Business Intelligence: Data Modeling (Part VI: On the Cusps of Complexity)

Business Intelligence Series

We live in a complex world, which makes it difficult to model and work with the complex models that attempt to represent it. Thus, we try to simplify it to the degree that it becomes processable and understandable for us, while further simplification is needed when we try to depict it by digital means that make it processable by machines, respectively by us. Whenever we simplify something, we lose some aspects, which might be acceptable in many cases, but create issues in a broader number of ways.

With each layer of simplification results a model that addresses some parts while ignoring some parts of it, which restricts models’ usability to the degree that makes them unusable. The more one moves toward the extremes of oversimplification or complexification, the higher the chances for models to become unusable.

This aspect is relevant also in what concerns the business processes we deal with. Many processes are oversimplified to the degree that we track the entry and exit points, respectively the quantitative aspects we are interested in. In theory this information should be enough when answering some business questions, though might be insufficient when one dives deeper into processes. One can try to approximate, however there are high chances that such approximations deviate too much from the value approximated, which can lead to strange outcomes.

Therefore, when a date or other values are important, organizations consider adding more fields to reflect the implemented process with higher accuracy. Unfortunately, unless we save a history of all the important changes in the data, it becomes challenging to derive the snapshots we need for our analyses. Moreover, it is more challenging to obtain consistent snapshots. There are systems which attempt to obtain such snapshots through the implementation of the processes, though also this approach involves some complexity and other challenges.

Looking at the way business processes are implemented (see ERP, CRM and other similar systems), the systems track the created, modified and a few other dates that allow only limited perspectives. The fields typically provide the perspectives we need for data analysis. For many processes, it would be interesting to track other events and maybe other values taken in between.

There is theoretical potential in tracking more detailed data, but also a complexity that’s difficult to transpose into useful information about the processes themselves. Despite tracking more data and the effort involved in such activities, processes can still behave like black boxes, especially when we have no or minimal information about the processes implemented in Information Systems.

There’s another important aspect - even if systems provide similar implementations of similar processes, the behavior of users can make an important difference. The best example is the behavior of people entering the relevant data only when a process closes and ignoring the steps happening in between (dates, price or quantity changes).

There is a lot of missing data/information not tracked by such a system, especially in what concerns users’ behavior. It’s true that such behavior can be tracked to some degree, though that happens only when data are modified physically. One can suppose that there are many activities happening outside of the system.

The data gathered represents only the projection of certain events, which might not represent accurately and completely the processes or users’ behavior. We have the illusion of transparency, though we work with black boxes. There can be a lot of effort happening outside of these borders.  

Fortunately, we can handle oversimplified processes and data maintenance, though one can but wonder how many important things can be found beyond the oversimplifications we work with, respectively what we miss in the process. 

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Book Review: Rolf Hichert & Jürgen Faisst's International Business Communication Standards (IBCS Version 1.2)

Over the last months I found several references to Rolf Hichert & Jürgen Faisst's booklet on business communication standards [1]. It draw my attention especially because it attempts to provide a standard for reports and data visualizations, which frankly it seems like a tremendous endeavor if done right. The two authors founded the IBCS institute 20 years ago, which is a host, training institute, and certification body of the Creative Commons project called IBCS.

The 150 pages booklet considers various standardization techniques with the help of more than 180 instructive figures, the overall structure being based on a set of principles and rules rooted in an acronym that spells "SUCCESS" - Say, Unify, Condense, Check, Express, Simplify, Structure. On one side the principles seem to form a solid fundament, however the fundament seems to suffer from the same rigidity resulted from fitting something in a nicely-spelled acronym. 

Say or conveying a message reflects the principle that each report should convey a message, otherwise the report is just a data collection. According to this "definition" most of the operational reports are just collections of data. Conversely, lot of communication in organizations revolve around issues, metrics and decision making, scenarios in which the messages conveyed can be powerful though dependent on the business context. Settling on only one message can make the message fall short.

Unifying or applying semantic notation reflects the principle that things that have same meaning should look the same. There are many patterns out there that can be standardized, however it's questionable how much complex visualizations can be standardized, respectively how much liberty of expressing certain aspects the standardization allows. 

Condense or increasing the information density reflects the requirements that all information necessary to understanding the content should, if possible, be included on one page. This allows to easier navigate the content and prioritize what the audience is able to see. The principle however seems to have more to do with the ink-information ratio principle (see [2]). 

Check or ensuring the visual integrity reflects the principle that the information should be presented in the most truthful and the most easily understood way. This is something that many data visualizations out there lack.

Express or choosing the proper visualizations is based on the principle that the visuals considered should be as intuitive as possible. In theory, the more intuitive a visual the easier is to be understood and reused, however this depends on the "visual vocabulary" and "visual grammar" of each individual. Intuition is something that needs to grow through the interplay of these two areas. Having the expectation of displaying everything in terms of basic elements is unrealistic and suboptimal. 

Simplify or avoiding clutter refers to eliminating the unnecessary from a visualization, when there's nothing to take out without changing the meaning of a visualization. At least, the principle is correctly considered even if is in general difficult to apply because quite often one needs to build something more complex and reduce the complexity through iterative steps until the simple is obtained. 

Structure or organizing the content is based on the principle that content should follow (a logical consistent) structure. The interplay between function and structure is an important topic in itself.

Browsing through the many data visualizations given as example, I'd say that many of the recommendations make sense, though from there to a standardization is still a long way. The reader should evaluate against his/her own judgements the practices described and consider what seems to work. 

The book is available on the IBS website as PDF, though the Kindle version is 40% cheaper. Overall, it is worth a read. 

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Resources:
[1] Rolf Hichert & Jürgen Faisst (2022) "International Business Communication Standards (IBCS Version 1.2): Conceptual, perceptual, and semantic design of comprehensible business reports, presentations, and dashboards" (link)
[2] Edward R Tufte (1983) "The Visual Display of Quantitative Information"
[3] IBCS Institude (2024) About (link)

ERP Implementations: Simplifying the Implementation Project

 

ERPimplementations are complex projects and a way to manage their complexity is to attempt reducing their complexity (instead of answering to complexity by complexity). A project implementation’s methodology is probably the most important area that allows project’s simplification, though none of the available methodologies seems to work well with such projects.

The point that differentiates the various methodologies is solution’s conceptualization. In general, the expectation is to have a set of functional design documents (FDDs) that describe how the system operates and that can be used for programming the customizations, if any. The customer must review and sign-off the FDDs before the setup is done, respectively the development starts. Moreover, given the dependencies between documents, they often need to be signed off together.

Unfortunately, FDDs reflect the degree of understanding of the target system and business requirements, gaps that can prove to be a challenge for the parties involved, requiring many iterations until they are brought to the expected quality level. The higher the accuracy considered; the more iterations are needed. FDDs tend to consume a considerable percent of the available financial resources, in extremis the whole budget being exhausted just for 'printed paper'. Moreover, the key users see late in the project the working functionality.

In agile methodologies, FDDs are replaced by user stories, and, if still needed, can be written as part of the sprints or later. Unfortunately, agile methodologies have their own challenges and constraints in ERP implementations. As functionality is explored, understood, and negotiated with the customer during the implementation, it’s seldom possible to provide a realistic cost estimation upfront. Given that most ERP implementations exceed their budget, starting a journey without having an idea how much the project costs seems to be a prohibitive approach for many customers. Moreover, the negotiations have the character of Change Requests, which can easily become a bottleneck for the project.

On the other hand, agile methodologies involve the customer earlier and the development could start earlier as well. The earlier the customer is involved, the earlier the key users understand how the system works, and thus they can be more efficient in performing their activities, respectively in identifying the gaps in understanding, trapping functional issues early in the process, at least in theory. Some projects address this need by having the key user trained, though the training environment usually has a different setup and data than needed by the customer. Wouldn’t be a good idea to have the key users trained in an environment that reflects to a higher or lower degree the customer’s data and setup requirements?

In theory the setup for such an environment can be done upfront based on one standard configuration frequently met in customer’s industry. With this the functional consultants can start to configure the system together with the key users exploring the data and setup existing in the legacy system(s). This would allow increasing on both sides the depth of understanding and has the potential of speeding up the implementation. This can be started in the early phases, during the time in which the requirements are gathered. Ideally, a basic setup can exist already when the requirements are signed off. It’s true that this approach would mean a higher investment upfront, though the impact could be considerable. Excepting Data Migration and customizations the customer already has a good basis for Go-Live.

Of course, there can be further challenges, though the customer can make thus sure that the financial resources are well spent – having a usable system, respectively a good system understanding outweighs by far the extreme alternative of having high-quality unimplemented FDDs!

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Strategic Management: Simplicity VI (ERP Implementations' Story II)

Besides the witty sayings and theories advanced in defining what simplicity is about, life shows that there’s a considerable gap between theory and praxis. In the attempt at a definition, one is forced to pull more concepts like harmony, robustness, variety, balance, economy, or proportion, which can be grouped under organic unity or similar concepts. However, intuitionally one can advance the idea that from a cybernetic perspective simplicity is achieved when the information flows are not disrupted and don’t meet unnecessary resistance. By information here are considered the various data aggregations – data, information, knowledge, and eventually wisdom (aka DIKW pyramid) – though it can be extended to encompass materials, cash and vital energy.

One can go further and say that an organization is healthy when the various flows mentioned above run smoothly through the organization nourishing it. The comparison with the human body can go further and say that a blockage in the flow can cause minor headaches or states that can take a period of convalescence to recover from them. Moreover, the sustained effort applied by an organization can result in fatigue or more complex ailments or even diseases if the state is prolonged. 

For example, big projects like ERP implementations tend to suck the vital energy of an organization to the degree that it will take months to recover from the effort, while the changes in the other types of flow can lead to disruptions, especially when the change is not properly managed. Even if ERP implementations provide standard solutions for the value-added processes, they represent vendors’ perspective into the respective processes, which don’t necessarily fit an organization’s needs. One is forced then to make compromises either by keeping close to the standard or by expanding the standard processes to close the gap. Either way processual changes are implied, which affect the information flow, especially for the steps where further coordination is needed, respectively the data flow in respect to implementation or integration with the further systems. A new integration as well as a missing integration have the potential of disrupting the data and information flows.

The processual changes can imply changes in the material flow as the handling of the materials can change, however the most important impact is caused maybe by the processual bottlenecks, which can cause serious disruptions (e.g. late deliveries, production is stopped), and upon case also in the cash-flow (e.g. penalties for late deliveries, higher inventory costs). The two flows can be impacted by the data and information flows independently of the processual changes (e.g. when they have poor quality, when not available, respectively when don’t reach the consumer in timely manner). 

With a new ERP solution, the organization needs to integrate the new data sources into the existing BI infrastructure, or when not possible, to design and implement a new one by taking advantage of the technological advancements. Failing to exploit this potential will impact the other flows, however the major disruptions appear when the needed knowledge about business processes is not available in-house, in explicit and/or implicit form, before, during and after the implementation. 

Independently on how they are organized – in center of excellence or ad-hoc form – is needed a group of people who can manage the various flows and ideally, they should have the appropriate level of empowerment. Typically, the responsibility resides with key users, IT and one or two people from the management. Without a form of ‘organization’ to manage the flows, the organization will reside only on individual effort, which seldom helps reaching the potential. Independently of the number of resources involved, simplicity is achieved when the activities flow naturally. 

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Written: Sep-2020, Last Reviewed: Mar-2024

Strategic Management: Simplicity IV (Designing for Simplicity)

More than two centuries ago, in his course on the importance of Style in Literature, George Lewes wisely remarked that 'the first obligation of Simplicity is that of using the simplest means to secure the fullest effect' [1]. This is probably the most important aspect the adopters of the KISS mantra seem to ignore – solutions need to be simple while covering all or most important aspects to assure the maximum benefit. The challenge for many resides in defining what the maximum benefit is about. This state of art is typically poorly understood, especially when people don’t understand what’s possible, respectively of what’s necessary to make things work smoothly. 

To make the simplicity principle work, one must envision the desired state of a product or solution and trace back what’s needed to achieve that vision. One can aim for the maximum or for the minimum possible, respectively for anything in between. That’s at least true in theory, in praxis there are constraints that limit the range of achievement, constraints ranging from the availability of resources, their maturity or the available time, respectively to the limits for growth - the learning capacity of individuals and organization as a whole. 

On the other side following the 80/20 principle, one could achieve in theory 80% of a working solution with 20% of the effort needed in achieving the full 100%. This principle comes with a trick too because one needs to focus on the important components or aspects of the solution for this to work. Otherwise, one is forced to do exploratory work in which the learning is gradually assimilated into the solution. This implies continuous feedback, respectively changing the targets as one progresses in multiple iterations. The approach is typically common to ERP implementations, BI and Data Management initiatives, or similar transformative projects which attempt changing an organization’s data, information, or knowledge flows - the backbones organizations are built upon.     

These two principles can be used together to shape an organization. While simplicity sets a target or compass for quality, the 80/20 principle provides the means of splitting the roadmap and effort into manageable targets while allowing to identify and prioritize the critical components, and they seldom resume only to technology. While technologies provide a potential for transformation, in the end is an organization’s setup that has the transformative role. 

For transformational synergies to happen, each person involved in the process must have a minimum of necessary skillset, knowledge and awareness of what’s required and how a solution can be harnessed. This minimum can be initially addressed through training and self-learning, however without certain mechanisms in place, the magic will not happen by itself. Change needs to be managed from within as part of an organization’s culture, by the people close to the flow, and when necessary, also from the outside, by the ones who can provide guiding direction. Ideally, a strategic approach is needed the vision, mission, goals, objectives, and roadmap are sketched, where intermediary targets are adequately mapped and pursued, and the progress is adequately tracked.

Thus, besides the technological components is needed to consider the required organizational components to support and manage change. These components form a structure which needs to adhere by design to the same principle of simplicity. According to Lewes, the 'simplicity of structure means organic unity' [1], which can imply harmony, robustness, variety, balance, economy or proportion. Without these qualities the structure of the resulting edifice can break under its own weight. Moreover, paraphrasing Eric Hoffer, simplicity marks the end of a continuous process of designing, building, and refining, while complexity marks a primitive stage.

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Written: Sep-2020, Last Reviewed: Mar-2024

References:
[1] George H Lewes (1865) "The Principles of Success in Literature"

Considered quotes:
"Simplicity of structure means organic unity, whether the organism be simple or complex; and hence in all times the emphasis which critics have laid upon Simplicity, though they have not unfrequently confounded it with narrowness of range." (George H Lewes, "The Principles of Success in Literature", 1865)
"The first obligation of Simplicity is that of using the simplest means to secure the fullest effect. But although the mind instinctively rejects all needless complexity, we shall greatly err if we fail to recognise the fact, that what the mind recoils from is not the complexity, but the needlessness." (George H Lewes, "The Principles of Success in Literature", 1865)
"In products of the human mind, simplicity marks the end of a process of refining, while complexity marks a primitive stage." (Eric Hoffer, 1954)

Strategic Management: Simplicity II (A System's View)

Each time one discusses in IT about software and hardware components interacting with each other, one talks about a composite referred to as a system. Even if the term Information System (IS) is related to it, a system is defined as a set of interrelated and interconnected components that can be considered together for specific purposes or simple convenience.

A component can be a piece of software or hardware, as well persons or groups if we extend the definition. The consideration of people becomes relevant especially in the context of ecologies, in which systems are placed in a broader context that considers people’s interaction with them, as this raises to important behavior that impacts system’s functioning.

Within a system each part has a role or function determined in respect to the whole as well as to the other parts. The role or function of the component is typically fixed, predefined, though there are also exceptions especially when the scope of a component is enlarged, respectively reduced to the degree that the component can be removed or ignored. What one considers or not considers as part of system defines a system’s boundaries; it’s what distinguishes it from other systems within the environment(s) considered.

The interaction between the components resumes in the exchange, transmission and processing of data found in different aggregations ranging from signals to complex data structures. If in non-IT-based systems the changes are determined by inflow, respectively outflow of energy, in IT the flow is considered in terms of data in its various aggregations (information, knowledge).  The data flow (also information flow) represents the ‘fluid’ that nourishes a system’s ‘organism’.

One can grasp the complexity in the moment one attempts to describe a system in terms of components, respectively the dependencies existing between them in term of data and processes. If in nature the processes are extrapolated, in IT they are predefined (even if the knowledge about them is not available). In addition, the less knowledge one has about the infrastructure, the higher the apparent complexity. Even if the system is not necessarily complex, the lack of knowledge and certainty about it makes it complex. The more one needs to dig for information and knowledge to get an acceptable level of knowledge and logical depth, the more time is needed for designing a solution.

Saint Exupéry’s definition of simplicity applies from a system’s functional point of view, though it doesn’t address the relative knowledge about the system, which often is implicit (in people’s heads). People have only fragmented knowledge about the system which makes it difficult to create the whole picture. It’s typically the role of system or process operational manuals, respectively of data descriptions, to make that knowledge explicit, also establishing a fundament for common knowledge and further communication and understanding.

Between the apparent (perceived) and real complexity of a system there’s an important gap that needs to be addressed if one wants to manage the systems adequately, respectively to simplify the systems. Often simplification happens when components or whole systems are replaced, consolidated, or migrated, a mix between these approaches existing as well. Simplifications at data level (aka data harmonization) or process level (aka process optimization and redesign) can have an important impact, being inherent to the good (optimal) functioning of systems.

Whether these changes occur in big-bang or gradual iterations it’s a question of available resources, organizational capabilities, including the ability to handle such projects, respectively the impact, opportunities and risks associated with such endeavors. Beyond this, it’s important to regard the problems from a systemic and systematic point of view, in which ecology’s role is important.

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Written: Jun-2020, Last Reviewed: Mar-2024

Project Management: The Choice of Tools in Project Management

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

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

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

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

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

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

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

Project Management: Planning Correctly Misundersood II

Even if planning is the most critical activity in Project Management it seems to be also one of the most misunderstood concepts. Planning is critical because it charters the road ahead in terms of what, when, why and who, being used as a basis for action, communication, for determining the current status in respect to the initial plan, as well the critical activities ahead.

The misunderstandings derive maybe also from the fact that each methodology introduces its own approach to planning. PMI as traditional approach talks about baseline planning with respect to scope schedule and costs, about management plans, which besides the theme covered in the baseline, focus also on quality, human resources, risks, communication and procurement, and separate plans can be developed for requirements, change and configuration management, respectively process improvement. To them one can consider also action and contingency planning.

In Prince2 the product-based planning is done at three levels – at project, stage, respectively team level – while separate plans are done for exceptions in case of deviations from any of these plans; in addition there are plans for communication, quality and risk management. Scrum uses an agile approach looking at the product and sprint backlog, the progress being reviewed in stand-up meetings with the help of a burn-down chart. There are also other favors of planning like rapid application planning considered in Extreme Programming (XP), with an open, elastic and undeterministic approach. In Lean planning the focus is on maximizing the value while minimizing the waste, this being done by focusing on the value stream, the complete list of activities involved in delivering the end-product, value stream's flow being mapped with the help of visualization techniques such as Kanban, flowcharts or spaghetti diagrams.

With so many types of planning nothing can go wrong, isn’t it? However, just imagine customers' confusion when dealing with a change of methodology, especially when the concepts sound fuzzy and cryptic! Unfortunately, also the programmers and consultants seem to be bewildered by the various approaches and the philosophies supporting the methodologies used, their insecurity bringing no service for the project and customers’ peace of mind. A military strategist will more likely look puzzled at the whole unnecessary plethora of techniques. On the field an army has to act with the utmost concentration and speed, to which add principles like directedness, maneuver, unity, economy of effort, collaboration, flexibility, simplicity and sustainability. It’s what Project Management fails to deliver.

Similarly to projects, the plan made before the battle seldom matches the reality in the field. Planning is an exercise needed to divide the strategy in steps, echelon and prioritize them, evaluate the needed resources and coordinate them, understand the possible outcomes and risks, evaluate solutions and devise actions for them. With a good training, planning and coordination, each combatant knows his role in the battle, has a rough idea about difficulties, targets and possible ways to achieve them; while a good combatant knows always the next action. At the same time, the leader must have visibility over fight’s unfold, know the situation in the field and how much it diverged from the initial plan, thus when the variation is considerable he must change the plan by changing the priorities and make better use the resources available.

Even if there are multiple differences between the two battlefields, the projects follow the same patterns of engagement at different scales. Probably, Project Managers can learn quite of a deal by studying the classical combat strategists, and hopefully the management of projects would be more effective and efficient if the imperatives of planning, respectively management, were better understood and addressed.

Data Science: Phenomena (Just the Quotes)

"The word ‘chance’ then expresses only our ignorance of the causes of the phenomena that we observe to occur and to succeed one another in no apparent order. Probability is relative in part to this ignorance, and in part to our knowledge.” (Pierre-Simon Laplace, "Mémoire sur les Approximations des Formules qui sont Fonctions de Très Grands Nombres", 1783)

"The aim of every science is foresight. For the laws of established observation of phenomena are generally employed to foresee their succession. All men, however little advanced make true predictions, which are always based on the same principle, the knowledge of the future from the past." (Auguste Compte, "Plan des travaux scientifiques nécessaires pour réorganiser la société", 1822)

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

"Theories usually result from the precipitate reasoning of an impatient mind which would like to be rid of phenomena and replace them with images, concepts, indeed often with mere words." (Johann Wolfgang von Goethe, "Maxims and Reflections", 1833)

"[…] in order to observe, our mind has need of some theory or other. If in contemplating phenomena we did not immediately connect them with principles, not only would it be impossible for us to combine these isolated observations, and therefore to derive profit from them, but we should even be entirely incapable of remembering facts, which would for the most remain unnoted by us." (Auguste Comte, "Cours de Philosophie Positive", 1830-1842)

"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) 

"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)

"If statistical graphics, although born just yesterday, extends its reach every day, it is because it replaces long tables of numbers and it allows one not only to embrace at glance the series of phenomena, but also to signal the correspondences or anomalies, to find the causes, to identify the laws." (Émile Cheysson, cca. 1877) 

"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)

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

"A model, like a novel, may resonate with nature, but it is not a ‘real’ thing. Like a novel, a model may be convincing - it may ‘ring true’ if it is consistent with our experience of the natural world. But just as we may wonder how much the characters in a novel are drawn from real life and how much is artifice, we might ask the same of a model: How much is based on observation and measurement of accessible phenomena, how much is convenience? Fundamentally, the reason for modeling is a lack of full access, either in time or space, to the phenomena of interest." (Kenneth Belitz, Science, Vol. 263, 1944)

"The principle of complementarity states that no single model is possible which could provide a precise and rational analysis of the connections between these phenomena [before and after measurement]. In such a case, we are not supposed, for example, to attempt to describe in detail how future phenomena arise out of past phenomena. Instead, we should simply accept without further analysis the fact that future phenomena do in fact somehow manage to be produced, in a way that is, however, necessarily beyond the possibility of a detailed description. The only aim of a mathematical theory is then to predict the statistical relations, if any, connecting the phenomena." (David Bohm, "A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden’ Variables", 1952)

"The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work" (John Von Neumann, "Method in the Physical Sciences", 1955)

"As shorthand, when the phenomena are suitably simple, words such as equilibrium and stability are of great value and convenience. Nevertheless, it should be always borne in mind that they are mere shorthand, and that the phenomena will not always have the simplicity that these words presuppose." (W Ross Ashby, "An Introduction to Cybernetics", 1956)

"Can there be laws of chance? The answer, it would seem should be negative, since chance is in fact defined as the characteristic of the phenomena which follow no law, phenomena whose causes are too complex to permit prediction." (Félix E Borel, "Probabilities and Life", 1962)

"Theories are usually introduced when previous study of a class of phenomena has revealed a system of uniformities. […] Theories then seek to explain those regularities and, generally, to afford a deeper and more accurate understanding of the phenomena in question. To this end, a theory construes those phenomena as manifestations of entities and processes that lie behind or beneath them, as it were." (Carl G Hempel, "Philosophy of Natural Science", 1966)

"The less we understand a phenomenon, the more variables we require to explain it." (Russell L Ackoff, "Management Science", 1967)

 "As soon as we inquire into the reasons for the phenomena, we enter the domain of theory, which connects the observed phenomena and traces them back to a single ‘pure’ phenomena, thus bringing about a logical arrangement of an enormous amount of observational material." (Georg Joos, "Theoretical Physics", 1968)

"A model is an abstract description of the real world. It is a simple representation of more complex forms, processes and functions of physical phenomena and ideas." (Moshe F Rubinstein & Iris R Firstenberg, "Patterns of Problem Solving", 1975)

"A real change of theory is not a change of equations - it is a change of mathematical structure, and only fragments of competing theories, often not very important ones conceptually, admit comparison with each other within a limited range of phenomena." (Yuri I Manin, "Mathematics and Physics", 1981)

"In all scientific fields, theory is frequently more important than experimental data. Scientists are generally reluctant to accept the existence of a phenomenon when they do not know how to explain it. On the other hand, they will often accept a theory that is especially plausible before there exists any data to support it." (Richard Morris, 1983)

"Nature is disordered, powerful and chaotic, and through fear of the chaos we impose system on it. We abhor complexity, and seek to simplify things whenever we can by whatever means we have at hand. We need to have an overall explanation of what the universe is and how it functions. In order to achieve this overall view we develop explanatory theories which will give structure to natural phenomena: we classify nature into a coherent system which appears to do what we say it does." (James Burke, "The Day the Universe Changed", 1985) 

"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 simplest hypothesis proposed as an explanation of phenomena is more likely to be the true one than is any other available hypothesis, that its predictions are more likely to be true than those of any other available hypothesis, and that it is an ultimate a priori epistemic principle that simplicity is evidence for truth." (Richard Swinburne, "Simplicity as Evidence for Truth", 1997)

"The point is that scientific descriptions of phenomena in all of these cases do not fully capture reality they are models. This is not a shortcoming but a strength of science much of the scientist's art lies in figuring out what to include and what to exclude in a model, and this ability allows science to make useful predictions without getting bogged down by intractable details." (Philip Ball," The Self-Made Tapestry: Pattern Formation in Nature", 1998)

"A scientific theory is a concise and coherent set of concepts, claims, and laws (frequently expressed mathematically) that can be used to precisely and accurately explain and predict natural phenomena." (Mordechai Ben-Ari, "Just a Theory: Exploring the Nature of Science", 2005)

"Complexity arises when emergent system-level phenomena are characterized by patterns in time or a given state space that have neither too much nor too little form. Neither in stasis nor changing randomly, these emergent phenomena are interesting, due to the coupling of individual and global behaviours as well as the difficulties they pose for prediction. Broad patterns of system behaviour may be predictable, but the system's specific path through a space of possible states is not." (Steve Maguire et al, "Complexity Science and Organization Studies", 2006)

"Humans have difficulty perceiving variables accurately […]. However, in general, they tend to have inaccurate perceptions of system states, including past, current, and future states. This is due, in part, to limited ‘mental models’ of the phenomena of interest in terms of both how things work and how to influence things. Consequently, people have difficulty determining the full implications of what is known, as well as considering future contingencies for potential systems states and the long-term value of addressing these contingencies. " (William B. Rouse, "People and Organizations: Explorations of Human-Centered Design", 2007)

"A theory is a speculative explanation of a particular phenomenon which derives it legitimacy from conforming to the primary assumptions of the worldview of the culture in which it appears. There can be more than one theory for a particular phenomenon that conforms to a given worldview. […]  A new theory may seem to trigger a change in worldview, as in this case, but logically a change in worldview must precede a change in theory, otherwise the theory will not be viable. A change in worldview will necessitate a change in all theories in all branches of study." (M G Jackson, "Transformative Learning for a New Worldview: Learning to Think Differently", 2008)

"[...] construction of a data model is precisely the selective relevant depiction of the phenomena by the user of the theory required for the possibility of representation of the phenomenon."  (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)

"Put simply, statistics is a range of procedures for gathering, organizing, analyzing and presenting quantitative data. […] Essentially […], statistics is a scientific approach to analyzing numerical data in order to enable us to maximize our interpretation, understanding and use. This means that statistics helps us turn data into information; that is, data that have been interpreted, understood and are useful to the recipient. Put formally, for your project, statistics is the systematic collection and analysis of numerical data, in order to investigate or discover relationships among phenomena so as to explain, predict and control their occurrence." (Reva B Brown & Mark Saunders, "Dealing with Statistics: What You Need to Know", 2008)

"A theory is a set of deductively closed propositions that explain and predict empirical phenomena, and a model is a theory that is idealized." (Jay Odenbaugh, "True Lies: Realism, Robustness, and Models", Philosophy of Science, Vol. 78, No. 5, 2011)

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

"Repeated observations of the same phenomenon do not always produce the same results, due to random noise or error. Sampling errors result when our observations capture unrepresentative circumstances, like measuring rush hour traffic on weekends as well as during the work week. Measurement errors reflect the limits of precision inherent in any sensing device. The notion of signal to noise ratio captures the degree to which a series of observations reflects a quantity of interest as opposed to data variance. As data scientists, we care about changes in the signal instead of the noise, and such variance often makes this problem surprisingly difficult." (Steven S Skiena, "The Data Science Design Manual", 2017)

"The first epistemic principle to embrace is that there is always a gap between our data and the real world. We fall headfirst into a pitfall when we forget that this gap exists, that our data isn't a perfect reflection of the real-world phenomena it's representing. Do people really fail to remember this? It sounds so basic. How could anyone fall into such an obvious trap?" (Ben Jones, "Avoiding Data Pitfalls: How to Steer Clear of Common Blunders When Working with Data and Presenting Analysis and Visualizations", 2020) 

"Although to penetrate into the intimate mysteries of nature and hence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena." (Leonhard Euler)

Data Science: Error (Just the Quotes)

"The probable is something which lies midway between truth and error" (Christian Thomasius, "Institutes of Divine Jurisprudence", 1688)

"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 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)

"Men are often led into errors by the love of simplicity, which disposes us to reduce things to few principles, and to conceive a greater simplicity in nature than there really is." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)

"The orbits of certainties touch one another; but in the interstices there is room enough for error to go forth and prevail." (Johann Wolfgang von Goethe, "Maxims and Reflections", 1833)

"Nothing hurts a new truth more than an old error." (Johann Wolfgang von Goethe, "Sprüche in Prosa", 1840)

"Every detection of what is false directs us towards what is true: every trial exhausts some tempting form of error. Not only so; but scarcely any attempt is entirely a failure; scarcely any theory, the result of steady thought, is altogether false; no tempting form of error is without some latent charm derived from truth." (William Whewell, "Lectures on the History of Moral Philosophy in England", 1852)

"[…] ideas may be both novel and important, and yet, if they are incorrect - if they lack the very essential support of incontrovertible fact, they are unworthy of credence. Without this, a theory may be both beautiful and grand, but must be as evanescent as it is beautiful, and as unsubstantial as it is grand." (George Brewster, "A New Philosophy of Matter", 1858)

"When a power of nature, invisible and impalpable, is the subject of scientific inquiry, it is necessary, if we would comprehend its essence and properties, to study its manifestations and effects. For this purpose simple observation is insufficient, since error always lies on the surface, whilst truth must be sought in deeper regions." (Justus von Liebig," Familiar Letters on Chemistry", 1859)

"As in the experimental sciences, truth cannot be distinguished from error as long as firm principles have not been established through the rigorous observation of facts." (Louis Pasteur, "Étude sur la maladie des vers à soie", 1870)

"It would be an error to suppose that the great discoverer seizes at once upon the truth, or has any unerring method of divining it. In all probability the errors of the great mind exceed in number those of the less vigorous one. Fertility of imagination and abundance of guesses at truth are among the first requisites of discovery; but the erroneous guesses must be many times as numerous as those that prove well founded. The weakest analogies, the most whimsical notions, the most apparently absurd theories, may pass through the teeming brain, and no record remain of more than the hundredth part. […] The truest theories involve suppositions which are inconceivable, and no limit can really be placed to the freedom of hypotheses." (W Stanley Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1877)

"Perfect readiness to reject a theory inconsistent with fact is a primary requisite of the philosophic mind. But it, would be a mistake to suppose that this candour has anything akin to fickleness; on the contrary, readiness to reject a false theory may be combined with a peculiar pertinacity and courage in maintaining an hypothesis as long as its falsity is not actually apparent." (William S Jevons, "The Principles of Science", 1887)

"One is almost tempted to assert that quite apart from its intellectual mission, theory is the most practical thing conceivable, the quintessence of practice as it were, since the precision of its conclusions cannot be reached by any routine of estimating or trial and error; although given the hidden ways of theory, this will hold only for those who walk them with complete confidence." (Ludwig E Boltzmann, "On the Significance of Theories", 1890)

"[…] to kill an error is as good a service as, and sometimes even better than, the establishing of a new truth or fact." (Charles R Darwin, "More Letters of Charles Darwin", Vol 2, 1903)

"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)

"The aim of science is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest. The guiding motto in the life of every natural philosopher should be, ‘Seek simplicity and distrust it’." (Alfred N Whitehead, "The Concept of Nature", 1919)

"Errors may also creep into the information transfer stage when the originator of the data is unconsciously looking for a particular result. Such situations may occur in interviews or questionnaires designed to gather original data. Improper wording of the question, or improper voice inflections. and other constructional errors may elicit nonobjective responses. Obviously, if the data is incorrectly gathered, any graph based on that data will contain the original error - even though the graph be most expertly designed and beautifully presented." (Cecil H Meyers, "Handbook of Basic Graphs: A modern approach", 1970)

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

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

"A mature science, with respect to the matter of errors in variables, is not one that measures its variables without error, for this is impossible. It is, rather, a science which properly manages its errors, controlling their magnitudes and correctly calculating their implications for substantive conclusions." (Otis D Duncan, "Introduction to Structural Equation Models", 1975)

"Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you'll never notice the flaws; if you doubt too much you won't get started. It requires a lovely balance." (Richard W Hamming, "You and Your Research", 1986) 

"We have found that some of the hardest errors to detect by traditional methods are unsuspected gaps in the data collection (we usually discovered them serendipitously in the course of graphical checking)." (Peter Huber, "Huge data sets", Compstat '94: Proceedings, 1994)

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

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

"In error analysis the so-called 'chi-squared' is a measure of the agreement between the uncorrelated internal and the external uncertainties of a measured functional relation. The simplest such relation would be time independence. Theory of the chi-squared requires that the uncertainties be normally distributed. Nevertheless, it was found that the test can be applied to most probability distributions encountered in practice." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"[myth:] Random errors can always be determined by repeating measurements under identical conditions. […] this statement is true only for time-related random errors ." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"[myth:] Systematic errors can be determined inductively. It should be quite obvious that it is not possible to determine the scale error from the pattern of data values." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"What is so unconventional about the statistical way of thinking? First, statisticians do not care much for the popular concept of the statistical average; instead, they fixate on any deviation from the average. They worry about how large these variations are, how frequently they occur, and why they exist. [...] Second, variability does not need to be explained by reasonable causes, despite our natural desire for a rational explanation of everything; statisticians are frequently just as happy to pore over patterns of correlation. [...] Third, statisticians are constantly looking out for missed nuances: a statistical average for all groups may well hide vital differences that exist between these groups. Ignoring group differences when they are present frequently portends inequitable treatment. [...] Fourth, decisions based on statistics can be calibrated to strike a balance between two types of errors. Predictably, decision makers have an incentive to focus exclusively on minimizing any mistake that could bring about public humiliation, but statisticians point out that because of this bias, their decisions will aggravate other errors, which are unnoticed but serious. [...] Finally, statisticians follow a specific protocol known as statistical testing when deciding whether the evidence fits the crime, so to speak. Unlike some of us, they don’t believe in miracles. In other words, if the most unusual coincidence must be contrived to explain the inexplicable, they prefer leaving the crime unsolved." (Kaiser Fung, "Numbers Rule the World", 2010) 

"A key difference between a traditional statistical problems and a time series problem is that often, in time series, the errors are not independent." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)

 "A wide variety of statistical procedures (regression, t-tests, ANOVA) require three assumptions: (i) Normal observations or errors. (ii) Independent observations (or independent errors, which is equivalent, in normal linear models to independent observations). (iii) Equal variance - when that is appropriate (for the one-sample t-test, for example, there is nothing being compared, so equal variances do not apply)." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)

"If the observations/errors are not independent, the statistical formulations are completely unreliable unless corrections can be made." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)

"Once a model has been fitted to the data, the deviations from the model are the residuals. If the model is appropriate, then the residuals mimic the true errors. Examination of the residuals often provides clues about departures from the modeling assumptions. Lack of fit - if there is curvature in the residuals, plotted versus the fitted values, this suggests there may be whole regions where the model overestimates the data and other whole regions where the model underestimates the data. This would suggest that the current model is too simple relative to some better model." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)

 "The random element in most data analysis is assumed to be white noise - normal errors independent of each other. In a time series, the errors are often linked so that independence cannot be assumed (the last examples). Modeling the nature of this dependence is the key to time series." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)

"When data is not normal, the reason the formulas are working is usually the central limit theorem. For large sample sizes, the formulas are producing parameter estimates that are approximately normal even when the data is not itself normal. The central limit theorem does make some assumptions and one is that the mean and variance of the population exist. Outliers in the data are evidence that these assumptions may not be true. Persistent outliers in the data, ones that are not errors and cannot be otherwise explained, suggest that the usual procedures based on the central limit theorem are not applicable." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)

"Bias is error from incorrect assumptions built into the model, such as restricting an interpolating function to be linear instead of a higher-order curve. [...] Errors of bias produce underfit models. They do not fit the training data as tightly as possible, were they allowed the freedom to do so. In popular discourse, I associate the word 'bias' with prejudice, and the correspondence is fairly apt: an apriori assumption that one group is inferior to another will result in less accurate predictions than an unbiased one. Models that perform lousy on both training and testing data are underfit." (Steven S Skiena, "The Data Science Design Manual", 2017)

"Repeated observations of the same phenomenon do not always produce the same results, due to random noise or error. Sampling errors result when our observations capture unrepresentative circumstances, like measuring rush hour traffic on weekends as well as during the work week. Measurement errors reflect the limits of precision inherent in any sensing device. The notion of signal to noise ratio captures the degree to which a series of observations reflects a quantity of interest as opposed to data variance. As data scientists, we care about changes in the signal instead of the noise, and such variance often makes this problem surprisingly difficult." (Steven S Skiena, "The Data Science Design Manual", 2017)

"Variance is error from sensitivity to fluctuations in the training set. If our training set contains sampling or measurement error, this noise introduces variance into the resulting model. [...] Errors of variance result in overfit models: their quest for accuracy causes them to mistake noise for signal, and they adjust so well to the training data that noise leads them astray. Models that do much better on testing data than training data are overfit." (Steven S Skiena, "The Data Science Design Manual", 2017)

"Machine learning bias is typically understood as a source of learning error, a technical problem. […] Machine learning bias can introduce error simply because the system doesn’t 'look' for certain solutions in the first place. But bias is actually necessary in machine learning - it’s part of learning itself." (Erik J Larson, "The Myth of Artificial Intelligence: Why Computers Can’t Think the Way We Do", 2021)

Data Science: The Science in Data Science (Just the Quotes)

"The aim of every science is foresight. For the laws of established observation of phenomena are generally employed to foresee their succession. All men, however little advanced make true predictions, which are always based on the same principle, the knowledge of the future from the past." (Auguste Compte, "Plan des travaux scientifiques nécessaires pour réorganiser la société", 1822)

"Science is nothing but the finding of analogy, identity, in the most remote parts." (Ralph W Emerson, 1837)

"Therefore science always goes abreast with the just elevation of the man, keeping step with religion and metaphysics; or, the state of science is an index of our self-knowledge." (Ralph W Emerson, "The Poet", 1844)

"It may sound quite strange, but for me, as for other scientists on whom these kinds of imaginative images have a greater effect than other poems do, no science is at its very heart more closely related to poetry, perhaps, than is chemistry." (Just Liebig, 1854)

"Science is the systematic classification of experience." (George H Lewes, "The Physical Basis of Mind", 1877)

"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)

"While science is pursuing a steady onward movement, it is convenient from time to time to cast a glance back on the route already traversed, and especially to consider the new conceptions which aim at discovering the general meaning of the stock of facts accumulated from day to day in our laboratories." (Dmitry Mendeleyev, "The Periodic Law of the Chemical Elements", Journal of the Chemical Society Vol. 55, 1889)

"The aim of science is always to reduce complexity to simplicity." (William James, "The Principles of Psychology", 1890)

"Science is not the monopoly of the naturalist or the scholar, nor is it anything mysterious or esoteric. Science is the search for truth, and truth is the adequacy of a description of facts." (Paul Carus, "Philosophy as a Science", 1909)

"Science is reduction. Mathematics is its ideal, its form par excellence, for it is in mathematics that assimilation, identification, is most perfectly realized. The universe, scientifically explained, would be a certain formula, one and eternal, regarded as the equivalent of the entire diversity and movement of things." (Émile Boutroux, "Natural law in Science and Philosophy", 1914)

"Abstract as it is, science is but an outgrowth of life. That is what the teacher must continually keep in mind. […] Let him explain […] science is not a dead system - the excretion of a monstrous pedantism - but really one of the most vigorous and exuberant phases of human life." (George A L Sarton, "The Teaching of the History of Science", The Scientific Monthly, 1918)

"The aim of science is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest. The guiding motto in the life of every natural philosopher should be, ‘Seek simplicity and distrust it’." (Alfred N Whitehead, "The Concept of Nature", 1919)

"Science is simply setting out on a fishing expedition to see whether it cannot find some procedure which it can call measurement of space and some procedure which it can call the measurement of time, and something which it can call a system of forces, and something which it can call masses." (Alfred N Whitehead, "The Concept of Nature", 1920)

"Science is a magnificent force, but it is not a teacher of morals. It can perfect machinery, but it adds no moral restraints to protect society from the misuse of the machine. It can also build gigantic intellectual ships, but it constructs no moral rudders for the control of storm tossed human vessel. It not only fails to supply the spiritual element needed but some of its unproven hypotheses rob the ship of its compass and thus endangers its cargo." (William J Bryan, "Undelivered Trial Summation Scopes Trial", 1925)

"Science is but a method. Whatever its material, an observation accurately made and free of compromise to bias and desire, and undeterred by consequence, is science." (Hans Zinsser, "Untheological Reflections", The Atlantic Monthly, 1929)

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

"The common view of science is that it is a sort of machine for increasing the race’s store of dependable facts. It is that only in part; in even larger part it is a machine for upsetting undependable facts." (Will Durant, 1931)

"One has to recognize that science is not metaphysics, and certainly not mysticism; it can never bring us the illumination and the satisfaction experienced by one enraptured in ecstasy. Science is sobriety and clarity of conception, not intoxicated vision."(Ludwig Von Mises, "Epistemological Problems of Economics", 1933)

"Modern positivists are apt to see more clearly that science is not a system of concepts but rather a system of statements." (Karl R Popper, "The Logic of Scientific Discovery", 1934)

"Science is a system of statements based on direct experience, and controlled by experimental verification. Verification in science is not, however, of single statements but of the entire system or a sub-system of such statements." (Rudolf Carnap, "The Unity of Science", 1934)

"Science is the attempt to discover, by means of observation, and reasoning based upon it, first, particular facts about the world, and then laws connecting facts with one another and (in fortunate cases) making it possible to predict future occurrences." (Bertrand Russell, "Religion and Science, Grounds of Conflict", 1935)

"[…] that all science is merely a game can be easily discarded as a piece of wisdom too easily come by. But it is legitimate to enquire whether science is not liable to indulge in play within the closed precincts of its own method. Thus, for instance, the scientist’s continuous penchant for systems tends in the direction of play." (Johan Huizinga, "Homo Ludens", 1938)

"Science makes no pretension to eternal truth or absolute truth; some of its rivals do. That science is in some respects inhuman may be the secret of its success in alleviating human misery and mitigating human stupidity." (Eric T Bell, "Mathematics: Queen and Servant of Science", 1938)

"Science is the attempt to make the chaotic diversity of our sense experience correspond to a logically uniform system of thought." (Albert Einstein, "Considerations Concerning the Fundaments of Theoretical Physics", Science Vol. 91 (2369), 1940)

"Science is the organised attempt of mankind to discover how things work as causal systems. The scientific attitude of mind is an interest in such questions. It can be contrasted with other attitudes, which have different interests; for instance the magical, which attempts to make things work not as material systems but as immaterial forces which can be controlled by spells; or the religious, which is interested in the world as revealing the nature of God." (Conrad H Waddington, "The Scientific Attitude", 1941)

"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)

"Science is an interconnected series of concepts and schemes that have developed as a result of experimentation and observation and are fruitful of further experimentation and observation."(James B Conant, "Science and Common Sense", 1951)

"[…] theoretical science is essentially disciplined exploitation of metaphor." (Anatol Rapoport, "Operational Philosophy", 1953)

"Prediction is all very well; but we must make sense of what we predict. The mainspring of science is the conviction that by honest, imaginative enquiry we can build up a system of ideas about Nature which has some legitimate claim to ‘reality’." (Stephen Toulmin, "The Philosophy of Science: An Introduction", 1953)

"An engineering science aims to organize the design principles used in engineering practice into a discipline and thus to exhibit the similarities between different areas of engineering practice and to emphasize the power of fundamental concepts. In short, an engineering science is predominated by theoretical analysis and very often uses the tool of advanced mathematics." (Qian Xuesen, "Engineering cybernetics", 1954))

"The true aim of science is to discover a simple theory which is necessary and sufficient to cover the facts, when they have been purified of traditional prejudices." (Lancelot L Whyte, "Accent on Form", 1954)

"Science is the creation of concepts and their exploration in the facts. It has no other test of the concept than its empirical truth to fact." (Jacob Bronowski, "Science and Human Values", 1956)

"The progress of science is the discovery at each step of a new order which gives unity to what had seemed unlike." (Jacob Bronowski, "Science and Human Values", 1956)

"[…] any serious examination of the basic concepts of any science is far more difficult than the elaboration of their ultimate consequences." (George F J Temple, "Turning Points in Physics", 1959)

"Science is usually understood to depict a universe of strict order and lawfulness, of rigorous economy - one whose currency is energy, convertible against a service charge into a growing common pool called entropy." (Paul A Weiss,"Organic Form: Scientific and Aesthetic Aspects", 1960)

"[…] the progress of science is a little like making a jig-saw puzzle. One makes collections of pieces which certainly fit together, though at first it is not clear where each group should come in the picture as a whole, and if at first one makes a mistake in placing it, this can be corrected later without dismantling the whole group." (Sir George Thomson, "The Inspiration of Science", 1961)

"Science is the reduction of the bewildering diversity of unique events to manageable uniformity within one of a number of symbol systems, and technology is the art of using these symbol systems so as to control and organize unique events. Scientific observation is always a viewing of things through the refracting medium of a symbol system, and technological praxis is always handling of things in ways that some symbol system has dictated. Education in science and technology is essentially education on the symbol level." (Aldous L Huxley, "Essay", Daedalus, 1962)

"The important distinction between science and those other systematizations [i.e., art, philosophy, and theology] is that science is self-testing and self-correcting. Here the essential point of science is respect for objective fact. What is correctly observed must be believed [...] the competent scientist does quite the opposite of the popular stereotype of setting out to prove a theory; he seeks to disprove it." (George G Simpson, "Notes on the Nature of Science", 1962)

"What, then, is science according to common opinion? Science is what scientists do. Science is knowledge, a body of information about the external world. Science is the ability to predict. Science is power, it is engineering. Science explains, or gives causes and reasons." (John Bremer "What Is Science?" [in "Notes on the Nature of Science"], 1962)

"Science is a matter of disinterested observation, patient ratiocination within some system of logically correlated concepts. In real-life conflicts between reason and passion the issue is uncertain. Passion and prejudice are always able to mobilize their forces more rapidly and press the attack with greater fury; but in the long run (and often, of course, too late) enlightened self-interest may rouse itself, launch a counterattack and win the day for reason." (Aldous L Huxley, "Literature and Science", 1963)

"Science is a way to teach how something gets to be known, what is not known, to what extent things are known (for nothing is known absolutely), how to handle doubt and uncertainty, what the rules of evidence are, how to think about things so that judgments can be made, how to distinguish truth from fraud, and from show." (Richard P Feynman, "The Problem of Teaching Physics in Latin America", Engineering and Science, 1963)

"The aim of science is to apprehend this purely intelligible world as a thing in itself, an object which is what it is independently of all thinking, and thus antithetical to the sensible world. [...] The world of thought is the universal, the timeless and spaceless, the absolutely necessary, whereas the world of sense is the contingent, the changing and moving appearance which somehow indicates or symbolizes it." (Robin G Collingwood, "Essays in the Philosophy of Art", 1964)

"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." (Herbert A Simon, "The Sciences of the Artificial", 1969)

"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." (Herbert A Simon, "The Sciences of the Artificial", 1969)

"Science is a product of man, of his mind; and science creates the real world in its own image." (Frank E Egler, "The Way of Science", 1970)

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

"Science is systematic organisation of knowledge about the universe on the basis of explanatory hypotheses which are genuinely testable. Science advances by developing gradually more comprehensive theories; that is, by formulating theories of greater generality which can account for observational statements and hypotheses which appear as prima facie unrelated." (Francisco J Ayala, "Studies in the Philosophy of Biology: Reduction and Related Problems", 1974)

"A mature science, with respect to the matter of errors in variables, is not one that measures its variables without error, for this is impossible. It is, rather, a science which properly manages its errors, controlling their magnitudes and correctly calculating their implications for substantive conclusions." (Otis D Duncan, "Introduction to Structural Equation Models", 1975)

"The very nature of science is such that scientists need the metaphor as a bridge between old and new theories." (Earl R MacCormac, "Metaphor and Myth in Science and Religion", 1976)

"Facts do not ‘speak for themselves’; they are read in the light of theory. Creative thought, in science as much as in the arts, is the motor of changing opinion. Science is a quintessentially human activity, not a mechanized, robot-like accumulation of objective information, leading by laws of logic to inescapable interpretation." (Stephen J Gould, "Ever Since Darwin", 1977)

"Science is not a heartless pursuit of objective information. It is a creative human activity, its geniuses acting more as artists than information processors. Changes in theory are not simply the derivative results of the new discoveries but the work of creative imagination influenced by contemporary social and political forces." (Stephen J Gould, "Ever Since Darwin: Reflections in Natural History", 1977)

"Engineering or Technology is the making of things that did not previously exist, whereas science is the discovering of things that have long existed." (David Billington, "The Tower and the Bridge: The New Art of Structural Engineering", 1983)

"Science is a process. It is a way of thinking, a manner of approaching and of possibly resolving problems, a route by which one can produce order and sense out of disorganized and chaotic observations. Through it we achieve useful conclusions and results that are compelling and upon which there is a tendency to agree." (Isaac Asimov, "‘X’ Stands for Unknown", 1984)

"If doing mathematics or science is looked upon as a game, then one might say that in mathematics you compete against yourself or other mathematicians; in physics your adversary is nature and the stakes are higher." (Mark Kac, "Enigmas Of Chance", 1985)

"Science is defined as a set of observations and theories about observations." (F Albert Matsen, "The Role of Theory in Chemistry", Journal of Chemical Education Vol. 62 (5), 1985)

"We expect to learn new tricks because one of our science based abilities is being able to predict. That after all is what science is about. Learning enough about how a thing works so you'll know what comes next. Because as we all know everything obeys the universal laws, all you need is to understand the laws." (James Burke, "The Day the Universe Changed", 1985)

"Science is human experience systematically extended (by intent, methodology and instrumentation) for the purpose of learning more about the natural world and for the critical empirical testing and possible falsification of all ideas about the natural world. Scientific hypotheses may incorporate only elements of the natural empirical world, and thus may contain no element of the supernatural." (Robert E Kofahl, Correctly Redefining Distorted Science: A Most Essential Task", Creation Research Society Quarterly Vol. 23, 1986)

"Science is not a given set of answers but a system for obtaining answers. The method by which the search is conducted is more important than the nature of the solution. Questions need not be answered at all, or answers may be provided and then changed. It does not matter how often or how profoundly our view of the universe alters, as long as these changes take place in a way appropriate to science. For the practice of science, like the game of baseball, is covered by definite rules." (Robert Shapiro, "Origins: A Skeptic’s Guide to the Creation of Life on Earth", 1986)

"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)

"Science doesn’t purvey absolute truth. Science is a mechanism, 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." (Isaac Asimov, [interview with Bill Moyers in The Humanist] 1989)

"The view of science is that all processes ultimately run down, but entropy is maximized only in some far, far away future. The idea of entropy makes an assumption that the laws of the space-time continuum are infinitely and linearly extendable into the future. In the spiral time scheme of the timewave this assumption is not made. Rather, final time means passing out of one set of laws that are conditioning existence and into another radically different set of laws. The universe is seen as a series of compartmentalized eras or epochs whose laws are quite different from one another, with transitions from one epoch to another occurring with unexpected suddenness." (Terence McKenna, "True Hallucinations", 1989)

"Science is (or should be) a precise art. Precise, because data may be taken or theories formulated with a certain amount of accuracy; an art, because putting the information into the most useful form for investigation or for presentation requires a certain amount of creativity and insight." (Patricia H Reiff, "The Use and Misuse of Statistics in Space Physics", Journal of Geomagnetism and Geoelectricity 42, 1990)

"In science if you know what you are doing you should not be doing it. In engineering if you do not know what you are doing you should not be doing it. Of course, you seldom, if ever, see either pure state." (Richard W Hamming, "The Art of Probability for Scientists and Engineers", 1991)

"On this view, we recognize science to be the search for algorithmic compressions. We list sequences of observed data. We try to formulate algorithms that compactly represent the information content of those sequences. Then we test the correctness of our hypothetical abbreviations by using them to predict the next terms in the string. These predictions can then be compared with the future direction of the data sequence. Without the development of algorithmic compressions of data all science would be replaced by mindless stamp collecting - the indiscriminate accumulation of every available fact. Science is predicated upon the belief that the Universe is algorithmically compressible and the modern search for a Theory of Everything is the ultimate expression of that belief, a belief that there is an abbreviated representation of the logic behind the Universe's properties that can be written down in finite form by human beings." (John D Barrow, New Theories of Everything", 1991)

"The goal of science is to make sense of the diversity of Nature." (John D Barrow, "Theories of Everything: The Quest for Ultimate Explanation", 1991)

"Science is not about control. It is about cultivating a perpetual condition of wonder in the face of something that forever grows one step richer and subtler than our latest theory about it. It is about  reverence, not mastery." (Richard Power, "Gold Bug Variations", 1993)

"Statistics as a science is to quantify uncertainty, not unknown." (Chamont Wang, "Sense and Nonsense of Statistical Inference: Controversy, Misuse, and Subtlety", 1993)

"Clearly, science is not simply a matter of observing facts. Every scientific theory also expresses a worldview. Philosophical preconceptions determine where facts are sought, how experiments are designed, and which conclusions are drawn from them." (Nancy R Pearcey & Charles B. Thaxton, "The Soul of Science: Christian Faith and Natural Philosophy", 1994)

"Science is distinguished not for asserting that nature is rational, but for constantly testing claims to that or any other affect by observation and experiment." (Timothy Ferris, "The Whole Shebang: A State-of-the Universe’s Report", 1996)

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

"The art of science is knowing which observations to ignore and which are the key to the puzzle." (Edward W Kolb, "Blind Watchers of the Sky", 1996)

"Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don’t look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding." (Gian-Carlo Rota, "Indiscrete Thoughts", 1997)

"Religion is the antithesis of science; science is competent to illuminate all the deep questions of existence, and does so in a manner that makes full use of, and respects the human intellect. I see neither need nor sign of any future reconciliation." (Peter W Atkins, "Religion - The Antithesis to Science", 1997)

"[…] the pursuit of science is more than the pursuit of understanding. It is driven by the creative urge, the urge to construct a vision, a map, a picture of the world that gives the world a little more beauty and coherence than it had before." (John A Wheeler, "Geons, Black Holes, and Quantum Foam: A Life in Physics", 1998)

"The rate of the development of science is not the rate at which you make observations alone but, much more important, the rate at which you create new things to test." (Richard Feynman, "The Meaning of It All", 1998)

"The passion and beauty and joy of science is that we humans have invented a process to understand the universe in a way that is true for everyone. We are finding universal truths." (Bill Nye, 2000)

"The poetry of science is in some sense embodied in its great equations, and these equations can also be peeled. But their layers represent their attributes and consequences, not their meanings." (Graham Farmelo, 2002)

"Science is the art of the appropriate approximation. While the flat earth model is usually spoken of with derision it is still widely used. Flat maps, either in atlases or road maps, use the flat earth model as an approximation to the more complicated shape." (Byron K. Jennings, "On the Nature of Science", Physics in Canada Vol. 63 (1), 2007)

"It is ironic but true: the one reality science cannot reduce is the only reality we will ever know. This is why we need art. By expressing our actual experience, the artist reminds us that our science is incomplete, that no map of matter will ever explain the immateriality of our consciousness." (Jonah Lehrer, "Proust Was a Neuroscientist", 2011)

"Science isn’t about being right. It is about convincing others of the correctness of an idea through a methodology all will accept using data everyone can trust. New ideas take time to be accepted because they compete with others that have already passed the test." (Tom Koch, "Commentary: Nobody loves a critic: Edmund A Parkes and John Snow’s cholera", International Journal of Epidemiology Vol. 42 (6), 2013)

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

More quotes on "Science" at quotablemath.blogspot.com.