📦Data Migrations (DM): Conceptualization (Part III: Heuristics)

Probably one of the most difficult things to learn as a technical person is using the right technology for a given purpose, this mainly because one’s inclined using the tools one knows best. Moreover, technologies’ overlapping makes the task more and more challenging, the difference between competing technologies often residing in the details. Thus, identifying the gaps resumes in understanding the details of the problem(s) or need(s), respectively the advantages or disadvantages of a technology over the other. This is true especially about competing technologies, including the ones that replace other technologies.

There are simple heuristics, that can allow approaching such challenges. For example, heavy data processing belongs usually in databases, while import/export functionality belongs in an ETL tool.  Therefore, one can start looking at the problems from these two perspectives. Would the solution benefit from these two approaches or are there more appropriate technologies (e.g. data streaming, ELT, non-relational databases)? How much effort would involve building the solution? 

Commercial Off-The-Shelf (COTS) tools provided by third-party vendors usually offer specialized functionality in each area. Gartner and Forrester provide regular analyses of the main players in the important areas, analyses which can be used in theory as basis for further research. Even if COTS tend to be more expensive and can have some important functionality gaps, as long they are extensible, they can prove a good starting point for developing a solution. 

Sometimes it helps researching on the web what other people or organizations did, how they approached the same aspects, what technologies, techniques and best practices they used to overcome the challenges. One doesn’t need to reinvent the wheel even if it’s sometimes fun to do so. Moreover, a few hours of research can give one a basis of useful information and a better understanding over the work ahead.

On the other side sometimes it’s advisable to use the tools one knows best, however this can lead also to unusable and less performant solutions. For example, MS Excel and Access have been for years the tools of choice for building personal solutions that later grew into maintenance nightmares for the IT team. Ideally, they can still be used for data entry or data cleaning, though building solutions exclusively based on (one of) them can prove to be far than optimal. 

When one doesn’t know whether a technology or mix of technologies can be used to provide a solution, it’s recommended to start a proof-of-concept (PoC) that would allow addressing most important aspects of the needed solution. One can start small by focusing on the minimal functionality needed to check the main aspects and evolve the PoC during several iterations as needed.

For example, in the case of a Data Migration (DM) this would involve building the data extraction layer for an entity, implement several data transformations based on the defined mappings, consider building a few integrity rules for validation, respectively attempt importing the data into the target system. Once this accomplished, one can start increasing the volume of data to check how the solution behaves under stress. The volume of data can be increased incrementally or by considering all the data available. 

As soon the skeleton was built one can consider all the mappings, respectively add several entities to build the dependencies existing between them and other functionality. The prototype might not address all the requirements from the beginning, therefore consider the problems as they arise. For example, if the volume of data seems to cause problems then attempt splitting the data during processing in batches or considering specific optimization techniques like indexing or scaling techniques like increasing computing resources. 

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🔭Data Science: Mathematical Models (Just the Quotes)

"Experience teaches that one will be led to new discoveries almost exclusively by means of special mechanical models." (Ludwig Boltzmann, "Lectures on Gas Theory", 1896)

"If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming."  (George Dantzig, "Linear Programming and Extensions", 1959)

“In fact, the construction of mathematical models for various fragments of the real world, which is the most essential business of the applied mathematician, is nothing but an exercise in axiomatics.” (Marshall Stone, cca 1960)

"[...] sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work - that is, correctly to describe phenomena from a reasonably wide area. Furthermore, it must satisfy certain aesthetic criteria - that is, in relation to how much it describes, it must be rather simple.” (John von Neumann, “Method in the physical sciences”, 1961)

“Mathematical statistics provides an exceptionally clear example of the relationship between mathematics and the external world. The external world provides the experimentally measured distribution curve; mathematics provides the equation (the mathematical model) that corresponds to the empirical curve. The statistician may be guided by a thought experiment in finding the corresponding equation.” (Marshall J Walker, “The Nature of Scientific Thought”, 1963)

"Thus, the construction of a mathematical model consisting of certain basic equations of a process is not yet sufficient for effecting optimal control. The mathematical model must also provide for the effects of random factors, the ability to react to unforeseen variations and ensure good control despite errors and inaccuracies." (Yakov Khurgin, "Did You Say Mathematics?", 1974)

"A mathematical model is any complete and consistent set of mathematical equations which are designed to correspond to some other entity, its prototype. The prototype may be a physical, biological, social, psychological or conceptual entity, perhaps even another mathematical model." (Rutherford Aris, "Mathematical Modelling", 1978)

"Mathematical model making is an art. If the model is too small, a great deal of analysis and numerical solution can be done, but the results, in general, can be meaningless. If the model is too large, neither analysis nor numerical solution can be carried out, the interpretation of the results is in any case very difficult, and there is great difficulty in obtaining the numerical values of the parameters needed for numerical results." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)

“Theoretical scientists, inching away from the safe and known, skirting the point of no return, confront nature with a free invention of the intellect. They strip the discovery down and wire it into place in the form of mathematical models or other abstractions that define the perceived relation exactly. The now-naked idea is scrutinized with as much coldness and outward lack of pity as the naturally warm human heart can muster. They try to put it to use, devising experiments or field observations to test its claims. By the rules of scientific procedure it is then either discarded or temporarily sustained. Either way, the central theory encompassing it grows. If the abstractions survive they generate new knowledge from which further exploratory trips of the mind can be planned. Through the repeated alternation between flights of the imagination and the accretion of hard data, a mutual agreement on the workings of the world is written, in the form of natural law.” (Edward O Wilson, “Biophilia”, 1984)

“The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?” (Stephen Hawking, "A Brief History of Time", 1988)

“Mathematical modeling is about rules - the rules of reality. What distinguishes a mathematical model from, say, a poem, a song, a portrait or any other kind of ‘model’, is that the mathematical model is an image or picture of reality painted with logical symbols instead of with words, sounds or watercolors.” (John L Casti, "Reality Rules, The Fundamentals", 1992)

“Pedantry and sectarianism aside, the aim of theoretical physics is to construct mathematical models such as to enable us, from the use of knowledge gathered in a few observations, to predict by logical processes the outcomes in many other circumstances. Any logically sound theory satisfying this condition is a good theory, whether or not it be derived from ‘ultimate’ or ‘fundamental’ truth.” (Clifford Truesdell & Walter Noll, “The Non-Linear Field Theories of Mechanics” 2nd Ed., 1992)

"Nature behaves in ways that look mathematical, but nature is not the same as mathematics. Every mathematical model makes simplifying assumptions; its conclusions are only as valid as those assumptions. The assumption of perfect symmetry is excellent as a technique for deducing the conditions under which symmetry-breaking is going to occur, the general form of the result, and the range of possible behaviour. To deduce exactly which effect is selected from this range in a practical situation, we have to know which imperfections are present." (Ian Stewart & Martin Golubitsky, "Fearful Symmetry", 1992)

“A model is an imitation of reality and a mathematical model is a particular form of representation. We should never forget this and get so distracted by the model that we forget the real application which is driving the modelling. In the process of model building we are translating our real world problem into an equivalent mathematical problem which we solve and then attempt to interpret. We do this to gain insight into the original real world situation or to use the model for control, optimization or possibly safety studies." (Ian T Cameron & Katalin Hangos, “Process Modelling and Model Analysis”, 2001)

"Formulation of a mathematical model is the first step in the process of analyzing the behaviour of any real system. However, to produce a useful model, one must first adopt a set of simplifying assumptions which have to be relevant in relation to the physical features of the system to be modelled and to the specific information one is interested in. Thus, the aim of modelling is to produce an idealized description of reality, which is both expressible in a tractable mathematical form and sufficiently close to reality as far as the physical mechanisms of interest are concerned." (Francois Axisa, "Discrete Systems" Vol. I, 2001)

"[…] interval mathematics and fuzzy logic together can provide a promising alternative to mathematical modeling for many physical systems that are too vague or too complicated to be described by simple and crisp mathematical formulas or equations. When interval mathematics and fuzzy logic are employed, the interval of confidence and the fuzzy membership functions are used as approximation measures, leading to the so-called fuzzy systems modeling." (Guanrong Chen & Trung Tat Pham, "Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems", 2001)

"Modeling, in a general sense, refers to the establishment of a description of a system (a plant, a process, etc.) in mathematical terms, which characterizes the input-output behavior of the underlying system. To describe a physical system […] we have to use a mathematical formula or equation that can represent the system both qualitatively and quantitatively. Such a formulation is a mathematical representation, called a mathematical model, of the physical system." (Guanrong Chen & Trung Tat Pham, "Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems", 2001)

“What is a mathematical model? One basic answer is that it is the formulation in mathematical terms of the assumptions and their consequences believed to underlie a particular ‘real world’ problem. The aim of mathematical modeling is the practical application of mathematics to help unravel the underlying mechanisms involved in, for example, economic, physical, biological, or other systems and processes.” (John A Adam, “Mathematics in Nature”, 2003)

“Mathematical modeling is as much ‘art’ as ‘science’: it requires the practitioner to (i) identify a so-called ‘real world’ problem (whatever the context may be); (ii) formulate it in mathematical terms (the ‘word problem’ so beloved of undergraduates); (iii) solve the problem thus formulated (if possible; perhaps approximate solutions will suffice, especially if the complete problem is intractable); and (iv) interpret the solution in the context of the original problem.” (John A Adam, “Mathematics in Nature”, 2003)

“Mathematical modeling is the application of mathematics to describe real-world problems and investigating important questions that arise from it.” (Sandip Banerjee, “Mathematical Modeling: Models, Analysis and Applications”, 2014)

“A mathematical model is a mathematical description (often by means of a function or an equation) of a real-world phenomenon such as the size of a population, the demand for a product, the speed of a falling object, the concentration of a product in a chemical reaction, the life expectancy of a person at birth, or the cost of emission reductions. The purpose of the model is to understand the phenomenon and perhaps to make predictions about future behavior. [...] A mathematical model is never a completely accurate representation of a physical situation - it is an idealization." (James Stewart, “Calculus: Early Transcedentals” 8th Ed., 2016)

"Machine learning is about making computers learn and perform tasks better based on past historical data. Learning is always based on observations from the data available. The emphasis is on making computers build mathematical models based on that learning and perform tasks automatically without the intervention of humans." (Umesh R Hodeghatta & Umesha Nayak, "Business Analytics Using R: A Practical Approach", 2017)

"Mathematical modeling is the modern version of both applied mathematics and theoretical physics. In earlier times, one proposed not a model but a theory. By talking today of a model rather than a theory, one acknowledges that the way one studies the phenomenon is not unique; it could also be studied other ways. One's model need not claim to be unique or final. It merits consideration if it provides an insight that isn't better provided by some other model." (Reuben Hersh, ”Mathematics as an Empirical Phenomenon, Subject to Modeling”, 2017)

🔬Data Science: Mathematical Model (Definitions)

"A mathematical model is any complete and consistent set of mathematical equations which are designed to correspond to some other entity, its prototype. The prototype may be a physical, biological, social, psychological or conceptual entity, perhaps even another mathematical model."  (Rutherford Aris, "Mathematical Modelling", 1978)

"The identification and selection of important descriptor variables to be used within an equation or process that can generate useful predictions." (Glenn J Myatt, "Making Sense of Data: A Practical Guide to Exploratory Data Analysis and Data Mining", 2006)

"Mathematical model is an abstract model that describes a problem, environment, or system using a mathematical language." (Giusseppi Forgionne & Stephen Russell, "Unambiguous Goal Seeking Through Mathematical Modeling", 2008)

"A set of equations, usually ordinary differential equations, the solution of which gives the time course behaviour of a dynamical system." (Peter Wellstead et al, "Systems and Control Theory for Medical Systems Biology", 2009)

"An abstract model that uses mathematical language to describe the behaviour of a system. Mathematical models are used particularly in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social sciences (such as economics, sociology and political science). It can be defined as the representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form." (Roberta Alfieri & Luciano Milanesi, "Multi-Level Data Integration and Data Mining in Systems Biology", Handbook of Research on Systems Biology Applications in Medicine, 2009)

"Mathematical description of a physical system. In the framework of this work mathematical models pursue the descriptions of mechanisms underlying stuttering, putting emphasis in the dynamics of neuronal regions involved in the disorder." (Manuel Prado-Velasco & Carlos Fernández-Peruchena "An Advanced Concept of Altered Auditory Feedback as a Prosthesis-Therapy for Stuttering Founded on a Non-Speech Etiologic Paradigm", 2011)

"Simplified description of a real world system in mathematical terms, e. g., by means of differential equations or other suitable mathematical structures." (Benedetto Piccoli, Andrea Tosin, "Vehicular Traffic: A Review of Continuum Mathematical Models" [Mathematics of Complexity and Dynamical Systems, 2012])

"Stated loosely, models are simplified, idealized and approximate representations of the structure, mechanism and behavior of real-world systems. From the standpoint of set-theoretic model theory, a mathematical model of a target system is specified by a nonempty set - called the model’s domain, endowed with some operations and relations, delineated by suitable axioms and intended empirical interpretation." (Zoltan Domotor, "Mathematical Models in Philosophy of Science" [Mathematics of Complexity and Dynamical Systems, 2012])

"The standard view among most theoretical physicists, engineers and economists is that mathematical models are syntactic (linguistic) items, identified with particular systems of equations or relational statements. From this perspective, the process of solving a designated system of (algebraic, difference, differential, stochastic, etc.) equations of the target system, and interpreting the particular solutions directly in the context of predictions and explanations are primary, while the mathematical structures of associated state and orbit spaces, and quantity algebras – although conceptually important, are secondary." (Zoltan Domotor, "Mathematical Models in Philosophy of Science" [Mathematics of Complexity and Dynamical Systems, 2012])

"They are a set of mathematical equations that explain the behaviour of the system under various operating conditions, and determine the dominant factors that govern the rules of the process. Mathematical modeling is also associated with data collection, data interpretation, parameter estimation, optimization, and provide tools for identifying possible approaches to control and for assessing the potential impact of different intervention measures." (Eldon R Rene et al, "ANNs for Identifying Shock Loads in Continuously Operated Biofilters", 2012)

"An abstract representation of the real-world system using mathematical concepts." (R Sridharan & Vinay V Panicker, "Ant Colony Algorithm for Two Stage Supply Chain", 2014)

"Is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling. Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models. A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour." (M T Benmessaoud et al, "Modeling and Simulation of a Stand-Alone Hydrogen Photovoltaic Fuel Cell Hybrid System", 2014)

"A mathematical model is a model built using the language and tools of mathematics. A mathematical model is often constructed with the aim to provide predictions on the future ‘state’ of a phenomenon or a system." (Crescenzio Gallo, "Artificial Neural Networks Tutorial", 2015)

"A mathematical model consists of an equation or a set of equations belonging to a certain class of mathematical models to describe the dynamic behavior of the corresponding system. The parameters involved in this mathematical model are related to a certain mathematical structure. This mathematical model is characterized by its class, its structure and its parameters." (Houda Salhi & Samira Kamoun, "State and Parametric Estimation of Nonlinear Systems Described by Wiener Sate-Space Mathematical Models", 2015)

"Description of a system using mathematical concepts and language." (Tomaž Kramberger, "A Contribution to Better Organized Winter Road Maintenance by Integrating the Model in a Geographic Information System", 2015)

"A description of a system using mathematical concepts and language." (Corrado Falcolini, "Algorithms for Geometrical Models in Borromini's San Carlino alle Quattro Fontane", 2016)

"A mathematical model is a mathematical description (often by means of a function or an equation) of a real-world phenomenon such as the size of a population, the demand for a product, the speed of a falling object, the concentration of a product in a chemical reaction, the life expectancy of a person at birth, or the cost of emission reductions. The purpose of the model is to understand the phenomenon and perhaps to make predictions about future behavior. [...] A mathematical model is never a completely accurate representation of a physical situation - it is an idealization." (James Stewart, "Calculus: Early Transcedentals" 8th Ed., 2016)

"Mathematical representation of a system to describe the behavior of certain variables for an indeterminate time." (Sergio S Juárez-Gutiérrez et al, "Temperature Modeling of a Greenhouse Environment", 2016)

"A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (e.g., computer science, artificial intelligence), but also in the social sciences (such as economics, psychology, sociology, and political science); physicists, engineers, statisticians, operations research analysts, and economists use mathematical models most extensively. A model may help to explain a system and to study the effects of different components, and to make predictions about behavior." (Addepalli V N Krishna & M Balamurugan, "Security Mechanisms in Cloud Computing-Based Big Data", 2019)

"A description of a system using mathematical symbols." (José I Gomar-Madriz et al, "An Analysis of the Traveling Speed in the Traveling Hoist Scheduling Problem for Electroplating Processes", 2020)

"An abstract mathematical representation of a process, device, or concept; it uses a number of variables to represent inputs, outputs and internal states, and sets of equations and inequalities to describe their interaction." (Alisher F Narynbaev, "Selection of an Information Source and Methodology for Calculating Solar Resources of the Kyrgyz Republic", 2020)

🏗️Software Engineering: Prototyping (Just the Quotes)

"The classical vertical arrangement for project management is characterized by an inherent self-sufficiency of operation. It has within its structure all the necessary specialized skills to provide complete engineering capabilities and it also has the ability to carry on its own laboratory investigations, preparation of drawings, and model or prototype manufacture. (Penton Publishing Company, Automation Vol 2, 1955)

"A mathematical model is any complete and consistent set of mathematical equations which are designed to correspond to some other entity, its prototype. The prototype may be a physical, biological, social, psychological or conceptual entity, perhaps even another mathematical model." (Rutherford Aris, "Mathematical Modelling", 1978)

"Economic principles underlie the overall structure of the software lifecycle, and its primary refinements of prototyping, incremental development, and advancemanship. The primary economic driver of the life-cycle structure is the significantly increasing cost of making a software change or fixing a software problem, as a function of the phase in which the change or fix is made." (Barry Boehm, "Software Engineering Economics", 1981)

"A problem with this 'waterfall' approach is that there will then be no user interface to test with real users until this last possible moment, since the 'intermediate work products' do not explicitly separate out the user interface in a prototype with which users can interact. Experience also shows that it is not possible to involve the users in the design process by showing them abstract specifications documents, since they will not understand them nearly as well as concrete prototypes." (Jakob Nielsen, "Usability Engineering", 1993)

"One should not start full-scale implementation efforts based on early user interface designs. Instead, early usability evaluation can be based on prototypes of the final systems that can be developed much faster and much more cheaply, and which can thus be changed many times until a better understanding of the user interface design has been achieved." (Jakob Nielsen, "Usability Engineering", 1993)

"Scenarios are an especially cheap kind of prototype. […] Scenarios are the ultimate reduction of both the level of functionality and of the number of features: They can only simulate the user interface as long as a test user follows a previously planned path. […] Scenarios are the ultimate minimalist prototype in that they describe a single interaction session without any flexibility for the user. As such, they combine the limitations of both horizontal prototypes (users cannot interact with real data) and vertical prototypes (users cannot move freely through the system)." (Jakob Nielsen, "Usability Engineering", 1993)

"The entire idea behind prototyping is to cut down on the complexity of implementation by eliminating parts of the full system. Horizontal prototypes reduce the level of functionality and result in a user interface surface layer, while vertical prototypes reduce the number of features and implement the full functionality of those chosen (i.e., we get a part of the system to play with)." (Jakob Nielsen, "Usability Engineering", 1993)

"The entire idea behind prototyping is to save on the time and cost to develop something that can be tested with real users. These savings can only be achieved by somehow reducing the prototype compared with the full system: either cutting down on the number of features in the prototype or reducing the level of functionality of the features such that they seem to work but do not actually do anything." (Jakob Nielsen, "Usability Engineering", 1993)

"Although it might seem as though frittering away valuable time on sketches and models and simulations will slow work down, prototyping generates results faster." (Tim Brown, "Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation", 2009)

"Just as it can accelerate the pace of a project, prototyping allows the exploration of many ideas in parallel. Early prototypes should be fast, rough, and cheap. The greater the investment in an idea, the more committed one becomes to it. Overinvestment in a refined prototype has two undesirable consequences: First, a mediocre idea may go too far toward realization - or even, in the worst case, all the way. Second, the prototyping process itself creates the opportunity to discover new and better ideas at minimal cost." (Tim Brown, "Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation", 2009)

"Prototypes should command only as much time, effort, and investment as is necessary to generate useful feedback and drive an idea forward. The greater the complexity and expense, the more 'finished' it is likely to seem and the less likely its creators will be to profit from constructive feedback - or even to listen to it. The goal of prototyping is not to create a working model. It is to give form to an idea to learn about its strengths and weaknesses and to identify new directions for the next generation of more detailed, more refined prototypes. A prototype’s scope should be limited. The purpose of early prototypes might be to understand whether an idea has functional value." (Tim Brown, "Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation", 2009)

"Prototyping at work is giving form to an idea, allowing us to learn from it, evaluate it against others, and improve upon it." (Tim Brown, "Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation", 2009)

"Since openness to experimentation is the lifeblood of any creative organization, prototyping - the willingness to go ahead and try something by building it - is the best evidence of experimentation." (Tim Brown, "Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation", 2009)

"In analytics, it’s more important for individuals to be able to formulate problems well, to prototype solutions quickly, to make reasonable assumptions in the face of ill-structured problems, to design experiments that represent good investments, and to analyze results." (Foster Provost & Tom Fawcett, "Data Science for Business", 2013)

"Because of the short timeline, it’s tempting to jump into prototyping as soon as you’ve selected your winning ideas. But if you start prototyping without a plan, you’ll get bogged down by small, unanswered questions. Pieces won’t fit together, and your prototype could fall apart." (Jake Knapp et al, "Sprint: How to Solve Big Problems and Test New Ideas in Just Five Days", 2016)

"But perhaps the biggest problem is that the longer you spend working on something - whether it’s a prototype or a real product - the more attached you’ll become, and the less likely you’ll be to take negative test results to heart. After one day, you’re receptive to feedback. After three months, you’re committed." (Jake Knapp et al, "Sprint: How to Solve Big Problems and Test New Ideas in Just Five Days", 2016)

"Sometimes you can’t fit everything in. Remember that the sprint is great for testing risky solutions that might have a huge payoff. So you’ll have to reverse the way you would normally prioritize. If a small fix is so good and low-risk that you’re already planning to build it next week, then seeing it in a prototype won’t teach you much. Skip those easy wins in favor of big, bold bets." (Jake Knapp et al, "Sprint: How to Solve Big Problems and Test New Ideas in Just Five Days", 2016)

"The prototype is meant to answer questions, so keep it focused. You don’t need a fully functional product - you just need a real-looking façade to which customers can react." (Jake Knapp et al, "Sprint: How to Solve Big Problems and Test New Ideas in Just Five Days", 2016)

"You can prototype anything. Prototypes are disposable. Build just enough to learn, but not more. The prototype must appear real." (Jake Knapp, "Sprint: How to Solve Big Problems and Test New Ideas in Just Five Days", 2016)

"The intention behind prototypes is to explore the visualization design space, as opposed to the data space. A typical project usually entails a series of prototypes; each is a tool to gather feedback from stakeholders and help explore different ways to most effectively support the higher-level questions that they have. The repeated feedback also helps validate the operationalization along the way." (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)

"Rapid prototyping is a process of trying out many visualization ideas as quickly as possible and getting feedback from stakeholders on their efficacy. […] The design concept of 'failing fast' informs this: by exploring many different possible visual representations, it quickly becomes clear which tasks are supported by which techniques." (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)