🔖Knowledge Representation: Models (Part I: In Search of a Definition)

Introduction
 Imagine you are talking with another person, you ramble about models here and there, and suddenly in the middle of the conversation a question falls like thunder, freezing the discussion for a few seconds: “you are talking about models, what is a model?”. The word become so common nowadays that such a question might seem a menace for the conversation. You might remember then some of the dictionary definitions you heard so often, though they pull with them other terms that need further clarification. Some well-known approximate quotations on models might spring into your thinking process, though they don’t seem of any help now. The seconds pass and the time of silence looks like an eternity, while your interlocutor stares at you waiting for an answer. Unless you are prepared to give a definition on interlocutor’s understanding, you’ll more likely be in the chase of a such definition. Words and ideas succeed fast, the silence grows deeper, your interlocutor becomes more anxious, and is waiting for an answer.

What is a Model?

The easiest way to tackle such concepts is to start with a common representative example that can be used as scaffolding for a definition. If few people heard of “role models”, more likely almost all people having a TV, PC or similar device have heard of “top models” or “fashion models”. The “fashion model” as well the “role model” are idealized types of people, the first type considering mainly the appearance characteristics that makes a person attractive for presenting fashion, while the second considers mainly the characteristics that other people would want to copy. Both categories represent some idealizations in which some characteristics, qualities or features are evidenced.

When one speaks about fashion models one can easily come with some names of such models who were en vogue over the years. On the other side maybe for many will be more difficult to come with names of people who can be considered as role models, unless they had in their life people who functioned as role models. A “role model” seems to be more abstract as concept than the “fashion model”, as the physical qualities are easier to grasps then the inner qualities. There can be defined qualities like success, confidence, hardworking or sociability that are attributed to both roles. In fact the qualities of the two concepts can intertwine to the degree that for some people a fashion model and role model may be defined by the same qualities, or the differences are so small that they can be ignored.

Fashion mode vs role model

Based on the two examples we can construct now a definition. Let’s consider a model as an idealization of a concrete or abstract object, in which some characteristics, qualities or features are considered as important and definitory.

The definition seems to be concise, clear, objective and precise, as much such a definition can be, so it looks like a good definition one can work with. The question is whether the praxis might invalidate it, where the gap between it and other definitions from technical literature is so big that makes this definition unusable. At least the following definitions seem to accord:

“A model is a simplification of reality intended to promote understanding.” [1]
“Models are replicas or representations of particular aspects and segments of the real world.” [2]
“A model is a representation of reality intended for some definite purpose .”[3].
“A model is an imitation of reality.” [4]
“A model is a representation of some subject matter.” [5]

From my point of view all these definitions aren’t good definitions because by attempting to be too general they lack precision. Is it any representation of some subject, of reality or part of it a model? Probably not! This raises another question: what isn’t a model? Unfortunately the answer isn’t that simple. Not any representation of something can be considered a model. Is it for example a cubistic representation of an object a model? The answer is again no! The model needs to keep certain characteristics of the object intended to represent, though more about it in other posts.

 Here are a few other alternative definitions for models:
”A model is a physical, mathematical, or logical representation of a system entity, phenomenon, or process.” [6]
“model: the artificial object which explains all the empirical facts under consideration” [7]

Models in Context

Depending on the context in which is used, the concept of model is more elaborated and adapted as needed. One can talk about business, conceptual/thinking, mental, mathematical, statistical, scientific, mechanistic, behavioral, structural, social, political, logical, data or diagrammatic models. In fact models are the cornerstone of all sciences and pseudo-sciences, the foundation on which our understanding and knowledge is based upon. From the inner to the outer world, from simple to complex activities, from mathematics to religion, we use models on a daily basis. We think in models, or at least we use models in our thinking even if we are not aware of it.

 From the literature reviewed over the years it can be observed that most of the definitions converge within the same boundaries, the difference residing mainly in the vocabulary used – idealization and characteristics being replaced by the family of words from the below table:

idealization	characteristics
simplification miniature representation imitation likeness description approximation abstraction reduction	qualities features attributes properties variables dimensions parameters

In various sources the denomination of model is substituted with synonyms that make better appeal of people’s understanding: pattern, example, emulation, analogy, visualization, system, replica, mold, mock-up, sketch, prototype, wireframe, schema, blueprint, (visual) aid, image (also picture, depiction), map, theory, principle, approximation, representation, allegory, metaphor, archetype, etc. All these can be considered upon context models, even if they might refer to totally different things.

Conclusion:

Even if our thinking became more complex, the average individual juggling with increasingly abstract concepts, it seems that we fail to define basic concepts like the one of model. Starting from two examples I attempted to provide a good definition one can work with. I tried also to provide a mechanism that can be used to extrapolate definitions for similar concepts.

References:
[1] SystemsThinking.org (2004) Models, by Gene Bellinger  http://www.systems-thinking.org/simulation/model.htm
[2] Data Modeling Fundamentals: A Practical Guide for IT Professionals, by Paulraj Ponniah, John Wiley & Sons, ISBN: 978-0-471-79049-5, 2007
[3] Tools for Thinking: Modelling in Management Science, 3rd Ed., by Michael Pidd, John Wiley & Sons, ISBN-13: 978-0470721421, 2009
[4] Process Systems Engineering: Process Modelling and Model Analysis Vol. IV, by Ian T. Cameron, Katalin M Hangos, Academic Press, ISBN-13: 978-0121569310, 2001
[5] Workflow Modeling: Tools for Process Improvement and Applications Development, 2nd Ed, by Alec Sharp Patrick McDermott. Artech House, ISBN-13: 978-1-59693-192-3, 2009
[6] Systems Engineering Fundamentals. Defense Acquisition University Press, 2001
[7] The Concept of Model: An Introduction to the Materialist Epistemology of Mathematics, by Alain Badiou, re.press, ISBN-13: 978-0980305234, 2007

 

🔖Knowledge Representation: Mental Models’ Fallacies (Part I: Professional Defects and Thinking Models)

Mental Models

Professional Defects

I heard of “professional defect” almost 15-20 years back, in a colloquial discussion with an acquaintance. I don’t remember anymore the context entirely, though as I used it then, it became part of my vocabulary. With time “professional defect” meant for me “seeing and judging the world through the knowledge of our profession, and ignoring or misinterpreting thus some (important) aspects of our quotidian life”.  I’m not sure whether the term is actually in use or a similar term is used to reflect this aspect. I met occasionally similar constructs later, some of my German colleagues stressing the fact that sometimes we have to take out our professional glasses in order to see things differently (e.g. take out or put our managerial glasses). A generalization can be met in De Bono’s six thinking hats – the hats representing in De Bono’s perception the distinct six ways in which people think about the world, each of them stressing an import aspect of reality and our thinking patterns.

While in school, preparing for our profession, and especially later when we arrive to practice it, we acquire a knowledge base, the facts about the world, a set of thinking models that provide an approximation of the world in which our profession is anchored, and heuristics, “algorithms” of thinking and decision making that form with time thinking patterns. They help us understand situations and solve problems in our professional life. They add up to our previous personal experience accumulated over the years. 

In fact we’ll more likely attempt at first to use some of the experience we acquired before attempting a profession, some of the knowledge, models and heuristics being validated or invalidated in our professional life. With time we arrive to use some of the models we exclusively acquired and verified in professional life also in our personal life. This translation may seem natural as professional life extends itself sometimes beyond the borders of our profession – some coworkers become our friends, we spend more and more time in communities related to our profession, we meet similar problems in the two areas as of life, etc.

This extension from professional to personal life can have positive as well negative implications. It is true that some models from professional life can help us figure out some aspects from personal life, we arrive maybe to validate and improve our models, reaching somehow a deeper understanding of life. The problem comes when we ignore that we deal with a different type of environment, with its own characteristics, with different groups of people having higher diversity and other characteristics than the ones we meet in professional life. As the premises, the environment and its actors change, some of the models need some tweaking or they become unusable in our personal life. Maybe the number of such cases is incomparable small when we regard other type of thinking fallacies we fall into on a daily basis, though as long they arrive to define us and our choices in one way or another, we need to take a step back and look at them.

Some Examples

There could be found multiple examples in which the thinking patterns and models about the world we “learned” in our profession are used outside the professional life. Sometimes they look at the world by generalizing the characteristics of the individuals, focusing typically on a single aspect of the human nature, making totally or partially abstraction of the whole.  It’s also a sequel of the analytic way of thinking about the world we’ve been exposed from the early years of school. A more appropriate way of studying, understanding and modeling the human nature is by following the systemic thinking view in which the human being is more than the components that builds it – the body, the psychological, the language, the character, the behavior ranging from simple movements to complex forms of expression, the creativity, the ways of thinking transposed in decision making and the philosophy about life, that include the religious and the spiritual, the experience, the community the person belongs to, and so on. Some of these aspects are interrelated and mold together, and as the human they are a part of the complex web of life we belong to.

Unfortunately, our models about the world are quite simplistic and inflexible, as long we keep them so and as long we can’t discover and build more complex models. Before jumping to further aspects about models let’s look at a few examples. They might not be representative, they might be a little brought to extreme, though they are met in life and affect us in one form or another.

For example, a mathematician or somebody with strong mathematical background arrives to think of the world around him in terms of probability for an event to happen. On one side this can prove as a powerful tool to quantify and predict such events, though might make the person ignore the area of impossible, expressed maybe in opportunities with small chances to happen, opportunities that when considered could have a huge impact on his live. It’s a trivial example of the attempt to quantify and simplify the world to a degree that makes it understandable and predictable, mathematician’s luggage of models being more complex than that. Judging the words of wisdom of some mathematicians, they seemed to arrive to a deeper understanding of life - spirituality, philosophy, literature and wit melting in mathematician's life. Still anyone can be entrapped in the fallacies of the cold mathematical thinking about life in which everything is reduced to a representational model.

Not far from the previous example, a philosopher builds in his mind a world of ideas, and sooner or later arrives to evaluate the world around and his personal interactions with the world based on the philosophical currents he adheres to. No matter how complete and well-established a philosophy is, it’s a human based system of beliefs and models, with its loops and wholes. Sooner or later the philosopher will find himself trapped in the threads of his own philosophy as long he applies it too deep und unaware into his personal life. From this perspective it will be hard for a philosopher to be happy and content with his life.

A psychologist or somebody with a similar background may arrive to judge the people outside his praxis based on the traits they reveal. A chemist or biologist may see human’s constitution governed by a chain of chemical reactions, reducing thus feelings and behavior to them. A doctor may start to see in people the predispositions to or existence of a given disease, arriving maybe to judge people based on certain predispositions. A dentist might start evaluate people based on the denture they have. A sales person might start to acquire new friends (exclusively) based on the predisposition of buying a product. Accountants and the other financial professionals might see the world around them through financial models and wealth. An artist may treat as inferior people those who don’t exhibit any artistic skills. A priest may see the people around him as sinners.

There are many other examples, each profession comes with own type of similar fallacies. Think about your profession or the professional environment you belong to! More likely you’ll discover similar examples. How deep have they penetrated in the human society? How much have they influenced or still influence you? How could you escape them?

A Jump to Thinking Models Fallacies

Models are a good way to represent and approximate the world around us and predict behavior, though paraphrasing George Box, all models are to some degree wrong. Sometimes is enough if a model is right once in a while, other times we need to have reliable models. In general acceptance the success of a particular model is tied to its ability to cope capture the behavior of the real world, while its reliability is proportional to the number of cases it does so. When dealing with people often we need reliable models. It’s a question of ethics, but primordially of chances we lose to meet new interesting people, new experiences, and why not in overcoming our current condition.

Relying too much on a model make us vulnerable to a range of events that are not addressed by our models. Some of the presumptions on which such models are built upon, same as the limitations of our thinking models can get easily forgotten in our decision making process. We become then the prisoners of a set of (thinking) patterns from which will be impossible to exit unless we realize their traps. This actually applies to all type of models we built along the years. Some of them are rooted deeply in our beliefs on how the world (environment) around us works or is supposed to work.

Not only the beliefs we have, but also the models we acquired and use make us filter the signals, events or information from our environment. What we consider in a model is as important as what we leave out. The components removed by reducing the world to a model can be quintessential in what concerns the understanding and why not the living of life as a whole – the religious, the spiritual, the favorable chance, the free will, the tipping point, the random, the potential of people or groups to raise above some condition(s). No matter how well established some models, there will always be exceptions. We should expect for such exceptions to happen. They should make us challenge and enhance our models.

Going beyond the limitations of our models can prove to be a considerable challenge. We need to challenge our models on a daily basis, their visible and hidden premises, recognize their advantages, disadvantages and area of applicability. We need to detach ourselves from the models we’ve built, adapt them or learn new similar models that complement or counterbalance the existing models. Each model offers in the end a glimpse of truth, though we’ll mistake if we consider it the ultimate truth.

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🕸️Web x.0: Is the Dot-Com Bubble 2.0 on its Way?

 

 The First Dot-Com Bubble

The dot-com bubble (aka Internet bubble) refers to the time period between 1995 and early spring of 2000, when the American economy underwent through a considerable boom, fact reflected in the increase in stock prices, especially the one associated with Internet-related assets [1]. The principal fuel for dot-com bubble seems to be the Internet and its huge potential for high-tech as well for non-high-tech companies. Data were communicated in real time at affordable prices, through web sites companies were having the potential of being known and of reaching potential customers all over the world, universities and companies could easier collaborate. It was the naissance of Internet phone, multicasting, e-commerce and e-auction portals, online banking and collaborative tools. The enormous potential was increasingly reflected in the news. 

Forbes and Wall Street Journal were encouraging people to invest in risky companies [4]. The public awareness was increasing [1], and the offer was huge. If previously a company needed to have had at least several profitable quarters before it went public, by 1999 the restrictions were relaxed considerably, it was enough to have a sketchy business plan, an Internet address and a few people who could speak the right jargon [1]. Numerous start-ups entered the marked over night, their entry being facilitated by the lower entry cost associated with the innovation [3], the sudden appearance of new niche markets and the demand coming from early adopters, eager to make most of the new technologies.

Many start-up companies like Google, Amazon or Netscape haven’t made a profit during the first years, however the high IPO value of their stocks allowed them to raise a substantial amount of money [4]. As the stocks of many companies were skying high, more and more money were pushed in the economy, many of the investments being driven by the mirage of getting rich over night. The investments in software, computer and communication equipment companies grow, IT becoming an important component of the US economy [2]. In fact, by October 1999, the stock value of the six biggest IT companies – Microsoft, Intel, IBM, Cisco, Lucent and Dell - was 20 percent of the US GDP [5]. Cities in US, trapped by the dream of becoming a new “Silicon Valley”, invested in their communication infrastructure and built network enabled offices to attract internet entrepreneurs [4]. Europe joined the rush as well, telecommunication companies investing in 3G licenses [4], companies were expanding to accommodate the increase demand coming from US.

Excessive IT investment, overconfidence and other factors made the bubble to burst in the spring of 2000. It was a turning point for the American economy as well for Europe, the dot-com stocks falling down, following the exit and bankruptcy of many dot-com companies. It was also the chance for other IT and non-IT companies to take over the assets of fallen companies. It was the time for acquisitions and mergers in order to survive the crisis. It was an opportunity for innovation to propagate and workforce to migrate from company to company. The investments in IT infrastructure continued moderately also after the burst, the economy revigorating itself slowly but steadily.

The Second Dot-Com Bubble?
 
Marc Andreeson, founder of Netscape, pointed out recently that “the ideas on the internet in the 1990s are all happening now” [7], and he seems to be right. The overevaluated IPOs of social networking companies like LinkedIn, Facebook or Groupon [6] seem to support the premises of a second dot-com bubble (aka dot-com bubble 2.0, to follow the trend, social networking bubble or social media bubble). Of course, social networks companies have a huge potential especially in what concerns the harnessing of collective intelligence and the diffusion of information, with application in multiple domains, but there is lot of work ahead until harnessing this potential. The boom of fancier and miniaturized electronic devices, plus the promises of Social Media, Web 2.0 and thinking further of the Semantic Web (aka Web 3,0), Big Data, Cloud Computing, Personal Cloud, Integrated Ecosystems, Enterprise App Stores and other technologies (e.g. in-memory computing, HTML5, Silverlight) seems to multiply exponentially the value of data, technology and networks. 

There are lots of opportunities for companies to appear over night, for small and average companies to grow, and for big companies to consolidate their position on the market. There is also lot of optimism in what concerns the future of the Web on one side, and the Web-centric organizations and business models on the other side, but is this optimism entitled? Could the boom of these technologies corroborated with the “this-time-is-different” syndrome and ignorance of history, facilitate the appearance of a second Internet bubble?  For sure that’s possible, but hopefully it won’t become reality, at least not in the near future. Hopefully the markets have learned something from the past…

Beyond Bubbles

Despite the negative effects the dot-com bubble had or might have at micro and macro level, I strongly believe that on the long term economies have the capacity to recover, and sometimes such bursts are necessary for the restructuring and re-leveling of values. Despite any future crisis, the Internet will continue its development fueled by the need for more capable technologies and, where technologies and needs are, investments more likely will follow.

References:
[1] G. Callahan, R. W. Garrison () Does Austrian Business Cycle Theory explain the Dot-Com Boom and Bust? [Online] Available from: http://mises.org/journals/qjae/pdf/qjae6_2_3.pdf (Accessed: 31.08.2012).
[2] Wikipedia (2012) Web Development. [Online] Available from: http://en.wikipedia.org/wiki/Web_development (Accessed: 31.08.2012).
[3] http://www.aeaweb.org/annual_mtg_papers/2007/0107_1300_0902.pdf
[4] Wikipedia (2012) Dot-com bubble. [Online] Available from: http://en.wikipedia.org/wiki/Dot-com_bubble (Accessed: 01.09.2012).
[5] M. Buttel (2010) 10 Years On: When the bubble burst. Financial Services Technologies. [Online] Available from: http://www.fsteurope.com/news/when-the-bubble-burst/ (Accessed: 01.09.2012).
[6] North American Value Investing. (2012). Are We in Another Dot Com Bubble? [Online] Available from: http://navinvesting.blogspot.de/2012/05/are-we-in-another-dot-com-bubble.html (Accessed: 02.01.2013)
[7] D. Soskin, (2012) Is the dotcom bubble 2.0 set to burst? [Online] Available from:  http://www.growingbusiness.co.uk/dot-com-bubble-2-0.html (Accessed: 02.01.2013)

Note: The current post was adapted after my assignment submission for the Internet History Technology and Security Coursera Course.

🏷️Knowledge Representation: On Decision-Making (Quotes)

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

"Great decisions in the realms of thought and momentous discoveries and solutions of problems are only possible to an individual working in solitude." (Sigmund Freud, "Group Psychology and the Analysis of the Ego", 1921)

“The fundamental gospel of statistics is to push back the domain of ignorance, prejudice, rule-of-thumb, arbitrary or premature decisions, tradition, and dogmatism and to increase the domain in which decisions are made and principles are formulated on the basis of analyzed quantitative facts.” (Robert W Burgess, “The Whole Duty of the Statistical Forecaster”, Journal of the American Statistical Association , Vol. 32, No. 200, 1937)

"Years ago a statistician might have claimed that statistics deals with the processing of data [...]today’s statistician will be more likely to say that statistics is concerned with decision making in the face of uncertainty." (Herman Chernoff & Lincoln E Moses, "Elementary Decision Theory", 1959) 

"[Game theory is] essentially a structural theory. It uncovers the logical structure of a great variety of conflict situations and describes this structure in mathematical terms. Sometimes the logical structure of a conflict situation admits rational decisions; sometimes it does not." (Anatol Rapoport, "Prisoner's Dilemma: A study in conflict and cooperation", 1965)E

"Now we are looking for another basic outlook on the world - the world as organization. Such a conception - if it can be substantiated - would indeed change the basic categories upon which scientific thought rests, and profoundly influence practical attitudes. This trend is marked by the emergence of a bundle of new disciplines such as cybernetics, information theory, general system theory, theories of games, of decisions, of queuing and others; in practical applications, systems analysis, systems engineering, operations research, etc. They are different in basic assumptions, mathematical techniques and aims, and they are often unsatisfactory and sometimes contradictory. They agree, however, in being concerned, in one way or another, with ‘systems’, ‘wholes’ or ‘organizations’; and in their totality, they herald a new approach." (Ludwig von Bertalanffy, "General System Theory", 1968)

"Each of us uses models constantly. Every person in his private life and in his business life instinctively uses models for decision making. The mental image of the world around you which you carry in your head is a model. […] A mental image is a model. All our decisions are taken on the basis of models." (Jay W Forrester, "Counter-Intuitive Behaviour of Social Systems", Technological Review 73, 1971)

"A somewhat deeper analysis suggests that a decision is a deliberate act of selection, by the mind, of an alternative from a set of competing alternatives in the hope, expectation, or belief that the actions envisioned in carrying out the selected alternative will accomplish certain goals. Decision is the selection of a mental state: it is a commitment to certain actions or inactions. Other people may observe our actions but they do not directly observe our decisions." (Peter C Fishburn, "Personalistic Decision Theory: Exposition and Critique", 1972)

"The human condition can almost be summed up in the observation that, whereas all experiences are of the past, all decisions are about the future. It is the great task of human knowledge to bridge this gap and to find those patterns in the past which can be projected into the future as realistic images." (Kenneth E Boulding, [foreword] 1972)

"Decision-making problems (hypothesis testing) involve situations where it is desired to make a choice among various alternative decisions (hypotheses). Such problems can be viewed as generalized state estimation problems where the definition of state has simply been expanded." (Fred C Scweppe, "Uncertain dynamic systems", 1973)

"Statistics is a body of methods and theory applied to numerical evidence in making decisions in the face of uncertainty." (Lawrence Lapin, "Statistics for Modern Business Decisions", 1973)

"The science of statistics may be described as exploring, analyzing and summarizing data; designing or choosing appropriate ways of collecting data and extracting information from them; and communicating that information. Statistics also involves constructing and testing models for describing chance phenomena. These models can be used as a basis for making inferences and drawing conclusions and, finally, perhaps for making decisions." (Fergus Daly et al, "Elements of Statistics", 1995)

"The major fault in this process - and thus, in the way we were making decisions - is that it lacks an organizing framework. In pursuing a variety of goals and objectives, in whatever situation we manage, we often fail to see that some of them are in conflict and that the achievement of one might come at the expense of achieving another. In weighing up the actions we might take to reach our goals and objectives, we have no way to account for nature's complexity and only rarely factor it in." (Allan Savory & Jody Butterfield, "Holistic Management: A new framework for decision making", 1988)

"A holistic perspective is essential in management. If we base management decisions on any other perspective, we are likely to experience results different from those intended because only the whole is reality." (Allan Savory & Jody Butterfield, "Holistic Management: A new framework for decision making", 1988)

"Faced with the overwhelming complexity of the real world, time pressure, and limited cognitive capabilities, we are forced to fall back on rote procedures, habits, rules of thumb, and simple mental models to make decisions. Though we sometimes strive to make the best decisions we can, bounded rationality means we often systematically fall short, limiting our ability to learn from experience." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"Just as dynamics arise from feedback, so too all learning depends on feedback. We make decisions that alter the real world; we gather information feedback about the real world, and using the new information we revise our understanding of the world and the decisions we make to bring our perception of the state of the system closer to our goals." (John D Sterman, "Business dynamics: Systems thinking and modeling for a complex world", 2000)

"No plea about inadequacy of our understanding of the decision-making processes can excuse us from estimating decision making criteria. To omit a decision point is to deny its presence - a mistake of far greater magnitude than any errors in our best estimate of the process." (Jay W Forrester, "Perspectives on the modelling process", 2000)

"The robustness of the misperceptions of feedback and the poor performance they cause are due to two basic and related deficiencies in our mental model. First, our cognitive maps of the causal structure of systems are vastly simplified compared to the complexity of the systems themselves. Second, we are unable to infer correctly the dynamics of all but the simplest causal maps. Both are direct consequences of bounded rationality, that is, the many limitations of attention, memory, recall, information processing capability, and time that constrain human decision making." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"Diversity and independence are important because the best collective decisions are the product of disagreement and contest, not consensus or compromise." (James Surowiecki, "The Wisdom of Crowds", 2005)

"The fact that cognitive diversity matters does not mean that if you assemble a group of diverse but thoroughly uninformed people, their collective wisdom will be smarter than an expert's. But if you can assemble a diverse group of people who possess varying degrees of knowledge and insight, you're better off entrusting it with major decisions rather than leaving them in the hands of one or two people, no matter how smart those people are." (James Surowiecki, "The Wisdom of Crowds", 2005)

"[...] under the right circumstances, groups are remarkably intelligent, and are often smarter than the smartest people in them. Groups do not need to be dominated by exceptionally intelligent people in order to be smart. Even if most of the people within a group are not especially well-informed or rational, it can still reach a collectively wise decision." (James Surowiecki, "The Wisdom of Crowds", 2005)

"[...] a model is a tool for taking decisions and any decision taken is the result of a process of reasoning that takes place within the limits of the human mind. So, models have eventually to be understood in such a way that at least some layer of the process of simulation is comprehensible by the human mind. Otherwise, we may find ourselves acting on the basis of models that we don’t understand, or no model at all.” (Ugo Bardi, “The Limits to Growth Revisited”, 2011)

"In general, when building statistical models, we must not forget that the aim is to understand something about the real world. Or predict, choose an action, make a decision, summarize evidence, and so on, but always about the real world, not an abstract mathematical world: our models are not the reality - a point well made by George Box in his oft-cited remark that "all models are wrong, but some are useful". (David Hand, "Wonderful examples, but let's not close our eyes", Statistical Science 29, 2014)

"So everyone has and uses mental representations. What sets expert performers apart from everyone else is the quality and quantity of their mental representations. Through years of practice, they develop highly complex and sophisticated representations of the various situations they are likely to encounter in their fields - such as the vast number of arrangements of chess pieces that can appear during games. These representations allow them to make faster, more accurate decisions and respond more quickly and effectively in a given situation. This, more than anything else, explains the difference in performance between novices and experts." (Anders Ericsson & Robert Pool, "Peak: Secrets from  the  New  Science  of  Expertise" , 2016)

🏷️Knowledge Representation: On Knowledge (Quotes)

"The mathematician speculates the causes of a certain sensible effect, without considering its actual existence; for the contemplation of universals excludes the knowledge of particulars; and he whose intellectual eye is fixed on that which is general and comprehensive, will think but little of that which is sensible and singular." (Proclus Lycaeus, cca 5th century)

"Knowledge, then, is a state of capacity to demonstrate, and has the other limiting characteristics which we specify in the Analytics; for it is when one believes in a certain way and the principles are known to him that he has knowledge, since if they are not better known to him than the conclusion, he will have his knowledge only on the basis of some concomitant." (Aristotle," Nicomachean Ethics", cca. 340 BC)

"What we know is not capable of being otherwise; of things capable of being otherwise we do not know, when they have passed outsideour observation, whether they exist or not. Therefore the object of knowledge is of necessity. Therefore it is eternal; for things that are of necessity in the unqualified sense are all eternal; and things that are eternal are ungenerated and imperishable. " (Aristotle, "Nicomachean Ethics", cca. 340 BC)

"There are four great sciences, without which the other sciences cannot be known nor a knowledge of things secured […] Of these sciences the gate and key is mathematics […] He who is ignorant of this [mathematics] cannot know the other sciences nor the affairs of this world." (Roger Bacon, "Opus Majus", 1267)

"There are two modes of acquiring knowledge, namely, by reasoning and experience. Reasoning draws a conclusion and makes us grant the conclusion, but does not make the conclusion certain, nor does it remove doubt so that the mind may rest on the intuition of truth unless the mind discovers it by the path of experience." (Roger Bacon, "Opus Majus", 1267)

"Knowledge being to be had only of visible and certain truth, error is not a fault of our knowledge, but a mistake of our judgment, giving assent to that which is not true." (John Locke, "An Essay Concerning Human Understanding", 1689)

"[…] the highest probability amounts not to certainty, without which there can be no true knowledge." (John Locke, "An Essay Concerning Human Understanding", 1689)

"Mathematical knowledge adds vigor to the mind, frees it from prejudice, credulity, and superstition." (John Arbuthnot, "An Essay on the Usefulness of Mathematical Learning", 1701)

"It is your opinion, the ideas we perceive by our senses are not real things, but images, or copies of them. Our knowledge therefore is no farther real, than as our ideas are the true representations of those originals. But as these supposed originals are in themselves unknown, it is impossible to know how far our ideas resemble them; or whether they resemble them at all. We cannot therefore be sure we have any real knowledge." (George Berkeley, "Three Dialogues", 1713)

"There is nothing more pleasant for man than the certainty of knowledge; whoever has once tasted of it is repelled by everything in which he perceives nothing but uncertainty. This is why the mathematicians who always deal with certain knowledge have been repelled by philosophy and other things, and have found nothing more pleasant than to spend their time with lines and letters." (Christian Wolff, 1741)

"He that would make a real progress in knowledge must dedicate his age as well as first fruits - the latter growth as well as the first-fruits - at the altar of truth." (Bishop George Berkeley, "Siris", 1744)

"Those who have not imbibed the prejudices of philosophers, are easily convinced that natural knowledge is to be founded on experiment and observation." (Colin Maclaurin, "An Account of Sir Isaac Newton’s Philosophical Discoveries", 1748)

"Our knowledge springs from two fundamental sources of the mind; the first is the capacity of receiving representations (receptivity for impressions), the second is the power of knowing an object through these representations (spontaneity [in the production] of concepts)." (Immanuel Kant, "Critique of Pure Reason", 1781)

"Philosophical knowledge is the knowledge gained by reason from concepts; mathematical knowledge is the knowledge gained by reason from the construction of concepts." (Immanuel Kant, "Critique of Pure Reason", 1781)

"Thoughts without content are empty, intuitions without concepts are blind. The understanding can intuit nothing, the senses can think nothing. Only through their unison can knowledge arise." (Immanuel Kant, "Critique of Pure Reason", 1781)

"The mathematician pays not the least regard either to testimony or conjecture, but deduces everything by demonstrative reasoning, from his definitions and axioms. Indeed, whatever is built upon conjecture, is improperly called science; for conjecture may beget opinion, but cannot produce knowledge." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)

"On completing one discovery we never fail to get an imperfect knowledge of others of which you could have no idea before […]" (Joseph Priestley, 1786)

"As there is no study which may be so advantageously entered upon with a less stock of preparatory knowledge than mathematics, so there is none in which a greater number of uneducated men have raised themselves, by their own exertions, to distinction and eminence. […] Many of the intellectual defects which, in such cases, are commonly placed to the account of mathematical studies, ought to be ascribed to the want of a liberal education in early youth." (Dugald Stewart, "Elements of the Philosophy of the Human Mind", 1792)

"The power of Reason […] is unquestionably the most important by far of those which are comprehended under the general title of Intellectual. It is on the right use of this power that our success in the pursuit of both knowledge and of  happiness depends; and it is by the exclusive possession of it that man is distinguished, in the most essential respects, from the lower animals. It is, indeed, from their subserviency to its operations, that the other faculties […] derive their chief value." (Dugald Stewart, "Elements of the Philosophy of the Human Mind", 1792)

"Each item of knowledge involves a second, a third step, and so on ad infinitum. If we pursue the life of the tree in its roots, or in its branches and twigs, one thing always follows from another. And the more vitally any concern of knowledge takes hold of us, the more we find ourselves driven to pursue it in its ramifications, both up and down." (Johann Wolfgang von Goethe, "Annals", 1807)

"Knowledge is only real and can only be set forth fully in the form of science, in the form of system." (G W Friedrich Hegel, "The Phenomenology of Mind", 1807)

"One may even say, strictly speaking, that almost all our knowledge is only probable; and in the small number of things that we are able to know with certainty, in the mathematical sciences themselves, the principal means of arriving at the truth - induction and analogy - are based on probabilities, so that the whole system of human knowledge is tied up with the theory set out in this essay." (Pierre-Simon Laplace, "Philosophical Essay on Probabilities", 1814) 

"[...] all knowledge, and especially the weightiest knowledge of the truth, to which only a brief triumph is allotted between the two long periods in which it is condemned as paradoxical or disparaged as trivial." (Arthur Schopenhauer, "The World as Will and Representation", 1819)

"The highest knowledge can be nothing more than the shortest and clearest road to truth; all the rest is pretension, not performance, mere verbiage and grandiloquence, from which we can learn nothing." (Charles C Colton, "Lacon", 1820)

"We [...] are profiting not only by the knowledge, but also by the ignorance, not only by the discoveries, but also by the errors of our forefathers; for the march of science, like that of time, has been progressing in the darkness, no less than in the light." (Charles C Colton, "Lacon", 1820)

"The first steps in the path of discovery, and the first approximate measures, are those which add most to the existing knowledge of mankind." (Charles Babbage, "Reflections on the Decline of Science in England", 1830)

"Our knowledge of circumstances has increased, but our uncertainty, instead of having diminished, has only increased. The reason of this is, that we do not gain all our experience at once, but by degrees; so our determinations continue to be assailed incessantly by fresh experience; and the mind, if we may use the expression, must always be under arms." (Carl von Clausewitz, "On War", 1832)

"Truth in itself is rarely sufficient to make men act. Hence the step is always long from cognition to volition, from knowledge to ability. The most powerful springs of action in men lie in his emotions." (Carl von Clausewitz, "On War", 1832)

"Science and knowledge are subject, in their extension and increase, to laws quite opposite to those which regulate the material world. Unlike the forces of molecular attraction, which cease at sensible distances; or that of gravity, which decreases rapidly with the increasing distance from the point of its origin; the farther we advance from the origin of our knowledge, the larger it becomes, and the greater power it bestows upon its cultivators, to add new fields to its dominions." (Charles Babbage, "On the Economy of Machinery and Manufactures", 1832)

"The peculiar character of mathematical truth is that it is necessarily and inevitably true; and one of the most important lessons which we learn from our mathematical studies is a knowledge that there are such truths." (William Whewell, "Principles of English University Education", 1838)

"[…] in order that the facts obtained by observation and experiment may be capable of being used in furtherance of our exact and solid knowledge, they must be apprehended and analysed according to some Conception which, applied for this purpose, gives distinct and definite results, such as can be steadily taken hold of and reasoned from […]" (William Whewell, "The Philosophy of the Inductive Sciences Founded Upon their History" Vol. 2, 1840)

"[…] there do exist among us doctrines of solid and acknowledged certainty, and truths of which the discovery has been received with universal applause. These constitute what we commonly term Sciences; and of these bodies of exact and enduring knowledge, we have within our reach so large and varied a collection, that we may examine them, and the history of their formation, with good prospect of deriving from the study such instruction as we seek." (William Whewell, "The Philosophy of the Inductive Sciences Founded upon Their History" Vol. 1, 1847)

"Remember that accumulated knowledge, like accumulated capital, increases at compound interest: but it differs from the accumulation of capital in this; that the increase of knowledge produces a more rapid rate of progress, whilst the accumulation of capital leads to a lower rate of interest. Capital thus checks its own accumulation: knowledge thus accelerates its own advance. Each generation, therefore, to deserve comparison with its predecessor, is bound to add much more largely to the common stock than that which it immediately succeeds." (Charles Babbage, "The Exposition of 1851: Or the Views of Industry, Science and Government of England", 1851)

"All knowledge is profitable; profitable in its ennobling effect on the character, in the pleasure it imparts in its acquisition, as well as in the power it gives over the operations of mind and of matter. All knowledge is useful; every part of this complex system of nature is connected with every other. Nothing is isolated. The discovery of to-day, which appears unconnected with any useful process, may, in the course of a few years, become the fruitful source of a thousand inventions." (Joseph Henry, "Report of the Secretary" [Sixth Annual Report of the Board of Regents of the Smithsonian Institution for 1851], 1852)

"SYSTEM (σύστημα, σύν ἵστημιavu, to place together) - is a full and connected view of all the truths of some department of knowledge. An organized body of truth, or truths arranged under one and the same idea, which idea is as the life or soul which assimilates all those truths. No truth is altogether isolated. Every truth has relation to some other. And we should try to unite the facts of our knowledge so as to see them in their several bearings. This we do when we frame them into a system. To do so legitimately we must begin by analysis and end with synthesis. But system applies not only to our knowledge, but to the objects of our knowledge. Thus we speak of the planetary system, the muscular system, the nervous system. We believe that the order to which we would reduce our ideas has a foundation in the nature of things. And it is this belief that encourages us to reduce our knowledge of things into systematic order. The doing so is attended with many advantages. At the same time a spirit of systematizing may be carried too far. It is only in so far as it is in accordance with the order of nature that it can be useful or sound." (William Fleming, "Vocabulary of philosophy, mental, moral, and metaphysical; with quotations and references; for the use of students", 1857)

"Science asks no questions about the ontological pedigree or a priori character of a theory, but is content to judge it by its performance; and it is thus that a knowledge of nature, having all the certainty which the senses are competent to inspire, has been attained - a knowledge which maintains a strict neutrality toward all philosophical systems and concerns itself not with the genesis or a priori grounds of ideas." (Chauncey Wright, "The Philosophy of Herbert Spencer", North American Review, 1865)

"One of the greatest obstacles to the free and universal movement of human knowledge is the tendency that leads different kinds of knowledge to separate into systems." (Claude Bernard, "An Introduction to the Study of Experimental Medicine", 1865)

"Isolated facts and experiments have in themselves no value, however great their number may be. They only become valuable in a theoretical or practical point of view when they make us acquainted with the law of a series of uniformly recurring phenomena, or, it may be, only give a negative result showing an incompleteness in our knowledge of such a law, till then held to be perfect." (Hermann von Helmholtz, "The Aim and Progress of Physical Science", 1869)

"Simplification of modes of proof is not merely an indication of advance in our knowledge of a subject, but is also the surest guarantee of readiness for farther progress." (William T Kelvin, "Elements of Natural Philosophy", 1873)

"The whole value of science consists in the power which it confers upon us of applying to one object the knowledge acquired from like objects; and it is only so far, therefore, as we can discover and register resemblances that we can turn our observations to account." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"Science is the observation of things possible, whether present or past; prescience is the knowledge of things which may come to pass, though but slowly." (Leonardo da Vinci, "The Notebooks of Leonardo da Vinci", 1883)

"[…] when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of science." (William T Kelvin, "Electrical Units of Measurement", 1883)

"I am convinced that it is impossible to expound the methods of induction in a sound manner, without resting them on the theory of probability. Perfect knowledge alone can give certainty, and in nature perfect knowledge would be infinite knowledge, which is clearly beyond our capacities. We have, therefore, to content ourselves with partial knowledge, - knowledge mingled with ignorance, producing doubt." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1887)

"The smallest group of facts, if properly classified and logically dealt with, will form a stone which has its proper place in the great building of knowledge, wholly independent of the individual workman who has shaped it." (Karl Pearson, "The Grammar of Science", 1892)

"The true aim of the teacher must be to impart an appreciation of method and not a knowledge of facts." (Karl Pearson, "The Grammar of Science", 1892)

"There is no short cut to truth, no way to gain a knowledge of the universe except through the gateway of scientific method." (Karl Pearson, "The Grammar of Science", 1892)

"Mature knowledge regards logical clearness as of prime importance: only logically clear images does it test as to correctness; only correct images does it compare as to appropriateness. By pressure of circumstances the process is often reversed. Images are found to be suitable for a certain purpose; are next tested as to their correctness ; and only in the last place purged of implied contradictions." (Heinrich Hertz, "The Principles of Mechanics Presented in a New Form", 1894)

"Without a theory all our knowledge of nature would be reduced to a mere inventory of the results of observation. Every scientific theory must be regarded as an effort of the human mind to grasp the truth, and as long as it is consistent with the facts, it forms a chain by which they are linked together and woven into harmony." (Thomas Preston, "The Theory of Heat", 1894)

"A system is not so important as a method. A system is of significance because it brings order and clearness into our knowledge, but he who hopes by its help to reach something more, he who thinks to extend his knowledge by means of a system is self-deceived." (Harald Høffding, "A history of modern philosophy", 1900)

"Man's determination not to be deceived is precisely the origin of the problem of knowledge. The question is always and only this: to learn to know and to grasp reality in the midst of a thousand causes of error which tend to vitiate our observation." (Federigo Enriques, "Problems of Science", 1906)

"Knowledge is the distilled essence of our intuitions, corroborated by experience." (Elbert Hubbard, "A Thousand & One Epigrams, 1911)

"It is experience which has given us our first real knowledge of Nature and her laws. It is experience, in the shape of observation and experiment, which has given us the raw material out of which hypothesis and inference have slowly elaborated that richer conception of the material world which constitutes perhaps the chief, and certainly the most characteristic, glory of the modern mind." (Arthur J Balfour, "The Foundations of Belief", 1912)

"The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another." (Henri Poincaré, 1913)

"By intuition is frequently understood perception, or the knowledge of actual reality, the apprehension of something as real. […] Intuition is the undifferentiated unity of the perception of the real and of the simple image of the possible. " (Benedetto Croce, "The Essence of Æsthetic", 1921)

"Observed facts must be built up, woven together, ordered, arranged, systematized into conclusions and theories by reflection and reason, if they are to have full bearing on life and the universe. Knowledge is the accumulation of facts. Wisdom is the establishment of relations. And just because the latter process is delicate and perilous, it is all the more delightful." (Gamaliel Bradford, "Darwin", 1926)

"With fuller knowledge we should sweep away the references to probability and substitute the exact facts." (Sir Arthur S Eddington, "The Nature of the Physical World", 1928)

"Scientific discovery and scientific knowledge have been achieved only by those who have gone in pursuit of them without any practical purpose whatsoever in view." (Max Planck, "Where is Science Going?", 1932)

"As facts and knowledge accumulate, the claim of the scientist to an understanding of the world in a certain sense diminishes." (Werner K Heisenberg, "Zur Geschichte der physikalischen Naturerklärung", 1933)

"The urge to knowledge is so deeply rooted in man that it can scarcely be omitted from a list of life's important needs." (Hans Reichenbach, "Atom and Cosmos: The World of Modern Physics", 1933)

"The laws of science are the permanent contributions to knowledge - the individual pieces that are fitted together in an attempt to form a picture of the physical universe in action. As the pieces fall into place, we often catch glimpses of emerging patterns, called theories; they set us searching for the missing pieces that will fill in the gaps and complete the patterns. These theories, these provisional interpretations of the data in hand, are mere working hypotheses, and they are treated with scant respect until they can be tested by new pieces of the puzzle." (Edwin P Whipple, "Experiment and Experience", [Commencement Address, California Institute of Technology] 1938)

"We have discovered that it is actually an aid in the search for knowledge to understand the nature of the knowledge we seek." (Arthur S Eddington, "The Philosophy of Physical Science", 1938)

"It is by abstraction that one can separate movements, knowledge, and affectivity. And the analysis is, here, so far from being a real dismemberment that it is given only as probable. One can never effectively reduce an [mental] image to its elements, for the reason that an image, like all other psychic syntheses, is something more and different from the sum of its elements. […] We will always go from image to image. Comprehension is a movement which is never-ending, it is the reaction of the mind to an image by another image, to this one by another image and so on, in principle to infinity. "(Jean-Paul Sartre, "The Imaginary: A phenomenological psychology of the imagination", 1940)

"In perception, a knowledge forms itself slowly; in the [mental] image the knowledge is immediate. We see now that the image is a synthetic act which unites a concrete, nonimagined, knowledge to elements which are more actually representative. The image teaches nothing: it is organized exactly like the objects which do produce knowledge, but it is complete at the very moment of its appearance." (Jean-Paul Sartre, "The Psychology of Imagination", 1940)

"Science, in the broadest sense, is the entire body of the most accurately tested, critically established, systematized knowledge available about that part of the universe which has come under human observation. For the most part this knowledge concerns the forces impinging upon human beings in the serious business of living and thus affecting man’s adjustment to and of the physical and the social world. […] Pure science is more interested in understanding, and applied science is more interested in control […]" (Austin L Porterfield, "Creative Factors in Scientific Research", 1941)

"Our theory has some bleaker consequences. [...] What is knowledge, if we are but a part of the mechanical system of the world we seek to know? What becomes of our ceaseless effort to explain the universe we live in, if explanation is but a part of the mechanical process?" (Kenneth Craik, "The Nature of Explanation", 1943)

"Whenever a man increases the content of his mind he gains new knowledge, and this occurs each time a new relation is established between the worlds on the two sides of the sense-organs - the world of ideas in an individual mind, and the world of objects existing outside individual minds which is common to us all." (James H Jeans, "Physics and Philosophy" 3rd Ed., 1943)

"Science usually advances by a succession of small steps, through a fog in which even the most keen-sighted explorer can seldom see more than a few paces ahead. Occasionally the fog lifts, an eminence is gained, and a wider stretch of territory can be surveyed - sometimes with startling results. A whole science may then seem to undergo a kaleidoscopic ‘rearrangement’, fragments of knowledge being found to fit together in a hitherto unsuspected manner. Sometimes the shock of readjustment may spread to other sciences; sometimes it may divert the whole current of human thought." (James H Jeans, "Physics and Philosophy" 3rd Ed., 1943)

"Every bit of knowledge we gain and every conclusion we draw about the universe or about any part or feature of it depends finally upon some observation or measurement. Mankind has had again and again the humiliating experience of trusting to intuitive, apparently logical conclusions without observations, and has seen Nature sail by in her radiant chariot of gold in an entirely different direction." (Oliver J Lee, "Measuring Our Universe: From the Inner Atom to Outer Space", 1950)

"The essence of knowledge is generalization. That fire can be produced by rubbing wood in a certain way is a knowledge derived by generalization from individual experiences; the statement means that rubbing wood in this way will always produce fire. The art of discovery is therefore the art of correct generalization." (Hans Reichenbach, "The Rise of Scientific Philosophy", 1951)

"Knowledge rests on knowledge; what is new is meaningful because it departs slightly from what was known before; this is a world of frontiers, where even the liveliest of actors or observers will be absent most of the time from most of them." (J Robert Oppenheimer, "Science and the Common Understanding", 1954)

"Science, then, is the attentive consideration of common experience; it is common knowledge extended and refined. Its validity is of the same order as that of ordinary perception; memory, and understanding. Its test is found, like theirs, in actual intuition, which sometimes consists in perception and sometimes in intent." (George Santayana, "The Life of Reason, or the Phases of Human Progress", 1954)

Science cannot be based on dogma or authority of any kind, nor on any institution or revelation, unless indeed it be of the Book of Nature that lies open before our eyes. We need not dwell on the processes of acquiring knowledge by observation, experiment, and inductive and deductive reasoning. The study of scientific method both in theory and practice is of great importance. It is inherent in the philosophy that the record may be imperfect and the conceptions erroneous; the potential fallibility of our science is not only acknowledged but also insisted upon." (Sir Robert Robinson, "Science and the Scientist", Nature Vol. 176 (4479), 1955)

"There comes a point where the mind takes a leap - call it intuition or what you will - and comes out upon a higher plane of knowledge, but can never prove how it got there. All great discoveries have involved such a leap." (Albert Einstein, [interview in Life, "Death of a Genius"] 1955)

"Knowledge is not something which exists and grows in the abstract. It is a function of human organisms and of social organization. Knowledge, that is to say, is always what somebody knows: the most perfect transcript of knowledge in writing is not knowledge if nobody knows it. Knowledge however grows by the receipt of meaningful information - that is, by the intake of messages by a knower which are capable of reorganising his knowledge." (Kenneth E Boulding, "General Systems Theory - The Skeleton of Science", Management Science Vol. 2 (3), 1956)

"The mathematical formulas indeed no longer portray nature, but rather our knowledge of nature." (Werner K Heisenberg, "The Representation of Nature in Contemporary Physics", Daedalus Vol. 87 (3), 1958)

"Science does not mean an idle resting upon a body of certain knowledge; it means unresting endeavor and continually progressing development toward an end which the poetic intuition may apprehend, but which the intellect can never fully grasp." (Max Planck, "The New Science", 1959)

"Incomplete knowledge must be considered as perfectly normal in probability theory; we might even say that, if we knew all the circumstances of a phenomenon, there would be no place for probability, and we would know the outcome with certainty." (Félix E Borel, Probability and Certainty", 1963)

"In its efforts to learn as much as possible about nature, modem physics has found that certain things can never be ‘known’ with certainty. Much of our knowledge must always remain uncertain. The most we can know is in terms of probabilities." (Richard P Feynman, "The Feynman Lectures on Physics", 1964)

"Knowing reality means constructing systems of transformations that correspond, more or less adequately, to reality. They are more or less isomorphic to transformations of reality. The transformational structures of which knowledge consists are not copies of the transformations in reality; they are simply possible isomorphic models among which experience can enable us to choose. Knowledge, then, is a system of transformations that become progressively adequate." (Jean Piaget, "Genetic Epistemology", 1968)

"Scientific knowledge is not created solely by the piecemeal mining of discrete facts by uniformly accurate and reliable individual scientific investigations. The process of criticism and evaluation, of analysis and synthesis, are essential to the whole system. It is impossible for each one of us to be continually aware of all that is going on around us, so that we can immediately decide the significance of every new paper that is published. The job of making such judgments must therefore be delegated to the best and wisest among us, who speak, not with their own personal voices, but on behalf of the whole community of Science. […] It is impossible for the consensus - public knowledge - to be voiced at all, unless it is channeled through the minds of selected persons, and restated in their words for all to hear." (John M Ziman, "Public Knowledge: An Essay Concerning the Social Dimension of Science", 1968)

"The idea of knowledge as an improbable structure is still a good place to start. Knowledge, however, has a dimension which goes beyond that of mere information or improbability. This is a dimension of significance which is very hard to reduce to quantitative form. Two knowledge structures might be equally improbable but one might be much more significant than the other." (Kenneth E Boulding, "Beyond Economics: Essays on Society", 1968)

"Models constitute a framework or a skeleton and the flesh and blood will have to be added by a lot of common sense and knowledge of details."(Jan Tinbergen, "The Use of Models: Experience," 1969)

"Inductive inference is the only process known to us by which essential new knowledge comes into the world." (Sir Ronald A Fisher, "The Design of Experiments", 1971)

"A discovery must be, by definition, at variance with existing knowledge." (Albert Szent-Gyorgyi, "Dionysians and Apollonians", Science 176, 1972)

"The human condition can almost be summed up in the observation that, whereas all experiences are of the past, all decisions are about the future. It is the great task of human knowledge to bridge this gap and to find those patterns in the past which can be projected into the future as realistic images." (Kenneth E Boulding, [foreword] 1972)

"Human knowledge is personal and responsible, an unending adventure at the edge of uncertainty." (Jacob Bronowski, "The Ascent of Man", 1973)

"Discoveries are made by pursuing possibilities suggested by existing knowledge." (Michael Polanyi, "Meaning", 1975)

"Knowledge is not a series of self-consistent theories that converges toward an ideal view; it is rather an ever increasing ocean of mutually incompatible (and perhaps even incommensurable) alternatives, each single theory, each fairy tale, each myth that is part of the collection forcing the others into greater articulation and all of them contributing, via this process of competition, to the development of our consciousness." (Paul K Feyerabend, "Against Method: Outline of an Anarchistic Theory of Knowledge", 1975)

"Every judgment teeters on the brink of error. To claim absolute knowledge is to become monstrous. Knowledge is an unending adventure at the edge of uncertainty." (Frank Herbert, "Children of Dune", 1976)

"Certainty, simplicity, vividness originate in popular knowledge. That is where the expert obtains his faith in this triad as the ideal of knowledge. Therein lies the general epistemological significance of popular science." (Ludwik Fleck, "Genesis and Development of a Scientific Fact", 1979)

"The thinking person goes over the same ground many times. He looks at it from varying points of view - his own, his arch-enemy’s, others’. He diagrams it, verbalizes it, formulates equations, constructs visual images of the whole problem, or of troublesome parts, or of what is clearly known. But he does not keep a detailed record of all this mental work, indeed could not. […] Deep understanding of a domain of knowledge requires knowing it in various ways. This multiplicity of perspectives grows slowly through hard work and sets the state for the re-cognition we experience as a new insight." (Howard E Gruber, "Darwin on Man", 1981)

"Contrary to the impression students acquire in school, mathematics is not just a series of techniques. Mathematics tells us what we have never known or even suspected about notable phenomena and in some instances even contradicts perception. It is the essence of our knowledge of the physical world. It not only transcends perception but outclasses it." (Morris Kline, "Mathematics and the Search for Knowledge", 1985)

"Knowledge is the appropriate collection of information, such that it's intent is to be useful. Knowledge is a deterministic process. When someone 'memorizes' information (as less-aspiring test-bound students often do), then they have amassed knowledge. This knowledge has useful meaning to them, but it does not provide for, in and of itself, an integration such as would infer further knowledge." (Russell L Ackoff, "Towards a Systems Theory of Organization", 1985)

"There is no coherent knowledge, i.e. no uniform comprehensive account of the world and the events in it. There is no comprehensive truth that goes beyond an enumeration of details, but there are many pieces of information, obtained in different ways from different sources and collected for the benefit of the curious. The best way of presenting such knowledge is the list - and the oldest scientific works were indeed lists of facts, parts, coincidences, problems in several specialized domains." (Paul K Feyerabend, "Farewell to Reason", 1987)

"We admit knowledge whenever we observe an effective (or adequate) behavior in a given context, i.e., in a realm or domain which we define by a question (explicit or implicit)." (Humberto Maturana & Francisco J Varela, "The Tree of Knowledge", 1987)

"Science doesn't purvey absolute truth. Science is a mechanism. It's a way of trying to improve your knowledge of nature. It's a system for testing your thoughts against the universe and seeing whether they match. And this works, not just for the ordinary aspects of science, but for all of life. I should think people would want to know that what they know is truly what the universe is like, or at least as close as they can get to it." (Isaac Asimov, [Interview by Bill Moyers] 1988)

"We live on an island surrounded by a sea of ignorance. As our island of knowledge grows, so does the shore of our ignorance." (John A Wheeler, Scientific American Vol. 267, 1992)

"Indeed, knowledge that one will be judged on some criterion of ‘creativeness’ or ‘originality’ tends to narrow the scope of what one can produce (leading to products that are then judged as relatively conventional); in contrast, the absence of an evaluations seems to liberate creativity." (Howard Gardner,  "Creating Minds", 1993)

"Knowledge is theory. We should be thankful if action of management is based on theory. Knowledge has temporal spread. Information is not knowledge. The world is drowning in information but is slow in acquisition of knowledge. There is no substitute for knowledge." (William E Deming, "The New Economics for Industry, Government, Education", 1993) 

"Discourses are ways of referring to or constructing knowledge about a particular topic of practice: a cluster (or formation) of ideas, images and practices, which provide ways of talking about, forms of knowledge and conduct associated with, a particular topic, social activity or institutional site in society. These discursive formations, as they are known, define what is and is not appropriate in our formulation of, and our practices in relation to, a particular subject or site of social activity." (Stuart Hall, "Representation: Cultural Representations and Signifying Practices", 1997)

"The social constructivist thesis is that mathematics is a social construction, a cultural product, fallible like any other branch of knowledge."  (Paul Ernest, "Social Constructivism as a Philosophy of Mathematics", 1998)

"An individual understands a concept, skill, theory, or domain of knowledge to the extent that he or she can apply it appropriately in a new situation." (Howard Gardner, "The Disciplined Mind", 1999)

"All human knowledge - including statistics - is created  through people's actions; everything we know is shaped by our language, culture, and society. Sociologists call this the social construction of knowledge. Saying that knowledge is socially constructed does not mean that all we know is somehow fanciful, arbitrary, flawed, or wrong. For example, scientific knowledge can be remarkably accurate, so accurate that we may forget the people and social processes that produced it." (Joel Best, Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists, 2001)

"Knowledge is factual when evidence supports it and we have great confidence in its accuracy. What we call 'hard fact' is information supported by  strong, convincing evidence; this means evidence that, so far as we know, we cannot deny, however we examine or test it. Facts always can be questioned, but they hold up under questioning. How did people come by this information? How did they interpret it? Are other interpretations possible? The more satisfactory the answers to such questions, the 'harder' the facts."(Joel Best, Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists, 2001)

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

"All knowledge that is not the real product of observation, or of consequences deduced from observation, is entirely groundless and illusory." (Jean-Baptiste Lamarck)

"By observation, facts are distinctly and minutely impressed in the mind; by analogy, similar facts are connected ; by experiment, new facts are discovered ; and, in the progression of knowledge, observation, guided by analogy, leads to experiment, and analogy, confirmed by experiment, becomes scientific truth." (Sir Humphry Davy)

"In imaginative thought there is no real knowledge of anything but similarities (ultimately identities): knowledge of differences is merely a transition to a new knowledge of similarities."  (Northrop Frye)

"Real wisdom is not the knowledge of everything, but the knowledge of which things in life are necessary, which are less necessary, and which are completely unnecessary to know." (Lev N Tolstoy)

"The goal of education is not to increase the amount of knowledge but to create the possibilities for a child to invent and discover, to create men who are capable of doing new things." (Jean Piaget)

"We call it 'explanation', but it is 'description' which distinguishes us from earlier stages of knowledge and science. We describe better - we explain just as little who came before us [...] We operate with nothing but things which do not exist, with lines, planes, bodies, atoms, divisible time, divisible space - how should explanation even be possible when we first make everything into an image, into our image!" (Friedrich W Nietzsche)

You know how the divine Simplicity enfolds all things. Mind is the image of this enfolding Simplicity. If, then, you called this divine Simplicity infinite Mind, it will be the exemplar of our mind. If you called the divine mind the totality of the truth of things, you will call our mind the totality of the assimilation of things, so that it may be a totality of ideas. In the divine Mind conception is the production of things; in our mind conception is the knowledge of things. If the divine Mind is absolute Being, then its conception is the creation of beings; and conception in the human mind is the assimilation of beings." (Nicholas of Cusa)

🏷️Knowledge Representation: On Definitions (Quotes)

"The errors of definitions multiply themselves according as the reckoning proceeds; and lead men into absurdities, which at last they see but cannot avoid, without reckoning anew from the beginning." (Thomas Hobbes, "The Moral and Political Works of Thomas Hobbes of Malmesbury", 1750)

"Definitions might be good if we did not employ words in making them." (Jean-Jacques Rousseau, "Emile, or, Treatise on Education", 1762)

"A definition is nothing else but an explication of the meaning of a word, by words whose meaning is already known. Hence it is evident that every word cannot be defined; for the definition must consist of words; and there could be no definition, if there were not words previously understood without definition." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)

"There is nothing more difficult than a good definition, for it is scarcely possible to express, in a few words, the abstracted view of an infinite variety of facts." (Humphry Davy, "Consolations in Travel, or the Last Days of a Philosopher" , 1830)

"It is the essence of a scientific definition to be causative, not by introduction of imaginary somewhats, natural or supernatural, under the name of causes, but by announcing the law of action in the particular case, in subordination to the common law of which all the phenomena are modifications or results." (Samuel T Coleridge, "Hints Towards the Formation of a More Comprehensive Theory of Life, The Nature of Life", 1847)

"The dimmed outlines of phenomenal things all merge into one another unless we put on the focusing-glass of theory, and screw it up sometimes to one pitch of definition and sometimes to another, so as to see down into different depths through the great millstone of the world." (James C Maxwell, "Are There Real Analogies in Nature?", 1856)

"Questions of Definition are of the very highest importance in Philosophy, and they need to be watched accordingly." (George Campbell, "A Fourth State of Matter, Nature", 1880)

"The more elevated a culture, the richer its language. The number of words and their combinations depends directly on a sum of conceptions and ideas; without the latter there can be no understandings, no definitions, and, as a result, no reason to enrich a language. (Anton Chekhov, [letter to A.S. Suvorin] 1892)

"A definition is the enclosing a wilderness of idea within a wall of words." (Samuel Butler, "The Note-Books of Samuel Butler", 1912)

"In every new and growing science there are many working hypotheses that never attain to any sort of reality. On the other hand, in the old and abstract sciences of mathematics, where it is hard to tell how much is mere definition or convention, the problem of reality is not so much doubtful as it is meaningless." (Gilbert N Lewis, "The Anatomy of Science", 1926)

"Logic issues in tautologies, mathematics in identities, philosophy in definitions; all trivial, but all part of the vital work of clarifying and organising our thought. (Frank P Ramsey, 'Last Papers: Philosophy', 1929)

"A Weltanschauung [worldview] is an intellectual construction which solves all the problems of our existence uniformly on the basis of one overriding hypothesis, which, accordingly, leaves no question unanswered and in which everything that interests us finds its fixed place [...] the worldview of science already departs noticeably from our definition. It is true that it too assumes the uniformity of the explanation of the universe; but it does so only as a programme, the fulfillment of which is relegated to the future." Sigmund Freud, "New introductory lectures on psycho-analysis", 1932)

"Scientific Ideas can often be adequately exhibited for all the purposes of reasoning, by means of Definitions and Axioms; all attempts to reason by means of Definitions from common Notions, lead to empty forms or entire confusion." (William Whewell, "History of the Inductive Sciences from the Earliest to the Present Time", 1937)

"The view is often defended that sciences should be built up on clear and sharply defined basal concepts. In actual fact no science, not even the most exact, begins with such definitions. The true beginning of scientific activity consists rather in describing phenomena and then in proceeding to group, classify and correlate them." (Sigmund Freud, "Collected Papers", 1950)

"Being built on concepts, hypotheses, and experiments, laws are no more accurate or trustworthy than the wording of the definitions and the accuracy and extent of the supporting experiments." (Gerald Holton, "Introduction to Concepts and Theories in Physical Science", 1952)

"The word 'definition' has come to have a dangerously reassuring sound, owing no doubt to its frequent occurrence in logical and mathematical writings." (Willard van Orman Quine, From a Logical Point of View, 1953)

"We cannot define truth in science until we move from fact to law. And within the body of laws in turn, what impresses us as truth is the orderly coherence of the pieces. They fit together like the characters of a great novel, or like the words of a poem. Indeed, we should keep that last analogy by us always, for science is a language, and like a language it defines its parts by the way they make up a meaning. Every word in a sentence has some uncertainty of definition, and yet the sentence defines its own meaning and that of its words conclusively. It is the internal unity and coherence of science which gives it truth, and which makes it a better system of prediction than any less orderly language." (Jacob Bronowski, "The Common Sense of Science", 1953)

"The view is often defended that sciences should be built up on clear and sharply defined basal concepts. In actual fact no science, not even the most exact, begins with such definitions. The true beginning of scientific activity consists rather in describing phenomena and then in proceeding to group, classify and correlate them." (Sigmund Freud, "General Psychological Theory", 1963)

"This other world is the so-called physical world image; it is merely an intellectual structure. To a certain extent it is arbitrary. It is a kind of model or idealization created in order to avoid the inaccuracy inherent in every measurement and to facilitate exact definition." (Max Planck, "The Philosophy of Physics", 1963)

"Definitions are the guardians of rationality, the first line of defense against the chaos of mental disintegration. (Ayn Rand, The Romantic Manifesto, 1969)

"Concepts form the basis for any science. These are ideas, usually somewhat vague (especially when first encountered), which often defy really adequate definition. The meaning of a new concept can seldom be grasped from reading a one-paragraph discussion. There must be time to become accustomed to the concept, to investigate it with prior knowledge, and to associate it with personal experience. Inability to work with details of a new subject can often be traced to inadequate understanding of its basic concepts." (William C Reynolds & Harry C Perkins, "Engineering Thermodynamics", 1977)

"Definitions, like questions and metaphors, are instruments for thinking. Their authority rests entirely on their usefulness, not their correctness. We use definitions in order to delineate problems we wish to investigate, or to further interests we wish to promote. In other words, we invent definitions and discard them as suits our purposes." (Neil Postman, "Language Education in a Knowledge Context", 1980)

"When terms [...] evolve and change definition with time; and when the social reality which terms are intended to organize and render intelligible is also seen to be in flux, capturing the truth in a net of words becomes a matter of intuition and style more than of any scientific method that can be replicated by others and made to achieve the same result every time someone asks the same question, or undertakes the same operations." (William H McNeill, "Discrepancies among the Social Sciences", 1981)

"Definitions are temporary verbalizations of concepts, and concepts - particularly difficult concepts - are usually revised repeatedly as our knowledge and understanding grows." (Ernst Mayr, "The Growth of Biological Thought", 1982) 

"A full definition of an object must include the whole of human experience, both as a criterion of truth and a practical indicator of its connection with human wants." (Vladimir Lenin) 

"Fundamental definitions do not arise at the start but at the end of the exploration, because in order to define a thing you must know what it is and what it is good for." (Hans Freudenthal)

"We begin to reason from sensible objects, and definition is the end and epilogue of science. It is not the beginning of our knowing, but only of our teaching." (Tommaso Campanella)

🏷️Knowledge Representation: On Patterns (Quotes)

"Most surprising and far-reaching analogies revealed themselves between apparently quite disparate natural processes. It seemed that nature had built the most various things on exactly the same pattern; or, in the dry words of the analyst, the same differential equations hold for the most various phenomena." (Ludwig Boltzmann, "On the methods of theoretical physics", 1892)

"It [knowledge] is clearly related to information, which we can now measure; and an economist especially is tempted to regard knowledge as a kind of capital structure, corresponding to information as an income flow. Knowledge, that is to say, is some kind of improbable structure or stock made up essentially of patterns - that is, improbable arrangements, and the more improbable the arrangements, we might suppose, the more knowledge there is." (Kenneth Boulding, "Beyond Economics: Essays on Society", 1968)

"The central task of a natural science is to make the wonderful commonplace: to show that complexity, correctly viewed, is only a mask for simplicity; to find pattern hidden in apparent chaos. […] This is the task of natural science: to show that the wonderful is not incomprehensible, to show how it can be comprehended - but not to destroy wonder. For when we have explained the wonderful, unmasked the hidden pattern, a new wonder arises at how complexity was woven out of simplicity. The aesthetics of natural science and mathematics is at one with the aesthetics of music and painting - both inhere in the discovery of a partially concealed pattern." (Herbert A Simon, "The Sciences of the Artificial", 1968)

"Faced with information overload, we have no alternative but pattern-recognition."(Marshall McLuhan, "Counterblast", 1969) 

"Without the hard little bits of marble which are called 'facts' or 'data' one cannot compose a mosaic; what matters, however, are not so much the individual bits, but the successive patterns into which you arrange them, then break them up and rearrange them." (Arthur Koestler, "The Act of Creation", 1970) 

"To do science is to search for repeated patterns, not simply to accumulate facts […]" (Robert H. MacArthur, "Geographical Ecology", 1972)

"A pattern has an integrity independent of the medium by virtue of which you have received the information that it exists. Each of the chemical elements is a pattern integrity. Each individual is a pattern integrity. The pattern integrity of the human individual is evolutionary and not static." (Buckminster Fuller, "Synergetics: Explorations in the Geometry of Thinking", 1975) 

"In everyday language, the words 'pattern' and 'symmetry' are used almost interchangeably, to indicate a property possessed by a regular arrangement of more-or-less identical units […]” (Ian Stewart & Martin Golubitsky, “Fearful Symmetry: Is God a Geometer?”, 1992)

"The methods of science include controlled experiments, classification, pattern recognition, analysis, and deduction. In the humanities we apply analogy, metaphor, criticism, and (e)valuation. In design we devise alternatives, form patterns, synthesize, use conjecture, and model solutions." (Béla H Bánáthy, "Designing Social Systems in a Changing World", 1996)

"Complexity is looking at interacting elements and asking how they form patterns and how the patterns unfold. It’s important to point out that the patterns may never be finished. They’re open-ended. In standard science this hit some things that most scientists have a negative reaction to. Science doesn’t like perpetual novelty." (W Brian Arthur, 1999)

"Knowledge is encoded in models. Models are synthetic sets of rules, and pictures, and algorithms providing us with useful representations of the world of our perceptions and of their patterns." (Didier Sornette, "Why Stock Markets Crash - Critical Events in Complex Systems", 2003) 

"[...] when data is presented in certain ways, the patterns can be readily perceived. If we can understand how perception works, our knowledge can be translated into rules for displaying information. Following perception‐based rules, we can present our data in such a way that the important and informative patterns stand out. If we disobey the rules, our data will be incomprehensible or misleading." (Colin Ware, "Information Visualization: Perception for Design" 2nd Ed., 2004)

"Perceiving the world as well designed and thus the product of a designer, and even seeing divine providence in the daily affairs of life, may be the product of a brain adapted to finding patterns in nature. We are pattern seeking and pattern-finding animals." (Michael Shermer, "Why Darwin Matters: The Case Against Intelligent Design", 2007) 

"It is the consistency of the information that matters for a good story, not its completeness. Indeed, you will often find that knowing little makes it easier to fit everything you know into a coherent pattern." (Daniel Kahneman, "Thinking, Fast and Slow", 2011) 

"Randomness might be defined in terms of order - its absence, that is. […] Everything we care about lies somewhere in the middle, where pattern and randomness interlace." (James Gleick, "The Information: A History, a Theory, a Flood", 2011)

"Finding patterns is easy in any kind of data-rich environment […] The key is in determining whether the patterns represent signal or noise." (Nate Silver, "The Signal and the Noise: Why So Many Predictions Fail-but Some Don’t", 2012)

"Another way to secure statistical significance is to use the data to discover a theory. Statistical tests assume that the researcher starts with a theory, collects data to test the theory, and reports the results - whether statistically significant or not. Many people work in the other direction, scrutinizing the data until they find a pattern and then making up a theory that fits the pattern." (Gary Smith, "Standard Deviations", 2014)

"If somebody ransacks data to find a pattern, we still need a theory that makes sense. On the other hand, a theory is just a theory until it is tested with persuasive data." (Gary Smith, "Standard Deviations", 2014)

"[…] regard it in fact as the great advantage of the mathematical technique that it allows us to describe, by means of algebraic equations, the general character of a pattern even where we are ignorant of the numerical values which will determine its particular manifestation." (Friedrich A von Hayek, "The Market and Other Orders", 2014)

"Remember that even random coin flips can yield striking, even stunning, patterns that mean nothing at all. When someone shows you a pattern, no matter how impressive the person’s credentials, consider the possibility that the pattern is just a coincidence. Ask why, not what. No matter what the pattern, the question is: Why should we expect to find this pattern?" (Gary Smith, "Standard Deviations", 2014)

"We are genetically predisposed to look for patterns and to believe that the patterns we observe are meaningful. […] Don’t be fooled into thinking that a pattern is proof. We need a logical, persuasive explanation and we need to test the explanation with fresh data." (Gary Smith, "Standard Deviations", 2014)

"We are hardwired to make sense of the world around us - to notice patterns and invent theories to explain these patterns. We underestimate how easily pat - terns can be created by inexplicable random events - by good luck and bad luck." (Gary Smith, "Standard Deviations", 2014)

"We are seduced by patterns and we want explanations for these patterns. When we see a string of successes, we think that a hot hand has made success more likely. If we see a string of failures, we think a cold hand has made failure more likely. It is easy to dismiss such theories when they involve coin flips, but it is not so easy with humans. We surely have emotions and ailments that can cause our abilities to go up and down. The question is whether these fluctuations are important or trivial." (Gary Smith, "Standard Deviations", 2014)

"A pattern is a design or model that helps grasp something. Patterns help connect things that may not appear to be connected. Patterns help cut through complexity and reveal simpler understandable trends. […] Patterns can be temporal, which is something that regularly occurs over time. Patterns can also be spatial, such as things being organized in a certain way. Patterns can be functional, in that doing certain things leads to certain effects. Good patterns are often symmetric. They echo basic structures and patterns that we are already aware of." (Anil K. Maheshwari, "Business Intelligence and Data Mining", 2015)