🧭Business Intelligence: Perspectives (Part XV: From Data to Storytelling III)

Business Intelligence Series 

As children we heard or later read many stories, and even if few remained imprinted in memory, we can still recognize some of the metaphors and ideas used. Stories prepared us for life, and one can suppose that the business stories we hear nowadays have similar intent, charge and impact. However, if we dig deeper into each story and dissect it, we may be disappointed by its simplicity, the resemblance to other stories, to what we've heard over time. Moreover, stories can bring also negative connotations, that can impact any other story we hear. 

From the scores or hundreds of distinct stories that have been told, few reach a magnitude that can become more than the stories themselves, few become a catalyst for the auditorium, and even then they tend to manipulate. Conversely, well-written transformative stories can move mountains when they resonate with the auditorium. In a leader’s motivational speech such stories can become a catalyst that moves people in the intended direction.

Children stories are quite simple and apparently don’t need special constructs even if the choice of words, structure and messages is important. Moving further into organizations, storytelling becomes more complex, upon case, structures and messages need to follow certain conventions within some politically correct scripts. Facts become important to the degree they serve the story, though the purposes they serve change with time, becoming secondary to the story. Storytelling becomes thus just of way of changing the facts as seems fit to the storyteller. 

Storytelling has its role in organizations for channeling the multitude of messages across various structures. However, the more one hears the word storytelling, the more likely one is closer to fiction than to business decision-making. It's also true that the word in itself carries a power we all tasted during childhood and why not much later. The word has a magic power that appeals to our memories, to our feelings, to our expectations. However, as soon one's expectations are not met, the fight with the chimeras turns into a battle of our own. Yes, storytelling has great power when used right, when there's a story to tell, when the business narratives are worth telling. 

The problem with stories is that no matter how much they are based on real facts or happenings, they become fictitious in time, to the degree that they lose some of the most important facts they were based on. That’s valid especially when there’s no written track of the story, though even then various versions of the story can multiply outside of the standard channels and boundaries. 

Even if the author tried to keep the story as close to the facts, the way stories are understood, remembered and retold depend on too many factors - the words used, the degree to which metaphors and similar elements are understood, remembered and transmitted correctly, the language used, the mental structure existing in the auditorium, the association of words, ideas or metaphors, etc.

Unfortunately, the effect of stories can be negative too, especially when stories are designed to manipulate the auditorium beyond any ethical norms. When they don’t resonate with the crowd or are repeated unnecessary, the narratives may have adverse effects and the messages can get lost in the crowd or create resistance. Moreover, stories may have a multifold and opposite effect within different segments of the auditorium. 

Storytelling can make hearts and minds resonate with the carried messages, though misdirected, improper or poorly conceived stories have also the power to destroy all that have been built over the years. Between the two extremes there’s a small space to send the messages across!

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🧭Business Intelligence: Data Culture (Part I: Generative AI - No Silver Bullet)

Business Intelligence Series

Talking about holy grails in Data Analytics, another topic of major importance for an organization’s "infrastructure" is data culture, that can be defined as the collective beliefs, values, behaviors, and practices of an organization’s employees in harnessing the value of data for decision-making, operations, or insight. Rooted in data literacy, data culture is an extension of an organization’s culture in respect to data that acts as enabler in harnessing the value of data. It’s about thinking critically about data and how data is used to create value. 

The current topic was suggested by PowerBI.tips’s webcast from today [3] and is based on Brent Dykes’ article from Forbes ‘Why AI Isn’t Going to Solve All Your Data Culture Problems’ [1]. Dykes’ starting point for the discussion is Wavestone's annual data executive survey based on which the number of companies that reported they had "created a data-driven organization" rose sharply from 23.9 percent in 2023 to 48.1 percent in 2024 [2]. The report’s authors concluded that the result is driven by the adoption of Generative AI, the capabilities of OpenAI-like tools to generate context-dependent meaningful text, images, and other content in response to prompts. 

I agree with Dykes that AI technologies can’t be a silver bullet for an organization data culture given that AI either replaces people’s behaviors or augments existing ones, being thus a substitute and not a cure [1]. Even for a disruptive technology like Generative AI, it’s impossible to change so much employees’ mindset in a so short period of time. Typically, a data culture matures over years with sustained effort. Therefore, the argument that the increase is due to respondent’s false perception is more than plausible. There’s indeed a big difference between thinking about an organization as being data-driven and being data-driven. 

The three questions-based evaluation considered in the article addresses this difference, thinking vs. being. Changes in data culture don’t occur just because some people or metrics say so, but when people change their mental models based on data, when the interpersonal relations change, when the whole dynamics within the organization changes (positively). If people continue the same behavior and practices, then there are high chances that no change occurred besides the Brownian movement in a confined space of employees, that’s just chaotic motion.  

Indeed, a data culture should encourage the discovery, exploration, collaboration, discussions [1] respectively knowledge sharing and make people more receptive and responsive about environmental or circumstance changes. However, just involving leadership and having things prioritized and funded is not enough, no matter how powerful the drive. These can act as enablers, though more important is to awaken and guide people’s interest, working on people’s motivation and supporting the learning process through mentoring. No amount of brute force can make a mind move and evolve freely unless the mind is driven by an inborn curiosity!

Driving a self-driving car doesn’t make one a better driver. Technology should challenge people and expand their understanding of how data can be used in different contexts rather than give solutions based on a mass of texts available as input. This is how people grow meaningfully and how an organization’s culture expands. Readily available answers make people become dull and dependent on technology, which in the long-term can create more problems. Technology can solve problems when used creatively, when problems and their context are properly understood, and the solutions customized accordingly.

Unfortunately, for many organizations data culture will be just a topic to philosophy about. Data culture implies a change of mindset, perception, mental models, behavior, and practices based on data and not only consulting the data to confirm one’s biases on how the business operates!

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Resources:
[1] Forbes (2024) Why AI Isn’t Going To Solve All Your Data Culture Problems, by Brent Dykes (link)
[2] Wavestone (2024) 2024 Data and AI Leadership Executive Survey (link)
[3] Power BI tips (2024) Ep.299: AI & Data Culture Problems (link)

🧭Business Intelligence: A Software Engineer's Perspective (Part V: From Process Management to Mental Models in Knowledge Gaps)

Business Intelligence Series 

An organization's business processes are probably one of its most important assets because they reflect the business model, philosophy and culture, respectively link the material, financial, decisional, informational and communicational flows across the whole organization with implication in efficiency, productivity, consistency, quality, adaptability, agility, control or governance. A common practice in organizations is to document the business-critical processes and manage them accordingly over their lifetime, making sure that the employees understand and respect them, respectively improve them continuously. 

In what concerns the creation of data artifacts, data without the processual context are often meaningless, no matter how much a data professional knows about data structures/models. Processes allow to delimit the flow and boundaries of data, respectively delimit the essential from non-essential. Moreover, it's the knowledge of processes that allows to reengineer the logic behind systems especially when no proper documentation about the logic is available. 

Therefore, the existence of documented processes allows to bridge the knowledge gaps existing on the factual side, and occasionally also on the technical side. In theory, the processes should provide a complete overview of the procedures, rules, policies and responsibilities existing in the organization, respectively how the business operates. However, even if people tend to understand how the world works locally, when broken down into parts, their understanding is systemically flawed, missing the implications of causal relationships that span time with delays, feedback, variable confusion, chaotic behavior, and/or other characteristics borrowed from the vocabulary of complex systems.  

Jay W Forrester [3], Peter M Senge [1], John D Sterman [2] and several other systems-thinking theoreticians stressed the importance of mental models in making-sense about the world especially in setups that reflect the characteristics of complex systems. Mental models frame our experience about the world in congruent mental constructs that are further used to think, understand and navigate the world. They are however tacit, fuzzy, incomplete, imprecisely stated, inaccurate, evolving simplifications with dual character, enabling on one side, while impeding on the other side cognitive processes like sense-making, learning, thinking or decision-making, limiting the range of action to what is familiar and comfortable. 

On one side one of the primary goals of Data Analytics is to provide new insights, while on the other side the new insights fail to be recognized and put into practice because they conflict with existing mental models, limiting employees to familiar ways of thinking and acting. 

Externalizing and sharing mental models allow besides making assumptions explicit and creating a world view also to strategize, make tests and simulations, respectively make sure that the barriers and further constraints don't impact the decisional process. Sange goes further and advances that mental models, especially at management level, offer a competitive advantage, allowing to maintain coherence and direction, people becoming more perceptive and responsive about environmental or circumstance changes.

The whole process isn't about creating a unique congruent mental model, even if several mental models may converge toward one or more holistic models, but of providing different diverse perspectives and enabling people to make leaps in abstraction (by moving from direct observations to generalizations) while blending advocacy and inquiry to promote collaborative learning. Gradually, people and organizations should recognize a shift from mental models dominated by events to mental models that recognize longer-tern patterns of change and the underlying structures producing those patterns [1].

Probably, for many the concept of mental models seems to be still too abstract, respectively that the effort associated with it is unnecessary, or at least questionable on whether it can make a difference. Conversely, being aware of the positive and negative implications the mental models hold, can makes us explore, even if ad-hoc, the roads they open.

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Resources:
[1] Peter M Senge (1990) The Fifth Discipline: The Art & Practice of The Learning Organization
[2] John D Sterman (2000) "Business Dynamics: Systems thinking and modeling for a complex world"
[3] Jay W Forrester (1971) "Counterintuitive Behaviour of Social Systems", Technology Review

🧭Business Intelligence: A Software Engineer's Perspective (Part II: Major Knowledge Gaps)

Business Intelligence Series

Solving a problem requires a certain degree of knowledge in the areas affected by the problem, degree that varies exponentially with problem's complexity. This requirement applies to scientific fields with low allowance for errors, as well as to business scenarios where the allowance for errors is in theory more relaxed. Building a report or any other data artifact is closely connected with problem solving as the data artifacts are supposed to model the whole or parts of what is needed for solving the problem(s) in scope.

In general, creating data artifacts requires: (1) domain knowledge - knowledge of the concepts, processes, systems, data, data structures and data flows as available in the organization; (2) technical knowledge - knowledge about the tools, techniques, processes and methodologies used to produce the artifacts; (3) data literacy - critical thinking, the ability to understand and explore the implications of data, respectively communicating data in context; (4) activity management - managing the activities involved. 

At minimum, creating a report may require only narrower subsets from the areas mentioned above, depending on the complexity of the problem and the tasks involved. Ideally, a single person should be knowledgeable enough to handle all this alone, though that's seldom the case. Commonly, two or more parties are involved, though let's consider the two-parties scenario: on one side is the customer who has (in theory) a deep understanding of the domain, respectively on the other side is the data professional who has (in theory) a deep understanding of the technical aspects. Ideally, both parties should be data literates and have some basic knowledge of the other party's domain. 

To attack a business problem that requires one or more data artifacts both parties need to have a common understanding of the problem to be solved, of the requirements, constraints, assumptions, expectations, risks, and other important aspects associated with it. It's critical for the data professional to acquire the domain knowledge required by the problem, otherwise the solution has high chances to deviate from the expectations. The general issue is that there are multiple interactions that are iterative. Firstly, the interactions for building the needed common ground. Secondly, the interaction between the problem and reality. Thirdly, the interaction between the problem and parties’ mental models und understanding about the problem. 

The outcome of these interactions is that the problem and its requirements go through several iterations in which knowledge from the previous iterations are incorporated successively. With each important piece of knowledge gained, it's important to revise and refine the question(s), respectively the problem. If in each iteration there are also programming and further technical activities involved, the effort and costs resulted in the process can explode, while the timeline expands accordingly. 

There are several heuristics that could be devised to address these challenges: (1) build all the required knowledge in one person, either on the business or the technical side; (2) make sure that the parties have the required knowledge for approaching the problems in scope; (3) make sure that the gaps between reality and parties' mental models is minimal; (4) make sure that the requirements are complete and understood before starting the development; (5) adhere to methodologies that accommodate the necessary iterations and endeavor's particularities; (6) make sure that there's a halt condition for regularly reviewing the progress, respectively halting the work; (7) build an organizational culture to support all this. 

The list is open, and the heuristics aren't exclusive, so in theory any combination of them can be considered. Ideally, an organization should reflect all these heuristics in one form or another. The higher the coverage, the more mature the organization is. The question is how organizations with a suboptimal setup can change the status quo?

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💼Project Management: Tools (Part I: The Choice of Tools in Project Management)

“Beware the man of one book” (in Latin, “homo unius libri”), a warning generally attributed to Thomas Aquinas and having a twofold meaning. In its original interpretation it was referring to the people mastering a single chosen discipline, however the meaning degenerated in expressing the limitations of people who master just one book, and thus having a limited toolset of perspectives, mental models or heuristics. This later meaning is better reflected in Abraham Maslow adage: “If the only tool you have is a hammer, you tend to see every problem as a nail”, as people tend to use the tools they are used to also in situations in which other tools are more appropriate.

It’s sometimes admirable people and even organizations’ stubbornness in using the same tools in totally different scenarios, expecting though the same results, as well in similar scenarios expecting different results. It’s true, Mathematics has proven that the same techniques can be used successfully in different areas, however a mathematician’s universe and models are idealistically fractionalized to a certain degree from reality, full of simplified patterns and never-ending approximations. In contrast, the universe of Software Development and Project Management has a texture of complex patterns with multiple levels of dependencies and constraints, constraints highly sensitive to the initial conditions.

Project Management has managed to successfully derive tools like methodologies, processes, procedures, best practices and guidelines to address the realities of projects, however their use in praxis seems to be quite challenging. Probably, the challenge resides in stubbornness of not adapting the tools to the difficulties and tasks met. Even if the same phases and multiple similarities seems to exist, the process of building a house or other tangible artefact is quite different than the approaches used in development and implementation of software.

Software projects have high variability and are often explorative in nature. The end-product looks totally different than the initial scaffold. The technologies used come with opportunities and limitations that are difficult to predict in the planning phase. What on paper seems to work often doesn’t work in praxis as the devil lies typically in details. The challenges and limitations vary between industries, businesses and even projects within the same organization.

Even if for each project type there’s a methodology more suitable than another, in the end project particularities might pull the choice in one direction or another. Business Intelligence projects for example can benefit from agile approaches as they enable to better manage and deliver value by adapting the requirements to business needs as the project progresses. An agile approach works almost always better than a waterfall process. In contrast, ERP implementations seldom benefit from agile methodologies given the complexity of the project which makes from planning a real challenge, however this depends also on an organization’s dynamicity.

Especially when an organization has good experience with a methodology there’s the tendency to use the same methodology across all the projects run within the organization. This results in chopping down a project to fit an ideal form, which might be fine as long the particularities of each project are adequately addressed. Even if one methodology is not appropriate for a given scenario it doesn’t mean it can’t be used for it, however in the final equation enter also the cost, time, effort, and the quality of the end-results.

In general, one can cope with complexity by leveraging a broader set of mental models, heuristics and set of tools, and this can be done only though experimentation, through training and exposing employees to new types of experiences, through openness, through adapting the tools to the challenges ahead.

🔭Data Science: Estimation (Just the Quotes)

"The scientific value of a theory of this kind, in which we make so many assumptions, and introduce so many adjustable constants, cannot be estimated merely by its numerical agreement with certain sets of experiments. If it has any value it is because it enables us to form a mental image of what takes place in a piece of iron during magnetization." (James C Maxwell, "Treatise on Electricity and Magnetism" Vol. II, 1873)

"It [probability] is the very guide of life, and hardly can we take a step or make a decision of any kind without correctly or incorrectly making an estimation of probabilities." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"A statistical estimate may be good or bad, accurate or the reverse; but in almost all cases it is likely to be more accurate than a casual observer’s impression, and the nature of things can only be disproved by statistical methods." (Arthur L Bowley, "Elements of Statistics", 1901)

"Great numbers are not counted correctly to a unit, they are estimated; and we might perhaps point to this as a division between arithmetic and statistics, that whereas arithmetic attains exactness, statistics deals with estimates, sometimes very accurate, and very often sufficiently so for their purpose, but never mathematically exact." (Arthur L Bowley, "Elements of Statistics", 1901)

“Some of the common ways of producing a false statistical argument are to quote figures without their context, omitting the cautions as to their incompleteness, or to apply them to a group of phenomena quite different to that to which they in reality relate; to take these estimates referring to only part of a group as complete; to enumerate the events favorable to an argument, omitting the other side; and to argue hastily from effect to cause, this last error being the one most often fathered on to statistics. For all these elementary mistakes in logic, statistics is held responsible.” (Sir Arthur L Bowley, “Elements of Statistics”, 1901)

"A good estimator will be unbiased and will converge more and more closely (in the long run) on the true value as the sample size increases. Such estimators are known as consistent. But consistency is not all we can ask of an estimator. In estimating the central tendency of a distribution, we are not confined to using the arithmetic mean; we might just as well use the median. Given a choice of possible estimators, all consistent in the sense just defined, we can see whether there is anything which recommends the choice of one rather than another. The thing which at once suggests itself is the sampling variance of the different estimators, since an estimator with a small sampling variance will be less likely to differ from the true value by a large amount than an estimator whose sampling variance is large." (Michael J Moroney, "Facts from Figures", 1951)

"The enthusiastic use of statistics to prove one side of a case is not open to criticism providing the work is honestly and accurately done, and providing the conclusions are not broader than indicated by the data. This type of work must not be confused with the unfair and dishonest use of both accurate and inaccurate data, which too commonly occurs in business. Dishonest statistical work usually takes the form of: (1) deliberate misinterpretation of data; (2) intentional making of overestimates or underestimates; and (3) biasing results by using partial data, making biased surveys, or using wrong statistical methods." (John R Riggleman & Ira N Frisbee, "Business Statistics", 1951)

"Statistics is the fundamental and most important part of inductive logic. It is both an art and a science, and it deals with the collection, the tabulation, the analysis and interpretation of quantitative and qualitative measurements. It is concerned with the classifying and determining of actual attributes as well as the making of estimates and the testing of various hypotheses by which probable, or expected, values are obtained. It is one of the means of carrying on scientific research in order to ascertain the laws of behavior of things - be they animate or inanimate. Statistics is the technique of the Scientific Method." (Bruce D Greenschields & Frank M Weida, "Statistics with Applications to Highway Traffic Analyses", 1952)

"We realize that if someone just 'grabs a handful', the individuals in the handful almost always resemble one another (on the average) more than do the members of a simple random sample. Even if the 'grabs' [sampling] are randomly spread around so that every individual has an equal chance of entering the sample, there are difficulties. Since the individuals of grab samples resemble one another more than do individuals of random samples, it follows (by a simple mathematical argument) that the means of grab samples resemble one another less than the means of random samples of the same size. From a grab sample, therefore, we tend to underestimate the variability in the population, although we should have to overestimate it in order to obtain valid estimates of variability of grab sample means by substituting such an estimate into the formula for the variability of means of simple random samples. Thus using simple random sample formulas for grab sample means introduces a double bias, both parts of which lead to an unwarranted appearance of higher stability." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)

"The usefulness of the models in constructing a testable theory of the process is severely limited by the quickly increasing number of parameters which must be estimated in order to compare the predictions of the models with empirical results" (Anatol Rapoport, "Prisoner's Dilemma: A study in conflict and cooperation", 1965)

"Pencil and paper for construction of distributions, scatter diagrams, and run-charts to compare small groups and to detect trends are more efficient methods of estimation than statistical inference that depends on variances and standard errors, as the simple techniques preserve the information in the original data." (William E Deming, "On Probability as Basis for Action" American Statistician Vol. 29 (4), 1975)

"In physics it is usual to give alternative theoretical treatments of the same phenomenon. We construct different models for different purposes, with different equations to describe them. Which is the right model, which the 'true' set of equations? The question is a mistake. One model brings out some aspects of the phenomenon; a different model brings out others. Some equations give a rougher estimate for a quantity of interest, but are easier to solve. No single model serves all purposes best." (Nancy Cartwright, "How the Laws of Physics Lie", 1983)

"Probability is the mathematics of uncertainty. Not only do we constantly face situations in which there is neither adequate data nor an adequate theory, but many modem theories have uncertainty built into their foundations. Thus learning to think in terms of probability is essential. Statistics is the reverse of probability (glibly speaking). In probability you go from the model of the situation to what you expect to see; in statistics you have the observations and you wish to estimate features of the underlying model." (Richard W Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985)

"A mechanistic model has the following advantages: 1. It contributes to our scientific understanding of the phenomenon under study. 2. It usually provides a better basis for extrapolation (at least to conditions worthy of further experimental investigation if not through the entire range of all input variables). 3. It tends to be parsimonious (i. e, frugal) in the use of parameters and to provide better estimates of the response." (George E P Box, "Empirical Model-Building and Response Surfaces", 1987)

"A tendency to drastically underestimate the frequency of coincidences is a prime characteristic of innumerates, who generally accord great significance to correspondences of all sorts while attributing too little significance to quite conclusive but less flashy statistical evidence." (John A Paulos, "Innumeracy: Mathematical Illiteracy and its Consequences", 1988)

"A model for simulating dynamic system behavior requires formal policy descriptions to specify how individual decisions are to be made. Flows of information are continuously converted into decisions and actions. No plea about the inadequacy of our understanding of the decision-making processes can excuse us from estimating decision-making criteria. To omit a decision point is to deny its presence - a mistake of far greater magnitude than any errors in our best estimate of the process." (Jay W Forrester, "Policies, decisions and information sources for modeling", 1994)

"In constructing a model, we always attempt to maximize its usefulness. This aim is closely connected with the relationship among three key characteristics of every systems model: complexity, credibility, and uncertainty. This relationship is not as yet fully understood. We only know that uncertainty (predictive, prescriptive, etc.) has a pivotal role in any efforts to maximize the usefulness of systems models. Although usually (but not always) undesirable when considered alone, uncertainty becomes very valuable when considered in connection to the other characteristics of systems models: in general, allowing more uncertainty tends to reduce complexity and increase credibility of the resulting model. Our challenge in systems modelling is to develop methods by which an optimal level of allowable uncertainty can be estimated for each modelling problem." (George J Klir & Bo Yuan, "Fuzzy Sets and Fuzzy Logic: Theory and Applications", 1995)

"Delay time, the time between causes and their impacts, can highly influence systems. Yet the concept of delayed effect is often missed in our impatient society, and when it is recognized, it’s almost always underestimated. Such oversight and devaluation can lead to poor decision making as well as poor problem solving, for decisions often have consequences that don’t show up until years later. Fortunately, mind mapping, fishbone diagrams, and creativity/brainstorming tools can be quite useful here." (Stephen G Haines, "The Manager's Pocket Guide to Strategic and Business Planning", 1998)

“Accurate estimates depend at least as much upon the mental model used in forming the picture as upon the number of pieces of the puzzle that have been collected.” (Richards J. Heuer Jr, “Psychology of Intelligence Analysis”, 1999)

“[…] we underestimate the share of randomness in about everything […]  The degree of resistance to randomness in one’s life is an abstract idea, part of its logic counterintuitive, and, to confuse matters, its realizations nonobservable.” (Nassim N Taleb, “Fooled by Randomness”, 2001)

"Most long-range forecasts of what is technically feasible in future time periods dramatically underestimate the power of future developments because they are based on what I call the 'intuitive linear' view of history rather than the 'historical exponential' view." (Ray Kurzweil, "The Singularity is Near", 2005)

"[myth:] Accuracy is more important than precision. For single best estimates, be it a mean value or a single data value, this question does not arise because in that case there is no difference between accuracy and precision. (Think of a single shot aimed at a target.) Generally, it is good practice to balance precision and accuracy. The actual requirements will differ from case to case." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"As uncertainties of scientific data values are nearly as important as the data values themselves, it is usually not acceptable that a best estimate is only accompanied by an estimated uncertainty. Therefore, only the size of nondominant uncertainties should be estimated. For estimating the size of a nondominant uncertainty we need to find its upper limit, i.e., we want to be as sure as possible that the uncertainty does not exceed a certain value." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Before best estimates are extracted from data sets by way of a regression analysis, the uncertainties of the individual data values must be determined.In this case care must be taken to recognize which uncertainty components are common to all the values, i.e., those that are correlated (systematic)." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"[myth:] Counting can be done without error. Usually, the counted number is an integer and therefore without (rounding) error. However, the best estimate of a scientifically relevant value obtained by counting will always have an error. These errors can be very small in cases of consecutive counting, in particular of regular events, e.g., when measuring frequencies." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Due to the theory that underlies uncertainties an infinite number of data values would be necessary to determine the true value of any quantity. In reality the number of available data values will be relatively small and thus this requirement can never be fully met; all one can get is the best estimate of the true value." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"It is the aim of all data analysis that a result is given in form of the best estimate of the true value. Only in simple cases is it possible to use the data value itself as result and thus as best estimate." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"It is the nature of an uncertainty that it is not known and can never be known, whether the best estimate is greater or less than the true value." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"The methodology of feedback design is borrowed from cybernetics (control theory). It is based upon methods of controlled system model’s building, methods of system states and parameters estimation (identification), and methods of feedback synthesis. The models of controlled system used in cybernetics differ from conventional models of physics and mechanics in that they have explicitly specified inputs and outputs. Unlike conventional physics results, often formulated as conservation laws, the results of cybernetical physics are formulated in the form of transformation laws, establishing the possibilities and limits of changing properties of a physical system by means of control." (Alexander L Fradkov, "Cybernetical Physics: From Control of Chaos to Quantum Control", 2007)

"A good estimator has to be more than just consistent. It also should be one whose variance is less than that of any other estimator. This property is called minimum variance. This means that if we run the experiment several times, the 'answers' we get will be closer to one another than 'answers' based on some other estimator." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"An estimate (the mathematical definition) is a number derived from observed values that is as close as we can get to the true parameter value. Useful estimators are those that are 'better' in some sense than any others." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"Estimators are functions of the observed values that can be used to estimate specific parameters. Good estimators are those that are consistent and have minimum variance. These properties are guaranteed if the estimator maximizes the likelihood of the observations." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"GIGO is a famous saying coined by early computer scientists: garbage in, garbage out. At the time, people would blindly put their trust into anything a computer output indicated because the output had the illusion of precision and certainty. If a statistic is composed of a series of poorly defined measures, guesses, misunderstandings, oversimplifications, mismeasurements, or flawed estimates, the resulting conclusion will be flawed." (Daniel J Levitin, "Weaponized Lies", 2017)

"One final warning about the use of statistical models (whether linear or otherwise): The estimated model describes the structure of the data that have been observed. It is unwise to extend this model very far beyond the observed data." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"One kind of probability - classic probability - is based on the idea of symmetry and equal likelihood […] In the classic case, we know the parameters of the system and thus can calculate the probabilities for the events each system will generate. […] A second kind of probability arises because in daily life we often want to know something about the likelihood of other events occurring […]. In this second case, we need to estimate the parameters of the system because we don’t know what those parameters are. […] A third kind of probability differs from these first two because it’s not obtained from an experiment or a replicable event - rather, it expresses an opinion or degree of belief about how likely a particular event is to occur. This is called subjective probability […]." (Daniel J Levitin, "Weaponized Lies", 2017)

"Samples give us estimates of something, and they will almost always deviate from the true number by some amount, large or small, and that is the margin of error. […] The margin of error does not address underlying flaws in the research, only the degree of error in the sampling procedure. But ignoring those deeper possible flaws for the moment, there is another measurement or statistic that accompanies any rigorously defined sample: the confidence interval." (Daniel J Levitin, "Weaponized Lies", 2017)

"The margin of error is how accurate the results are, and the confidence interval is how confident you are that your estimate falls within the margin of error." (Daniel J Levitin, "Weaponized Lies", 2017)

🔭Data Science: Problem Solving (Just the Quotes)

"Reflexion is careful and laborious thought, and watchful attention directed to the agreeable effect of one's plan. Invention, on the other hand, is the solving of intricate problems and the discovery of new principles by means of brilliancy and versatility." (Marcus Vitruvius Pollio, "De architectura" ["On Architecture], cca. 15BC)

"The insights gained and garnered by the mind in its wanderings among basic concepts are benefits that theory can provide. Theory cannot equip the mind with formulas for solving problems, nor can it mark the narrow path on which the sole solution is supposed to lie by planting a hedge of principles on either side. But it can give the mind insight into the great mass of phenomena and of their relationships, then leave it free to rise into the higher realms of action." (Carl von Clausewitz, "On War", 1832)

"The correct solution to any problem depends principally on a true understanding of what the problem is." (Arthur M Wellington, "The Economic Theory of Railway Location", 1887)

"He who seeks for methods without having a definite problem in mind seeks for the most part in vain." (David Hilbert, 1902)

"This diagrammatic method has, however, serious inconveniences as a method for solving logical problems. It does not show how the data are exhibited by cancelling certain constituents, nor does it show how to combine the remaining constituents so as to obtain the consequences sought. In short, it serves only to exhibit one single step in the argument, namely the equation of the problem; it dispenses neither with the previous steps, i.e., 'throwing of the problem into an equation' and the transformation of the premises, nor with the subsequent steps, i.e., the combinations that lead to the various consequences. Hence it is of very little use, inasmuch as the constituents can be represented by algebraic symbols quite as well as by plane regions, and are much easier to deal with in this form." (Louis Couturat, "The Algebra of Logic", 1914)

"A great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery." (George Polya, "How to solve it", 1944)

"Success in solving the problem depends on choosing the right aspect, on attacking the fortress from its accessible side." (George Polya, "How to Solve It", 1944)

"[The] function of thinking is not just solving an actual problem but discovering, envisaging, going into deeper questions. Often, in great discovery the most important thing is that a certain question is found." (Max Wertheimer, "Productive Thinking", 1945)

"We can scarcely imagine a problem absolutely new, unlike and unrelated to any formerly solved problem; but if such a problem could exist, it would be insoluble. In fact, when solving a problem, we should always profit from previously solved problems, using their result or their method, or the experience acquired in solving them." (George Polya, 1945)

"I believe, that the decisive idea which brings the solution of a problem is rather often connected with a well-turned word or sentence. The word or the sentence enlightens the situation, gives things, as you say, a physiognomy. It can precede by little the decisive idea or follow on it immediately; perhaps, it arises at the same time as the decisive idea. […]  The right word, the subtly appropriate word, helps us to recall the mathematical idea, perhaps less completely and less objectively than a diagram or a mathematical notation, but in an analogous way. […] It may contribute to fix it in the mind." (George Pólya [in a letter to Jaque Hadamard, "The Psychology of Invention in the Mathematical Field", 1949])

"The problems are solved, not by giving new information, but by arranging what we have known since long." (Ludwig Wittgenstein, "Philosophical Investigations", 1953)

"Solving problems is the specific achievement of intelligence." (George Pólya, 1957)

"Systems engineering embraces every scientific and technical concept known, including economics, management, operations, maintenance, etc. It is the job of integrating an entire problem or problem to arrive at one overall answer, and the breaking down of this answer into defined units which are selected to function compatibly to achieve the specified objectives." (Instrumentation Technology, 1957)

"A problem that is located and identified is already half solved!" (Bror R Carlson, "Managing for Profit", 1961)

"If we view organizations as adaptive, problem-solving structures, then inferences about effectiveness have to be made, not from static measures of output, but on the basis of the processes through which the organization approaches problems. In other words, no single measurement of organizational efficiency or satisfaction - no single time-slice of organizational performance can provide valid indicators of organizational health." (Warren G Bennis, "General Systems Yearbook", 1962)

"Solving problems can be regarded as the most characteristically human activity." (George Pólya, "Mathematical Discovery", 1962)

"The final test of a theory is its capacity to solve the problems which originated it." (George Dantzig, "Linear Programming and Extensions", 1963)

"It is a commonplace of modern technology that there is a high measure of certainty that problems have solutions before there is knowledge of how they are to be solved." (John K Galbraith, "The New Industrial State", 1967)

"An expert problem solver must be endowed with two incompatible qualities, a restless imagination and a patient pertinacity.” (Howard W Eves, “In Mathematical Circles”, 1969)

"The problem-solving approach allows for mental double-clutching. It does not require a direct switch from one point of view to another. It provides a period 'in neutural' where there is an openness to facts and, therefore, a willingness to consider alternative views." (William Reddin, "Managerial Effectiveness", 1970)

"In general, complexity and precision bear an inverse relation to one another in the sense that, as the complexity of a problem increases, the possibility of analysing it in precise terms diminishes. Thus 'fuzzy thinking' may not be deplorable, after all, if it makes possible the solution of problems which are much too complex for precise analysis." (Lotfi A Zadeh, "Fuzzy languages and their relation to human intelligence", 1972)

"If we deal with our problem not knowing, or pretending not to know the general theory encompassing the concrete case before us, if we tackle the problem "with bare hands", we have a better chance to understand the scientist's attitude in general, and especially the task of the applied mathematician." (George Pólya, "Mathematical Methods in Science", 1977)

"Systems represent someone's attempt at solution to problems, but they do not solve problems; they produce complicated responses." (Melvin J Sykes, Maryland Law Review, 1978)

“Solving problems can be regarded as the most characteristically human activity.” (George Polya, 1981)

"The problem solver needs to stand back and examine problem contexts in the light of different 'Ws' (Weltanschauungen). Perhaps he can then decide which 'W' seems to capture the essence of the particular problem context he is faced with. This whole process needs formalizing if it is to be carried out successfully. The problem solver needs to be aware of different paradigms in the social sciences, and he must be prepared to view the problem context through each of these paradigms." (Michael C Jackson, "Towards a System of Systems Methodologies", 1984)

"People in general tend to assume that there is some 'right' way of solving problems. Formal logic, for example, is regarded as a correct approach to thinking, but thinking is always a compromise between the demands of comprehensiveness, speed, and accuracy. There is no best way of thinking." (James L McKenney & Peter G W Keen, Harvard Business Review on Human Relations, 1986)

"A great many problems are easier to solve rigorously if you know in advance what the answer is." (Ian Stewart, "From Here to Infinity", 1987)

"Define the problem before you pursue a solution." (John Williams, Inc. Magazine's Guide to Small Business Success, 1987)

"No matter how complicated a problem is, it usually can be reduced to a simple, comprehensible form which is often the best solution." (Dr. An Wang, Nation's Business, 1987)

"There are many things you can do with problems besides solving them. First you must define them, pose them. But then of course you can also refi ne them, depose them, or expose them or even dissolve them! A given problem may send you looking for analogies, and some of these may lead you astray, suggesting new and different problems, related or not to the original. Ends and means can get reversed. You had a goal, but the means you found didn’t lead to it, so you found a new goal they did lead to. It’s called play. Creative mathematicians play a lot; around any problem really interesting they develop a whole cluster of analogies, of playthings." (David Hawkins, "The Spirit of Play", Los Alamos Science, 1987)

"A scientific problem can be illuminated by the discovery of a profound analogy, and a mundane problem can be solved in a similar way." (Philip Johnson-Laird, "The Computer and the Mind", 1988)

"Anecdotes may be more useful than equations in understanding the problem." (Robert Kuttner, "The New Republic", The New York Times, 1988)

"Most people would rush ahead and implement a solution before they know what the problem is." (Q T Wiles, Inc. Magazine, 1988)

“A mental model is a knowledge structure that incorporates both declarative knowledge (e.g., device models) and procedural knowledge (e.g., procedures for determining distributions of voltages within a circuit), and a control structure that determines how the procedural and declarative knowledge are used in solving problems (e.g., mentally simulating the behavior of a circuit).” (Barbara Y White & John R Frederiksen, “Causal Model Progressions as a Foundation for Intelligent Learning Environments”, Artificial Intelligence 42, 1990)

"An important symptom of an emerging understanding is the capacity to represent a problem in a number of different ways and to approach its solution from varied vantage points; a single, rigid representation is unlikely to suffice." (Howard Gardner, “The Unschooled Mind”, 1991)

“[By understanding] I mean simply a sufficient grasp of concepts, principles, or skills so that one can bring them to bear on new problems and situations, deciding in which ways one’s present competencies can suffice and in which ways one may require new skills or knowledge.” (Howard Gardner, “The Unschooled Mind”, 1991)

"We consider the notion of ‘system’ as an organising concept, before going on to look in detail at various systemic metaphors that may be used as a basis for structuring thinking about organisations and problem situations." (Michael C Jackson, "Creative Problem Solving: Total Systems Intervention", 1991)

“But our ways of learning about the world are strongly influenced by the social preconceptions and biased modes of thinking that each scientist must apply to any problem. The stereotype of a fully rational and objective ‘scientific method’, with individual scientists as logical (and interchangeable) robots, is self-serving mythology.” (Stephen Jay Gould, “This View of Life: In the Mind of the Beholder”, Natural History Vol. 103 (2), 1994)

"The term mental model refers to knowledge structures utilized in the solving of problems. Mental models are causal and thus may be functionally defined in the sense that they allow a problem solver to engage in description, explanation, and prediction. Mental models may also be defined in a structural sense as consisting of objects, states that those objects exist in, and processes that are responsible for those objects’ changing states." (Robert Hafner & Jim Stewart, "Revising Explanatory Models to Accommodate Anomalous Genetic Phenomena: Problem Solving in the ‘Context of Discovery’", Science Education 79 (2), 1995)

"The purpose of a conceptual model is to provide a vocabulary of terms and concepts that can be used to describe problems and/or solutions of design. It is not the purpose of a model to address specific problems, and even less to propose solutions for them. Drawing an analogy with linguistics, a conceptual model is analogous to a language, while design patterns are analogous to rhetorical figures, which are predefined templates of language usages, suited particularly to specific problems." (Peter P Chen [Ed.], "Advances in Conceptual Modeling", 1999)

"The three basic mechanisms of averaging, feedback and division of labor give us a first idea of a how a CMM [Collective Mental Map] can be developed in the most efficient way, that is, how a given number of individuals can achieve a maximum of collective problem-solving competence. A collective mental map is developed basically by superposing a number of individual mental maps. There must be sufficient diversity among these individual maps to cover an as large as possible domain, yet sufficient redundancy so that the overlap between maps is large enough to make the resulting graph fully connected, and so that each preference in the map is the superposition of a number of individual preferences that is large enough to cancel out individual fluctuations. The best way to quickly expand and improve the map and fill in gaps is to use a positive feedback that encourages individuals to use high preference paths discovered by others, yet is not so strong that it discourages the exploration of new paths." (Francis Heylighen, "Collective Intelligence and its Implementation on the Web", 1999)

"What it means for a mental model to be a structural analog is that it embodies a representation of the spatial and temporal relations among, and the causal structures connecting the events and entities depicted and whatever other information that is relevant to the problem-solving talks. […] The essential points are that a mental model can be nonlinguistic in form and the mental mechanisms are such that they can satisfy the model-building and simulative constraints necessary for the activity of mental modeling." (Nancy J Nersessian, "Model-based reasoning in conceptual change", 1999)

"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)

"[...] a general-purpose universal optimization strategy is theoretically impossible, and the only way one strategy can outperform another is if it is specialized to the specific problem under consideration." (Yu-Chi Ho & David L Pepyne, "Simple explanation of the no-free-lunch theorem and its implications", Journal of Optimization Theory and Applications 115, 2002)

"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)

"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)

"Alternative models are neither right nor wrong, just more or less useful in allowing us to operate in the world and discover more and better options for solving problems." (Andrew Weil," The Natural Mind: A Revolutionary Approach to the Drug Problem", 2004)

“A conceptual model is a mental image of a system, its components, its interactions. It lays the foundation for more elaborate models, such as physical or numerical models. A conceptual model provides a framework in which to think about the workings of a system or about problem solving in general. An ensuing operational model can be no better than its underlying conceptualization.” (Henry N Pollack, “Uncertain Science … Uncertain World”, 2005)

"Graphics is the visual means of resolving logical problems." (Jacques Bertin, "Graphics and Graphic Information Processing", 2011)

"In specific cases, we think by applying mental rules, which are similar to rules in computer programs. In most of the cases, however, we reason by constructing, inspecting, and manipulating mental models. These models and the processes that manipulate them are the basis of our competence to reason. In general, it is believed that humans have the competence to perform such inferences error-free. Errors do occur, however, because reasoning performance is limited by capacities of the cognitive system, misunderstanding of the premises, ambiguity of problems, and motivational factors. Moreover, background knowledge can significantly influence our reasoning performance. This influence can either be facilitation or an impedance of the reasoning process." (Carsten Held et al, "Mental Models and the Mind", 2006)

"Every problem has a solution; it may sometimes just need another perspective.” (Rebecca Mallery et al, "NLP for Rookies", 2009)

"Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.” (Paul Lockhart, "A Mathematician's Lament", 2009)

"Mostly we rely on stories to put our ideas into context and give them meaning. It should be no surprise, then, that the human capacity for storytelling plays an important role in the intrinsically human-centered approach to problem solving, design thinking." (Tim Brown, "Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation", 2009)

"Mental models are formed over time through a deep enculturation process, so it follows that any attempt to align mental models must focus heavily on collective sense making. Alignment only happens through a process of socialisation; people working together, solving problems together, making sense of the world together." (Robina Chatham & Brian Sutton, "Changing the IT Leader’s Mindset", 2010)

"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)

"Mental imagery is often useful in problem solving. Verbal descriptions of problems can become confusing, and a mental image can clear away excessive detail to bring out important aspects of the problem. Imagery is most useful with problems that hinge on some spatial relationship. However, if the problem requires an unusual solution, mental imagery alone can be misleading, since it is difficult to change one’s understanding of a mental image. In many cases, it helps to draw a concrete picture since a picture can be turned around, played with, and reinterpreted, yielding new solutions in a way that a mental image cannot." (James Schindler, "Followership", 2014)

“Framing the right problem is equally or even more important than solving it.” (Pearl Zhu, “Change, Creativity and Problem-Solving”, 2017)

🎓Knowledge Management: Cognitive Map (Definitions)

"A cognitive map is a specific way of representing a person's assertions about some limited domain, such as a policy problem. It is designed to capture the structure of the person's causal assertions and to generate the consequences that follow front this structure." (Robert M Axelrod, "Structure of Decision: The cognitive maps of political elites", 1976)

"A cognitive map is the representation of thinking about a problem that follows from the process of mapping." (Colin Eden, "Analyzing cognitive maps to help structure issues or problems", 2002)

"A mental representation of a portion of the physical environment and the relative locations of points within it." (Andrew M Colman, "A Dictionary of Psychology" 3rd Ed, 2008)

"A mental model (or map) of the external environment which may be constructed following exploratory behaviour." (Michael Allaby, "A Dictionary of Zoology" 3rd Ed., 2009)

"An FCM [Fuzzy Cognitive Map] is a directed graph with concepts like policies, events etc. as nodes and causalities as edges. It represents causal relationship between concepts." (Florentin Smarandache &  W B Vasantha Kandasamy, "Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps", 2014)

"A conceptual tool that provides a representation of particular natural or social environments in the form of a model." (Evangelos C Papakitsos et al, "The Challenges of Work-Based Learning via Systemic Modelling in the European Union", 2020)

"A representation of the conceptualization that the subject constructs of the system in which he evolves. The set of cognitive representations that emerge make it possible to understand his actions, the links between the factors structuring the cognitive patterns dictating his behaviors." (Henda E Karray & Souhaila Kammoun, "Strategic Orientation of the Managers of a Tunisian Family Group Before and After the Revolution", 2020)

"A cognitive map is a type of mental representation which serves an individual to acquire, code, store, recall, and decode information about the relative locations and attributes of phenomena in their everyday or metaphorical spatial environment." (Wikipedia) [source]