🤖〽️Prompt Engineering: Copilot Unabridged (Part 180: How AI Can Detect Conditional Complex Patterns That Appear Only in Specific Contexts)

Prompt Engineering Series

Prompt: "write a post of 600 words on how AI can detect conditional complex patterns that appear only in specific contexts"

Introduction

One of the most subtle and powerful capabilities of modern Artificial Intelligence (AI) is its ability to detect conditional complex patterns - relationships that appear only under certain circumstances, within specific subgroups, or when multiple contextual factors align. Humans are naturally inclined to search for general rules that apply broadly. We prefer simplicity, coherence, and universality. Yet the world rarely behaves that way. Many important patterns are conditional: they emerge only in particular environments, at certain thresholds, or when specific combinations of variables interact. AI is uniquely equipped to uncover these context‑dependent structures, revealing insights that lie beyond the reach of intuition.

The first reason AI can detect conditional patterns is its ability to partition data into meaningful subspaces. Humans tend to look at datasets as unified wholes, but AI models - especially decision trees, random forests, and gradient boosting machines - excel at dividing data into smaller regions where different rules apply. A relationship that is invisible in the aggregate may become obvious within a specific subgroup. For example, a medical treatment might be effective only for patients with a particular genetic marker, or a marketing strategy might work only for customers in a certain demographic. AI can automatically identify these pockets of conditional behavior by recursively splitting the data along the most informative dimensions.

A second advantage lies in AI’s capacity to model interactions between variables, which is essential for detecting conditional patterns. Many relationships appear only when two or more variables interact in specific ways. A variable may have no effect on its own but become highly predictive when combined with another. Humans struggle to reason about such interactions because they require tracking multiple dependencies simultaneously. AI systems, however, can evaluate thousands of potential interactions, identifying the precise conditions under which a pattern emerges. This ability is crucial in fields like finance, where risk factors interact in nonlinear ways, or in climate science, where environmental variables combine to produce rare but significant events.

Another key factor is AI’s ability to detect local nonlinearities. Conditional patterns often involve nonlinear relationships that change direction depending on context. A variable might increase an outcome up to a point and then decrease it beyond that threshold. Neural networks, kernel methods, and spline‑based models can capture these curved, context‑dependent relationships without requiring explicit assumptions. They learn the shape of the pattern directly from the data, allowing them to detect subtle shifts that humans would overlook.

AI also excels at temporal and sequential context detection, which is essential for identifying patterns that appear only at certain times or in specific sequences. Models like transformers and recurrent neural networks can track long‑range dependencies, recognizing when a pattern emerges only after a particular sequence of events. This is especially valuable in fields like cybersecurity, where certain attack signatures appear only after a chain of precursor actions, or in behavioral analytics, where user actions form meaningful patterns only when viewed in order.

A further strength comes from AI’s ability to integrate multimodal context. Conditional patterns often span different types of data - text, images, numerical signals, or categorical variables. Humans struggle to synthesize such diverse information streams. AI systems, however, can fuse them into unified representations, allowing conditional patterns to emerge across modalities. For example, a manufacturing defect might occur only when a specific sensor reading coincides with a particular visual anomaly. AI can detect this cross‑modal condition effortlessly.

Finally, AI’s ability to detect conditional patterns is amplified by continuous learning. As new data arrives, AI systems can update their internal models, refining their understanding of when and where certain patterns appear. This dynamic adaptation allows them to track evolving systems where conditional relationships shift over time.

AI’s ability to detect conditional complex patterns is not a replacement for human insight. Instead, it expands our analytical reach, revealing structures that only emerge under specific contexts. When humans and AI collaborate - combining human judgment with machine‑level pattern detection - we gain a deeper, more accurate understanding of the complex systems that shape our world.

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 179: How AI Can Detect Interactions Between Multiple Variables in Complex Patterns)

Prompt Engineering Series

Prompt: "write a post of 600 words on how AI can detect interactions between multiple variables in complex patterns"

Introduction

One of the most powerful capabilities of modern Artificial Intelligence (AI) is its ability to detect interactions between multiple variables - interactions that are subtle, nonlinear, and often invisible to human intuition. Humans are good at spotting simple relationships: when one variable increases, another tends to rise or fall. But real‑world systems rarely behave so cleanly. Instead, outcomes often emerge from the interplay of many factors acting together, sometimes reinforcing each other, sometimes canceling each other out, and sometimes producing effects that only appear under very specific conditions. AI excels in precisely this territory. Its architecture allows it to uncover complex, multi‑variable interactions that would otherwise remain hidden.

The first reason AI can detect these interactions is its ability to analyze high‑dimensional data without cognitive limits. Humans can reason about two or three variables at a time, but beyond that, our intuition collapses. AI systems, especially deep learning models, can process hundreds or thousands of variables simultaneously. They can map how changes in one variable influence another, not in isolation, but in combination with many others. This is essential in fields like genomics, where the effect of a single gene may depend on the presence of dozens of others, or in economics, where market behavior emerges from the interplay of countless signals.

A second advantage lies in AI’s capacity to model nonlinear relationships. Interactions between variables are rarely linear. The effect of one variable may depend on the level of another, creating curved, threshold‑based, or conditional relationships. Traditional statistical methods often struggle with these nonlinearities unless explicitly instructed to look for them. AI models, by contrast, naturally capture nonlinear interactions through their layered structure. Neural networks, for example, learn complex transformations at each layer, allowing them to detect relationships that bend, twist, or reverse depending on context. This flexibility enables AI to uncover interactions that humans would never think to test.

Another key factor is AI’s ability to detect higher‑order interactions - relationships that involve not just pairs of variables, but combinations of three, four, or more. These higher‑order interactions are common in complex systems. For example, a medical treatment might be effective only when a patient has a specific genetic profile and a particular environmental exposure and a certain lifestyle pattern. Humans rarely detect such interactions because they require examining an enormous number of possible combinations. AI, however, can explore these combinations efficiently, identifying the rare configurations that produce meaningful effects.

AI also excels at local pattern detection, which is crucial for identifying interactions that appear only under specific conditions. Humans tend to look for global rules that apply everywhere. AI can break a dataset into many small regions and learn different relationships in each one. A variable might matter only when another variable crosses a certain threshold, or only within a particular subgroup. Models like decision trees, random forests, and gradient boosting machines are particularly good at uncovering these conditional interactions. They reveal patterns that are invisible when looking at the dataset as a whole.

A further strength comes from AI’s ability to integrate heterogeneous data sources. Interactions often span different types of information - numerical measurements, text, images, signals, or categorical variables. Humans struggle to combine such diverse inputs. AI systems, however, can fuse them into a unified representation, allowing interactions to emerge across modalities. This is especially valuable in fields like healthcare, where symptoms, lab results, imaging data, and patient history interact in complex ways.

Finally, AI’s ability to detect multi‑variable interactions is amplified by continuous learning. As new data arrives, AI systems can update their internal models, refining their understanding of how variables interact. This dynamic adaptation allows them to track evolving systems where interactions shift over time.

AI’s ability to detect interactions between multiple variables is not a replacement for human insight. Instead, it expands our analytical reach, revealing structures that lie beyond the limits of intuition. When humans and AI collaborate - combining human judgment with machine‑level pattern detection - we gain a deeper, more accurate understanding of the complex systems that shape our world.

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 178: How AI Can Detect Curved Relationships in Complex Patterns)

Prompt Engineering Series

Prompt: "write a post of 600 words on how AI can detect curved relationships in complex patterns"

Introduction

One of the most intriguing strengths of modern Artificial Intelligence (AI) is its ability to detect curved, nonlinear relationships hidden inside complex datasets. Humans are naturally inclined toward linear thinking. We look for straight‑line connections: more of X leads to more of Y, or less of X leads to less of Y. This bias toward linearity is cognitively efficient, but it blinds us to the deeper structure of many real‑world systems. In nature, economics, biology, psychology, and technology, relationships often bend, twist, and loop in ways that defy simple intuition. AI, however, is uniquely equipped to uncover these curved patterns - relationships that change direction, accelerate, plateau, or reverse depending on context.

The first reason AI can detect curved relationships is its ability to model nonlinear functions directly. Traditional statistical tools often assume linearity unless explicitly told otherwise. AI models, especially neural networks, do the opposite: they assume nothing. Their architecture allows them to approximate any function - straight, curved, or wildly irregular - by adjusting internal parameters. This flexibility enables AI to capture relationships that humans overlook because they do not fit our mental templates. For example, a medical variable might increase risk up to a point and then decrease it beyond that threshold. A human analyst might miss this U‑shaped curve, but an AI model can detect it naturally.

A second advantage lies in AI’s capacity to explore high‑dimensional interactions. Curved relationships often emerge only when multiple variables interact. A single variable may appear to have no meaningful effect, but when combined with two or three others, a curved pattern suddenly becomes visible. Humans struggle to visualize relationships beyond two dimensions. AI systems, by contrast, can analyze hundreds of variables simultaneously, mapping how they bend and twist together. This is particularly valuable in fields like genomics, where the effect of one gene may depend on the presence or absence of many others, creating curved interactions that only appear in high‑dimensional space.

Another key factor is AI’s ability to detect local patterns rather than forcing global assumptions. Humans tend to look for one overarching rule that explains everything. AI models can break a dataset into many small regions and learn different relationships in each one. A relationship might be linear in one region, curved in another, and flat in a third. Decision trees, random forests, and gradient boosting machines excel at this kind of local pattern detection. They can identify subtle bends in the data that only appear under specific conditions. This ability to adapt to local curvature allows AI to uncover patterns that would otherwise remain hidden.

AI also benefits from its capacity to learn from noise rather than be overwhelmed by it. Curved relationships are often subtle, emerging only after filtering out randomness. Humans tend to see noise as a distraction; AI treats it as part of the landscape. By analyzing massive datasets, AI can distinguish between random fluctuations and genuine curvature. This is essential in fields like climate science, where long‑term curved trends are buried beneath short‑term variability.

Finally, AI’s ability to detect curved relationships is strengthened by continuous learning and iterative refinement. As new data arrives, AI systems can update their internal models, refining the shape of the relationships they detect. Curved patterns often evolve over time - markets shift, ecosystems adapt, diseases mutate. Humans struggle to update their mental models quickly. AI can adjust in real time, capturing new bends and inflection points as they emerge.

The ability of AI to detect curved relationships in complex patterns is not merely a technical achievement. It expands our understanding of the world, revealing structures that lie beyond the reach of intuition. When humans and AI work together - combining human insight with machine‑level pattern detection - we gain a richer, more accurate view of the systems that shape our lives.

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 177: How AI Can Detect Multi‑Step Relationships That Span Many Variables)

Prompt Engineering Series

Prompt: "write a post of 600 words on how AI can detect multi‑step relationships that span many variables"

Introduction

One of the most remarkable capabilities of modern Artificial Intelligence (AI) is its ability to uncover multi‑step relationships that span across many variables - patterns so complex, layered, and indirect that they remain invisible to human reasoning. Humans excel at intuitive leaps and conceptual understanding, but we struggle when relationships unfold across multiple dimensions, involve subtle dependencies, or require tracking interactions over long chains of influence. AI, by contrast, thrives in precisely these environments. Its computational architecture allows it to map relationships that are not linear, not obvious, and not easily captured by traditional analytical methods.

The first reason AI can detect multi‑step relationships is its ability to operate in high‑dimensional spaces. Humans can mentally juggle only a handful of variables at once before cognitive overload sets in. But many real‑world systems - biological networks, financial markets, climate dynamics - operate across hundreds or thousands of interacting factors. AI models, especially deep neural networks, are designed to navigate these high‑dimensional landscapes. They can track how small changes in one variable propagate through a chain of dependencies, eventually influencing outcomes far removed from the original cause. This ability to follow long causal threads is something human intuition simply cannot replicate at scale.

A second advantage lies in AI’s capacity to model nonlinear interactions. Multi‑step relationships often involve nonlinearities: effects that amplify, dampen, or transform as they move through a system. Humans tend to assume linearity because it is cognitively simple. AI does not make this assumption. Neural networks, decision trees, and attention‑based architectures can capture nonlinear transformations at every layer. This allows AI to detect relationships where the influence of one variable depends on the state of several others - patterns that only emerge when multiple conditions align in specific ways.

Another key factor is AI’s ability to learn hierarchical representations. Deep learning models build understanding layer by layer. Early layers detect simple features; deeper layers combine these features into more abstract concepts. This hierarchical structure mirrors the multi‑step nature of complex relationships. For example, in medical diagnostics, an AI system might first detect subtle biomarkers, then combine them into intermediate patterns, and finally infer a higher‑level diagnosis. Each step builds on the previous one, allowing the model to trace relationships that unfold across multiple conceptual levels.

AI also excels at temporal reasoning, which is essential for detecting multi‑step relationships that evolve over time. Recurrent neural networks, transformers, and sequence models can track dependencies across long time horizons. They can identify how an event today influences outcomes weeks or months later, even when the connection is indirect. This is particularly valuable in fields like supply chain forecasting, epidemiology, and macroeconomic modeling, where delayed effects are the norm rather than the exception.

A further strength comes from AI’s ability to integrate heterogeneous data sources. Multi‑step relationships often span different types of information - numerical data, text, images, signals, or categorical variables. Humans struggle to synthesize such diverse inputs. AI systems, however, can fuse them into a unified representation. This multimodal integration allows AI to detect relationships that cross boundaries between data types, revealing patterns that would remain hidden if each source were analyzed in isolation.

Finally, AI’s ability to detect multi‑step relationships is amplified by continuous learning and iterative refinement. As new data arrives, AI systems can update their internal models, strengthening or revising the relationships they have inferred. This dynamic adaptation allows them to track evolving systems where relationships shift over time. Humans, by contrast, tend to cling to outdated mental models, even when the underlying reality has changed.

AI’s ability to detect multi‑step relationships across many variables is not a replacement for human judgment. Instead, it expands our analytical reach, revealing structures that lie beyond the limits of intuition. When humans and AI collaborate - combining human understanding with machine‑level pattern detection - we gain a deeper, more accurate view of the complex systems that shape our world.

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 176: How AI Can Detect Rare Patterns That Humans Might Overlook)

Prompt Engineering Series

Prompt: "write a post of 600 words on how AI can detect rare patterns that humans might overlook"

Introduction

One of the most transformative capabilities of modern Artificial Intelligence (AI) is its ability to detect patterns that are too subtle, too rare, or too complex for humans to notice. While humans excel at intuitive reasoning, contextual understanding, and creative interpretation, we are limited by cognitive bandwidth, memory constraints, and perceptual biases. AI, by contrast, thrives in environments where scale, precision, and exhaustive analysis are essential. Understanding how AI uncovers rare patterns reveals not only its technical power but also its potential to reshape scientific discovery, business strategy, and our understanding of complex systems.

The first reason AI can detect rare patterns is its ability to process massive datasets without fatigue or bias. Humans can analyze only a small number of variables at once, and our attention is easily overwhelmed by noise. AI systems, especially those built on deep learning or advanced statistical models, can examine millions of data points simultaneously. They can identify correlations that occur only once in a million cases - signals so faint that they disappear into the background for human observers. This ability is particularly valuable in fields like fraud detection, where unusual behavior is intentionally hidden, or in medical diagnostics, where early signs of disease may be nearly invisible.

A second advantage lies in AI’s capacity to operate beyond human intuition. Humans rely heavily on heuristics - mental shortcuts that help us navigate the world efficiently but can blind us to unexpected relationships. AI does not share these cognitive shortcuts. It does not assume which variables matter or which patterns are plausible. Instead, it evaluates all possibilities, including those that defy conventional wisdom. This openness allows AI to uncover patterns that humans would never think to look for. In scientific research, for example, AI has identified previously unknown relationships between genetic markers and diseases, not because it 'understood' biology, but because it was not constrained by human assumptions about what should or should not be related.

Another key factor is AI’s ability to detect patterns across multiple scales simultaneously. Humans tend to focus on either the big picture or the fine details, but rarely both at once. AI can analyze micro‑patterns—minute fluctuations, rare anomalies, subtle deviations - while also tracking macro‑patterns that unfold across long time horizons. This multi‑scale analysis is essential in fields like climate modeling, financial forecasting, and cybersecurity. A human analyst might notice a sudden spike in activity, but an AI system can detect the faint precursors that occurred months earlier, revealing a pattern that only becomes meaningful when viewed across scales.

AI also excels at identifying nonlinear relationships, which are notoriously difficult for humans to detect. Many real‑world systems - ecosystems, markets, neural networks - do not behave in simple, linear ways. Small changes can produce disproportionate effects, and interactions between variables can create emergent behavior. AI models, especially neural networks, are designed to capture these nonlinearities. They can map complex relationships that would be invisible to traditional statistical methods or human intuition. This capability allows AI to detect rare patterns that emerge only when multiple variables interact in specific, unusual ways.

Finally, AI’s ability to detect rare patterns is amplified by continuous learning. Humans learn slowly and forget quickly. AI systems can update their models in real time, incorporating new data as it arrives. This allows them to detect emerging patterns before they become obvious. In cybersecurity, for example, AI can identify a new type of attack based on a handful of early signals. In healthcare, AI can detect subtle shifts in patient data that indicate a rare complication long before symptoms appear.

The ability of AI to detect rare patterns is not a replacement for human judgment. Instead, it is a complement - a way to extend our perceptual reach and reveal structures hidden beneath the surface of complexity. When humans and AI work together, combining intuition with computation, we gain a deeper, more nuanced understanding of the world.

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 166: How AI Recognizes Subtle Relationships in Data)

Prompt Engineering Series

Prompt: "write a post of 600 words on how AI can recognize subtle relationships in data"

Introduction

Artificial Intelligence (AI) has become a powerful tool for uncovering patterns in data - patterns that are too complex, too hidden, or too high‑dimensional for humans to detect on their own. While humans excel at intuitive reasoning and contextual understanding, AI excels at scale. It can analyze millions of data points simultaneously, identify faint correlations, and detect relationships that would otherwise remain invisible. Understanding how AI recognizes subtle relationships in data reveals why these systems are so transformative - and why they must be used thoughtfully.

1. AI Learns Patterns Through High‑Dimensional Representations

At the heart of modern AI is the ability to represent information in high‑dimensional space. Instead of viewing data as simple numbers or labels, AI models encode concepts as vectors - mathematical points with hundreds or thousands of dimensions.

This allows the model to capture:

• Nuanced similarities between concepts
• Gradients of meaning rather than binary categories
• Relationships that span multiple variables at once

For example, a language model can understand that 'king' and 'queen' are related not because it knows gender or royalty, but because their vector representations share structural patterns learned from data.

2. AI Detects Patterns Across Massive Datasets

Humans can only process a limited amount of information at once. AI, however, can analyze enormous datasets containing millions of examples. This scale allows it to detect:

• Weak correlations that appear only across large samples
• Rare patterns that humans might overlook
• Multi‑step relationships that span many variables

In fields like medicine or finance, these subtle patterns can reveal early warning signs, hidden risks, or emerging trends.

3. AI Identifies Non‑Linear Relationships

Traditional statistical methods often assume linear relationships - simple, straight‑line connections between variables. AI models, especially neural networks, can capture far more complex patterns:

• Curved relationships
• Interactions between multiple variables
• Conditional patterns that appear only in specific contexts

This ability to model non‑linear relationships is one reason AI can outperform traditional analytics in tasks like image recognition, fraud detection, and natural language processing.

4. AI Learns Through Layered Abstraction

Deep learning models recognize subtle relationships by building layers of abstraction. Each layer transforms the data into a more meaningful representation:

• Early layers detect simple features
• Middle layers combine features into patterns
• Higher layers capture concepts and relationships

This hierarchical structure allows AI to detect relationships that are not obvious at the surface level. For example, in image analysis, early layers detect edges, while deeper layers detect shapes, objects, and even emotional expressions.

5. AI Uses Attention Mechanisms to Focus on What Matters

Modern AI models often include attention mechanisms - components that help the model identify which parts of the data are most relevant to a given task. Attention allows AI to:

• Highlight subtle but important signals
• Ignore irrelevant noise
• Understand relationships across long sequences

In language models, attention helps the system track relationships between words that are far apart in a sentence, enabling it to understand nuance, tone, and context.

6. AI Learns From Patterns It Was Not Explicitly Taught

One of the most surprising aspects of AI is its ability to discover relationships that were never explicitly labeled. Through unsupervised or self‑supervised learning, AI can:

• Cluster similar items
• Infer categories
• Detect anomalies
• Reveal hidden structure in data

This makes AI a powerful tool for exploration and discovery.

Closing Statement

AI recognizes subtle relationships in data by combining high‑dimensional representations, massive computational scale, non‑linear modeling, layered abstraction, and attention mechanisms. These capabilities allow AI to uncover patterns that humans cannot easily see, making it invaluable in fields ranging from science and medicine to business and communication. Yet with this power comes responsibility: subtle patterns can illuminate truth, but they can also reflect bias or noise. Understanding how AI detects these relationships helps us use it wisely - leveraging its strengths while ensuring its insights remain grounded, fair, and meaningful.

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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🧭Business Intelligence: Perspectives (Part 23: In between the Many Destinations)

Business Intelligence Series

In too many cases the development of queries, respectively reports or data visualizations (aka artifacts) becomes a succession of drag & drops, formatting, (re)ordering things around, a bit of makeup, configuring a set of parameters, and the desired product is good to go! There seems nothing wrong with this approach as long as the outcomes meet users’ requirements, though it also gives the impression that’s all what the process is about. 

Given a set of data entities, usually there are at least as many perspectives into the data as entities’ number. Further perspectives can be found in exceptions and gaps in data, process variations, and the further aspects that can influence an artifact’s logic. All these aspects increase the overall complexity of the artifact, respectively of the development process. One guideline in handling all this is to keep the process in focus, and this starts with requirements’ elicitation and ends with the quality assurance and actual use.

Sometimes, the two words, the processes and their projection into the data and (data) models don’t reflect the reality adequately and one needs to compromise, at least until the gaps are better addressed. Process redesign, data harmonization and further steps need to be upon case considered in multiple iterations that should converge to optimal solutions, at least in theory. 

Therefore, in the development process there should be a continuous exploration of the various aspects until an optimum solution is reached. Often, there can be a couple of competing forces that can pull the solution in two or more directions  and then compromising is necessary. Especially as part of continuous improvement initiatives there’s the tendency of optimizing locally processes in the detriment of the overall process, with all the consequences resulting from this. 

Unfortunately, many of the problems existing in organizations are ill-posed and misunderstood to the degree that in extremis more effort is wasted than the actual benefits. Optimization is a process of putting in balance all the important aspects, respectively of answering with agility to the changing nature of the business and environment. Ignoring the changing nature of the problems and their contexts is a recipe for failure on the long term. 

This implies that people in particular and organizations in general need to become and  remain aware of the micro and macro changes occurring in organizations. Continuous learning is the key to cope with change. Organizations must learn to compromise and focus on what’s important, achievable and/or probable. Identifying, defining and following the value should be in an organization’s ADN. It also requires pragmatism (as opposed to idealism). Upon case, it may even require to say “no”, at least until the changes in the landscape offer a reevaluation of the various aspects.

One requires a lot from organizations when addressing optimization topics, especially when misalignment or important constraints or challenges may exist. Unfortunately, process related problems don’t always admit linear solutions. The nonlinear aspects are reflected especially when changing the scale, perspective or translating the issues or solutions from one are area to another.

There are probably answers available in the afferent literature or in the approaches followed by other organizations. Reinventing the wheel is part of the game, though invention may require explorations outside of the optimal paths. Conversely, an organization that knows itself has more chances to cope with the challenges and opportunities altogether. 

A lot from what organizations do in a consistent manner looks occasionally like inertia, self-occupation, suboptimal or random behavior, in opposition to being self-driven, self-aware, or in self-control. It’s also true that these are ideal qualities or aspects of what organizations should become in time. 

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🔭Data Science: Approximation (Just the Quotes)

"Man’s mind cannot grasp the causes of events in their completeness, but the desire to find those causes is implanted in man’s soul. And without considering the multiplicity and complexity of the conditions any one of which taken separately may seem to be the cause, he snatches at the first approximation to a cause that seems to him intelligible and says: ‘This is the cause!’" (Leo Tolstoy, "War and Peace", 1867)

"[It] may be laid down as a general rule that, if the result of a long series of precise observations approximates a simple relation so closely that the remaining difference is undetectable by observation and may be attributed to the errors to which they are liable, then this relation is probably that of nature." (Pierre-Simon Laplace, "Mémoire sur les Inégalites Séculaires des Planètes et des Satellites", 1787)

"Although this may seem a paradox, all exact science is dominated by the idea of approximation. When a man tells you that he knows the exact truth about anything, you are safe in inferring that he is an inexact man." (Bertrand Russell, "The Scientific Outlook", 1931)

"We live in a system of approximations. Every end is prospective of some other end, which is also temporary; a round and final success nowhere. We are encamped in nature, not domesticated." (Ralph W Emerson, "Essays", 1865)

"It is well to notice in this connection [the mutual relations between the results of counting and measuring] that a natural law, in the statement of which measurable magnitudes occur, can only be understood to hold in nature with a certain degree of approximation; indeed natural laws as a rule are not proof against sufficient refinement of the measuring tools." (Luitzen E J Brouwer, "Intuitionism and Formalism", Bulletin of the American Mathematical Society, Vol. 20, 1913)

"[…] as the sciences have developed further, the notion has gained ground that most, perhaps all, of our laws are only approximations." (William James, "Pragmatism: A New Name for Some Old Ways of Thinking", 1914)

"Science does not aim at establishing immutable truths and eternal dogmas; its aim is to approach the truth by successive approximations, without claiming that at any stage final and complete accuracy has been achieved." (Bertrand Russell, "The ABC of Relativity", 1925)

"[…] reality is a system, completely ordered and fully intelligible, with which thought in its advance is more and more identifying itself. We may look at the growth of knowledge […] as an attempt by our mind to return to union with things as they are in their ordered wholeness. […] and if we take this view, our notion of truth is marked out for us. Truth is the approximation of thought to reality […] Its measure is the distance thought has travelled […] toward that intelligible system […] The degree of truth of a particular proposition is to be judged in the first instance by its coherence with experience as a whole, ultimately by its coherence with that further whole, all comprehensive and fully articulated, in which thought can come to rest." (Brand Blanshard, "The Nature of Thought" Vol. II, 1939) 

"The most important maxim for data analysis to heed, and one which many statisticians seem to have shunned is this: ‘Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.’ Data analysis must progress by approximate answers, at best, since its knowledge of what the problem really is will at best be approximate." (John W Tukey, "The Future of Data Analysis", Annals of Mathematical Statistics, Vol. 33, No. 1, 1962)

"Because engineering is science in action - the practice of decision making at the earliest moment - it has been defined as the art of skillful approximation. No situation in engineering is simple enough to be solved precisely, and none worth evaluating is solved exactly. Never are there sufficient facts, sufficient time, or sufficient money for an exact solution, for if by chance there were, the answer would be of academic and not economic interest to society. These are the circumstances that make engineering so vital and so creative." (Ronald B Smith, "Engineering Is…", Mechanical Engineering Vol. 86 (5), 1964)

"Each piece, or part, of the whole of nature is always merely an approximation to the complete truth, or the complete truth so far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet. Therefore, things must be learned only to be unlearned again or, more likely, to be corrected." (Richard Feynman, "The Feynman Lectures on Physics" Vol. 1, 1964)

"Engineering is the art of skillful approximation; the practice of gamesmanship in the highest form. In the end it is a method broad enough to tame the unknown, a means of combing disciplined judgment with intuition, courage with responsibility, and scientific competence within the practical aspects of time, of cost, and of talent." (Ronald B Smith, "Professional Responsibility of Engineering", Mechanical Engineering Vol. 86 (1), 1964)

"Measurement, we have seen, always has an element of error in it. The most exact description or prediction that a scientist can make is still only approximate." (Abraham Kaplan, "The Conduct of Inquiry: Methodology for Behavioral Science", 1964)

"One grievous error in interpreting approximations is to allow only good approximations." (Preston C Hammer, "Mind Pollution", Cybernetics, Vol. 14, 1971)

"The fact that [the model] is an approximation does not necessarily detract from its usefulness because models are approximations. All models are wrong, but some are useful." (George Box, 1987)

"Science is more than a mere attempt to describe nature as accurately as possible. Frequently the real message is well hidden, and a law that gives a poor approximation to nature has more significance than one which works fairly well but is poisoned at the root." (Robert H March, "Physics for Poets", 1996)

"Most physical systems, particularly those complex ones, are extremely difficult to model by an accurate and precise mathematical formula or equation due to the complexity of the system structure, nonlinearity, uncertainty, randomness, etc. Therefore, approximate modeling is often necessary and practical in real-world applications. Intuitively, approximate modeling is always possible. However, the key questions are what kind of approximation is good, where the sense of 'goodness' has to be first defined, of course, and how to formulate such a good approximation in modeling a system such that it is mathematically rigorous and can produce satisfactory results in both theory and applications." (Guanrong Chen & Trung Tat Pham, "Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems", 2001)

"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)

"All models are approximations. Essentially, all models are wrong, but some are useful. However, the approximate nature of the model must always be borne in mind." (George E P Box & Norman R Draper, "Response Surfaces, Mixtures, and Ridge Analyses", 2007)

"Science, at its core, is simply a method of practical logic that tests hypotheses against experience. Scientism, by contrast, is the worldview and value system that insists that the questions the scientific method can answer are the most important questions human beings can ask, and that the picture of the world yielded by science is a better approximation to reality than any other." (John M Greer, "After Progress: Reason and Religion at the End of the Industrial Age", 2015)

"Science is about finding ever better approximations rather than pretending you have already found ultimate truth." (Friedrich Nietzsche)

More quotes on "Approximation" at the-web-of-knowledge.blogspot.com. 

🔭Data Science: Neural Networks (Just the Quotes)

"The terms 'black box' and 'white box' are convenient and figurative expressions of not very well determined usage. I shall understand by a black box a piece of apparatus, such as four-terminal networks with two input and two output terminals, which performs a definite operation on the present and past of the input potential, but for which we do not necessarily have any information of the structure by which this operation is performed. On the other hand, a white box will be similar network in which we have built in the relation between input and output potentials in accordance with a definite structural plan for securing a previously determined input-output relation." (Norbert Wiener, "Cybernetics: Or Control and Communication in the Animal and the Machine", 1948)

"A neural network is a massively parallel distributed processor that has a natural propensity for storing experiential knowledge and making it available for use. It resembles the brain in two respects: 1. Knowledge is acquired by the network through a learning process. 2. Interneuron connection strengths known as synaptic weights are used to store the knowledge." (Igor Aleksander, "An introduction to neural computing", 1990) 

"Neural Computing is the study of networks of adaptable nodes which through a process of learning from task examples, store experiential knowledge and make it available for use." (Igor Aleksander, "An introduction to neural computing", 1990)

"A neural network is characterized by (1) its pattern of connections between the neurons (called its architecture), (2) its method of determining the weights on the connections (called its training, or learning, algorithm), and (3) its activation function." (Laurene Fausett, "Fundamentals of Neural Networks", 1994)

"An artificial neural network is an information-processing system that has certain performance characteristics in common with biological neural networks. Artificial neural networks have been developed as generalizations of mathematical models of human cognition or neural biology, based on the assumptions that: (1) Information processing occurs at many simple elements called neurons. (2) Signals are passed between neurons over connection links. (3) Each connection link has an associated weight, which, in a typical neural net, multiplies the signal transmitted. (4) Each neuron applies an activation function (usually nonlinear) to its net input (sum of weighted input signals) to determine its output signal." (Laurene Fausett, "Fundamentals of Neural Networks", 1994)

"An artificial neural network (or simply a neural network) is a biologically inspired computational model that consists of processing elements (neurons) and connections between them, as well as of training and recall algorithms." (Nikola K Kasabov, "Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering", 1996)

"Many of the basic functions performed by neural networks are mirrored by human abilities. These include making distinctions between items (classification), dividing similar things into groups (clustering), associating two or more things (associative memory), learning to predict outcomes based on examples (modeling), being able to predict into the future (time-series forecasting), and finally juggling multiple goals and coming up with a good- enough solution (constraint satisfaction)." (Joseph P Bigus,"Data Mining with Neural Networks: Solving business problems from application development to decision support", 1996)

"More than just a new computing architecture, neural networks offer a completely different paradigm for solving problems with computers. […] The process of learning in neural networks is to use feedback to adjust internal connections, which in turn affect the output or answer produced. The neural processing element combines all of the inputs to it and produces an output, which is essentially a measure of the match between the input pattern and its connection weights. When hundreds of these neural processors are combined, we have the ability to solve difficult problems such as credit scoring." (Joseph P Bigus,"Data Mining with Neural Networks: Solving business problems from application development to decision support", 1996)

"Neural networks are a computing model grounded on the ability to recognize patterns in data. As a consequence, they have many applications to data mining and analysis." (Joseph P Bigus,"Data Mining with Neural Networks: Solving business problems from application development to decision support", 1996)

"Neural networks are a computing technology whose fundamental purpose is to recognize patterns in data. Based on a computing model similar to the underlying structure of the human brain, neural networks share the brains ability to learn or adapt in response to external inputs. When exposed to a stream of training data, neural networks can discover previously unknown relationships and learn complex nonlinear mappings in the data. Neural networks provide some fundamental, new capabilities for processing business data. However, tapping these new neural network data mining functions requires a completely different application development process from traditional programming." (Joseph P Bigus, "Data Mining with Neural Networks: Solving business problems from application development to decision support", 1996)

"The most familiar example of swarm intelligence is the human brain. Memory, perception and thought all arise out of the nett actions of billions of individual neurons. As we saw earlier, artificial neural networks (ANNs) try to mimic this idea. Signals from the outside world enter via an input layer of neurons. These pass the signal through a series of hidden layers, until the result emerges from an output layer. Each neuron modifies the signal in some simple way. It might, for instance, convert the inputs by plugging them into a polynomial, or some other simple function. Also, the network can learn by modifying the strength of the connections between neurons in different layers." (David G Green, "The Serendipity Machine: A voyage of discovery through the unexpected world of computers", 2004)

"A neural network is a particular kind of computer program, originally developed to try to mimic the way the human brain works. It is essentially a computer simulation of a complex circuit through which electric current flows." (Keith J Devlin & Gary Lorden, "The Numbers behind NUMB3RS: Solving crime with mathematics", 2007)

 "Neural networks are a popular model for learning, in part because of their basic similarity to neural assemblies in the human brain. They capture many useful effects, such as learning from complex data, robustness to noise or damage, and variations in the data set. " (Peter C R Lane, Order Out of Chaos: Order in Neural Networks, 2007)

"A network of many simple processors ('units' or 'neurons') that imitates a biological neural network. The units are connected by unidirectional communication channels, which carry numeric data. Neural networks can be trained to find nonlinear relationships in data, and are used in various applications such as robotics, speech recognition, signal processing, medical diagnosis, or power systems." (Adnan Khashman et al, "Voltage Instability Detection Using Neural Networks", 2009)

"An artificial neural network, often just called a 'neural network' (NN), is an interconnected group of artificial neurons that uses a mathematical model or computational model for information processing based on a connectionist approach to computation. Knowledge is acquired by the network from its environment through a learning process, and interneuron connection strengths (synaptic weighs) are used to store the acquired knowledge." (Larbi Esmahi et al, "Adaptive Neuro-Fuzzy Systems", 2009)

"Generally, these programs fall within the techniques of reinforcement learning and the majority use an algorithm of temporal difference learning. In essence, this computer learning paradigm approximates the future state of the system as a function of the present state. To reach that future state, it uses a neural network that changes the weight of its parameters as it learns." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)

"The simplest basic architecture of an artificial neural network is composed of three layers of neurons - input, output, and intermediary (historically called perceptron). When the input layer is stimulated, each node responds in a particular way by sending information to the intermediary level nodes, which in turn distribute it to the output layer nodes and thereby generate a response. The key to artificial neural networks is in the ways that the nodes are connected and how each node reacts to the stimuli coming from the nodes it is connected to. Just as with the architecture of the brain, the nodes allow information to pass only if a specific stimulus threshold is passed. This threshold is governed by a mathematical equation that can take different forms. The response depends on the sum of the stimuli coming from the input node connections and is 'all or nothing'." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)

"Neural networks can model very complex patterns and decision boundaries in the data and, as such, are very powerful. In fact, they are so powerful that they can even model the noise in the training data, which is something that definitely should be avoided. One way to avoid this overfitting is by using a validation set in a similar way as with decision trees.[...] Another scheme to prevent a neural network from overfitting is weight regularization, whereby the idea is to keep the weights small in absolute sense because otherwise they may be fitting the noise in the data. This is then implemented by adding a weight size term (e.g., Euclidean norm) to the objective function of the neural network." (Bart Baesens, "Analytics in a Big Data World: The Essential Guide to Data Science and Its Applications", 2014)

"A neural network consists of a set of neurons that are connected together. A neuron takes a set of numeric values as input and maps them to a single output value. At its core, a neuron is simply a multi-input linear-regression function. The only significant difference between the two is that in a neuron the output of the multi-input linear-regression function is passed through another function that is called the activation function." (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"Just as they did thirty years ago, machine learning programs (including those with deep neural networks) operate almost entirely in an associational mode. They are driven by a stream of observations to which they attempt to fit a function, in much the same way that a statistician tries to fit a line to a collection of points. Deep neural networks have added many more layers to the complexity of the fitted function, but raw data still drives the fitting process. They continue to improve in accuracy as more data are fitted, but they do not benefit from the 'super-evolutionary speedup'."  (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)

"A neural-network algorithm is simply a statistical procedure for classifying inputs (such as numbers, words, pixels, or sound waves) so that these data can mapped into outputs. The process of training a neural-network model is advertised as machine learning, suggesting that neural networks function like the human mind, but neural networks estimate coefficients like other data-mining algorithms, by finding the values for which the model’s predictions are closest to the observed values, with no consideration of what is being modeled or whether the coefficients are sensible." (Gary Smith & Jay Cordes, "The 9 Pitfalls of Data Science", 2019)

"Deep neural networks have an input layer and an output layer. In between, are “hidden layers” that process the input data by adjusting various weights in order to make the output correspond closely to what is being predicted. [...] The mysterious part is not the fancy words, but that no one truly understands how the pattern recognition inside those hidden layers works. That’s why they’re called 'hidden'. They are an inscrutable black box - which is okay if you believe that computers are smarter than humans, but troubling otherwise." (Gary Smith & Jay Cordes, "The 9 Pitfalls of Data Science", 2019)

"Neural-network algorithms do not know what they are manipulating, do not understand their results, and have no way of knowing whether the patterns they uncover are meaningful or coincidental. Nor do the programmers who write the code know exactly how they work and whether the results should be trusted. Deep neural networks are also fragile, meaning that they are sensitive to small changes and can be fooled easily." (Gary Smith & Jay Cordes, "The 9 Pitfalls of Data Science", 2019)

"The label neural networks suggests that these algorithms replicate the neural networks in human brains that connect electrically excitable cells called neurons. They don’t. We have barely scratched the surface in trying to figure out how neurons receive, store, and process information, so we cannot conceivably mimic them with computers." (Gary Smith & Jay Cordes, "The 9 Pitfalls of Data Science", 2019)

More quotes on "Neural Networks" at the-web-of-knowledge.blogspot.com.

🔭Data Science: Nonlinearity (Just the Quotes)

"The term chaos is used in a specific sense where it is an inherently random pattern of behaviour generated by fixed inputs into deterministic (that is fixed) rules (relationships). The rules take the form of non-linear feedback loops. Although the specific path followed by the behaviour so generated is random and hence unpredictable in the long-term, it always has an underlying pattern to it, a 'hidden' pattern, a global pattern or rhythm. That pattern is self-similarity, that is a constant degree of variation, consistent variability, regular irregularity, or more precisely, a constant fractal dimension. Chaos is therefore order (a pattern) within disorder (random behaviour)." (Ralph D Stacey, "The Chaos Frontier: Creative Strategic Control for Business", 1991)

"In nonlinear systems - and the economy is most certainly nonlinear - chaos theory tells you that the slightest uncertainty in your knowledge of the initial conditions will often grow inexorably. After a while, your predictions are nonsense." (M Mitchell Waldrop, "Complexity: The Emerging Science at the Edge of Order and Chaos", 1992)

"In addition to dimensionality requirements, chaos can occur only in nonlinear situations. In multidimensional settings, this means that at least one term in one equation must be nonlinear while also involving several of the variables. With all linear models, solutions can be expressed as combinations of regular and linear periodic processes, but nonlinearities in a model allow for instabilities in such periodic solutions within certain value ranges for some of the parameters." (Courtney Brown, "Chaos and Catastrophe Theories", 1995)

"The dimensionality and nonlinearity requirements of chaos do not guarantee its appearance. At best, these conditions allow it to occur, and even then under limited conditions relating to particular parameter values. But this does not imply that chaos is rare in the real world. Indeed, discoveries are being made constantly of either the clearly identifiable or arguably persuasive appearance of chaos. Most of these discoveries are being made with regard to physical systems, but the lack of similar discoveries involving human behavior is almost certainly due to the still developing nature of nonlinear analyses in the social sciences rather than the absence of chaos in the human setting."  (Courtney Brown, "Chaos and Catastrophe Theories", 1995)

"So we pour in data from the past to fuel the decision-making mechanisms created by our models, be they linear or nonlinear. But therein lies the logician's trap: past data from real life constitute a sequence of events rather than a set of independent observations, which is what the laws of probability demand. [...] It is in those outliers and imperfections that the wildness lurks." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"There is a new science of complexity which says that the link between cause and effect is increasingly difficult to trace; that change (planned or otherwise) unfolds in non-linear ways; that paradoxes and contradictions abound; and that creative solutions arise out of diversity, uncertainty and chaos." (Andy P Hargreaves & Michael Fullan, "What’s Worth Fighting for Out There?", 1998)

"A system may be called complex here if its dimension (order) is too high and its model (if available) is nonlinear, interconnected, and information on the system is uncertain such that classical techniques can not easily handle the problem." (M Jamshidi, "Autonomous Control on Complex Systems: Robotic Applications", Current Advances in Mechanical Design and Production VII, 2000)

"Most physical systems, particularly those complex ones, are extremely difficult to model by an accurate and precise mathematical formula or equation due to the complexity of the system structure, nonlinearity, uncertainty, randomness, etc. Therefore, approximate modeling is often necessary and practical in real-world applications. Intuitively, approximate modeling is always possible. However, the key questions are what kind of approximation is good, where the sense of 'goodness' has to be first defined, of course, and how to formulate such a good approximation in modeling a system such that it is mathematically rigorous and can produce satisfactory results in both theory and applications." (Guanrong Chen & Trung Tat Pham, "Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems", 2001)

"Swarm intelligence can be effective when applied to highly complicated problems with many nonlinear factors, although it is often less effective than the genetic algorithm approach discussed later in this chapter. Swarm intelligence is related to swarm optimization […]. As with swarm intelligence, there is some evidence that at least some of the time swarm optimization can produce solutions that are more robust than genetic algorithms. Robustness here is defined as a solution’s resistance to performance degradation when the underlying variables are changed." (Michael J North & Charles M Macal, "Managing Business Complexity: Discovering Strategic Solutions with Agent-Based Modeling and Simulation", 2007)

"Thus, nonlinearity can be understood as the effect of a causal loop, where effects or outputs are fed back into the causes or inputs of the process. Complex systems are characterized by networks of such causal loops. In a complex, the interdependencies are such that a component A will affect a component B, but B will in general also affect A, directly or indirectly.  A single feedback loop can be positive or negative. A positive feedback will amplify any variation in A, making it grow exponentially. The result is that the tiniest, microscopic difference between initial states can grow into macroscopically observable distinctions." (Carlos Gershenson, "Design and Control of Self-organizing Systems", 2007)

"All forms of complex causation, and especially nonlinear transformations, admittedly stack the deck against prediction. Linear describes an outcome produced by one or more variables where the effect is additive. Any other interaction is nonlinear. This would include outcomes that involve step functions or phase transitions. The hard sciences routinely describe nonlinear phenomena. Making predictions about them becomes increasingly problematic when multiple variables are involved that have complex interactions. Some simple nonlinear systems can quickly become unpredictable when small variations in their inputs are introduced." (Richard N Lebow, "Forbidden Fruit: Counterfactuals and International Relations", 2010)

"Given the important role that correlation plays in structural equation modeling, we need to understand the factors that affect establishing relationships among multivariable data points. The key factors are the level of measurement, restriction of range in data values (variability, skewness, kurtosis), missing data, nonlinearity, outliers, correction for attenuation, and issues related to sampling variation, confidence intervals, effect size, significance, sample size, and power." (Randall E Schumacker & Richard G Lomax, "A Beginner’s Guide to Structural Equation Modeling" 3rd Ed., 2010)

"Complexity is a relative term. It depends on the number and the nature of interactions among the variables involved. Open loop systems with linear, independent variables are considered simpler than interdependent variables forming nonlinear closed loops with a delayed response." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity A Platform for Designing Business Architecture" 3rd Ed., 2011)

"We have minds that are equipped for certainty, linearity and short-term decisions, that must instead make long-term decisions in a non-linear, probabilistic world." (Paul Gibbons, "The Science of Successful Organizational Change", 2015)

"Random forests are essentially an ensemble of trees. They use many short trees, fitted to multiple samples of the data, and the predictions are averaged for each observation. This helps to get around a problem that trees, and many other machine learning techniques, are not guaranteed to find optimal models, in the way that linear regression is. They do a very challenging job of fitting non-linear predictions over many variables, even sometimes when there are more variables than there are observations. To do that, they have to employ 'greedy algorithms', which find a reasonably good model but not necessarily the very best model possible." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

"Exponentially growing systems are prevalent in nature, spanning all scales from biochemical reaction networks in single cells to food webs of ecosystems. How exponential growth emerges in nonlinear systems is mathematically unclear. […] The emergence of exponential growth from a multivariable nonlinear network is not mathematically intuitive. This indicates that the network structure and the flux functions of the modeled system must be subjected to constraints to result in long-term exponential dynamics." (Wei-Hsiang Lin et al, "Origin of exponential growth in nonlinear reaction networks", PNAS 117 (45), 2020)

"Non-linear associations are also quantifiable. Even linear regression can be used to model some non-linear relationships. This is possible because linear regression has to be linear in parameters, not necessarily in the data. More complex relationships can be quantified using entropy-based metrics such as mutual information. Linear models can also handle interaction terms. We talk about interaction when the model’s output depends on a multiplicative relationship between two or more variables." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

🔭Data Science: Linearity (Just the Quotes)

"In addition to dimensionality requirements, chaos can occur only in nonlinear situations. In multidimensional settings, this means that at least one term in one equation must be nonlinear while also involving several of the variables. With all linear models, solutions can be expressed as combinations of regular and linear periodic processes, but nonlinearities in a model allow for instabilities in such periodic solutions within certain value ranges for some of the parameters." (Courtney Brown, "Chaos and Catastrophe Theories", 1995)

"So we pour in data from the past to fuel the decision-making mechanisms created by our models, be they linear or nonlinear. But therein lies the logician's trap: past data from real life constitute a sequence of events rather than a set of independent observations, which is what the laws of probability demand. [...] It is in those outliers and imperfections that the wildness lurks." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"All forms of complex causation, and especially nonlinear transformations, admittedly stack the deck against prediction. Linear describes an outcome produced by one or more variables where the effect is additive. Any other interaction is nonlinear. This would include outcomes that involve step functions or phase transitions. The hard sciences routinely describe nonlinear phenomena. Making predictions about them becomes increasingly problematic when multiple variables are involved that have complex interactions. Some simple nonlinear systems can quickly become unpredictable when small variations in their inputs are introduced." (Richard N Lebow, "Forbidden Fruit: Counterfactuals and International Relations", 2010)

"There are several key issues in the field of statistics that impact our analyses once data have been imported into a software program. These data issues are commonly referred to as the measurement scale of variables, restriction in the range of data, missing data values, outliers, linearity, and nonnormality." (Randall E Schumacker & Richard G Lomax, "A Beginner’s Guide to Structural Equation Modeling" 3rd Ed., 2010)

"Complexity is a relative term. It depends on the number and the nature of interactions among the variables involved. Open loop systems with linear, independent variables are considered simpler than interdependent variables forming nonlinear closed loops with a delayed response." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity A Platform for Designing Business Architecture" 3rd Ed., 2011)

"Without precise predictability, control is impotent and almost meaningless. In other words, the lesser the predictability, the harder the entity or system is to control, and vice versa. If our universe actually operated on linear causality, with no surprises, uncertainty, or abrupt changes, all future events would be absolutely predictable in a sort of waveless orderliness." (Lawrence K Samuels, "Defense of Chaos", 2013)

"An oft-repeated rule of thumb in any sort of statistical model fitting is 'you can't fit a model with more parameters than data points'. This idea appears to be as wide-spread as it is incorrect. On the contrary, if you construct your models carefully, you can fit models with more parameters than datapoints [...]. A model with more parameters than datapoints is known as an under-determined system, and it's a common misperception that such a model cannot be solved in any circumstance. [...] this misconception, which I like to call the 'model complexity myth' [...] is not true in general, it is true in the specific case of simple linear models, which perhaps explains why the myth is so pervasive." (Jake Vanderplas, "The Model Complexity Myth", 2015) [source]

"Random forests are essentially an ensemble of trees. They use many short trees, fitted to multiple samples of the data, and the predictions are averaged for each observation. This helps to get around a problem that trees, and many other machine learning techniques, are not guaranteed to find optimal models, in the way that linear regression is. They do a very challenging job of fitting non-linear predictions over many variables, even sometimes when there are more variables than there are observations. To do that, they have to employ 'greedy algorithms', which find a reasonably good model but not necessarily the very best model possible." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

"Non-linear associations are also quantifiable. Even linear regression can be used to model some non-linear relationships. This is possible because linear regression has to be linear in parameters, not necessarily in the data. More complex relationships can be quantified using entropy-based metrics such as mutual information. Linear models can also handle interaction terms. We talk about interaction when the model’s output depends on a multiplicative relationship between two or more variables." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

See also the quotes on linearity in Graphical Representation

🔬Data Science: Swarm Intelligence (Definitions)

"Swarm systems generate novelty for three reasons: (1) They are 'sensitive to initial conditions' - a scientific shorthand for saying that the size of the effect is not proportional to the size of the cause - so they can make a surprising mountain out of a molehill. (2) They hide countless novel possibilities in the exponential combinations of many interlinked individuals. (3) They don’t reckon individuals, so therefore individual variation and imperfection can be allowed. In swarm systems with heritability, individual variation and imperfection will lead to perpetual novelty, or what we call evolution." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)

"Dumb parts, properly connected into a swarm, yield smart results." (Kevin Kelly, "New Rules for the New Economy", 1999)

"It is, however, fair to say that very few applications of swarm intelligence have been developed. One of the main reasons for this relative lack of success resides in the fact that swarm-intelligent systems are hard to 'program', because the paths to problem solving are not predefined but emergent in these systems and result from interactions among individuals and between individuals and their environment as much as from the behaviors of the individuals themselves. Therefore, using a swarm-intelligent system to solve a problem requires a thorough knowledge not only of what individual behaviors must be implemented but also of what interactions are needed to produce such or such global behavior." (Eric Bonabeau et al, "Swarm Intelligence: From Natural to Artificial Systems", 1999)

"Just what valuable insights do ants, bees, and other social insects hold? Consider termites. Individually, they have meager intelligence. And they work with no supervision. Yet collectively they build mounds that are engineering marvels, able to maintain ambient temperature and comfortable levels of oxygen and carbon dioxide even as the nest grows. Indeed, for social insects teamwork is largely self-organized, coordinated primarily through the interactions of individual colony members. Together they can solve difficult problems (like choosing the shortest route to a food source from myriad possible pathways) even though each interaction might be very simple (one ant merely following the trail left by another). The collective behavior that emerges from a group of social insects has been dubbed 'swarm intelligence'." (Eric Bonabeau & Christopher Meyer, Swarm Intelligence: A Whole New Way to Think About Business, Harvard Business Review, 2001)

"[…] swarm intelligence is becoming a valuable tool for optimizing the operations of various businesses. Whether similar gains will be made in helping companies better organize themselves and develop more effective strategies remains to be seen. At the very least, though, the field provides a fresh new framework for solving such problems, and it questions the wisdom of certain assumptions regarding the need for employee supervision through command-and-control management. In the future, some companies could build their entire businesses from the ground up using the principles of swarm intelligence, integrating the approach throughout their operations, organization, and strategy. The result: the ultimate self-organizing enterprise that could adapt quickly - and instinctively - to fast-changing markets." (Eric Bonabeau & Christopher Meyer, "Swarm Intelligence: A Whole New Way to Think About Business", Harvard Business Review, 2001)

"Swarm Intelligence can be defined more precisely as: Any attempt to design algorithms or distributed problem-solving methods inspired by the collective behavior of the social insect colonies or other animal societies. The main properties of such systems are flexibility, robustness, decentralization and self-organization." (Ajith Abraham et al, "Swarm Intelligence in Data Mining", 2006)

"Swarm intelligence can be effective when applied to highly complicated problems with many nonlinear factors, although it is often less effective than the genetic algorithm approach discussed later in this chapter. Swarm intelligence is related to swarm optimization […]. As with swarm intelligence, there is some evidence that at least some of the time swarm optimization can produce solutions that are more robust than genetic algorithms. Robustness here is defined as a solution’s resistance to performance degradation when the underlying variables are changed." (Michael J North & Charles M Macal, "Managing Business Complexity: Discovering Strategic Solutions with Agent-Based Modeling and Simulation", 2007)

[swarm intelligence] "Refers to a class of algorithms inspired by the collective behaviour of insect swarms, ant colonies, the flocking behaviour of some bird species, or the herding behaviour of some mammals, such that the behaviour of the whole can be considered as exhibiting a rudimentary form of 'intelligence'." (John Fulcher, "Intelligent Information Systems", 2009)

"The property of a system whereby the collective behaviors of unsophisticated agents interacting locally with their environment cause coherent functional global patterns to emerge." (M L Gavrilova, "Adaptive Algorithms for Intelligent Geometric Computing", 2009) 

[swarm intelligence] "Is a discipline that deals with natural and artificial systems composed of many individuals that coordinate using decentralized control and self-organization. In particular, SI focuses on the collective behaviors that result from the local interactions of the individuals with each other and with their environment." (Elina Pacini et al, "Schedulers Based on Ant Colony Optimization for Parameter Sweep Experiments in Distributed Environments", 2013). 

"Swarm intelligence (SI) is a branch of computational intelligence that discusses the collective behavior emerging within self-organizing societies of agents. SI was inspired by the observation of the collective behavior in societies in nature such as the movement of birds and fish. The collective behavior of such ecosystems, and their artificial counterpart of SI, is not encoded within the set of rules that determines the movement of each isolated agent, but it emerges through the interaction of multiple agents." (Maximos A Kaliakatsos-Papakostas et al, "Intelligent Music Composition", 2013)

"Collective intelligence of societies of biological (social animals) or artificial (robots, computer agents) individuals. In artificial intelligence, it gave rise to a computational paradigm based on decentralisation, self-organisation, local interactions, and collective emergent behaviours." (D T Pham & M Castellani, "The Bees Algorithm as a Biologically Inspired Optimisation Method", 2015)

"It is the field of artificial intelligence in which the population is in the form of agents which search in a parallel fashion with multiple initialization points. The swarm intelligence-based algorithms mimic the physical and natural processes for mathematical modeling of the optimization algorithm. They have the properties of information interchange and non-centralized control structure." (Sajad A Rather & P Shanthi Bala, "Analysis of Gravitation-Based Optimization Algorithms for Clustering and Classification", 2020)

"It [swarm intelligence] is the discipline dealing with natural and artificial systems consisting of many individuals who coordinate through decentralized monitoring and self-organization." (Mehmet A Cifci, "Optimizing WSNs for CPS Using Machine Learning Techniques", 2021)

Resources:
More quotes on "Swarm Intelligence" at the-web-of-knowledge.blogspot.com.