« (BSZ) research group in the Helmholtz Centre. Our investigation of archaeological findings and discoveries from the ancient Near East – the majority of which is still in the initial process of being catalogued* and is hence difficult to access – will benefit from the research questions and theses developed in an interdisciplinary exchange. As historical examples of success, error and aporia, tradition, innovation and development in the fields of counting, illustrating, writing and measuring, they will expand the material foundation for work in the BSZ research group.

Image, Script, Number in the Turing Galaxy. On the Technical and Socio-Cultural Backgrounds of Intellectual Property under the Conditions of Multimedia Digitalisation and Global Networking

Wolfgang Coy, Volker Grassmuck

A radical change can currently be observed in how intellectual property is handled. German copyright law has been adapted to digital technologies on the basis of international standards. Patent law is causing controversies in the European Parliament and is on the cusp of a fundamental expansion. It is not only media corporations that are making far-reaching economic claims; the scientific community and the public have vested cultural interests in having access to, and being able to use, knowledge. These intense debates have been prompted by digitalisation and networking and the ensuing technical changes in the production, storage and distribution of multimedia artefacts. The established knowledge order is consequently undergoing a structural change that is fundamentally transforming cultural practices, economic relationships, technological trajectories and the political regulatory framework. Even basic terms such as »author«, »work« and »knowledge« are affected. It is therefore necessary to look not only into the legal and economic conditions of »digitised« intellectual property but into its technical foundations and its cultural traditions as well.

At the centre of the project is the question of balancing different demands: the moral and the economic interests of authors and inventors, the interest in exploitation of publishers and other parties, and those of the public at large. Based on specific issues, we will explore the field of »Image–Script–Number« in its cultural-technological aspects in order to disentangle the current debate on intellectual property from its narrow juridical and economical confines and to encourage a more open discussion on the path to the Turing Galaxy.

Music and Mathematics

Friedrich Kittler, Philip v. Hilgers, Ana Ofak

The aim of the »Image–Script–Number« research group was and is to study the three elementary cultural techniques of showing, writing and counting, examining their historical combinations and transformations in order to arrive at a cultural history from below.

As with Brüning’s subproject, it is therefore imperative to investigate the foundations of the European sciences in ancient Greece. It was Pythagoras of Samos and his students in Southern Italy who took the basic concepts of music theory (harmony, octave, interval) and created mathematics as a science of general laws. The conceptual pair even/odd made it possible to conceive consonance per se, in other words, without actual numbers. The science thereby emerged as a generally practised cultural technique in the form it still has today in schools, academies and universities.

Taking elementary cultural techniques as our starting point promises to generate new, synthesising findings because this approach enables interactions between image, script and number to be identified. According to a new thesis (Powell, 1991), the Greek alphabet itself, the first and only alphabetic script in history, appears to be the reason why singing and music became the object of a new kind of writing and counting. They both employed the same cultural technique because Greek numbers were a superset of the alphabet.

Conversely, geometry emerged as a scientific image of objects distinct from arithmetics from one of the fundamental Pythagorean discoveries, namely that not all intervals or geometric lines are rational. But when arithmetics and geometry in this complementarity of theirs seek to capture »what« essentially »is«, then image, script and number combine to form an ontology – for the first time, as far as I can see.

From Script to Trace
Reading Traces as a Cultural Technique in the Disputed Territory of Media Theory, Genetic Research and Computer Technology

Sybille Krämer, Gernot Grube, Werner Kogge

For centuries, cultural theoretical debate was characterised by a movement that identified culture with text or language ability. The »Image–Script–Number« research group developed an alternative to this text-based concept of culture by reconstructing historically differing techniques of handling non-linguistic symbolic systems (image, script, number) as cultural techniques and simultaneously reconstructing knowledge-generating and knowledge-transforming achievements. The objective of this new project is to conceptually refine and provide a theoretical underpinning for the prototype of the cultural technique: the trace and reading traces. The transition from the ‘Script Project’ (2001–2003) to the ‘Trace Project’ (2004–2006) entails three shifts in focus with respect to the previous research funding period:

1. Reading, like the trace, is preceded by writing; hence reading is a central element of the concept of the trace. But unlike script, the idea of the trace emphasises the pragmatic dimension of reading because it is only when read as a trace that a trace can be identified as such.

2. Simultaneously, reading traces go beyond the domain of human culture – here, too, in contrast to script – and is also relevant to biological processes, especially genetic processes. Can a bridge be found here between cultural techniques and biological processes, a bridge that not only undermines the distinction between literal and metaphorical meaning but also opens up productive analogies between cultural and biological/cellular scenarios?

3. The computer is not just a machine for transforming scripts and symbols: it is also a visualisation machine, and this is becoming increasingly important epistemologically. What the computer »puts in the picture« also includes traces of that which fundamentally escapes our perception (e.g. nanotechnology). When computers read traces, »epistemic objects« – in other words, knowledge objects – are not merely visualised; they are simultaneously also generated.

By conceptually explicating the diverse processes of reading traces, the project aims to define the cultural technique of reading in such a way as to disentangle the equation of reading with »reading text« and to allow the non-hermeneutic dimensions of reading (etymology: »reading« as »gathering«, »catching«) to come to the fore.

Cultural Techniques of Synchronisation

Thomas Macho, Erich Hörl, Robert Dennhardt

The objective of this project is to conduct an exemplary study of the interdependencies and interactions between image, script and number in the cultural techniques of synchronisation. Our analysis will centre on historical shifts in the weighting of, and interferences between, the techniques of calculating time and measuring time. In the first application, the calendar was our central focus as a specific cultural technique for synchronising. Our objective now is to study in greater depth the perspectives on, and the conception of problems in, temporal synchronisation in the modern period. These were issues that emerged increasingly after the Gregorian Reform of 1582.

In order to be able to precisely describe the spectrum of shifts and interferences between calculating and measuring time in synchronisation techniques, we will select and examine three key examples of synchronisation that are typical of their period, with our focus being their visualisation strategies in images, texts and mathematical operations. These examples are (1) the cultural techniques of synchronising lunar and solar cycles in ancient advanced civilisations, primarily in relation to the establishment of binding solar calendar systems (here the keyword is »solarisation«); (2) the cultural techniques of synchronising cyclical and linear systems of calculating time, in other words, the whole problem of calculating long periods in the calendar systems of late antiquity to the early modern period (keyword: »the long year«); and (3) the cultural techniques of synchronisation in the modern period. Here we will focus on instrument-based techniques for synchronising processes and recordings of these processes, from phototelegraphy to computer clocking (keyword: »self-recording devices«). 

Defining the Concept of the Model

Bernd Mahr, Reinhard Wendler, Jens Gulden

The project seeks to pursue the hypothesis developed in our earlier work, namely that it is possible to reach a unified concept of the model. Our objective is to contribute to defining the concept of the model. Working collaboratively as three subprojects, we will (1) develop the foundations of a general theory of the model, based on a conceptual analysis and classification of the factual relationships that constitute the essence of models; (2) study the phenomenon of restructuring and rendering understandable through models in investigations into hierarchical structures grounded in cultural history and image theory; and (3) determine the conditions and techniques for a formal discipline and heuristics of modelling by studying diagrammatic forms of representation. Based on this work and studies of selected historical and contemporary examples, we will seek to identify forms of model development and use in prototypical, pragmatic contexts and to explore the question of whether models can be conceived as a fundamental cultural technique for abstracting and transferring. Our project work will centre on the orders and grids that make up the architecture of many models in the form of divisions, classifications, hierarchies, steps, trees, grids, matrices, triangulations and multidimensional grids. In this it follows the history of the concept of the model.

Reading and Grasping the World
Hand and Word – Hand and Techné

Horst Wenzel, Jörn Münkner, Moritz Wedell

In the initial funding period, we succeeded in providing an account of the representation of the hand in times of radical media changes, examining the transformation of the conceptual and semantic relationship of counting and telling, and in explaining the linking of hand, text, image and number as an early form of technologically mediated audiovisuality. In the second application for funding, the project aims to focus on a new question. The project leader will examine the connection between hand-writing and hand-work (poiésis and techné), primarily based on hand gestures in secular and religious textual and image evidence from the Middle Ages and early modern period. The focus of our enquiries is now on the actions/handlings/hand-usages manifested in both text and image, whilst the distribution of the word and its technical visualisation (using image, script and number) will be our fundamental research topic. With its two subproject work areas (UP I: »Accessing by Hand and Technical Showing in Illustrated Pamphlets«, Jörn Münkner; UP II: »Religious and Secular Manipulations of Numbers: Speaking – Writing – Counting«, Moritz Wedell), the project aims to contribute to a history of the cultural techniques of reading, telling/counting and showing/pointing out.

Image, Script and Number in the Tradition of Euclid’s »Elements«

Jochen Brüning

The tension between image, script and number is clearly of immense importance to cultural history, even if it appears to be as difficult to define the concept precisely as it is to formulate general laws for their interaction. A promising field of study must therefore be delimited sufficiently clearly and present a sufficiently long and significant development in which all three of the media under examination played an important role.

Euclid’s »Elements« and the history of its reception meet these criteria exceptionally well. Given the text’s age and the extent to which it is known, it is clear that only a few others could rival it; its technical nature, however, considerably limits its field of influence, at least on initial examination. The first parts of the work are formed of script and numbers, both of which are written in the same character set. They are joined by the image as the indispensable support in the abstract reflections, but from the outset, as befits the programme set out in the title, the images are composed of »elements«: the »point«, »straight line«, »triangle«, etc. Image, script and number are therefore similarly essential in constituting and communicating the work’s substantive content, yet their individual roles have been subject to diverse changes over the course of time. The large number of »proofs« supplied by the various editors can be seen as a special index of this interaction. To date, they have received scarcely any attention.

In order to analyse this cultural historical process, it is very helpful that the corpus of the »Elements« has remained largely stable over the course of its more than two-thousand-year history so that differences in the value placed on its constituent parts and their organisation are relatively easily identifiable. The proposed project seeks to explore the specific interactions of image, script and number in the presentation, reception and influence of Euclid’s »Elements«. We are particularly interested in the extent to which demonstrable phenomena are characteristic for the overall development of mathematics as this is the field where the most direct influences are to be expected, given the nature of the »Elements«. With this as our starting point, the study can be expanded to include cultural historical developments of a more general character.

On the Interdependence of Image, Script and Number in the Calendar

Thomas Macho

This project aims to conduct exemplary research into and to present the cultural history of the calendar from the perspective of the integration of image, script and number. One initial focus of our project work will be on the relationship between astronomy and geometry (in ancient Greece), and ancient Roman activities in calendar politics (primarily after the Julian calendar reform). The second area of enquiry will be the transition from late medieval computus to the astronomical visual language of the Renaissance; the third focus will be the problem of alternative, future calendar systems, a question primarily associated today with the »Y2K« debate. Our overall objective is to document the drivers of calendar calculation in scientific and cultural history as exemplified by selected examples from the past and present day.

Reading and Grasping the World
Image, Script and Number in the Tension between Bodily Memory and Written Memory

Horst Wenzel

Medieval manuscripts and early modern prints contain manifold combinations of the written word, image and number that refer back to the hand of God. At the same time, they are manifestations of the advanced (mnemo)techniques in a culture where scriptural and oral memory coexisted (scriptorality): the relationship between »counting« and »telling« (recall that »tell« can also mean to »count«, »enumerate«), the indexical, correlative juxtaposition of text and image. The planned project will seek to present the hand and number as the operators of mnemonics and to examine the »hidden« number in text and number. The aim is to demonstrate how the numerical connection of text and image foreshadows technologically mediated audiovisuality.

Representational Problems under Louis XIV
André Félibien versus Thomas Hobbes

Horst Bredekamp

The sovereign, usually portrayed in personalised form until the French Revolution, has been examined by political iconography with reference to many aspects of motifs and in many forms of media. The principles of the functioning and the iconographic pattern are regarded as extensively researched; however, mathematics has not been considered in this context. Based on an exemplary research design, this project aims to explore the role of mathematics in the representation of the sovereign.

It will address the founding of the modern theory of the state by Thomas Hobbes (1651) and the controversial debate over the course of the following two centuries on the representation of the sovereign. At its core is the conflict between a political science based on mathematics, as expounded by Hobbes in »Leviathan«, and an image of the sovereign grounded in metaphysics, as propounded by André Félibien, chronicler of the arts and culture under Louis XIV, in »Portrait du Roy« (1663).

The Trigonometry of Image and Sound 

Friedrich Kittler

In the context of the research project as a whole, a study that includes sounds and their digitalisation, as well as images and their digitalisation, is an exception because sound has never acted as a media of science, unlike the image, script and number. However, there are two reasons why the technological histories of linear perspective and tempered musical frequency should be seen as running strictly parallel to each other. Firstly, the distinction between them disappears under the technical universality of digital signals processing in computerised conditions; secondly, modern mathematics formalised optical phenomena with the same trigonometry as that applied to musical waves. This subproject is interested in this very relationship between an essential mathematicalisation, which resulted in a distinction between the arts in European modernity and those in other cultures, and a modern technicisation that has succeeded in converting these arts firstly into analogue media and ultimately into digital media. Drawing on this distinction, we can hypothesise as to the reasons for this fundamental separation, which since Kant has juxtaposed a philosophical aesthetics of linguistic exegesis with a physical aesthetics of measurement. Such a hypothesis could, by negative reasoning, contribute to bridging the gap between mathematics, computer science and cultural studies.

»Notational Iconicity« 
On the Potential in the Visuality of Texts as a Cultural Technique and Theory of Reading

Sybille Krämer

It is a truism in the humanities that how we handle symbols follows the pattern of the bifurcation of language and image. This division between the discursive and the iconic considers script as language and not as an image. This project seeks to develop a fundamental theory and to revise this language-centred concept of script. Put simply, our aim is to disentangle reflections on script from the influence of its origins in the oral/written debate. We shall achieve this by (1) rehabilitating a fundamental visual-iconic dimension in script, which we call »notational iconicity«. This is a dimension that both the representational potential of script and text make use of. What this potential represents becomes clear when script is examined in its function as a cultural technique. The cognitive and communicative role of notational iconicity manifests itself in the cultural technique of reading. The visually accessible surface of texts, their texture, can be seen as the score in reading performance. For this reason, we will (2) investigate how the conditions of notational iconicity change in electronic hypertext in relation to the classic text.

Arguing Visually. The Creation and Logic of Scientific/Technical Graphics and Images under the Conditions of Digital Production 

Wolfgang Coy

This project examines images (as opposed to texts) as a medium of technical/scientific communication. Our research will focus in particular on the logic and argumentative power of visual images – by this we mean graphical, schematic images but also images produced by sensors and computed images – in the natural and engineering sciences. Based on historical graphical and visual representational techniques (primarily the images in Diderot’s Encyclopedia), we will analyse technical images, ranging from graphics to analogue (autographic) imaging processes to computerised, digital imaging processes. We consider these to be essential argumentative tools in modern engineering disciplines and the natural sciences, and will compare them to text-based logics. The use of programmed processes in the analysis of complex sensor data is giving rise to new forms of argumentation (in medicine, the natural sciences and engineering). This is challenging both the written form of logic in the sciences and its definition as a formal logic in mathematics and the natural and engineering sciences; indeed, it even goes as far as to challenge Sir Karl Popper’s »Logic of the Social Sciences« and the theory of science. Based on new developments in image generation in computer science, we will present and analyse these transformations from a transdisciplinary perspective.

The Digitalisation of Image, Script, Number and Sound. Their Conceptualisation and Cultural Context

Bernd Mahr

Image, script, number and sound are the media of our daily communication and media we use every day. Their conventionalised use is a constituent part of our culture and science. With their digitalisation and automatic processing in information technology and telecommunications, image, script, number and sound are being reduced to that which is symbolically representable and effectively executable. This reduction encompasses how they are conceptualised, which is in essence subject to two influences: firstly, a particular conception of what they are and, secondly, a particular conception of what they should be in the context of their digitalised form. Digitalisation is thus placed in a cultural context that is instrumental in determining this conceptualisation on the one hand and is itself shaped by the same conceptualisation on the other. Statements about the cultural context of digitalisation are therefore impredicative.

Based on a reference model, this project aims to formulate the conceptual framework for the conceptualisations of image, script, number and tone inherent in digitalisation. The development of such a model requires insights into the cultural interdependence of digitalisation, an exploration of the profit and loss arising through digitalisation, an account of the relationships between image, script, number and sound, and a contribution to the theoretical debate in cultural studies. We expect the model to be capable of being applied practically as a heuristics for the documentation of collections using information technology.

Horst Bredekamp
Interdisciplinary Laboratory Director, Executive Board Principal Investigators
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Interdisciplinary Laboratory Principal Investigators
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Interdisciplinary Laboratory Principal Investigators
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Horst Wenzel
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Friedrich Kittler
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