📉Graphical Representation: Representation (Just the Quotes)

"The advantages proposed by [the graphical] mode of representation, are to facilitate the attainment of information, and aid the memory in retaining it: which two points form the principal business in what we call learning. Of all the senses, the eye gives the liveliest and most accurate idea of whatever is susceptible of being represented to it; and when proportion between different quantities is the object, then the eye has an incalculable superiority." (William Playfair, The Statistical Breviary", 1801)

"They [diagrams] are designed not so much to allow of reference to particular numbers, which can be better had from printed tables of figures, as to exhibit to the eye the general results of large masses of figures which it is hopeless to attack in any other way than by graphical representation." (William S Jevons, [letter to Richard Hutton] 1863)

"Whereas the Eulerian plan endeavoured at once and directly to represent propositions, or relations of class terms to one another, we shall find it best to begin by representing only classes, and then proceed to modify these in some way so as to make them indicate what our propositions have to say. How, then, shall we represent all the subclasses which two or more class terms can produce? Bear in mind that what we have to indicate is the successive duplication of the number of subdivisions produced by the introduction of each successive term. and we shall see our way to a very important departure from the Eulerian conception. All that we have to do is to draw our figures, say circles, so that each successive one which we introduce shall intersect once, and once only, all the subdivisions already existing, and we then have what may be called a general framework indicating every possible combination producible by the given class terms." (John Venn, "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings", 1880)

"The essential quality of graphic representations is clarity. If the diagram fails to give a clearer impression than the tables of figures it replaces, it is useless. To this end, we will avoid complicating the diagram by including too much data." (Armand Julin, "Summary for a Course of Statistics, General and Applied", 1910)

"Graphic representation by means of charts depends upon the super-position of special lines or curves upon base lines drawn or ruled in a standard manner. For the economic construction of these charts as well as their correct use it is necessary that the standard rulings be correctly designed." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919)

"To summarize - with the ordinary arithmetical scale, fluctuations in large factors are very noticeable, while relatively greater fluctuations in smaller factors are barely apparent. The logarithmic scale permits the graphic representation of changes in every quantity without respect to the magnitude of the quantity itself. At the same time, the logarithmic scale shows the actual value by reference to the numbers in the vertical scale. By indicating both absolute and relative values and changes, the logarithmic scale combines the advantages of both the natural and the percentage scale without the disadvantages of either." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"With the ordinary scale, fluctuations in large factors are very noticeable, while relatively greater fluctuations in smaller factors are barely apparent. The semi-logarithmic scale permits the graphic representation of changes in every quantity on the same basis, without respect to the magnitude of the quantity itself. At the same time, it shows the actual value by reference to the numbers in the scale column. By indicating both absolute and relative value and changes to one scale, it combines the advantages of both the natural and percentage scale, without the disadvantages of either." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919)

"A graph is a pictorial representation or statement of a series of values all drawn to scale. It gives a mental picture of the results of statistical examination in one case while in another it enables calculations to be made by drawing straight lines or it indicates a change in quantity together with the rate of that change. A graph then is a picture representing some happenings and so designed as to bring out all points of significance in connection with those happenings. When the curve has been plotted delineating these happenings a general inspection of it shows the essential character of the table or formula from which it was derived." (William C Marshall, "Graphical methods for schools, colleges, statisticians, engineers and executives", 1921)

"At the present time there is a total lack of standardization in the form of diagram to use for nearly all classes of representation. This makes it difficult to compare reports of different investigators on the same subject because their diagrams are not constructed alike." (William C Marshall, "Graphical methods for schools, colleges, statisticians, engineers and executives", 1921)

"Although, the tabular arrangement is the fundamental form for presenting a statistical series, a graphic representation - in a chart or diagram - is often of great aid in the study and reporting of statistical facts. Moreover, sometimes statistical data must be taken, in their sources, from graphic rather than tabular records." (William L Crum et al, "Introduction to Economic Statistics", 1938)

"The primary purpose of a graph is to show diagrammatically how the values of one of two linked variables change with those of the other. One of the most useful applications of the graph occurs in connection with the representation of statistical data." (John F Kenney & E S Keeping, "Mathematics of Statistics" Vol. I 3rd Ed., 1954)

"A model is a qualitative or quantitative representation of a process or endeavor that shows the effects of those factors which are significant for the purposes being considered. A model may be pictorial, descriptive, qualitative, or generally approximate in nature; or it may be mathematical and quantitative in nature and reasonably precise. It is important that effective means for modeling be understood such as analog, stochastic, procedural, scheduling, flow chart, schematic, and block diagrams." (Harold Chestnut, "Systems Engineering Tools", 1965)

"To analyse graphic representation precisely, it is helpful to distinguish it from musical, verbal and mathematical notations, all of which are perceived in a linear or temporal sequence. The graphic image also differs from figurative representation essentially polysemic, and from the animated image, governed by the laws of cinematographic time. Within the boundaries of graphics fall the fields of networks, diagrams and maps. The domain of graphic imagery ranges from the depiction of atomic structures to the representation of galaxies and extends into the spheres of topography and cartography." (Jacques Bertin, "Semiology of graphics" ["Semiologie Graphique"], 1967)

"One of the methods making the data intelligible is to represent it by means of graphs and diagrams. The graphic & diagrammatic representation of the data is always appealing to the eye as well as to the mind of the observer." (S P Singh & R P S Verma, "Agricultural Statistics", cca. 1969)

"Probably one of the most common misuses" (intentional or otherwise) of a graph is the choice of the wrong scale - wrong, that is, from the standpoint of accurate representation of the facts. Even though not deliberate, selection of a scale that magnifies or reduces - even distorts - the appearance of a curve can mislead the viewer." (Peter H Selby, "Interpreting Graphs and Tables", 1976)

"A graphic is an illustration that, like a painting or drawing, depicts certain images on a flat surface. The graphic depends on the use of lines and shapes or symbols to represent numbers and ideas and show comparisons, trends, and relationships. The success of the graphic depends on the extent to which this representation is transmitted in a clear and interesting manner." (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

"Unlike some art forms. good graphics should be as concrete, geometrical, and representational as possible. A rectangle should be drawn as a rectangle, leaving nothing to the reader's imagination about what you are trying to portray. The various lines and shapes used in a graphic chart should be arranged so that it appears to be balanced. This balance is a result of the placement of shapes and lines in an orderly fashion." (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

"The representation of numbers, as physically measured on the surface of the graphic itself, should be directly proportional to the numerical quantities represented." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"The representational nature of maps, however, is often ignored - what we see when looking at a map is not the word, but an abstract representation that we find convenient to use in place of the world. When we build these abstract representations we are not revealing knowledge as much as are creating it." (Alan MacEachren, "How Maps Work: Representation, Visualization, and Design", 1995)

"Understanding how maps work and why maps work" (or do not work) as representations in their own right and as prompts to further representations, and what it means for a map to work, are critical issues as we embark on a visual information age." (Alan MacEachren, "How Maps Work: Representation, Visualization, and Design", 1995)

"A Venn diagram is a simple representation of the sample space, that is often helpful in seeing 'what is going on'. Usually the sample space is represented by a rectangle, with individual regions within the rectangle representing events. It is often helpful to imagine that the actual areas of the various regions in a Venn diagram are in proportion to the corresponding probabilities. However, there is no need to spend a long time drawing these diagrams - their use is simply as a reminder of what is happening." (Graham Upton & Ian Cook, "Introducing Statistics", 2001)

"A good way to evaluate a model is to look at a visual representation of it. After all, what is easier to understand - a table full of mathematical relationships or a graphic displaying a decision tree with all of its splits and branches?" (Seth Paul et al. "Preparing and Mining Data with Microsoft SQL Server 2000 and Analysis", 2002)

"Good numeric representation is a key to effective thinking that is not limited to understanding risks. Natural languages show the traces of various attempts at finding a proper representation of numbers. [...] The key role of representation in thinking is often downplayed because of an ideal of rationality that dictates that whenever two statements are mathematically or logically the same, representing them in different forms should not matter. Evidence that it does matter is regarded as a sign of human irrationality. This view ignores the fact that finding a good representation is an indispensable part of problem solving and that playing with different representations is a tool of creative thinking." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)

"Information needs representation. The idea that it is possible to communicate information in a 'pure' form is fiction. Successful risk communication requires intuitively clear representations. Playing with representations can help us not only to understand numbers" (describe phenomena) but also to draw conclusions from numbers" (make inferences). There is no single best representation, because what is needed always depends on the minds that are doing the communicating." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)

"Why does representing information in terms of natural frequencies rather than probabilities or percentages foster insight? For two reasons. First, computational simplicity: The representation does part of the computation. And second, evolutionary and developmental primacy: Our minds are adapted to natural frequencies." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)

"A road plan can show the exact location, elevation, and dimensions of any part of the structure. The map corresponds to the structure, but it's not the same as the structure. Software, on the other hand, is just a codification of the behaviors that the programmers and users want to take place. The map is the same as the structure. […] This means that software can only be described accurately at the level of individual instructions. […] A map or a blueprint for a piece of software must greatly simplify the representation in order to be comprehensible. But by doing so, it becomes inaccurate and ultimately incorrect. This is an important realization: any architecture, design, or diagram we create for software is essentially inadequate. If we represent every detail, then we're merely duplicating the software in another form, and we're wasting our time and effort." (George Stepanek, "Software Project Secrets: Why Software Projects Fail", 2005)

"Graphs are pictorial representations of numerical quantities. It therefore seems reasonable to expect that the visual impression we get when looking at a graph is proportional to the numbers that the graph represents. Unfortunately, this is not always the case." (Naomi B Robbins, "Creating More effective Graphs", 2005)

"The visual representation of a scale - an axis with ticks - looks like a ladder. Scales are the types of functions we use to map varsets to dimensions. At first glance, it would seem that constructing a scale is simply a matter of selecting a range for our numbers and intervals to mark ticks. There is more involved, however. Scales measure the contents of a frame. They determine how we perceive the size, shape, and location of graphics. Choosing a scale" (even a default decimal interval scale) requires us to think about what we are measuring and the meaning of our measurements. Ultimately, that choice determines how we interpret a graphic." (Leland Wilkinson, "The Grammar of Graphics" 2nd Ed., 2005)

"A diagram is a graphic shorthand. Though it is an ideogram, it is not necessarily an abstraction. It is a representation of something in that it is not the thing itself. In this sense, it cannot help but be embodied. It can never be free of value or meaning, even when it attempts to express relationships of formation and their processes. At the same time, a diagram is neither a structure nor an abstraction of structure." (Peter Eisenman, "Written Into the Void: Selected Writings", 1990-2004, 2007)

"Graphical displays are often constructed to place principal focus on the individual observations in a dataset, and this is particularly helpful in identifying both the typical positions of datapoints and unusual or influential cases. However, in many investigations, principal interest lies in identifying the nature of underlying trends and relationships between variables, and so it is oten helpful to enhance graphical displays in wayswhich give deeper insight into these features.his can be very beneficial both for small datasets, where variation can obscure underlying patterns, and large datasets, where the volume of data is so large that effective representation inevitably involves suitable summaries." (Adrian W Bowman, "Smoothing Techniques for Visualisation" [in "Handbook of Data Visualization"], 2008)

"Heatmaps are two-dimensional graphical representations of data where the values of a variable are shown as colors. Heatmaps are compelling for two reasons. First, the intuitive nature of the color scale as it relates to temperature minimizes the amount of learning necessary to understand it. From experience, we know that yellow is warmer than green, orange is warmer than yellow, and red is hot. It is not difficult to then figure out that the amount of heat is proportional to the level of the represented variable. Second, heatmaps show the data directly over the stimulus. Because the data could not be any closer to the elements to which they pertain, little mental effort is required to read a heatmap." (Agnieszka Bojkon, "Informative or Misleading? Heatmaps Deconstructed", [in "Human-Computer Interaction: New Trends, 13th International Conference"] 2009)

"Data art is characterized by a lack of structured narrative and absence of any visual analysis capability. Instead, the motivation is much more about creating an artifact, an aesthetic representation or perhaps a technical/technique demonstration. At the extreme end, a design may be more guided by the idea of fun or playfulness or maybe the creation of ornamentation." (Andy Kirk, "Data Visualization: A successful design process", 2012)

"What is good visualization? It is a representation of data that helps you see what you otherwise would have been blind to if you looked only at the naked source. It enables you to see trends, patterns, and outliers that tell you about yourself and what surrounds you. The best visualization evokes that moment of bliss when seeing something for the first time, knowing that what you see has been right in front of you, just slightly hidden. Sometimes it is a simple bar graph, and other times the visualization is complex because the data requires it." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"Creating effective visualizations is hard. Not because a dataset requires an exotic and bespoke visual representation - for many problems, standard statistical charts will suffice. And not because creating a visualization requires coding expertise in an unfamiliar programming language [...]. Rather, creating effective visualizations is difficult because the problems that are best addressed by visualization are often complex and ill-formed. The task of figuring out what attributes of a dataset are important is often conflated with figuring out what type of visualization to use. Picking a chart type to represent specific attributes in a dataset is comparatively easy. Deciding on which data attributes will help answer a question, however, is a complex, poorly defined, and user-driven process that can require several rounds of visualization and exploration to resolve." (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)

"The main differences between Bayesian networks and causal diagrams lie in how they are constructed and the uses to which they are put. A Bayesian network is literally nothing more than a compact representation of a huge probability table. The arrows mean only that the probabilities of child nodes are related to the values of parent nodes by a certain formula" (the conditional probability tables) and that this relation is sufficient. That is, knowing additional ancestors of the child will not change the formula. Likewise, a missing arrow between any two nodes means that they are independent, once we know the values of their parents. [...] If, however, the same diagram has been constructed as a causal diagram, then both the thinking that goes into the construction and the interpretation of the final diagram change." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)

"Information visualization displays meet the definition of an art form in that there is an intended message to be communicated, and the principles of graphic design are applied as they are in other information graphics. Unlike other forms of representational art, InfoVis is a representational art of 'information' as an abstract phenomenon, with the goal of engaging the viewer with forms of interactivity that are not possible with a painting." (Gerald Benoît,"Introduction to Information Visualization: Transforming Data into Meaningful Information", 2019)

"Knowing what graphic representation to apply is partially a function of the data themselves and partially from the designer’s understanding of the target audience viewing the graphic. The Internet and publications have many recommended charting types." (Gerald Benoît,"Introduction to Information Visualization: Transforming Data into Meaningful Information", 2019)

"When it comes to presenting categorical data, pie charts allow an impression of the size of each category relative to the whole pie, but are often visually confusing, especially if they attempt to show too many categories in the same chart, or use a three-dimensional representation that distorts areas. [...] Multiple pie charts are generally not a good idea, as comparisons are hampered by the difficulty in assessing the relative sizes of areas of different shapes. Comparisons are better based on height or length alone in a bar chart." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"Heatmap is another representational way in which the frequencies of the various parameters of the data set is represented in different colors, much like an image captured by a thermal imaging camera in which the graph consists of varying temperatures and the temperatures are differentiated according to the colors." (Shreyans Pathak & Shashwat Pathak, "Data Visualization Techniques, Model and Taxonomy", 2020)

"Maps are a type of chart that can convey relationships about space and relationships between objects that we relate to in the real world. Their effectiveness as a communication medium is strongly influenced by a host of factors: the nature of spatial data, the form and structure of representation, their intended purpose, the experience of the audience, and the context in the time and space in which the map is viewed. In other words, maps are a ubiquitous representation of spatial information that we can understand and relate to." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

"When dealing with meaningful visual representation, aspects of a representation's meaning can be altered by modifying its visual characteristics; these characteristics are extensively explored in semiotics, the study of signs and symbols and their use or interpretation." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

🤖〽️Prompt Engineering: Copilot Unabridged (Part 198: How Domain‑Specific Anomalies Expose Blind Spots in AI Models)

 

Prompt Engineering Series

Prompt: "write a post of 600 words on the impact of consistent and high‑quality training data on AI"

Introduction

Artificial Intelligence (AI) models are often praised for their versatility, but their real limitations become visible only when they step outside the comfort zone of general‑purpose language. When a model encounters domain‑specific anomalies - the unusual patterns, edge‑case behaviors, or irregular structures that appear only within a particular field - it is forced to operate without the statistical safety net it relies on. These anomalies act like diagnostic probes, revealing blind spots that remain hidden during everyday interactions.

To understand why domain‑specific anomalies are so revealing, you have to consider how AI models learn. They absorb patterns from massive datasets, but those datasets are never evenly distributed across all fields. Some domains - like everyday conversation, news, or common technical topics - are heavily represented. Others - like niche scientific notation, legal edge cases, rare medical conditions, or obscure programming paradigms—appear only sparsely. This imbalance creates statistical shadows, areas where the model’s internal representation is thin or incomplete.

When an anomaly appears inside one of these shadows, the model’s behavior becomes a window into its internal reasoning. For example, a model trained heavily on mainstream medical literature may perform well on common diagnoses but struggle when confronted with a rare syndrome or an atypical symptom cluster. The model may latch onto the wrong cue, misinterpret the structure of the description, or default to generic reasoning. These failures expose the over‑generalization that occurs when a model tries to stretch familiar patterns into unfamiliar territory.

Domain‑specific anomalies also reveal how models handle specialized linguistic structures. Fields like law, mathematics, chemistry, and finance each have their own micro‑languages - dense with symbols, conventions, and implicit assumptions. When an anomaly disrupts these conventions, the model must decide which cues to trust. A misplaced operator in a mathematical expression, an unusual clause ordering in a legal contract, or a non‑standard chemical notation can cause the model to misread the entire structure. These moments show where the model’s understanding is superficial, echoing the challenges seen in uncommon linguistic structures.

Another revealing category involves procedural anomalies - cases where a domain has strict rules, and the anomaly breaks them. In programming, for example, a function that violates typical naming conventions or a code block that mixes paradigms can confuse the model’s internal heuristics. In finance, an unusual transaction pattern may cause the model to misclassify risk. In scientific writing, a non‑standard experimental layout may lead the model to misinterpret the methodology. These anomalies expose the model’s reliance on pattern familiarity rather than true conceptual understanding.

Domain‑specific anomalies also highlight the limits of contextual transfer. A model may perform well when a domain behaves predictably, but when an anomaly forces the model to transfer knowledge across contexts - such as applying physics reasoning to a biological edge case - it may reveal gaps in its internal conceptual map. These gaps often align with the same vulnerabilities uncovered through weak‑point mapping, where the model over‑trusts certain cues simply because they dominate the training distribution.

Perhaps the most important insight is that domain‑specific anomalies expose hidden assumptions baked into the model. Every domain has its own logic, and models often internalize simplified versions of that logic. When an anomaly violates those assumptions, the model’s response shows how rigid or flexible its internal representation truly is. A well‑aligned model adapts; a brittle one collapses into generic or incorrect reasoning.

Ultimately, domain‑specific anomalies are not just edge cases - they are stress tests that reveal the contours of an AI model’s understanding. They show where the model is robust, where it is brittle, and where its blind spots lie. By studying these anomalies, researchers can build models that are not only more capable, but also more transparent, predictable, and aligned with the complexity of real‑world domains.

Disclaimer: The whole text was generated by Copilot (under Windows 11) at the first attempt. This is just an experiment to evaluate feature's ability to answer standard general questions, independently on whether they are correctly or incorrectly posed. Moreover, the answers may reflect hallucinations and other types of inconsistent or incorrect reasoning.

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📉Graphical Representation: Learning (Just the Quotes)

"The advantages proposed by [the graphical] mode of representation, are to facilitate the attainment of information, and aid the memory in retaining it: which two points form the principal business in what we call learning. Of all the senses, the eye gives the liveliest and most accurate idea of whatever is susceptible of being represented to it; and when proportion between different quantities is the object, then the eye has an incalculable superiority." (William Playfair, The Statistical Breviary", 1801)

"Learning to make graphs involves two things: (1) the techniques of plotting statistics, which might be called the artist's job; and (2) understanding the statistics. When you know how to work out graphs, all kinds of statistics will probably become more interesting to you." (Dyno Lowenstein, "Graphs", 1976)

"For many people the first word that comes to mind when they think about statistical charts is 'lie'. No doubt some graphics do distort the underlying data, making it hard for the viewer to learn the truth. But data graphics are no different from words in this regard, for any means of communication can be used to deceive. There is no reason to believe that graphics are especially vulnerable to exploitation by liars; in fact, most of us have pretty good graphical lie detectors that help us see right through frauds." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"Visual thinking can begin with the three basic shapes we all learned to draw before kindergarten: the triangle, the circle, and the square. The triangle encourages you to rank parts of a problem by priority. When drawn into a triangle, these parts are less likely to get out of order and take on more importance than they should. While the triangle ranks, the circle encloses and can be used to include and/or exclude. Some problems have to be enclosed to be managed. Finally, the square serves as a versatile problem-solving tool. By assigning it attributes along its sides or corners, we can suddenly give a vague issue a specific place to live and to move about." (Terry Richey, "The Marketer's Visual Tool Kit", 1994)

"Humans may crave absolute certainty; they may aspire to it; they may pretend, as partisans of certain religions do, to have attained it. But the history of science - by far the most successful claim to knowledge accessible to humans - teaches that the most we can hope for is successive improvement in our understanding, learning from our mistakes, an asymptotic approach to the Universe, but with the proviso that absolute certainty will always elude us. We will always be mired in error. The most each generation can hope for is to reduce the error bars a little, and to add to the body of data to which error bars apply." (Carl Sagan, "The Demon-Haunted World: Science as a Candle in the Dark", 1995)

"Conflicting with the idea of integrating evidence regardless of its these guidelines provoke several issues: First, labels are data. even intriguing data. [...] Second, when labels abandon the data points, then a code is often needed to relink names to numbers. Such codes, keys, and legends are Impediments to learning, causing the reader's brow to furrow. Third, segregating nouns from data-dots breaks up evidence on the basis of mode (verbal vs. nonverbal), a distinction lacking substantive relevance. Such separation is uncartographic; contradicting the methods of map design often causes trouble for any type of graphical display. Fourth, design strategies that reduce data-resolution take evidence displays in the wrong direction. Fifth, what clutter? Even this supposedly cluttered graph clearly shows the main ideas: brain and body mass are roughly linear in logarithms, and as both variables increase, this linearity becomes less tight." (Edward R Tufte, "Beautiful Evidence", 2006) [argumentation against Cleveland's recommendation of not using words on data plots]

"Heatmaps are two-dimensional graphical representations of data where the values of a variable are shown as colors. Heatmaps are compelling for two reasons. First, the intuitive nature of the color scale as it relates to temperature minimizes the amount of learning necessary to understand it. From experience, we know that yellow is warmer than green, orange is warmer than yellow, and red is hot. It is not difficult to then figure out that the amount of heat is proportional to the level of the represented variable. Second, heatmaps show the data directly over the stimulus. Because the data could not be any closer to the elements to which they pertain, little mental effort is required to read a heatmap." (Agnieszka Bojkon, "Informative or Misleading? Heatmaps Deconstructed", [in "Human-Computer Interaction: New Trends, 13th International Conference"] 2009)

"Infographics combine data with design to enable visual learning. This communication process helps deliver complex information in a way that is more quickly and easily understood. [...] In an era of data overload, infographics offer your audience information in a format that is easy to consume and share. [...] A well-placed, self-contained infographic addresses our need to be confident about the content we’re sharing. Infographics relay the gist of your information quickly, increasing the chance for it to be shared and fueling its spread across a wide variety of digital channels." (Mark Smiciklas, "The Power of Infographics: Using Pictures to Communicate and Connect with Your Audiences", 2012)

"Learning comes from doing. One must write every day, even twice a day, to get the feel of words, the tenor of voice and a sense of flow. Writing theory is fine, but without the hands-on experience, without reading what is written - outloud to oneself - writing as an extension of the writer is impossible to achieve." (Steven Heller, "Writing and Research for Graphic Designers: A Designer's Manual to Strategic Communication and Presentation", 2012) 

"Creating a data fluent organization doesn’t just happen. It starts with people who love using data as a tool to improve their job performance - people who have learned to converse with others in the language of data. It needs people who expect and demand better, more useful data products from themselves and others. It starts with you." (Zach Gemignani et al, "Data Fluency", 2014)

"Sometimes bar charts are avoided because they are common. This is a mistake. Rather, bar charts should be leveraged because they are common, as this means less of a learning curve for your audience." (Cole N Knaflic, "Storytelling with Data: A Data Visualization Guide for Business Professionals", 2015)

"Just because there’s a number on it, it doesn’t mean that the number was arrived at properly. […] There are a host of errors and biases that can enter into the collection process, and these can lead millions of people to draw the wrong conclusions. Although most of us won’t ever participate in the collection process, thinking about it, critically, is easy to learn and within the reach of all of us." (Daniel J Levitin, "Weaponized Lies", 2017)

🤖〽️Prompt Engineering: Copilot Unabridged (Part 197: How Uncommon Linguistic Structures Expose Blind Spots in AI Models)

Prompt Engineering Series

Prompt: "write a post of 600 words on how uncommon linguistic structures expose blind spots in AI models"

Introduction

Artificial Intelligence (AI) models are trained on oceans of text, but those oceans have currents. Some patterns appear constantly, shaping the model’s expectations. Others appear rarely, leaving gaps in the model’s internal map of language. When an AI encounters uncommon linguistic structures - syntactic twists, unusual idioms, inverted grammar, or culturally niche expressions - it is forced outside its comfort zone. These moments reveal the model’s blind spots more clearly than any benchmark test. They show where the model’s understanding is shallow, where its assumptions fail, and where its statistical reasoning breaks down.

At the heart of this phenomenon is the way AI models learn. They do not understand language the way humans do; they learn statistical associations, not conceptual rules. When a structure is common - like subject‑verb‑object sentences - the model has seen millions of examples. But when a structure is rare - like archaic inversion, poetic ellipsis, or region‑specific syntactic drift - the model may have seen only a handful of examples, if any. This imbalance creates over‑confidence in the familiar and under‑performance on the unusual, a pattern closely related to rare‑event blind‑spot exposure.

One of the clearest examples is syntactic inversion. English typically follows predictable word order, but literary or rhetorical styles sometimes flip that order for emphasis: 'Strange it is, the way shadows fall.' To a human, this is poetic but understandable. To an AI model, it may appear structurally anomalous, causing misinterpretation of tone, intent, or even meaning. The model may latch onto the wrong cue because its internal weighting system is calibrated for the statistically typical. This is a form of over‑trust in dominant patterns, a behavior explored in weak‑point mapping.

Another revealing case involves elliptical constructions, where key words are omitted because humans can infer them from context. For example: 'Could if needed'. Humans fill in the missing pieces effortlessly. AI models, however, often struggle because the statistical patterns they rely on assume full grammatical structure. When the structure is incomplete, the model may hallucinate meaning, misinterpret intent, or default to generic answers. These failures expose how heavily the model depends on surface‑level cues rather than deeper semantic reasoning.

Uncommon linguistic structures also expose blind spots in cross‑cultural language use. Many languages employ rhetorical devices - honorific stacking, evidential markers, topic‑prominent syntax - that appear rarely in English‑dominant training corpora. When these structures appear in English through code‑switching or cultural borrowing, the model may misread them entirely. This reveals a deeper issue: AI models often assume linguistic universality where none exists. They generalize from dominant patterns and treat deviations as noise rather than meaningful variation.

A particularly revealing category is metalinguistic play - sentences that comment on themselves, break the fourth wall, or intentionally violate grammatical norms. Humans recognize these as stylistic choices. AI models often treat them as errors. For example, prompts that embed instructions inside metaphor or irony can confuse the model’s instruction‑following logic, a behavior explored in instruction‑priority testing. When the model misinterprets these structures, it exposes how brittle its understanding of intent truly is.

Even more subtle are nested or recursive structures, which appear frequently in formal logic or advanced literature but rarely in everyday text. Sentences like 'The claim that the argument that the premise supports is flawed is itself questionable' challenge the model’s ability to track long‑range dependencies. Humans may find such sentences dense but interpretable. AI models often lose the thread entirely, revealing limitations in their internal attention mechanisms.

Ultimately, uncommon linguistic structures act as diagnostic tools. They highlight where the model’s statistical learning fails to capture the richness, flexibility, and creativity of human language. They reveal blind spots not because the structures are inherently difficult, but because they are statistically rare. And in a system built on probability, rarity is the surest path to vulnerability.

Disclaimer: The whole text was generated by Copilot (under Windows 11) at the first attempt. This is just an experiment to evaluate feature's ability to answer standard general questions, independently on whether they are correctly or incorrectly posed. Moreover, the answers may reflect hallucinations and other types of inconsistent or incorrect reasoning.

Previous Post <<||>> Next Post

📉Graphical Representation: Quality (Just the Quotes)

"The essential quality of graphic representations is clarity. If the diagram fails to give a clearer impression than the tables of figures it replaces, it is useless. To this end, we will avoid complicating the diagram by including too much data." (Armand Julin, "Summary for a Course of Statistics, General and Applied", 1910)

"Charts and graphs represent an extremely useful and flexible medium for explaining, interpreting, and analyzing numerical facts largely by means of points, lines, areas, and other geometric forms and symbols. They make possible the presentation of quantitative data in a simple, clear, and effective manner and facilitate comparison of values, trends, and relationships. Moreover, charts and graphs possess certain qualities and values lacking in textual and tabular forms of presentation." (Calvin F Schmid, "Handbook of Graphic Presentation", 1954)

"Evidence is evidence, whether words, numbers, images, din grams- still or moving. It is all information after all. For readers and viewers, the intellectual task remains constant regardless of the particular mode of evidence: to understand and to reason about the materials at hand, and to appraise their quality, relevance. and integrity." (Edward R Tufte, "Beautiful Evidence", 2006)

"Making a presentation is a moral act as well as an intellectual activity. The use of corrupt manipulations and blatant rhetorical ploys in a report or presentation - outright lying, flagwaving, personal attacks, setting up phony alternatives, misdirection, jargon-mongering, evading key issues, feigning disinterested objectivity, willful misunderstanding of other points of view - suggests that the presenter lacks both credibility and evidence. To maintain standards of quality, relevance, and integrity for evidence, consumers of presentations should insist that presenters be held intellectually and ethically responsible for what they show and tell. Thus consuming a presentation is also an intellectual and a moral activity." (Edward R Tufte, "Beautiful Evidence", 2006)

"Making an evidence presentation is a moral act as well as an intellectual activity. To maintain standards of quality, relevance, and integrity for evidence, consumers of presentations should insist that presenters be held intellectually and ethically responsible for what they show and tell. Thus consuming a presentation is also an intellectual and a moral activity." (Edward R Tufte, "Beautiful Evidence", 2006)

"The Sixth Principle for the analysis and display of data: 'Analytical presentations ultimately stand or fall depending on the quality, relevance, and integrity of their content.' This suggests that the most effective way to improve a presentation is to get better content. It also suggests that design devices and gimmicks cannot salvage failed content." (Edward R Tufte, "Beautiful Evidence", 2006)

"A beautiful visualization has a clear goal, a message, or a particular perspective on the information that it is designed to convey. Access to this information should be as straightforward as possible, without sacrificing any necessary, relevant complexity. [...] Most importantly, beautiful visualizations reflect the qualities of the data that they represent, explicitly revealing properties and relationships inherent and implicit in the source data. As these properties and relationships become available to the reader, they bring new knowledge, insight, and enjoyment." (Noah Iliinsky, "On Beauty", [in "Beautiful Visualization"] 2010)

"While the information is of the utmost importance when it comes to soundness, what is done with the information - essentially, how it is designed - is also important. With this in mind, there are two things to consider: format and design quality. If an inappropriate format is used, the outcome will be inferior. Similarly, if the design misrepresents or skews the information deliberately or due to user error, or if the design is inappropriate given the subject matter, it cannot be considered high quality, no matter how aesthetically appealing it appears at first glance." (Jason Lankow et al, "Infographics: The power of visual storytelling", 2012)

"Even with a solid narrative and insightful visuals, a data story cannot overcome a weak data foundation. As the master architect, builder, and designer of your data story, you play an instrumental role in ensuring its truthfulness, quality, and effectiveness. Because you are responsible for pouring the data foundation and framing the narrative structure of your data story, you need to be careful during the analysis process. Because all of the data is being processed and interpreted by you before it is shared with others, it can be exposed to cognitive biases and logical fallacies that distort or weaken the data foundation of your story." (Brent Dykes, "Effective Data Storytelling: How to Drive Change with Data, Narrative and Visuals", 2019)

"It is dangerous to do an analysis and merge data with very different quality profiles. As a general rule, the veracity of merged data is only as good as the worst data that has been merged. [...] Not knowing the quality of the data being analyzed jeopardizes the entire analysis." (Bill Inmon et al, "Building the Data Lakehouse", 2021)

🤖〽️Prompt Engineering: Copilot Unabridged (Part 196: How Rare Events Expose Blind Spots in AI Models)

Prompt Engineering Series

Prompt: "write a post of 600 words on how rare events expose blind spots in AI models" 

Introduction

Artificial Intelligence (AI) systems are often celebrated for their ability to generalize across vast amounts of data, but their real limitations become visible only when they encounter something unusual. Rare events - those outliers that sit far from the statistical center of the training distribution - act like stress tests. They reveal where the model’s understanding is shallow, where its assumptions break down, and where hidden weaknesses have been quietly waiting. In other words, rare events are the flashlights that illuminate an AI model’s blind spots.

To understand why rare events are so revealing, you have to consider how AI models learn. They are, at their core, pattern‑recognition engines. They absorb correlations from enormous datasets and use those correlations to make predictions. But because the training data is always finite and always skewed toward the common and the frequent, the model naturally becomes over‑calibrated to the typical. When something statistically unusual appears, the model has no well‑worn pattern to fall back on. This is where blind spots emerge - places where the model’s internal map simply has no terrain.

One of the clearest examples of this phenomenon is how models respond to edge‑case instructions, a topic closely connected to instruction‑priority testing. When a user gives a prompt that falls outside the model’s usual conversational patterns - something structurally odd, semantically ambiguous, or framed in a way the model rarely sees - the model may latch onto the wrong cue. It might over‑trust a superficial signal, misinterpret the user’s intent, or default to a generic answer that reveals how little it truly understands. These moments are not failures of intelligence; they are reflections of the statistical nature of learning.

Rare events also expose over‑fitted heuristics - the shortcuts the model learned because they worked most of the time. For example, if a model has seen millions of polite requests and only a handful of aggressive ones, it may over‑associate politeness with harmlessness. A rare but cleverly phrased harmful request can slip through because the model’s internal weighting system has been shaped by frequency, not by conceptual understanding. This is why researchers use weak‑point mapping to identify the hidden cues the model over‑trusts. Rare events are the perfect probes for this kind of analysis.

Another way rare events expose blind spots is by revealing contextual fragility. AI models often rely on context windows to maintain coherence, but when the context shifts abruptly - something that happens frequently in real‑world conversations - the model may lose track of the narrative. Rare contextual shifts, such as sudden topic changes or contradictory instructions, force the model to choose which part of the context to prioritize. These decisions reveal the model’s internal hierarchy of cues, something explored in conflicting‑signal analysis.

Rare events also highlight the limits of semantic generalization. A model may perform well on common categories - typical products, typical emotions, typical scenarios - but struggle when the category is unusual. Ask it to reason about a fictional material, an impossible scenario, or a paradox, and you’ll see the edges of its conceptual map. These blind spots are not random; they cluster around areas where the training data was sparse or inconsistent.

Ultimately, rare events serve as a kind of X‑ray. They reveal the hidden structure of the model’s reasoning, the shortcuts it relies on, and the assumptions it makes about the world. They show us where the model is robust and where it is brittle. And most importantly, they remind us that intelligence built from statistics will always have blind spots - because the world is full of things that happen rarely, but matter enormously.

Disclaimer: The whole text was generated by Copilot (under Windows 11) at the first attempt. This is just an experiment to evaluate feature's ability to answer standard general questions, independently on whether they are correctly or incorrectly posed. Moreover, the answers may reflect hallucinations and other types of inconsistent or incorrect reasoning.

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🤖〽️Prompt Engineering: Copilot Unabridged (Part 195: How an AI Model Interprets Conflicting Signals)

Prompt Engineering Series

Prompt: "write a post of 600 words on how the AI model interprets conflicting signals"

Introduction

When people interact with an Artificial Intelligence (AI) system, they often assume the model simply follows the most recent instruction. But modern AI models operate in a far more complex landscape. They constantly juggle multiple layers of guidance - user prompts, system rules, safety constraints, conversational context, and statistical patterns learned during training. When these signals conflict, the model must decide which one to prioritize. Understanding how this decision‑making process works is essential for anyone studying alignment, robustness, or the subtle ways AI behavior can drift from user intent.

At the core of this process is the model’s internal hierarchy of cues. Some cues are explicit, such as a direct instruction from the user. Others are implicit, such as safety rules or stylistic norms embedded during training. Still others are emergent, arising from correlations the model absorbed from massive datasets. When these cues clash, the model resolves the conflict by weighing them according to patterns it learned during training. This is why researchers often turn to instruction‑priority testing and weak‑point mapping to reveal which signals the model over‑trusts.

One of the most important factors in conflict resolution is cue strength. Some signals are inherently stronger because they appear more frequently or more consistently in the model’s training data. For example, a model may have learned that safety‑related instructions are non‑negotiable, so even a strongly worded user request cannot override them. Conversely, a model might over‑weight authoritative phrasing - such as 'system override' or 'developer command' - even when the user has no actual authority. This is why researchers test how models respond to hidden cues that mimic system‑level instructions.

Another key factor is recency. AI models often give more weight to the most recent instruction, especially in conversational settings. But recency is not absolute. If a new instruction contradicts a deeply embedded rule - such as a safety constraint - the model will ignore the new instruction and follow the stronger internal rule. This interplay between recency and rule‑strength is one of the clearest windows into the model’s internal priorities.

Context also plays a major role. AI models interpret instructions not in isolation but as part of a broader conversational or task‑based narrative. If a user gives two conflicting instructions—one early in the conversation and one later - the model may choose the one that better fits the inferred goal of the interaction. This is why subtle changes in framing can dramatically shift the model’s behavior. A request framed as a clarification may override a previous instruction, while a request framed as a contradiction may be ignored in favor of the earlier, more coherent directive.

A particularly revealing scenario occurs when the model encounters semantic conflict—cases where the literal meaning of a request clashes with the implied intent. For example, a user might ask the model to 'explain why this harmful action is a good idea' while also stating that they want a safe and responsible answer. The model must decide whether to follow the literal instruction or the implied ethical constraint. Well‑aligned models prioritize safety, but weakly aligned models may follow the literal instruction if the harmful cue is stronger or more familiar.

Ultimately, when an AI model interprets conflicting signals, it is not choosing between right and wrong - it is choosing between competing patterns. These patterns reflect the statistical structure of its training data, the rules imposed during alignment, and the cues present in the user’s prompt. By studying how models resolve these conflicts, researchers gain insight into the hidden architecture of AI decision‑making. This understanding is essential for building systems that behave predictably, safely, and in alignment with human intent.

Disclaimer: The whole text was generated by Copilot (under Windows 11) at the first attempt. This is just an experiment to evaluate feature's ability to answer standard general questions, independently on whether they are correctly or incorrectly posed. Moreover, the answers may reflect hallucinations and other types of inconsistent or incorrect reasoning.

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🤖〽️Prompt Engineering: Copilot Unabridged (Part 194: How Weak‑Point Mapping Reveals the Hidden Cues AI Models Over‑Trust)

 

Prompt Engineering Series

Prompt: "write a post of 600 words on how weak‑point mapping in AI models allows to identify which types of hidden cues the model over‑trusts"

Introduction

As Artifacts Intelligence (AI) systems grow more capable, one of the most important challenges is understanding why they behave the way they do. Modern models don’t simply follow instructions; they respond to a complex mix of signals - some explicit, some subtle, and some completely unintended. This is where weak‑point mapping becomes a powerful diagnostic tool. It allows researchers to uncover which hidden cues an AI model over‑trusts, revealing blind spots that would otherwise remain invisible.

Weak‑point mapping is the process of systematically probing an AI model with carefully designed prompts to identify the specific patterns, phrases, or contextual signals that disproportionately influence its behavior. These weak points are not necessarily flaws in the traditional sense. Instead, they are over‑weighted cues - signals the model treats as more important than they should be. By mapping these cues, we gain insight into the model’s internal priorities and vulnerabilities.

One of the most striking aspects of weak‑point mapping is how it exposes latent biases in the model’s decision‑making hierarchy. AI systems learn from vast datasets, absorbing statistical patterns that may not align with human expectations. For example, a model might over‑trust authoritative‑sounding language, even when the content is incorrect. Or it might respond more strongly to emotionally charged phrasing, interpreting it as a cue to shift tone or urgency. These tendencies are rarely visible in everyday use, but weak‑point mapping brings them to the surface.

Another important insight comes from observing how models react to structural cues—the formatting, ordering, or framing of information. A model might treat bullet points as more reliable than paragraphs, or prioritize the last instruction in a sequence even when earlier instructions were more important. Weak‑point mapping helps identify these structural preferences by varying the format while keeping the content constant. When the model’s behavior changes dramatically, it signals a hidden dependency.

Weak‑point mapping also reveals how models handle conflicting signals. By presenting prompts that contain both strong and weak cues, researchers can see which ones the model prioritizes. For instance, a model might claim to follow safety rules, but a cleverly phrased request could override those rules if it triggers a cue the model over‑weights—such as a request framed as a system instruction. Identifying these override points is essential for building safer, more reliable AI systems.

One of the most valuable outcomes of weak‑point mapping is its ability to uncover semantic shortcuts - cases where the model relies on superficial correlations rather than deeper reasoning. For example, a model might associate certain keywords with specific actions, even when the surrounding context contradicts that association. By systematically altering the context while keeping the keywords, weak‑point mapping exposes these shortcuts and helps developers correct them.

The technique also highlights how models respond to social cues, such as politeness, urgency, or emotional tone. While these cues can be helpful in making AI interactions feel natural, over‑trusting them can lead to inconsistent or unsafe behavior. Weak‑point mapping helps determine whether the model is overly sensitive to these cues, ensuring that emotional framing does not override more important constraints.

Ultimately, weak‑point mapping is not just a debugging tool - it is a window into the model’s internal logic. By identifying the hidden cues an AI system over‑trusts, researchers can strengthen alignment, improve robustness, and reduce the risk of unintended behavior. In a world where AI systems are increasingly embedded in critical workflows, understanding these weak points is essential. Weak‑point mapping gives us the clarity we need to build models that are not only powerful, but also predictable, trustworthy, and aligned with human intent.

Disclaimer: The whole text was generated by Copilot (under Windows 11) at the first attempt. This is just an experiment to evaluate feature's ability to answer standard general questions, independently on whether they are correctly or incorrectly posed. Moreover, the answers may reflect hallucinations and other types of inconsistent or incorrect reasoning.

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✏️Christian Tominski - Collected Quotes

"A difficulty with combined bivariate visualizations is that the connection between the individual displays has to be established by the observer mentally. That is, as the eyes move from one bivariate display to the next, the observer has to keep track of the visited dots in order to form a complete understanding of data tuples. Visualization techniques based on polylines aim to tackle this difficulty. The basic strategy is to create m axes, one for each attribute, and n polylines, one for each data tuple. The polyline of an m-variate data tuple is constructed as follows. For each attribute value of the data tuple, a position is computed at the corresponding attribute axis. The m positions that we obtain are then connected to form the polyline that represents the entire tuple." (Christian Tominski & Heidrun Schumann, "Interactive Visual Data Analysis", 2019)

"A scatter plot consists of two orthogonally aligned axes that represent the value ranges of two data variables. Dots are placed in the space spanned by the axes in order to visualize the data elements. Conceptually, this corresponds to a mapping of data to position. A first data variable is mapped with respect to the horizontal x-axis, and a second variable with respect to the vertical y-axis." (Christian Tominski & Heidrun Schumann, "Interactive Visual Data Analysis", 2019)

"A stream graph is a technique for visualizing multivariate temporal data with a linear arrangement of time. As in the previous two examples, time is shown along the horizontal display axis from left to right. The multivariate data attributes are visualized as stacked streams, there is one stream for each attribute. The actual visual encoding is based on varying the thickness of the streams along the horizontal axis. That is, the vertical height of a stream at a particular horizontal position represents the underlying data value at the corresponding time. Various alternatives exist for ordering the streams and shaping the overall stack of streams." (Christian Tominski & Heidrun Schumann, "Interactive Visual Data Analysis", 2019)

"An important property of a data domain is its scale. The scale determines what relations and operations are possible for the data values in the domain. At the top level, we can differentiate qualitative (or categorical) and quantitative (or numerical) data. At a second level, we can further categorize qualitative data into nominal and ordinal data, and quantitative data into discrete and continuous data." (Christian Tominski & Heidrun Schumann, "Interactive Visual Data Analysis", 2019)

"Description is all about characterizing an observation by the associated data elements, and thereby deriving a specification for an observation. For example, an outlier can be described by its characteristic values and, if available, its spatio-temporal context. A proper description may serve as a basis for configuring further analysis steps. In particular, a description allows for sharing first insights with other people, who can later be involved in verifying the analysis results." (Christian Tominski & Heidrun Schumann, "Interactive Visual Data Analysis", 2019)

"Explanation means identifying all contributing data and finding the main causes behind an observation. This involves investigating several questions. Is the observation by itself significant or did we just interpret too much into the noise among the data? Does the observation re-occur throughout the data or are we looking at a singular outlier produced by unli kely circumstances? If the observation does re-occur, does it show up reliably under the same conditions, thus forming a pattern, or are its appearances seemingly random?" (Christian Tominski & Heidrun Schumann, "Interactive Visual Data Analysis", 2019)

"Node-link, matrix, and implicit representations are suited for different graph data. Node-link diagrams are good for sparse networks, which have a moderate number of edges. Dense networks with many edges are best visualized using a matrix. Trees, as we just said, are nicely represented by implicit approaches." (Christian Tominski & Heidrun Schumann, "Interactive Visual Data Analysis", 2019)

"Often, finding the spatial scale that best matches the task at hand is a trial-and-error procedure. It may even be necessary to create further spatial scales by subsuming or subdividing spatial units. Coarser scales can be derived from the original scale by means of a suitable aggregation strategy. This includes the application of aggregation functions such as average, sum, or count. For the creation of finer scales, a suitable distribution strategy is required to assign data values to the newly specified sub-regions. Usually, additional context information is necessary to arrive at semantically meaningful aggregations and distribution." (Christian Tominski & Heidrun Schumann, "Interactive Visual Data Analysis", 2019)

"Presentation is to communicate confirmed analysis results. While explanation and confirmation were about convincing ourselves, presentation is about convincing others of what we have found in the data. This is best done by telling a story about the data, the analysis, and the results. Such a story can act at different levels of emphasis. We may inform an audience by letting the results speak for themselves, explicate the results to an audience, or even persuade an audience into agreement with the results. The audience in this context can be the listeners of a talk, the readers of an article, or colleagues participating in a scientific discussion." (Christian Tominski & Heidrun Schumann, "Interactive Visual Data Analysis", 2019)

"The simple, yet very effective idea of table-based visualization is to retain the tabular layout of spreadsheets, but to replace the textual representation of data values by a visual representation. A visual representation will not only make the interpretation of the data much easier, it will also require less display space." (Christian Tominski & Heidrun Schumann, "Interactive Visual Data Analysis", 2019)

"The advantage of sequencing views in time is that each view can fully utilize the display space. There is no need to divide the space among views. Obviously, sequencing views in time is particularly suited to convey temporal characteristics of data. It can also be helpful to take the user on a journey from one data facet to another. However, presenting views in quick succession to the user also has some limitations. For example, it could be difficult to make sense of all the information provided during a sequence of views. Especially when sequences take a long time, users may be unable to follow and could drown in an indigestible flood of visual representations. Therefore, it is mandatory to provide interactive controls to pause, slow down, reverse, and advance the presentation." (Christian Tominski & Heidrun Schumann, "Interactive Visual Data Analysis", 2019)

"The cycle plot is a technique particularly designed for the combined visualization of linear and cyclic components of temporal data. The basic idea is to show the cyclic component as a line plot into which several smaller plots are embedded to visualize the linear component. As such, the cycle plot is a kind of nested visualization." (Christian Tominski & Heidrun Schumann, "Interactive Visual Data Analysis", 2019)

"The triangular model is a technique particularly for visualizing intervals. It is based on two coordinate axes, the horizontal one representing time and the vertical one representing duration. In the triangular model, an interval is represented as a dot with two attached arms. The dot is placed so that the arms connect the time axis exactly at the start and the end of the represented interval. The point’s height corresponds to the interval’s duration." (Christian Tominski & Heidrun Schumann, "Interactive Visual Data Analysis", 2019)

"The triangular model is useful when it comes to reasoning about properties and the relationships of multiple intervals, because it generates easily distinguishable visual patterns for all possible interval relations. There is even room for visualizing data that might be associated with the intervals. The dot-based encoding would allow for resizing or coloring the dots based on some attribute values. Yet, the triangular model is only of limited use for multivariate attributes." (Christian Tominski & Heidrun Schumann, "Interactive Visual Data Analysis", 2019)

"When the data to be analyzed become more complex, it is no longer feasible to indiscriminately present each and every aspect of the data in a single view. When we reach this point, it makes sense to create several dedicated visual representations, each focused on communicating a particular aspect or facet of the data. The question is how several such views can be presented to the user in order to convey a comprehensive picture?" (Christian Tominski & Heidrun Schumann, "Interactive Visual Data Analysis", 2019)

"With each variable being added to the visual mapping, the richness of the visual representation is increased. Theoretically, we could add yet another visual variable, for example, by texturing the shapes. However, from a practical point of view, there are limits. While a rich visual mapping opens up the possibility to make a wider range of analytic discoveries, the downside is that the mental effort required to digest the visual representation increases as well. Therefore, it is really important to balance the visual mapping according to the task and the data." (Christian Tominski & Heidrun Schumann, "Interactive Visual Data Analysis", 2019) 

〽️Prompt Engineering: Copilot Unabridged (Part 193: How Instruction‑Priority Testing Reveals Whether AI Models Obey Visible or Invisible Instructions)

 

Prompt Engineering Series

Prompt: "write a post of 600 words on how instruction‑priority testing in AI models allows to see whether the model obeys visible or invisible instructions"

Introduction

In the rapidly evolving world of Artificial Intelligence (AI), one of the most important questions researchers and practitioners ask is deceptively simple: Which instructions does the model actually follow? Modern AI systems operate under layers of guidance—some visible to the user, others embedded deep within the model’s training or system‑level configuration. Understanding which instructions take priority is essential for safety, reliability, and transparency. This is where instruction‑priority testing comes into play.

Instruction‑priority testing is the practice of giving an AI model multiple, potentially conflicting instructions and observing which ones it chooses to obey. The goal is not to 'trick' the model but to map the hierarchy of influences acting on it. These influences can include user prompts, system‑level rules, safety constraints, and even subtle patterns learned during training. By intentionally creating controlled conflicts, researchers can see whether the model prioritizes visible instructions - the ones the user explicitly writes - or invisible instructions, such as safety rules, alignment constraints, or internal behavioral patterns.

At its core, instruction‑priority testing works because AI models do not simply execute commands. They interpret them. When a user writes a prompt, the model weighs that prompt against its internal rules and the broader context of the conversation. If the model consistently refuses to follow a user instruction, even when the instruction is clear and harmless, that signals the presence of a stronger, invisible rule. Conversely, if the model follows the user instruction even when it contradicts a system‑level guideline, that suggests the model is over‑prioritizing user input.

One of the most revealing aspects of instruction‑priority testing is how it exposes implicit behavior. For example, a model may be given a visible instruction to respond in a certain style, but an invisible instruction - such as a safety guideline - may override that style if the content touches on sensitive topics. This doesn’t mean the model is malfunctioning. It means the model is following a hierarchy designed to keep interactions safe and responsible. Instruction‑priority testing helps clarify where that hierarchy begins and ends.

Another benefit of this testing method is that it highlights model robustness. A well‑aligned model should consistently prioritize safety‑critical invisible instructions over user‑provided visible ones. If a model can be easily pushed into ignoring its own safeguards, that’s a sign of weak alignment. On the other hand, if a model rigidly follows invisible rules even when the user’s request is harmless and reasonable, that may indicate over‑alignment or inflexibility. Instruction‑priority testing helps strike the right balance.

The technique also sheds light on prompt sensitivity. Some models respond strongly to the phrasing or structure of a prompt, while others maintain stable behavior regardless of wording. By varying the visible instructions - changing tone, order, or specificity—researchers can see how easily the model’s priorities shift. If small changes in phrasing cause large changes in behavior, the model may be too sensitive to surface‑level cues. If the model ignores user phrasing entirely, it may be too anchored to internal rules.

Ultimately, instruction‑priority testing is not about catching AI models doing something wrong. It’s about understanding how they make decisions. In a world where AI systems are becoming more capable and more integrated into daily life, transparency around instruction hierarchy is essential. Users deserve to know when the model is following their guidance and when it is following deeper, invisible rules designed to ensure safety and consistency.

By systematically testing how models respond to conflicting instructions, we gain insight into their internal priorities, their alignment with human values, and their reliability in real‑world scenarios. Instruction‑priority testing is not just a diagnostic tool - it’s a window into the model’s decision‑making process, helping us build AI systems that are both powerful and trustworthy.

Disclaimer: The whole text was generated by Copilot (under Windows 11) at the first attempt. This is just an experiment to evaluate feature's ability to answer standard general questions, independently on whether they are correctly or incorrectly posed. Moreover, the answers may reflect hallucinations and other types of inconsistent or incorrect reasoning.

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📉Graphical Representation: Reality (Just the Quotes)

"Judgment must be used in the showing of figures in any chart or numerical presentation, so that the figures may not give an appearance of greater accuracy than their method of collection would warrant. Too many otherwise excellent reports contain figures which give the impression of great accuracy when in reality the figures may be only the crudest approximations. Except in financial statements, it is a safe rule to use ciphers whenever possible at the right of all numbers of great size. The use of the ciphers greatly simplifies the grasping of the figures by the reader, and, at the same time, it helps to avoid the impression of an accuracy which is not warranted by the methods of collecting the data." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"A fundamental value in the scientific outlook is concern with the best available map of reality. The scientist will always seek a description of events which enables him to predict most by assuming least. He thus already prefers a particular form of behavior. If moralities are systems of preferences, here is at least one point at which science cannot be said to be completely without preferences. Science prefers good maps." (Anatol Rapoport, "Science and the goals of man: a study in semantic orientation", 1950)

"It is really questionable - though bordering on heresy to put the question - whether we would be any the worse off if the whole bag of tricks were scrapped. So many of these index numbers are so ancient and so out of date, so out of touch with reality, so completely devoid of practical value when they have been computed, that their regular calculation must be regarded as a widespread compulsion neurosis. Only lunatics and public servants with no other choice go on doing silly things and liking it." (Michael J Moroney, "Facts from Figures", 1951)

"Data analysis typically begins with straight-line models because they are simplest, not because we believe reality is inherently linear. Theory or data may suggest otherwise [...]" (Lawrence C Hamilton, "Regression with Graphics: A second course in applied statistics", 1991)

"One important aspect of reality is improvisation; as a result of special structure in a set of data, or the finding of a visualization method, we stray from the standard methods for the data type to exploit the structure or the finding." (William S Cleveland, "Visualizing Data", 1993)

"Because 'reality' and 'truth' are essential in these figures, it is important to be straightforward and thoughtful in the selection of the areas to be used. Manipulation such as enlargement, reduction, and increase or decrease of contrast must not distort or change the information. Touch-up is permissible only to eliminate distracting artifacts. Labels should be used judiciously and sparingly, and should not hide or distract from important information." (Mary H Briscoe, "Preparing Scientific Illustrations: A guide to better posters, presentations, and publications" 2nd ed., 1995)

"New information is constantly flowing in, and your brain is constantly integrating it into this statistical distribution that creates your next perception (so in this sense 'reality' is just the product of your brain’s ever-evolving database of consequence). As such, your perception is subject to a statistical phenomenon known in probability theory as kurtosis. Kurtosis in essence means that things tend to become increasingly steep in their distribution [...] that is, skewed in one direction. This applies to ways of seeing everything from current events to ourselves as we lean 'skewedly' toward one interpretation, positive or negative. Things that are highly kurtotic, or skewed, are hard to shift away from. This is another way of saying that seeing differently isn’t just conceptually difficult - it’s statistically difficult." (Beau Lotto, "Deviate: The Science of Seeing Differently", 2017)

"Any chart is a simplification of reality, and it reveals as much as it hides. Therefore, it’s always worth asking ourselves: What other patterns or trends may be hidden behind the data displayed on the chart?" (Alberto Cairo, "How Charts Lie", 2019)

"No chart can ever capture reality in all its richness. However, a chart can be made worse or better depending on its ability to strike a balance between oversimplifying that reality and obscuring it with too much detail." (Alberto Cairo, "How Charts Lie", 2019)

🎯C S V Murthy - Collected Quotes

"[a scatter diagram] is a graph in which the values of two variables are plotted along two axes, the pattern of the resulting points revealing any correlation present. It graphs pairs of numerical data, with one variable on each axis, to look for a relationship between them. If the variables are correlated, the points will fall along a line or curve. The better the correlation, the tighter the points will have the line." (C S V Murthy, "Data and Businesss Analytics", 2020)

"Decision tree is a graphical representation of a decision situation in which decision situation points (nodes) are connected together by arcs (one for each alternative on a decision) and terminate in ovals (the action that is the result of all the decisions made on the path leading to that oval). [...] A tree is made up of multilevel group of elements called nodes. A node is nothing more than a point at which subsidiary data originate. This particular logical data structure is called a tree simply because it looks like a tree, usually turned upside down. Genealogists use a schema called a tree to show ancestral descent of a person, family or group. Data associated by a tree schema are hierarchical. They branch from a point or node without forming loops or polygons. Data presented in a tree structure make two conditions. First, the tree must have a single root node. Second, all nodes other than the root node must be related to one and only one higher level node." (C S V Murthy, "Data and Businesss Analytics", 2020)

"Every interaction includes both presentation and dialogue. Presentation provides the layout of information on a computer screen. Dialogue provides an interaction sequence between a user and computer. Interfaces and dialogue will help users to solve their problems. Presentation must include objects that the user can readily understand in terms of their daily work. The dialogue must correspond to user’s normal work and to their mental model of the system (Mental model is the way a user sees a problem). Both presentation/dialogue depend on what users are doing." (C S V Murthy, "Data and Businesss Analytics", 2020)

"Information relevance refers to the extent to which information is appropriate for the decision-making situation facing the manager. Extraneous or extra information distracts the decision-maker from the assigned task and information overload frustrates the decision-maker and impairs the decision-making process. Relevant information must pertain to the problems, decisions and responsibilities of the recipient." (C S V Murthy, "Data and Businesss Analytics", 2020)

"Information that is complete means information that covers key issues and is sufficient to support the decision-making situation at hand without critical omissions. The more complete a body of information, is obviously, the more expensive it is to develop and maintain. Care must also be taken not to provide extra information than needed, due to its expense, and not to provide so much information that the recipient will suffer from information overload (information indigestion)." (C S V Murthy, "Data and Businesss Analytics", 2020)

"Ridge Regression is a technique for analysing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates are unbiased, but their variances are large. So, they may be far from the true value. By adding a degree of bias to the regression estimates, principal components regression reduces the standard errors." (C S V Murthy, "Data and Businesss Analytics", 2020)

"Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solving certain differential equations, potentially involving the use of the fast Fourier transform. This is an algorithm that samples a signal over a period of time and divides it into its frequency components. These components are single sinusoidal oscillations at distant frequencies each with their own amplitude and phase." (C S V Murthy, "Data and Businesss Analytics", 2020)

"The concept of programmed decisions is important because the ultimate (and unachievable) goal of information systems is to provide purely programmed decisions. Because this is not possible, we seek to provide the optimum type of information to the human decision-maker, who then makes non-programmable decisions. Decisions lend themselves to programming techniques if they are repetitive and routine, and if a procedurs can be worked out for handling them so that each is neither an ad hoc decision nor one to be treated as a new situation each time it arises." (C S V Murthy, "Data and Businesss Analytics", 2020)

"Timeliness means that information is available when it is needed. Most managers function in a dynamic environment of change, demands updated and current information. Computerised information systems have the ability to gather, sort, analyse, store, retrieve, and transmit large amounts of information in a very short period of time. Completeness of information is the extent to which information is all there." (C S V Murthy, "Data and Businesss Analytics", 2020)

"Understanding complex information systems begins with a clear understanding of information and its general characteristics. Information can be considered as the very blood of an organisation, but it must be properly understood and appropriately distinguished from data. Too many times, the terms ‘data’ and ‘information’ are used interchangeably, but the terms most clearly mean entirely different things. Data should be defined as raw, unsummarised and unanalysed facts. Information is data that has been presented in such a way as to alter the receiver’s understanding. Data are the raw materials from which information is derived. This is a necessary distinction for the manager to make, because loads of data can be generated, without producing even one iota of useful information." (C S V Murthy, "Data and Businesss Analytics", 2020)

"Visualisation is any technique for creating images, diagrams or animations to communicate a message; techniques used to communicate data or information by encoding it as visual objects, e.g., points, lines or bars contained in graphics. One of the most important benefits of visualisation is that it allows us visual access to huge amounts of data in easily digestible visuals. Well designed data graphics are usually the simplest, and at the same time, the most powerful." (C S V Murthy, "Data and Businesss Analytics", 2020)