Beauty as a Concept

Most of us would agree that watching the sun set over the horizon is a thing of beauty. In an instant, we are leaving our complex world behind and feel at peace for a moment or two…


Beauty as an Emotional Experience

What is it about a perfect sunset that makes us feel that way?  or why are we disappointed when clouds obscure the sunset’s final moments above the horizon?  Lots of folks have discussed the nature of “beauty”and how it holds our mind’s attention.  Researchers have found that people have similar beauty standards across China, India and the USA.  Back in the 1750’s, the German philosopher Immanuel Kant distinguished between beauty as an intuitive or sensible experience and a rational approach to aesthetics on the other.   In the first instance, beauty is an emotion.  In the second instance, we are trying to use logic to establish whether something- a painting, a song or a piece of clothing – is beautiful. Clearly, watching the sunset is an emotional experience, beyond logic.

Is Logic All We’ve Got?

Science and engineering are purely based on logic.  In fact, logic is the main human language of reasoning. The entire “digital” world of computers is based on logic. Moore and Parker argue that logic is the mode in which our mind reasons best about our reality. But there is another important way to think, and analyze, and feel: conceptual thinking.  I covered conceptual thinking briefly in another post.  Every day, we build, update or modify complex, flexible, abstract representations of reality called “concepts”. For instance, we recognize just about any cat by matching it to our concept of “cat”, even if the cat wears a costume!  Psychologists have tried to understand how we build these abstract models. Jean Piaget, the famous Swiss psychologist developed a theory about the nature and development of human intelligence which includes observations about how children develop concepts.  In general, however, these analyses fall short of explaining the mathematical and physical structure of concepts, how they are learned and how they work.

Beauty as a Concept

Conceptual thinking may not be as definitive or as accurate as logic (although logic based on bad assumptions will yield bad answers!) but it is much faster. We can figure out with near certainty that something is a cat much faster with conceptual thinking than with logic: Does it have fur? Does it have whiskers? Is its size compatible with that of a cat? Is it not a dog? Etc…

When we see the sun setting over the horizon, the scene before us, no matter where it is, reduces itself to a simple, timeless, abstract and moving concept:  beauty.

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Three skills for dealing with complexity

CT1Our World has generally become more complex, in part because of the many linkages and relationships between elements that make it a lot harder to figure out how things work and where they are going.  Let’s take the stock market for instance.  One day it is affected by the country of Greece, and the next by Amazon’s quarterly revenue. The price of an airline ticket to a particular destination is another good example. It depends on the time of year, the day of the week, the flight’s time of day, the airline’s particular network structure, the number of stops, how many seats remain in each fare class, what the competition charges, what the market will bear, etc…  Below are three important skills to help us deal with complexity:

Critical Thinking

Critical thinking is the ability to break down a complex system (my definition) and using analysis to understand its inner-workings.  Critical thinking requires research, critique, analysis and evaluation of the system and its sub-components. “Research” means gathering facts, information and opinions. “Critique” is the ability to discern what is important and what is not.  “Analysis” (from the Greek “αναλυειν”, meaning to “untie”) is the ability to understand how things work.  “Evaluate” means forming a quantitative assessment of a system, understanding how it may behave under various circumstances. Critical thinking is about identifying what, in the complex system under study, is important for the particular situation at hand.

Conceptual Thinking

cat dressed up

We all know this is a cat!

This is a tough one.  Conceptual thinking is the ability to reduce a complex system into a simple, critical model.  The concept of a cat, for instance, is a representation of knowledge in our brain about what makes a cat, and how a cat is different from a dog, or an elephant. Cats may be all very different, but we recognize them all as cats and not dogs.  We know it when we see it!   Things are a bit more complicated when we talk about complex systems.  Both experience and creative thinking help reduce a complex system into a simple conceptual model. We then intuitively understand how it works.   Take for instance the concept of “supply and demand”.   Conceptual thinking means that we recognize that the price of an airline ticket is highly driven by supply and demand.  Suddenly, we understand better what drives the price of an airline ticket.

Risk Management

Reducing a system to its critical relationships, or building a conceptual model to understand it, are key to decision-making and to management. Of course, it is possible that we do not understand perfectly the complex system we are looking at or that we are not able to predict how it will behave.  In particular, assumptions about what will happen in the future are likely be shattered by unforeseen developments.  That’s where risk management comes in.  Risk management is a systematic process of  addressing and understanding what can go wrong with our assumptions.  What can be done?  Typically we can build flexibility into our decisions, but that will likely cost us something.  For instance, we can buy a refundable air ticket in case we change our mind, but that’s more expensive as we know.

Thinking critically, conceptually and systematically addressing risks are important, lifelong skills that everyone should learn.

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The Universe is a ‘complexity machine’

I am reproducing below an article published on January 23rd, 2015 in Science Daily  about a Clemson University study entitled  “How does the universe creates reason, morality?.”   I am also adding to the article relevant links (in parentheses) to outside sources.

image_1940-Local-UniverseRecent developments in science (Origin of Complexity in the Universe,  The Universe is Complex) are beginning to suggest that the universe naturally produces complexity. The emergence of life in general and perhaps even rational life, with its associated technological culture, may be extremely common, argues Clemson researcher Kelly Smith (Selected Works) in a recently published paper in the journal Space Policy.

What’s more, he suggests, this universal tendency has distinctly religious overtones and may even establish a truly universal basis for morality.

Smith, a Philosopher and Evolutionary Biologist, applies recent theoretical developments in Biology and Complex Systems Theory ( On the interplay between mathematics and biology: Hallmarks toward a new systems biology) to attempt new answers to the kind of enduring questions about human purpose and obligation that have long been considered the sole province of the humanities.

He points out that scientists are increasingly beginning to discuss how the basic structure of the universe seems to favor the creation of complexity. The large scale history of the universe strongly suggests a trend of increasing complexity: disordered energy states produce atoms and molecules, which combine to form suns and associated planets, on which life evolves. Life then seems to exhibit its own pattern of increasing complexity, with simple organisms getting more complex over evolutionary time until they eventually develop rationality and complex culture.

And recent theoretical developments in Biology and complex systems theory suggest this trend may be real, arising from the basic structure of the universe in a predictable fashion.“If this is right,” says Smith, “you can look at the universe as a kind of ‘complexity machine’, which raises all sorts of questions about what this means in a broader sense. For example, does believing the universe is structured to produce complexity in general, and rational creatures in particular, constitute a religious belief? It need not imply that the universe was created by a God, but on the other hand, it does suggest that the kind of rationality we hold dear is not an accident.

And Smith feels another similarity to religion are the potential moral implications of this idea. If evolution tends to favor the development of sociality, reason, and culture as a kind of “package deal,” then it’s a good bet that any smart extraterrestrials we encounter will have similar evolved attitudes about their basic moral commitments. 

In particular, they will likely agree with us that there is something morally special about rational, social creatures. And such universal agreement, argues Smith, could be the foundation for a truly universal system of ethics. (Moral universalism)

Smith will soon take sabbatical to lay the groundwork for a book exploring these issues in more detail.

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The Return of Simplicity?

Phone designers have raced for many years to come up with more and more features, connecting with just about anything that emits…  These features are designed to differentiate one product from another, but are they?  They likely confuse more than anything else.  When was the last time you used NFC on your phone?

Feature Bloat

“Tacking features on to products makes them harder to use” say Roland T. Rust, Debora Viana Thompson and Rebecca Hamilton (Harvard Business Review), in part because we have to learn and remember where to find and how to use these features.   To me, the traditional KitchenAid stand mixer (see photo) is the ultimate response to “feature bloat”.  The current mixer was designed in 1949 and has not changed much since.  It has only two main controls (lock or lift and speed) and a few attachments. In 1997 the San Francisco Museum of Modern Art selected it as an icon of American design.

Uplifting the Brand

In a 2013 article entitled “The Secret to Successful Product Design? Simplicity.”, Debra Kaye articulates why simple products can be successful:

  • Clean, simple silhouettes with fewer bells and whistles reduce the message to an idea that is both immediate and clear
  • Icons that embody the prime characteristics of a brand or product are memorable and instantly identifiable on the shelf or online.
  • We are both culturally and biologically programmed to gravitate toward those things that we recognize. They give us a feeling of comfort and security.

Capability versus Usability

Developers and engineers (I am one of them) are still pushing for products and services with more capabilities when we really need greater usability.  Hopefully, marketing-savvy executives will learn from Kitchenaid’s success and happily return to more simplicity…

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Santa Fe Institute Complexity Classes Online Starting Sept 29 2014

The Santa Fe Institute is offering three free courses starting on September 29, 2014:

  • Introduction to Complexity is a re-offering of the popular introductory course, taught by Melanie Mitchell, with no prerequisites.   It’s appropriate for anyone with an interest in the field.
  • Nonlinear Dynamics:  Mathematical and Computational Approaches is a new course, taught by SFI’s Liz Bradley.  It will cover dynamics and chaos from both theoretical and practical perspectives, with emphasis on mathematical and computational tools.
  • Mathematics for Complex Systems is not so much a “course” as a set of mathematics tutorials covering the math topics most relevant to complex systems science.  If you sign up for this course, you’ll be informed when new units are ready

You can get more information on these courses at .

In addition to free courses, the Santa Fe site offers useful educational resources for complex systems under the “Explore” tab, including a glossary, a collection of web resources, and a set of course syllabi.  Check it out at

Complexity Explorer is a community project and the help of the community is vital for building it.  Get involved in this project by volunteering to submit additional resources, help create subtitles for videos, or even make a small donation to our efforts.  You can find information on all this at

Posted in Mathematics

Complexity of football (AKA soccer)

football_strategyBoth real and american #football are complex sports, primarily because they are team sports.   Skills and athleticism are required, of course but it is likely that teams and players at the #FIFA #WorldCup in #Brazil will all be top-notch athletes.   Italy’s defeat against Costa Rica today is a clear example of how complex dynamics are at play, making predictions difficult.

“The italians were caught offside 11 times, evidence of their failure to adjust and adapt”, said Marc Santora in the New York Times.   Adaptability is required because an important strategic feature of football is to optimize space when attacking and defending.   Players must adapt their positions and movements on the field not only based on where the opponents are and how and where they are moving, but also in relation to their own team players.  It’s like herding sheep!  In the 1970’s, “total football” further broke players’ spatial barriers by enabling them to assume different roles on the field.  Johan Cruyff, winner of the Ballon d’Or in 1971, 1973 and 1974, used to direct his teammates in real time while himself on the field.

It is the ability to adapt to the opponents’ tactics, and #complex interactions between players on the field, that, in the end, makes a World(cup)of difference.

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What Causes School Shootings?

Incidence of school shootings dead and woundedTake a look at the chart to the right.  It shows the number of school shootings in the U.S. by year (in blue), the number of dead (orange) and the number of wounded (grey). I just went to Wikipedia and tallied it up. I should say that I am not an expert on this at all.

After a fairly steady rate between 2000 and 2007, the number of school shootings, and the number of victims is increasing rapidly in the last few years.  The year 2014 is not half over, yet the number of incidents exceeds the number for the whole of last year.   I could not readily find recent numbers for gun availability and the ease of getting legal and illegal guns, but we know that the number has been going up.   The economy has rebounded and unemployment is down, and typically this tends to reduce crime rate.  But school shootings are not regular crimes, they are acts of desperation.  

Clearly, the chart suggests a certain dynamic, where factors influence one another to produce a curve that looks like a trend, not just spikes like in 2007 and 2008.  To me, this growth and this dynamic speak to complex interactions between multiple factors in play: the ease of getting fire arms,  cultural markers (“copy-cat” tendencies), and difficulties confronting the future.   This would suggest that curbing this dynamic (or complexity) will require a multi-pronged approach.  The first is clearly gun control.  How man shootings would have been prevented if guns were not readily available to their perpetrators?  But will that be enough?  The chart suggests to me otherwise.  Focus has to be placed on the dynamic between the factors and how this trend can be broken.

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