When Reality Matters Less.

—?—?—?
How the concept of ‘Abstraction’ is fundamental to our world-view, yet often it befuddles us. Explorations in the disciplines of?—?Design, Mathematics & Business.
[ Originally posted on medium.com ]
—?—?—

WHEN THE SILENT MOVIE The Passion of the Joan of Arc came out in 1928, its cinematographic brilliance stunned everyone. Throughout its sequence the director Carl Dreyer overtly employed abstraction?—?using close-up or low-angle shots of the characters—that depicted mostly their partial body-parts on-screen. Joan’s harrowing emotional journey is captured in shots of just her face or up to shoulders?—?and rarely of her entire figure?—?an effect claimed to create a supreme sense of intimacy with the audience. Dreyer had abstracted Joan into just a symbolic, victimised face of the human beings’ (the priests’) utter sham and savagery.

One extreme scene shows a priest unleashing his demonic fury on Joan. As the priest yells, all we are shown is an abstract close-up of just a pair of lips, which seem to bear no approximation of any human form. This extreme abstraction alternates with the shots of Joan?—?where we are rather shown her full face in contrast, frightened and vulnerable. The priest is reduced to a salivating mouth, glutton and animal-like, contrasting to Joan’s tender, emotive face of moral rectitude. Joan was eventually executed in public.

Some cinematic felicities jolt us from within. Dreyer demonstrated how filmmaking could leverage abstraction to totally de-humanize the characters, or achieve variously such converging effects that play-up with the reality.

And it worked like magic.

The Passion of the Joan of Arc is considered a masterpiece for its avant-garde application of abstraction; for its total departure from the other live-action cinema of its times. It ‘convinced the world that filmmaking could be art’.

Intuitive or apparent?—?now even an average movie-goer grasps the wizardry of abstraction in the virtual-screen reality, or in the craft of filmmaking.

But how do we view Abstraction in our practical lives—?if we leave apart the cinematic, illusion or metaphysical realms for the moment.

LET US COME OUT OF THE CINEMA. In 1931, a man in London named Harry Beck released a new map of the city’s Underground Metro (Tube). That Tube map?—?technically a diagram?—?looked strikingly different from the earlier versions. The older maps were physically accurate, in that they depicted the geographical and topographical realities of the city just as they exist. However, with their messy lines and crammed presentation, those maps were hard to decipher.

Until Harry produced a simplified, ‘abstracted’, even-more-inaccurate version of the map?—?with straightened lines and fixed angles?—?which were much easier and intuitive to read. In fact it was such a departure from older counterparts that the London’s Tube management was initially sceptical about its launch altogether.

It turned out that the public indeed loved it. The London Tube map we use today is not much different from Harry’s 1931 version. Just simplifying or ’tidying-up’ the old messy map into circuit-diagram-look might seem a small effortless idea. But don’t many beautiful ideas look simple in retrospect?

Harry Beck’s map-to-diagram abstraction was a huge design leap.

Harry had abstracted the reality even farther from the old messy map. He favoured function over form, practicality over geography. For a commuter the actual distances between stations matters relatively less than just knowing clear linkage between them all. It’s been claimed that ‘Harry Beck’s format was an innovation that would become essential for the comprehensibility of complex networks of today’s transport systems all over the world.’

AS IT TURNS OUT, cartography or map-making allows an imperiously intuitive grasp of abstraction as a concept and its departure from reality. Children early in schools should be introduced to the idea of abstraction—?before even learning counting—?through just Google maps: Zoom-in to reveal the specificity of a region; Zoom-out to reveal the ‘bigger-picture’ boundaries and context?—?where localised reality matters less. And more importantly, this conception should be articulated across all the disciplines that children are taught?—?from mathematics to languages.

In fact, one of the reasons mathematics is considered a tougher discipline where children struggle is because of the level of abstraction they have to deal with so early on in life?—?despite all of the story-problems in algebra and plethora of visual ways of teaching it.

Consider the foundations of mathematical learning for example. Numbers and Counting are the purest forms of abstractions that we take for granted. It is said that for prehistoric civilisations the raw numbers?—?One, Two, Three… didn’t even exist. Rather, they could only comprehend, say, One-moon, Two-eyes, Three-stones etc. In other words, they could never abstract out the object from numbers and counting process. Because numbers were (are) not something they could touch or hold. Neither can we, but we indeed totally ‘get’ numbers by themselves.

How?

Number and Counting abstractions have been a huge mental shift for the human civilisation.

If that seems hard to believe, consider why several isolated tribal worlds—?such as Brazil’s Pirah?s—?have no counting system, and cannot count without language, such as on their fingers?

Over the course of the civilisation, our conception of the Numeric system has in fact evolved from the family of Natural numbers (1, 2, 3…), to the Whole numbers (0, 1, 2, 3…) to Integers, Rational (Fractions/Decimals), Irrational (the entire Real numbers set)—?then finally to Imaginary numbers (Complex set).

Greeks for example doubted the existence of irrational numbers, such as Pi.

There’s a legend that once Hippasus, a pupil of Pythagoras (the legendary Greek Philosopher and Mathematician) ran-in to him in excitement to share about his new discovery of ‘irrational’ numbers. Pythagoras considered it a dire profanity, and ordered his pupil be abandoned in the middle of sea alone till he dies! As it has been stated: ‘Numbers may have originated from purely practical needs, but Pythagoreans attributed mystical significance to their ability to perceive the presence of rational numbers in everything, be it a sunrise or a musical harmony.’

Quite unsurprisingly, in high school all of us are totally flummoxed when introduced to the concept of Imaginary numbers for the first time (√-1, or i). It inherently feels so unreal. How can there be any square root of negative one? Imaginary numbers don’t even exist on the linear number line, except for the accommodated rotational representation. What are Imaginary numbers? And more importantly—why do we need them?

It’s best to think of them as further shortcut abstractions that help us model the reality easier and quicker. The Wi-Fi signals that you are relying on to connect to the internet at this very instant—they are in fact electromagnetic waves whose properties can most accurately be chronicled by complex number entities, with the electrical and magnetic field expressed together as real and imaginary sub-parts respectively. The electronic circuits of the mobile/laptop/tablet device on which you are reading this piece—their behaviours are again most easily captured by calculations through imaginary numbers (for the geeks—the capacitance and inductance of device circuit elements are best expressed together as a complex entity).

In this sense, imaginary numbers are not that different an abstraction as are the straight percentages and ratios—which even the non-educated brains save some intuition for.

Here’s an analogy (at the level of early-school elementary Mathematics): Suppose you want to compare the popularity of Justin Beiber in London against NY, through the concerts ticket sales to the adults against teenagers in both cities. Some fictional ticket sales data—In London: 7000 teenagers and 1500 adults, versus in NY: 5500 teenagers vs. 950 adults. Our intuition would point us to quickly hit the percentages, or the respective ratios of adults’ sales vs. total sales: 0.176 (17.6%) in London vs. 0.147 (14.7%) for NY—which would lead us to conclude—more adult popularity in the London concert.

But notice here—?in order to estimate this specific popularity we have used decimals—a number type (abstraction) that cannot be used to count or measure the adults themselves. For in real-life we can only count adults using natural numbers (1,2,3…); and not in any of its higher abstracted forms, such as fractions or decimals. Could there exist an 0.176 adult or even half-adult?! However, the abstracted numbers indeed furnish us with a better sense of the adults’ popularity—of their comparison, behaviour and nature…of our perceived reality!

Imaginary numbers are similar, yet another higher layer of number abstraction, which extend our numbers family and enable us to model the real world to a much more scrupulous degree—by providing a richer, quantified sense of the comparison, nature and behaviour of its infinitely many entities.

Consider engineering applications for example—say building a Jet Engine. The mathematical models and equations that best depict the circuit behaviours in such complex applications?—?they cannot be solved with only the real, non-imaginary numbers. However, the solutions to these equations do exist in the imaginary-number world. Solving them thereby could produce not one but sets of solutions?—?of which all we smartly keep only those solutions that are real-valued.

Hence the beginning and ending points of such model equation solutions involve only real numbers, but we cannot navigate through this ‘solution journey’ without dipping into the imaginary-number world!

We let ourselves drown into the realms of imaginary number-world for moments?—?as a shortcut trick and abstraction to model the objective real world?—?and then down below as the equations melt and imaginaries disunite—we sneak out, conjure, gamble, pretend, as if such imaginary world never existed! Just as we escape and hide under the canopy of fabulous fiction and arts?—?smitten away for moments—while unravelling the furtive fables and follies of the human nature, within the conceit of our subjective, uncertain real lives.

ABSTRACTION IS LIKE ONE MINISTRY OF MAGIC. It is so fundamentally entrenched into our thought-process and conception of the world that we often don’t realise when applying it within certain disciplines or contexts. At times it appears intrinsically weaved into our intuition, disarmingly docile (say interpreting road-signage); while at others it manifests itself within illimitable layers across reams of theoretical equations?—?demanding decades of learning and expertise to comprehend (say demystifying Quantum Physical equations or Price equations for selfish-gene theory).

Uniquely, we use abstraction as much in the objective realm as in the subjective realms?—?from applying scientific rigour, to separating object/matter from ideas, to synthesising human behaviour. There’s hardly any foundational discipline of studies, from physical sciences to humanities, which does not leverage abstraction. In several instances as our learning progresses from observation to heuristics to formulating theories, we move across ‘sedimentary layers’ of abstraction formed over centuries of learning. Any codification?—?frameworks, models, theories, archetypes et al.?—?results from an intense abstraction process, regardless of the applied method?—?scientific or empirical.

Consider human sciences. In psychology Carl Jung introduced four levels of abstraction relating to complementary psychological functions: sensation, intuition, feeling, and thinking. In language we heavily employ ‘abstraction hierarchy’ while moving across the generics and specifics. Consider the simple sentence: ‘All species have heart, but only birds can fly, and only vultures can fly high.’ In fiction and non-fiction writing, ‘ladder of abstraction’ technique is often considered a mastered art. In business strategy or other complex scenarios, the use and abuse of jargon and framework abstractions?—?say ’30,000-view’, ‘competitive-advantage’, ‘customer-centricity’?—?results from their varying interpretations among executives, even within the same context.

Levels of experience, aptitude, and quality of information refine abstraction layers in the human’s mind. We constantly judge an individual’s wisdom and critical-thinking abilities based on his depth, faculty, and agility across the abstraction layers within a topic. From specificity during constructing arguments, to bigger-picture visionary thinking, to identifying combinatorial patterns among unrelated areas in channelling creativity?—?all of these require vigorous juggling across the degrees of abstraction.

NOW CONSIDER DESIGN AGAIN FOR A MOMENT. The most ‘colloquial’ understanding of Design unfortunately tends to be towards the graphic, interaction and product design manifestations. And these cross over quite a lot with the field of the Arts, where abstraction is elemental—and also a movement of its own, say Cubism, Abstract Expressionism— dating back to its origins from the pre-historic times.

Most sketched symbols are abstractions. Any visual artefact results from the abstraction processes. To abstract in Arts and Design means to manipulate perceived visual stimuli and to reflect the outcome by the use of a medium. As it has been stated: “Through abstraction, a figure can gain another meaning and represent more than the element in reality it refers to. Abstraction is needed to reflect reality, but more over it enables visual expressions that exceed the representational world.”

Think about though the wider anatomy of Design as a discipline (lately popularised as 'design thinking', and closely aided by systems-thinking). In his seminal work published in 1992?—?‘Wicked problems in Design Thinking’ ?—?Richard Buchanan introduced four abstracted layers of applying design-thinking into real world problems: 1) Symbolic and visual communications 2) Material objects 3) Activities and organised services 4) Complex systems or environments for living, working, playing and learning.

This convergence of Design abstraction layers helps position the order of complexity while trying to solve the problems of reality or human behaviour. The challenge though is that the popular vernacular conception of Design is limited only to the first two layers of these abstractions.

Let us get deeper into the design anatomy to further grasp how it plays out abstraction.

Here’s an example, out of the millions out there in both commercial and social business contexts: A US consumer-goods company once wanted to gaze the price-levels that people in rural Ghana were willing to pay to buy health and beauty products. How would you find out? Common intuition would say: just go ask them directly, or do a survey.

However, is asking direct questions or conducting surveys the best way to listen to the people, or get the most out of them, all the time? It’s a well-established wisdom now that in plenty of situations human beings simply cannot articulate what they need or want, or why they think or behave the certain way. And therefore in order to listen to them better and generate richer insights we employ several techniques: spend relentless time in their environment; observe their behaviours indirectly; amass big-data and apply agent-based simulation models to predict behaviours; use established heuristics and biases, et al.

What are the other unique ways to creatively listen to the people?

In the above case, the supermarket partners went to a Ghanaian village roadside and designed and set-up a mock physical shop. It was a highly abstracted version of a future shop with ‘unknown’ details of groceries, brands and prices. It got the locals engaged and provoked them to elicit what sort of products would interest them?—?without the need of seeing the entire shop reality in detail. Could this be achieved through a survey?

For the supermarket, it eventually led to the market knowledge and insight that rural Ghanians would pay more for some higher-quality, branded products, such as vitamins and toothbrushes, and were reluctant to pay for others, such as detergent and toothpaste. This allowed the company to come up with the right basket of goods, a focused pricing and branding strategy, and finally an established micro-franchising business.

Techniques such as the mock shop above—or prototyping—are in fact heavily applied in various popular design-driven tasks. New Car concepts, Architect’s building renditions, and 3D Printing models?—?we see design prototypes in such manifestations just all around.

However, popular applications such as these characterize prototyping only in its limited scope, and not as a key conceptual technique—of the human thought process—that captures very many deceptive layers of abstraction. Prototypes need to be understood not just as testing samples, but also as abstracted realities?—?represented in the form of conceptual artefacts?—?that wittily work around the complexity and enhance the ways of listening to our sub-conscious, and influencing human behaviour.

For example, consider how various other non-design disciplines employ prototyping. In programming-languages, prototyping across layers of abstraction is a core foundation to tackle complexity (think of any Object Oriented Language). In engineering, it has largely taken the form of computer modelling over the past few decades, opening up entirely new frontiers of technological advancement. Of late, social scientists specifically the economists have heavily started to apply agent-based modelling to simulate a million possible realities (scenarios)—that require extensive prototyping at significantly higher level of abstraction to represent complex and complicated relationships and derive meaningful insights.

Design approach though rigorously promotes the application of rapid prototyping—which allows progressing through the layers of abstractions over several iterations—when trying to solve a human or reality problem. It entails producing early highly abstracted artefacts of the product/service (solution) to test and provoke feedback from the intended end-user. It makes ideas and thoughts tangible at the earliest in the form of those low-fidelity artefacts, and lets designers and problem-solvers fail early and fast.

How?

The fact that ideas and concepts presented before humans in the form of crude abstracted prototypes aren’t as good as they would like to see (or use) in the future reality—creates a temporary ownership of the object or issue among them. It induces them to react to the artefact stimuli and contribute dutifully. For the users as we noticed above—the abstracted artefact is enough to provoke imagination and bring forth their slow-dawning sub-conscious; the ultimate reality of the product/service matters less.

This is hard to achieve via insights through surveys, statistical modelling, indirect observations, big data analytics etc. (although these often can either complement or lead the process very well). As it has been rightly stated—Design drives people to come out of their trenches, to leap through the layers of abstraction that are otherwise inconceivable for them. Mainstream private and public sector have only recently getting to realise the potential of such design approaches; so no wonder it has been a catchphrase for the past few years. Not to claim either though that it is an entirely pristine approach to creative problem-solving.

Design thinking also further helps to tackle Highly Ambiguous Problems, where the abstraction layers are not visible enough, where there are too many unknown unknowns. For example, problems around human behaviour and engagement particularly are highly ambiguous. In such situations, analytical thinking, regression modelling and spreadsheets cannot always model the complexity.

Consider for example if one wants to figure out how to boost agriculture sector, say in a high-growth developing market (Sudan). More specifically, how to come up with the most efficient mechanism to allocate resources—capital, human and institutional expertise—to smallholders farmers in such remote markets. The complex problem is to model (abstract out) the working capital needs; develop on-lending schemes criteria; build short-term trade finance opportunities for such farmer groups etc. Pretty hard and complex problem indeed, right?

But now imagine that the objective is not just efficient resource allocation, but also to get willing participation from such farmer groups in the new proposed schemes; to positively influence and change their mindsets and behaviours—given the existing presence of ‘loan sharks’ and bureaucratic quagmire in securing government loan schemes. Such a problem would be highly ambiguous in nature and cannot be modelled using spreadsheets and simulation covering hundreds of parameters. There’s no singular way to abstract such problem scenarios. Ambiguous problems require empathy, engagement and consensus-building—unlocking the creative potential of entire groups and communities than an individual—where approaches such as design prototypes come handy. These approaches can either lead or complement and augment the modelling and analytical approaches well, such as in this smallholder farmer scenario.

Even the problems around the design, delivery and running of complex private or public services at scale are highly ambiguous in nature (hence the emerging focus on 'service design'). It is rightly stated that—in any society, the quality of life is highly underpinned in the way its public and private services are designed and delivered; in the way they speak.

There’s also some ingenious thinking and problem-framing that exists around such ambiguous problems that are gigantic in their scope and complexity—The Wicked Problems—or the over-arching socio-cultural problems which are “difficult or impossible to solve for as many as four reasons: incomplete or contradictory knowledge, the number of people and opinions involved, the large economic burden, and the interconnected nature of these problems with other problems.” Say the problems around gender-quality, poverty, disease or famine etc.

Attempting to carve out any abstraction layers within wicked problems into a simplified model is like asking—in terms of scientific equivalent—to accurately draw the quantum model of atom on a piece of sticky note. Originally coined by Horst Rittel in 1973—of late the design veterans such as Jon Kolko have been inspiring in championing the role of design in tackling such wicked problems at large scale.

IT IS INTRIGUING TO NOTE how in the earlier instance of rapid-prototyping iterations, we progress from simple to complex realities?—?reducing abstraction, filling-in the details from low-to-high fidelity?—?or ‘zooming-in’. Whereas notice that the creation of visual artefacts such as symbols?—?or the earlier Harry Beck’s map example?—?involves weeding-out or simplifying the unnecessary details, thus increasing the degree of abstraction or ‘zooming-out’. This nature is also visible in mathematical-modelling and equation solving, such as using the imaginary numbers discussed earlier.

In fact within any context of problem-solving or creation task across most of the disciplines?—?we rapidly scuttle through this ‘zoom-in’ and ‘zoom-out’ levels of abstraction?—?quick and fast ever so often, mindlessly. In a generic research or commercial task, when you are fact-finding, you are largely ‘zooming-in’ to fill the unknown details; when you are synthesizing information and insights, you are mostly ‘zooming-out’ to hunt down the emerging themes and patterns, and weed out the irrelevant.

Consider any objective or subjective exercise or exploration. Consider any problems in mathematics and physics, business and economics; any design or behavioural challenge; any discourses in logical reasoning and language or even fiction-writing. Consider calculating GDP ratios to establish country riches; modelling football flight to predict its projections; analysing competition to establish market position; building inductive/deductive reasoning or speech rhetoric…

Any such task involves frequent formulation, observation, conception, abduction, modelling, calculation, synthesis?—?where we rapidly move either unidirectional or incessantly fluctuate to-and-fro across in its degrees of abstraction. We cannot move from the beginning to the end of a creation/solution process without shifting between its non-static ‘zoom-in’ or ‘zoom-out’ abstraction states.

Which leads to the following rough hypothesis:

During any problem-solving or creation phase?—?we are always at any given instance either abstracting-in or abstracting-out. The degree of abstraction cannot stay static during any value-adding moment.

However primitive this may appear, it stands true probably for any discipline or context that deals with abstraction. Note though that the negation of the above makes less sense or is probably hard to validate:

The moment the degree of abstraction freezes static, we cease adding value in our solution or creation process.

Indeed ‘value-adding’ here is a contextual and dependent term (hence ‘rough’ hypothesis). And there is probably no singular definition of abstraction that is consistent and applicable across all the relevant disciplines simultaneously. However, this doesn’t mean it would be impossible to abstract the abstraction as a concept! What exists already are only different themes, categories and forms of abstraction depending on disciplines, but not a unifying whole.

Maybe we do not need one. Regardless of such a hypothesis, it’s a thing to wonder how no normal human being can deny possessing within himself an inherent intuition for abstraction across heterogeneous facets of life?—?in varying degrees based on his learning, wisdom and expertise.

ABSTRACTION IS LIKE one unmannered undercover agent of our thought-process. A capricious tastemaker. A sly spy. It allows abbreviations of complexity. It fiercely forces us into certain dulled delusions of adequacy. It helps establish quicker synaptic connections within the cells of our brain, in the latter’s unstoppable quest to devour all of the world’s realities in one swoop. In one dignified display of determinism and sovereignty.

Maps—one of the most intuitive abstractions as we observed above—are rightly called ‘at once misguided and brave’. In the same way that manned flight and other technological breakthroughs ‘embody the intellectual achievement and adventurous outlook of the twentieth century’, so too does abstraction. It is fitting to consider the following thought to conclude:

“However strange this may sound, humans are better wired for dealing with incomplete information and getting approximate, plausible results than dealing with complete information that requires exactitude of reasoning.”

Abstraction is the dark matter of our intellect. Dreyer took much delight in it.

Image Sources (In their order of Appearance):

closeupfilmcentre.com | humansinvent.com | collegehumor.com | brilliantscholars.com | xkcd.com | tattooxd.com | slideshare.net/folletto | ithinkidesign.com | slideshare.net/lcoorevits | smashingmagazine.com | uxmag.com | comphacker.org | radford.edu