Orthogonal Links

Let’s unpack the concept of orthogonal influences that we introduced in a recent post. Everyone is familiar with the word diagonal, but the word orthogonal could use a little introduction. Diagonal describes a line that intersects one or more lines to form one or more angles, like the line that connects two opposite corners of a square forming two 45-degree angles. Orthogonal describes a line that intersects another line at a right angle. For instance, the two lines that form the corner of the square are orthogonal to each other. They meet to form a 90-degree angle.

In statistics, orthogonal describes two factors or variables that are not correlated. The movement of one is unrelated to the movement of the other. In computer science and signal processing, orthogonal describes techniques or functions that are independent of one another. You get the point.

The term orthogonal has a broader application in the context of singular links. It speaks to things that are unrelated, whether they are in the same domain or not. They may be objects, ideas, elements, or influences that exist on different planes, in different dimensions, in different regions of the map or on different maps; they may hail from different families, different generations, different species; they’re not necessarily in the same ballpark and maybe not even in the same sport. They are unalike, unassociated, unfamiliar, and distinct. That’s why pairing them with one another can create uniqueness.

Importantly, things that are orthogonal are not opposite to one another. Opposites are very different but are most certainly related to each other. Heads and tails are opposite but related. Yin and yang are opposites but related, as are male and female, hero and villain, beauty and beast, heaven and hell, life and death, truth and lies, order and chaos. Opposites define each other. Each exists in opposition to the other. They are not orthogonal.

Zero and infinity are very far apart but they are mathematically related. Zero and infinity are symbolic quantities that exist beyond quantification, as improbable as that may sound, numbers beyond enumeration. If we were to count backward toward zero, searching for the smallest non-negative number in the universe, the teeniest, barely existing essence of the vanishingly tiniest fraction of a hint of a number… Well, zero is even smaller than that. If we were to count upward, searching for the largest number in the universe by counting all the tiniest elements of the universe such as protons and neutrons and electrons and all the mysterious quarks in the vastness of space, and then if we were to exponentiate that number to gargantuan proportions, exploding the size of that number larger and larger, and if we were to repeat that process a billion billion times over and over again every nanosecond from now until the last of our great great grandchildren breathed their last breath, creating a mind-bendingly huge number beyond our wildest imaginations… Well, infinity is even larger than that. Zero and infinity are far apart — exceedingly far apart — but they are not orthogonal. They both exist on a numerical continuum.

Infinity and zero share the same kind of special relationship as do the dualities of everything and nothing (the absence of everything), light and darkness (the absence of light) and sound and silence (the absence of sound). They are opposites but they are related.

Orthogonal influences are emphatically not related.

Orthogonal influences are all around us if we look for them. They are everywhere, in fact, and far too numerous to list. The number of discrete pairings of orthogonal influences is infinite (there’s that word again), and that would be true even if humanity wasn’t continually creating new information, which it is. The domain of collective human knowledge is expanding faster than our ability to assimilate the new knowledge and apply it to the things we already know. The things we know are a form of order in our lives, and the new things that influence what we know are a form of chaos. It is in this interplay of order and chaos where singular links are born. 

Given the infinite potential of singular links, the vastness of linkable ideas that swirl around us all the time, we need to start somewhere, and the best places to start are the places we already know. We begin with a field of familiarity, and then we introduce new, unfamiliar influences. We start with something known, and we introduce something new. We start with order, and then we inject a dose of chaos. That’s when things start to get interesting.

Look at the world of biomimicry in engineering. Biomimicry seeks to create designs by imitating natural systems and structures. Velcro was inspired by burrs that grew on bushes and tenaciously stuck to clothes. The Japanese bullet train was inspired by the aerodynamic bill of the king fisher bird. Spider webs and silk from silk worms have inspired researchers to make filaments stronger without adding proportionate weight. Designers of wind turbines borrowed the biological design of humpback-whale fins whose tubercles along their leading edges reduce drag and increase lift.

In each of these examples designers took what they knew (order) and introduced orthogonal influences from nature (chaos) to create engineering breakthroughs.

The classic example of orthogonal elements is the duality of form & function. Form pertains to the attractiveness of something. Function pertains to its usefulness. 

Form is the Tiffany diamond, the plunging back line of the bride’s dress and the bouquet of intricate sugar flowers on the wedding cake. It’s the groom’s symmetrical, toothy smile, his silk pocket square, the panache of his flare-rim glasses. Function is the credit card used to pay for the ballroom, the wedding-guest list, the marriage certificate, and the prenuptial contract.

Form is the elegant angled headlight of a sports car. Function is its gas pedal and its brake pedal.

Form is the the dreamy landscape zipping past the window of the moving train and the sound of the surf as heard from the beach house. Function is the printed train schedule and the house’d flood-insurance policy.

Form is the look of wonder in the eyes of a baby watching windshield wipers slosh back and forth across the car windshield. Function is the windshield wiper blade and the seatbelt holding the baby car seat in place. 

Form and function aren’t necessarily orthogonal. In certain contexts form can influence function and vice versa. Designers may strive to achieve both beauty and functionality, and many succeed. Think of the iPhone with its elegance and utility, or the Sydney Opera House with its concentric pointed arches and acoustic fidelity. Car manufacturers embrace form-function duality, as in the Porsche 911, the Mercedes Gullwing, and James Bond’s Aston Martin, to name a few.

In many domains, however, form and function are not intrinsically related. Something can be beautiful and either practical or practically useless. Likewise, a thing can be functional and either beautiful or repulsive. Form and function can be orthogonal.

In the context of starting with what we know, we can start with a practical object and then consciously search for ways to redesign it with aesthetics in mind. Charles and Ray Eames did this with the iconic Eames Lounge Chair, for instance, which they fashioned after a baseball glove (talk about orthogonal influences).

Alternatively, we can look for practical applications of things that are primarily aesthetic. Look at origami, for instance, the Japanese art of paper folding. Origami has traditionally been a decorative craft. However, in recent years it has found application in other fields. Engineers have used origami techniques to design folding solar panels that can be transported and deployed efficiently. Origami techniques have been used to efficiently fold automobile air bags into compact dashboard spaces. Medical researchers have also developed origami-inspired stents that are minimally invasive to insert and then expanded once inside the body.

I personally love the design of the old Italian Lambretta scooters (the now-defunct rival of Vespas) that fused elegance into a form of practical transportation for the masses. During World War II, the industrial Ferdinando Innocenti ran a company manufacturing metal tubes for the Italian Air Force. As part of the negotiated peace package, after the war he was forbidden to continue manufacturing military products. Looking to rebuild his factory from the rubble, he was inspired when he saw the Cushman scooters that the US army had imported to provide easy transportation for troops. He fashioned prototypes for new scooters using bent tubing for the frame and aviation landing gear for the front forks. Aviation tubing was what he knew. American scooters provided a new influence. Innocenti linked together these orthogonal influences to produce the iconic Lambretta scooter.